Research on the status and experience of women in academia in the last 30 years has challenged conventional explanations of persistent gender inequality, bringing into sharp focus the cumulative impact of small scale, often unintentional differences in recognition and response: the patterns of 'post-civil rights era' dis­crimination made famous by the 1999 report on the status of women in the MIT School of Science. I argue that feminist standpoint theory is a useful resource for understanding how this sea change in (...) understanding gender inequity was realized. At the same time, close attention to activist research on workplace environment issues suggests ways in which our understanding of standpoint theory can fruitfully be refined. I focus on the implications of two sets of distinctions: between types of epistemic injustice (and correlative advantage) that may affect marginalized knowers; and between the resources of situated knowledge and those of a critical standpoint on knowledge production. (shrink)

A core historical narrative about anthropological knowledge is that it is created in relations with others, with fieldwork seen as ‘a series of apprenticeships’ whose success is determined by the quality of those relations. An ethnographer connects with the conditions of those studied in ‘circulating exchange’; but on leaving the field a degree of closure is needed to formulate and communicate anthropological knowledge. These obligations and requirements in the creation of knowledge entail attachment and detachment, carrying the seeds of betrayal (...) that can compromise that knowledge. Each epistemological enquiry has its own core ethical imperatives, but as long as knowledge posits a knower, ‘the self of the knower will be at epistemological issue’. In discussing the ethics of knowledge creation I consider the following questions, among others: To what extent is the creation of a particular kind of ethical and epistemic person required for knowledge? How can ethnography produce knowledge about others without betraying them? Can relations of knowledge exchange confer or withhold ‘rights to speak’? Is it possible that unethical relations may destroy or hold up the unfolding of knowledge? And are there circumstances in which it is unethical to disclose knowledge? (shrink)

Feminist epistemology aims to propose epistemic reasons for increasing the representation of women or socially subordinated people in science. This is typically done—albeit often only implicitly—by positing a causal mechanism through which the representation of sociodemographic minorities exerts a positive effect on scientific advancement. Two types of causal theories can be identified. The “epistemic diversity thesis” presents a causal path from sociodemographic diversity to scientific progress mediated by epistemic diversity. The “thesis of epistemic advantage” proposes a causal path from (...) social subjugation to capacity for inquiry. The latter theory is defined with substantial ambiguity in the existing literature, and I present an explicit causal reformulation that disambiguates it. The epistemic diversity thesis focuses on the effect of group composition on collective epistemic performance and is largely silent about what kind of characteristics lead to individual epistemic excellence. On the other hand, the thesis of epistemic advantage seeks to identify sociodemographic background conditions that make certain epistemic agents strictly better knowers or inquirers than others and pays little attention to the synergistic effects of diverse group composition. Such a difference in the causal structure reflects the diverging political characteristics of the two theories. (shrink)

In this article it is argued that the optical metaphor and critical practice of diffraction further developed by Donna Haraway and Karen Barad might be no less significant than the widely spread notion of reflection, when the questions of various practices of knowledge are addressed. By considering Paul Ramsden’s approach to learning/teaching and its underlying theory in higher education alongside Karen Barad’s methodology of diffraction, it is shown that Ramsden’s understanding of learning/teaching is rather based on the theoretical assumptions of (...) diffractive practice. His notion that teaching/learning are closely related and actively shaping each other, and that learners are not disconnected from the environment and their previous experiences with the subject matter and learning process itself, adds to Barad’s onto-epistemological position that knowers know the world at the same time as being the part of the world in its ongoing intra-activity. Ramsden’s understanding of relation is diffractive, because it is not about predefined binary entities and their fixed identities, but about layers and entanglements of various previous experiences and reactions to the learning environment. In addition, looking at learning/teaching processes through a different perspective also leads to a different approach to teaching and other ways of problem-solving. Both Ramsden and Barad distrust homologies, analogies, and causality-based conceptions of knowledge sharing. Instead, the ability to respond to an always new learning/teaching environment is assessed, which implies a diffractive type of sensitivity to the context, iterative process of re-turning, and the creation of dangerously indeterminate relationships and commitments. In this way, some of Barad’s philosophical notions, i.e., the diffraction pattern, intra-activity, returning, and others, also may acquire new practical content. (shrink)

Abstract The present paper examines the role of epistemic virtues in the formation of intellectual identity and its impact on improving our truth-seeking behaviors. A epistemic virtue is a special faculty or trait of a person whose operation makes that person a thinker, believer, learner, scholar, knower, cognizer, perceiver, etc., or causes his intellectual development and perfection, and improves his truth-seeking and knowledge-acquiring behaviours and places him on the path to attain understanding, perception and wisdom. Virtue epistemology is a set (...) of approaches in contemporary epistemology that regards knowledge as "a true belief arising from humans epistemic virtues." Virtue responsibilism and Virtue reliabilism are two important approaches to virtue epistemology that differ together in their attitude to the nature of epistemic virtue. Responsibilisms regards epistemic virtues as an acquired character traits that must be attained through practice and training with plenty of effort from the agent who possesses the will. In contrast, virtue reliabilisms considers epistemic virtues as reliable and innate cognitive faculties, and believes that this natural faculties has been placed in the human being from the very beginning and, if used in the appropriate condition and in a proper environment, is reliably truth-conducive. So virtue epistemology, which is distinguished from belief-based analytical epistemology by focusing on the cognitive character of the agent rather than the belief, regards epistemic virtues as the constructive factor of the epistemic agent and the condition of reaching the truth. From the two approaches of virtue reliabilism and virtue responsibilism, this paper focuses on the second approach and with using of the nine-fold virtues, that Jason Baehr posed, shows how to make epistemically good and thinker human by utilizing these virtues and avoiding the corresponding vices and through this, gained the truth in various epistemic areas. After explaining these virtues and their role in the two mentioned domains based on the virtue epistemology, the significance of this relationship in the view of Mulla Sadra as an example of Islamic philosophy is examined, For the reason that he sees knowledge as the produce of some factors that epistemic virtues is considered part of them. In the view of Sadra, epistemic virtues is the specific attributes and traits of reason faculty that their function causes man to be a very good and strong perciever, and their actual possesion or their gradual acquisition leads to the perfection of the soul and the dignity of human existence. In a new theory of soul-  Ph.D. Student of Islamic Philosophy and Theology, Qom University, Qom, Iran (Responsible author) [email protected]  Associate Professor of Islamic Philosophy and Theology, Qom University, Qom, Iran. [email protected]  Professor of Islamic Philosophy and Theology, Qom University, Qom, Iran. [email protected] 2/ Comparative Theology, Vol: 9, No: 19, Spring & Summer 2018 knowledge, he considers the journey of the soul from the outset as evolutionary journey, and, on the other hand, he considers all human activities directly as an activity of the soul (epistemic agent), which he performs through his own faculties. As a result, the soul is a increasing and evolving being, while at the same time acquiring knowledge is also from its own activities, and therefore the factors that make up the soul are also influential in its products. Now, as knowledge comes from soul exposure to the outside world, the more this soul is refined from pollutions and adorned to virtues, the better reflection from reality will be. Undoubtedly, the desire to engage in the process of truth-seeking and the responsible use of cognitive virtues and skills lead man to a desirable goal (recognition of truth) and forms his true intellectual identity. In the end, the paper suggests that because of the importance of epistemic virtues in the improvement of truth-seeking behaviors, educating and cultivating of these types of virtues should be part of the spoken and written course content of universities and schools, and must be proper critical thinking is institutionalized and strengthened in the spirit of community members. Educational resources contain a wide range of information that can deeply influence our epistemic behaviors and actions. Hence, it is necessary to include praised cognitive skills and epistemic virtues training in them. Teachers play an important role in educating and developing epistemic virtues as part of the formal curriculum content of educational centers, perhaps as part of critical thinking and logic courses. The formal education of epistemic virtues and the creation of opportunities for practicing and exercising them will be a good starting point for institutionalizing and developing admired cognitive skills among members of the community. In a society where individuals in their epistemic processes use their own cognitive virtues and organize their beliefs on their basis, the community itself and the social relations will also be virtuous, because the necessity of such an virtues is that individuals interact with their peers and In these interactions, rule virtue. Observing fairness towards others, intellectual humility, intellectual generosity, courage against miscreant and one who has weak arguments, observance of neutrality and other epistemic virtues, if it is to be found in societies as a habit and praised skill, then that society will be virtuous and its relations will be healthier and with the cultivating of those virtues, Intellectual and moral development will also become easier and more common. Intellectual virtues (or praised cognitive skills) should be taught to the community members, so that they display such characteristics when engaging in social activities, whean expressing opinions, when doing research, and so on. It is important to change our education policies, because the decay of praised cognitive skills leads to devastating consequences for intellectual identity and the truth-seeking and knowledgeacquiring behavior of the community members. (shrink)

Epistemic injustices are wrongs that agents can suffer in their capacity as knowers. In this article, I offer a conceptualisation of a phenomenon I call anticipatory epistemic injustice, which I claim is a distinct and particularly pernicious type of epistemic injustice worthy of independent analysis. I take anticipatory epistemic injustice to consist in the wrongs that agents can suffer as a result of anticipated challenges in their process of taking up testimony-sharing opportunities. I distinguish my account from paradigmatic cases (...) of epistemic injustice, such as Miranda Fricker’s concepts of testimonial injustice and hermeneutical injustice; additionally, I differentiate my view from Kristie Dotson’s account of testimonial smothering. I argue, ultimately, that anticipatory epistemic injustice is a useful addition to our current taxonomy of epistemic injustices, as it has promising explanatory potential for a range of non-standard cases of epistemic injustice. (shrink)

The general concept of a trope – that of a non-shareable character-grounder – admits of a distinction between modifier tropes and module tropes. Roughly, a module trope is self-exemplifying whereas a modifier trope is not. This distinction has wide-ranging implications. Modifier tropes are uniquely eligible to be powers and fundamental determinables, whereas module tropes are uniquely eligible to play a direct role in perception and causation. Moreover, each type of trope theory faces unique challenges concerning character- grounding. Modifier trope theory (...) faces challenges concerning the inscrutability of predication and the incompatibility with bundle theory, whereas module trope theory faces challenges concerning character overdetermination and a collapse into austere nominalism. These differences indicate that the modifier/module distinction divides the advantages of general trope theory and thus presents the trope theorist with a pivotal choice. (shrink)

Technological innovation is almost always investigated from an economic perspective; with few exceptions, the specific technological and social nature of innovation is often ignored. We argue that a novel way to characterise and make sense of different types of technological innovation is to start considering uncertainty. This seems plausible since technological development and innovation almost always occur under conditions of uncertainty. We rely on the distinction between, on the one hand, uncertainty that can be quantified (e.g. probabilistic risk) and, (...) on the other, deep forms of uncertainty that may resist the possibility of being quantified (e.g. severe or fundamental uncertainties). On the basis of these different ingredients of uncertainty in technological innovation, we propose a new taxonomy that reveals the technological nature of innovation. Unlike previous taxonomies employed to handle different types of technological innovations, our taxonomy does not consider the economic value of innovation alone; it is much more oriented towards societal preferences and forms of technological uncertainty. Finally, we investigate the coherence of our proposal with the dual nature of technological artefacts, showing that innovation can be grounded on structural and functional factors and not just on economic ones. (shrink)

The replication crisis has caused researchers to distinguish between exact replications, which duplicate all aspects of a study that could potentially affect the results, and direct replications, which duplicate only those aspects of the study that are thought to be theoretically essential to reproduce the original effect. The replication crisis has also prompted researchers to think more carefully about the possibility of making Type I errors when rejecting null hypotheses. In this context, the present article considers the utility of two (...) types of Type I error probability: the Neyman–Pearson long run Type I error rate and the Fisherian sample-specific Type I error probability. It is argued that the Neyman–Pearson Type I error rate is inapplicable in social science because it refers to a long run of exact replications, and social science deals with irreversible units that make exact replications impossible. Instead, the Fisherian sample-specific Type I error probability is recommended as a more meaningful way to conceptualize false positive results in social science because it can be applied to each sample-specific decision about rejecting the same substantive null hypothesis in a series of direct replications. It is concluded that the replication crisis may be partly due to researchers’ unrealistic expectations about replicability based on their consideration of the Neyman–Pearson Type I error rate across a long run of exact replications. (shrink)

Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally (...) two types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

This is a review paper, where we recall the definitions together with practical applications of the Soft Set and its extensions to HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set.

”It is often assumed that knowledge claims must be justified. But what kind of justification is required for knowledge ? . . . ” (*) -/- presupposition: the kind of epistemic justification depends on the type of the knowledge claim and its respective knowledge claim tradeoff ’vague vs. precise’. -/- procedere: in two - almost purely logical - case studies I account for this tradeoff and question in each case what (if any) were its general outcome wrt justification -/- first (...) for basic measurement statements of the form ′′ϕ(x) = r ∈ IR ± δ′′ (wrt ”measurement accuracy realism” debate) -/- and secondly predication statements of the form ′′x is ( a case of )P′′ (wrt ”epistemic vagueness” debate). (shrink)

Xuanzang (602–664) is famous for his legendary life, his important translation works, and also his Discourse on the Realisation of Consciousness-Only (Vijñapti-mātratā-siddhi, 成唯識論). This text, which is considered as a synthesis of Yogācāra thought, has been diversely interpreted by modern scholars and is still discussed, in particular about the status of external things. Nevertheless, this issue seems to be of little interest for Yogācāra thinkers compared to other topics such as the Noble Path, or else the three types of (...) wisdom (trividhā prajñā, 三慧): learning (śruta, 聞), reasoning (cintā, 思), and cultivating (bhāvanā, 修). As emphasized in recent research, this topic represents a major issue for Buddhist practitioners. In an attempt to analyse it in Xuanzang’s Discourse, and more generally in Yogācāra thought, this paper will first discuss Asaṅga’s and Vasubandhu’s thought on the three types of wisdom. Secondly, since it is important to replace the three types of wisdom in the general argumentation of Xuanzang’s Discourse, we will present the structure of his text which is modelled on a “path” leading progressively to Supreme Awakening. Then, we will present the main elements of the Noble Path and situate the three types of wisdom into it. Finally, we will explain that Xuanzang follows Asaṅga’s and Vasubandhu’s conceptions and eventually confirm the importance of the three types of wisdom in Yogācāra thought. (shrink)

Epistemic instrumentalism views epistemic norms and epistemic normativity as essentially involving the instrumental relation between means and ends. It construes notions like epistemic normativity, norms, and rationality, as forms of instrumental or means-end normativity, norms, and rationality. I do two main things in this paper. In part 1, I argue that there is an under-appreciated distinction between two independent types of epistemic instrumentalism. These are instrumentalism about epistemic norms and instrumentalism about epistemic normativity. In part 2, I argue that (...) this under-appreciated distinction matters for the debate surrounding the plausibility of EI. Specifically, whether we interpret EI as norm-EI or as source-EI matters for the widely discussed universality or categoricity objection to EI, and for two important motivations for adopting EI, namely naturalism and the practical utility of epistemic norms. I will then conclude by drawing some lessons for epistemic instrumentalism going forward. (shrink)

Using tools like argument diagrams and profiles of dialogue, this paper studies a number of examples of everyday conversational argumentation where determination of relevance and irrelevance can be assisted by means of adopting a new dialectical approach. According to the new dialectical theory, dialogue types are normative frameworks with specific goals and rules that can be applied to conversational argumentation. In this paper is shown how such dialectical models of reasonable argumentation can be applied to a determination of whether (...) an argument in a specific case is relevant are not in these examples. The approach is based on a linguistic account of dialogue and text from congruity theory, and on the notion of a dialectical shift. Such a shift occurs where an argument starts out as fitting into one type of dialogue, but then it only continues to makes sense as a coherent argument if it is taken to be a part of a different type of dialogue. (shrink)

I develop a distinction between two types of psychological hedonism. Inferential hedonism (or “I-hedonism”) holds that each person only has ultimate desires regarding his or her own hedonic states (pleasure and pain). Reinforcement hedonism (or “R–hedonism”) holds that each person's ultimate desires, whatever their contents are, are differentially reinforced in that person’s cognitive system only by virtue of their association with hedonic states. I’ll argue that accepting R-hedonism and rejecting I-hedonism provides a conciliatory position on the traditional altruism debate, (...) and that it coheres well with the neuroscientist Anthony Dickinson’s theory about the evolutionary function of hedonic states, the “hedonic interface theory.” Finally, I’ll defend R-hedonism from potential objections. (shrink)

Although I agree with Sabine Muller’s conclusion that we should first seek to find alternatives to amputation for patients suffering from Body Integrity Identity Disorder (BIID), I disagree with one of the major premises that she uses to argue for her claim. Muller argues that patients with BIID are likely not autonomous when they request that the limb be amputated. Muller’s argument that BIID suffers are not autonomous is flawed because she conflates philosophical conceptions of autonomy with the conception of (...) autonomy that is operative in the context of medicine. (shrink)

Although the idea that sexual violence is a “structural” problem is not new, the lack of specification as to what that entails blocks effective responses to it. This paper illustrates the concept of sexual violence as structural in the sense of containing a type of moral wrong called “structural wrong” and discusses its practical implications. First, I introduce a distinction between two types of moral wrongs—interactional wrongs and structural wrongs—and I argue that the moral problem of sexual violence includes (...) both types, each of which calls for a different set of moral responses. Second, drawing on Iris Marion Young’s social connection model of responsibility, I argue that recognizing the structural-wrong element of sexual violence does not reduce individual perpetrators’ responsibility for it. Instead, it implies that a broader group of agents are required to join collective actions to reform the social structure. I conclude by evaluating some preventive programs against sexual violence through the lens of structural wrongs and providing directions to advance them. (shrink)

In the literature, new types of neutrosophic sets have been introduced in the meantime by the growing neutrosophic community. We present a few: Pythagorean Neutrosophic Set, Fermatean Neutrosophic Set, Generalized Fermatean Neutrosophic Set, n-power Neutrosophic Set, Cubic Spherical Neutrosophic Set, Spherical Neutrosophic Set, n-HyperSpherical Neutrosophic Set, Refined n-HyperSpherical Neutrosophic Set.

The aim of this essay is twofold. First, it outlines the concept of ontological frame. Secondly, two models are distinguished on this structure. The first one is connected to Kant’s concept of possible object and the second one relates to Leibniz’s. Leibniz maintains that the source of possibility is the mere logical consistency of the notions involved, so that possibility coincides with analytical possibility. Kant, instead, argues that consistency is only a necessary component of possibility. According to Kant, something is (...) possible if there is a cause capable of bringing it into existence; to this end consistency alone is not sufficient. Thus, while the Leibnizian notion of consistency is at the root of the concept of analytical possibility, the Kantian notion of possibility is the source of real possibility. This difference plays an important role in the discussion of Gödel’s ontological proof, which can be formally interpreted on the ontological frame of the pure perfections. While this proof, under some emendation condition, is conclusive in the context of Leibniz’s ontological model, it is not so within the Kantian one. This issue will be the subject of the second part of the present essay. (shrink)

This paper distinguishes two types of qualia theory, which I call Galilean and non-Galilean qualia theories. It also offers considerations against each type of theory. To my mind the considerations are powerful. In any case, they bring out the importance of distinguishing the two types of theory. For they show that different considerations come into play—or considerations come into play in quite different ways—in assessing the two types of theory.

An examination of conditionals in di¤erent languages leads to a distinction of three types of conditionals instead of the usual two (indicative and subjunctive). The three types can be explained by the degree of acceptance or as-if acceptance of the truth of the antecedent. The labels subjunctive and indicative are shown to be inadequate. So-called indicative conditionals comprise two classes, the very frequent uncertain-fact conditionals and the quite rare accepted-fact conditionals. Uncertain-fact conditionals may have a time shift in (...) contemporary English and the future subjunctive in Portuguese (though not all of them do). Moreover, paraphrases of if with in case or supposing are usually possible with approximately the same meaning. Accepted-fact conditionals never have these features. (shrink)

Do we live in a computer simulation? I will present an argument that the results of a certain experiment constitute empirical evidence that we do not live in, at least, one type of simulation. The type of simulation ruled out is very specific. Perhaps that is the price one must pay to make any kind of Popperian progress.

Note: Many types of nanosensors are designed using CP nanomaterials for nanobiological applications. (Conductive surface) The oxidation of conductive polymeric materials is easily altered by redox mechanisms, and the charge transfer properties of these materials are affected by structural parameters, such as diameter and dimensions. CP materials are able to provide sensitive and rapid responses to specific biological and chemical species. Techniques such as chemical polymerization are often used to make CP nanomaterials. Manufacturing strategies can be divided into three (...) categories: hard mold synthesis, soft mold synthesis, and mold-free synthesis. The most widely used conductive polymers in nanosensors are nanomaterials made from CP due to their unique chemical and electrical properties resulting from the properties of their pie-electron nanosystem. Many modeling and functionalization technologies are being developed to control the location, distribution, amount, or structure and orientation of biological nanomolecules at the nanomaterial level. Therefore, our level of contact between biological nanomolecules and nanomaterials is of particular importance in countless applications. Covalent and non-covalent modifications are two general methods for coupling biological molecules and CP nanomaterials. Covalent functionalization is a chemical process in which a strong bond or relationship between nanomaterials and biological molecules is formed. In many cases, surface chemical modifications are required to create active groups that can bind to biomolecules. Unlike covalent functionalization, in the non-covalent method, nanomolecules can be removed without destroying the geometric and electronic structure on the surface. Nanomaterials are formed. Conclusion : The large surface-to-volume ratio in nanostructures and the high potential for signal amplification provide ideal conditions for marking and detecting biological elements in the structure of nanosensors. (shrink)

Abstract: Tomatoes are part of the major crops in food security. Tomatoes are plants grown in temperate and hot regions of South American origin from Peru, and then spread to most countries of the world. Tomatoes contain a lot of vitamin C and mineral salts, and are recommended for people with constipation, diabetes and patients with heart and body diseases. Studies and scientific studies have proven the importance of eating tomato juice in reducing the activity of platelets in diabetics, which (...) helps in protecting them from developing deadly blood clots. A tomato classification approach is presented with a data set containing approximately 5,266 images with 7 species belonging to tomatoes. The Neural Network Algorithms (CNN), a deep learning technique applied widely in image recognition, is used for this task. (shrink)

Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference in there. The main goal of this article is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and (...) middle period dialogues. Though this is a kind of strengthening the developmentalistic approach corresponding the relation of the early and middle period dialogues, based on the fact that what is to be proved here is a essential development in Plato’ ontology and his epistemology, by expanding the grounds of development to the ontological and epistemological principles, it hints to a more profound development. The fact that the bipolar and split knowledge and being of the early period dialogues give way to the tripartite and bound knowledge and benig of the middle period dialogues indicates the development of the notions of being and knowledge in Plato’s philosophy before the dialogues of the middle period. -/- Keywords Plato; early dialogues; middle dialogues; being; knowledge; development -/- Introduction The differences between two groups of the early and middle period dialogues have always been a matter of dispute. Whereas the developmentalists like Vlastos, Silverman (2002), Teloh (1981), Dancy (2004) and Rickless (2007) think that from the early to the middle dialogues Plato’s philosophy changes, at least in some essential points, the unitarists like Kahn, Cherniss and Shorey believe that there happens no development and the differences must be taken as natural, ignorable and even pedagogic. In his well-known article, Socrates contra Socrates in PLATO, Vlastos lists ten theses of difference between two groups of dialogues. The first group which includes Plato’s early dialogues he divides to 'elenctic' (Apology, Charmides, Crito, Euthyphro, Gorgias, Hippias Minor, Ion, Laches, Protagoras and Republic I) and 'transitional' (Euthydemus, Hippias Major, Lysis, Menexenus and Meno) dialogues. These transitional come after all the elenctic dialogues and before all the dialogues of the second group which compose Plato’s middle period dialogues, including (with Vlastos' chronological order) Cratylus, Phaedo, Symposium, Republic II-X, Phaedrus, Parmenides and Theaetetus (1991, 46-49). Vlastos asserts strictly that his list of differences are 'so diverse in content and method that they contrast as sharply with one another as with any third philosophy you care to mention, beginning with Aristotole’s' (ibid, 46). Vlastos’ list of differences between two Socrateses is considered a view breaking sharply between the early and the middle dialogues. Besides all ten differences between the two Socrateses in Vlastos’ list that can be supportive for our doctrine here, we intend to focus on some ontological as well as epistemological distinctions that have not completely been discussed hitherto. Contrary to the developmentalist theory of Vlastos, unitarian theory of Charles Kahn wishes to eliminate any substantial difference between the early and the middle dialogues. He distinguishes seven 'pre-middle' or 'threshold' dialogues including Laches, Charmides, Euthyphro, Protagoras, Meno, Lysis and Euthydemus from the other Socratic dialogues which he calls 'earliest group' (1996, 41). The threshold dialogues, Kahn thinks, 'embarke upon a sustained project' that is to reach to its climax in the middle period dialogues, namely Phaedo, Symposium and Republic. Believing in that there is no 'fundamental shift'between the early and middle dialogues (ibid, 40), Kahn thinks the Socratic dialogues are just the 'first stage' with a 'deliberate silence' towards the theories of later periods (ibid, 339). One of the reasons of the surprising fact that Plato gives no hint of the metaphysics and epistemology of the Forms in the early dialogues, he thinks, is the pedagogical advantages of aporia. He thinks that Plato 'obscurely', and mostly because of education, hinted to some doctrines and conceptions in his early dialogues and with the aim of clarifying them only in the later ones (ibid, 66). The seven threshold dialogues, Kahn asserts, 'had been designed from the first' to prepare the pupils and readers for the views expounded in the middle period dialogues (ibid, 59-60). To show that the differences of the two Socrateses of the early and middle period dialogue are in their onto-epistemological grounds and thence cannot be explained by a unitaristic view, we try to draw the ontological and epistemological principles of the early dialogues in the first part below in order to show, in the second part, that those principles have been developed in the middle period dialogues. -/- A. The Onto-Epistemologic Principles of the Early Dialogues Socratic dialogues are paradoxical about knowledge because while being knowledge-oriented always searching for knowledge, they deny it and even never discuss it directly. Three elements of Socrates’ way of searching Knowledge throughout the early dialogues, i.e. Socratic 'what is X?' question, his disavowal of knowledge and his elenctic method combined together produce something like a circle which works, more or less, in the same way in these dialogues. Though this circle is an embaressing inquiry always resulting in ignorance instead of knowledge, its motivation is surprisingly Socrates’ passionate enthusiasm for knowledge, an intensive love of wisdom. The starting point of this circle is Socrates’ confession of having no knowledge which might be explicitly asserted or presupposed, maybe because it was one of the famous characteristics of Socrates; a confession always paradoxically accompanied with his intense longing for knowledge (e.g., Gorgias 505e4-5). Every time Socrates encounters with someone who thinks he knows something (οἴεταί τι εἰδέναι) (Apology 21d5) and tries to examine him. This examination seems to be the simplest one asking just what it is that he knows. Socrates’ elenchus, therefore, is always connected with 'what is X?' (τίς ποτέ ἐστιν) question, a question that most of the early dialogues of Plato are concerned with; 'what is courage?' in the Laches, 'what is piety?' in Euthydemus, 'what is temperance?' in Charmides and 'what is beauty?' in Hippias Major. This question we call here 'Socratic question' and probably is the very question the historical Socrates used to employ, is tightly interrelated with both his disavowal and his elenchus. He disclaims knowledge because he cannot find the answer to the question himself and he rejects others’ since they cannot offer the correct answer too. Every interlocutor can claim he knows X, if and only if he can answer the Socratic question. Otherwise, he is more of an ignorant than of a knower of τί ποτέ ἐστι X. Knowing the answer to this question is, thus, knowledge’s criterion for Socrates. Having found out that he cannot answer what it is which he would claim to know, the interlocutor comes to the point Socrates was there at the beginning. The least advantage of this circle is that he becomes as wise as Socrates does about the subject, becoming aware that he does not know it. At the end of the circle they are both still at the beginning, not knowing what X is. So let us first take a glance at these three elements. Socratic disavowal of knowledge is strictly asserted in some passages. At Apology 21b4-5, Socrates says: -/- I do not know of myself being wise at all (οὔτε μέγα οὔτε σμικρὸν σύνοιδα ἐμαυτῷ σοφὸς ὤν) -/- Moreover, at 21d4-6: -/- None of us knows anything worthwhile (καλὸν κἀγαθὸν εἰδέναι) …. I do not know (οἶδα) neither do I think I know. -/- In Charmides Socrates speaks about a fear about his probable mistake of thinking that he knows (εἰδέναι) something when he does not (166d1-2). The somehow generalization of this disavowal can be seen in Gorgias. After calling his disavowal 'an account that is always the same' (509a4-5), Socrates continues (a5-7): -/- I say that I do not know (οἶδα) how these things are, but no one I have ever met, like now, who can say anything else without being absurd. -/- At the end of Hippias Major (304d7-8), Socrates affirms his disavowal of knowledge of 'what is X?' this time about the fine: -/- I do not know (οἶδα) what that is itself (αὐτὸ τοῦτο ὅτι ποτέ ἐστιν). Some other passages, however, made a number of scholars dubious about Socrates’ disavowal. Vlastos mentions Apology 29b6-7 as an evidence : 'that to do wrong and to disobey one’s master, both god and men, I know (οἶδα) to be evil and shameful'. He thinks that if we give this single text 'its full weight' it can suffice to show that Socrates does claim knowledge of a moral truth (1985, 7). Vlastos’ claim is not admittable since it would be too strange, I think, for a man like Socrates to violate his disavowal claim just after emphasizing it. We can see his claim just before the already mentioned passage: -/- And surely it is the most blameworthy ignorance to believe that one knows what one does not know. It is perhaps on this point and in this respect, gentlemen, that I differ from the majority of men and if I were to claim that I am wiser than anyone in anything it world be in this, that, as I have no adequate knowledge (οὐκ εἰδὼς ἱκανῶς) of things in the underworld, so I do not think I have (οὐκ εἰδέναι) (Apology 29b1-6) Vlastos tries to solve what he calls the 'paradox' of Socrates’ disavowal of knowledge distinguishing the 'certain' knowledge from 'elenctic' knowledge (1985, 11) and thinking that when Socrates avows knowledge, we must perceive it as an elenctic knowledge, a knowledge its content 'must be propositions he thinks elenctically justifiable' (ibid, 18). Irwin’s solution is the distinction of knowledge and belief. He approves that Socrates does not 'explicitly' make such a distinction, but still thinks that Socrates’ 'test for knowledge would make it reasonable for him to recognize true belief without knowledge, and his own claims are easily understood if they are claims to true belief alone' (1977, 40). While I agree with Vlastos up to a point, I strongly disagree with Irwin about the early dialogues. As I will try to show below, we are not permitted to consider any kind of distinction within knowledge in Socratic dialogues because only one category of knowledge is alluded to there and the distinction of knowledge and belief thoroughly belongs to the second Sorcates. Although no kind of distinction can be admittable here, I think Vlastos’ distinction can be accepted only if we regard it as a distinction between knowledge, which is unique and without any, even incomparable, rival, and a semi-idiomatic and ordinary one that is a necessary requirement for any argument, and thus, unavoidable even for someone who does not claim any kind of knowledge. An apparent evidence of this is Gorgias 505e6-506a4: -/- I go through the discussion as I think it is (ὡς ἄν μοι δοκῇ ἔχειν), if any of you do not agree with admissions I am making to myself, you must object and refute me. For I do not say what I say as I know (οὐδὲ γάρ τοι ἔγωγε εἰδὼς λέγω ἃ λέγω) but as searching jointly with you (ζητῶ κοινῇ μεθ᾽ ὑμῶν). -/- The minimal degree of knowledge everyone must have to take part in an argument, conduct it and use the phrase "I know" when it is necessary is what Socrates cannot deny. We can call it elenctic knowledge only if we agree that it is not the kind of knowledge that Socrates has always been searching, the one that can be accepted as the answer of Socratic 'what is X?' question. His disavowal of knowledge is applied only to the knowledge which can truly be the answer of Socratic question and pass the elenctic exam; a knowledge that, I believe, is never claimed by first Socrates. Socrates conducts his method of examining his interlocutors’ knowledge, our second element here, by almost the same method repeated in Socratic dialogues. That whether we are allowed to regard all the examinations of Socrates in the early dialogues as based on the same or not has been a matter of dispute. Vlastos himself (1994, 31) distinguished Euthydemas, Lysis, Menexenns and Hippias Major from the other Socratic dialogues because he thinks Socrates has lost his faith to elenchus in there. Irwin (1977, 38) distinguishes Apology and Crito where Socrates’ own convictions is present. Contrary to some scholars like Benson (2002, 107) who take elenchus in all the Socratic dialogues as a unique method, Michelle Carpenter and Ronald M. Polansky (2002, 89-100) argue pro the variety of methods of elenchus. Thomas C. Brickhouse and Nicholas D. Smith (2002, 145-160) even reject such a thing as Socratic elenchus which can gather all of the Socrates’ various arguments under such a heading. There can be no solution for the problem of elenchus, they think, is due to 'the simple reason that there is no such thing as 'the Socratic elenchos"'(p.147). Though we consider elenchus a somehow determined process and a part of Socratic circle in the early dialogues, all we assume is that whatever differences it might have in different dialogues, it has the same onto-epistemological principles and, thus, we are not going to take it necessarily as a unique method. This method sets out to prove that the interlocutors are as ignorant as Socrates himself is. That whether elenchus is constructive, capable of establishing doctrines as Vlastos (1994) or Brickhouse and Smith (1994, 20-21) believe or not is another issue to which this paper is not to claim anything. What is crucial for our discussion here is that elenchus does not reach to the very knowledge Socrates is looking for. This is strictly against Irwin who thinks that not only elenchus leads to positive results, 'it should even yield knowledge to match Socrates’ conditions'(1977, 68, cf. 48). He does not explain where and how they really yield to that kind of knowledge. He explains his elenctic method in his apology in the court (Apology 21-22), that how he used to examine wise men, politicians, poets and all those who had the highest reputation for their knowledge and every time found that they have no knowledge. If we accept, as I strongly do, that Socrates’ disavowal of his knowledge is not irony, it might seem more reasonable to agree that the process that has that disavowal as its first step cannot be irony as well. The key of the circle which can explain why Socrates disclaims knowledge and how he can reject others’ claim of having any kind of knowledge lies in the third element, Socratic question. In Hippias Major (287c1-2), Socrates asks: 'Is it not by Justice that just people are Just? (ἆρ᾽ οὐ δικαιοσύνῃ δίκαιοί εἰσιν οἱ δίκαιοι). He insists at 294b1 that they were searching for that by which (ᾧ) all beautiful things are beautiful (cf. b4-5, 8). At Euthyphro 6d10-11 it is said that the Socratic question is waiting for 'the form itself (αὐτὸ τὸ εἶδος) by which (ᾧ) all the pious actions are pious; and at 6d11-e1: -/- Through one form (που μιᾷ ἰδέᾳ) impious actions are impious and pious actions pious. -/- Since the X itself is that by which X is X, knowing 'X itself' is the only way of knowing X. It is probably because of this that Socrates makes the distinction between the ousia as a right answer to the question and effect as a wrong one: -/- I am afraid, Euthyphro, that when you were asked what piety is (τὸ ὅσιον ὅτι ποτ᾽ ἐστίν) you did not wish to make clear its nature itself (οὐσίαν … αὐτοῦ) to me, but you said some effect (πάθος) about it. (Euthp. 11a6-9) -/- 1. Knowledge of what X is Now it is time to look for the onto-epistemological principles of Socratic circle and its three elements. It cannot reasonably be expected from the first Socrates to present us explicitly and clearly formulated principles of his onto-epistemology when such explications cannot be found even in the second Socrates who has some obviously positive theoris. Since there must be some principles underlying this first systematic inqury of knowledge, we must seek to them and be satisfied with elicitation of the first Socratas’ principle. What will be drawn out as his principles cannot and must not, thus, be taken as very fix and dogmatic principles. Some very slightest principles and grounds suffice for our purposes here. The first principle that is the prima facie significance of the Socratic question and his implementation of all those elenctic arguments I call the principle of 'Knowledge of What X is' (KWX): -/- KWX To know X, it is required to know what X is. -/- Aristotle (Metaphysics 1078b23-25, 27-29, 987b4-8) takes Plato’s τί ἐστι question as seeking the definition of a thing that is the same as historical Socrates’ search but applying to a different field. That Plato’s 'what is X?' question was a search for definition became the prevailed understanding of this question up to now. I am going neither to discuss the answer of Socratic question nor to challenge taking it as definition. What I am to insist is that knowledge is attached firmly to the answer of the question: Knowledge of X is not anything but the knowledge of what X is. It entails, certainly, the priority of this knowledge to any other kind of knowledge about X but it also has something more fundamental about the relation of knowledge and Socratic question. Socrates’ exclusive focus on the answer of his question can authorize the consideration of such an essential role for KWX in his epistemolgoy. The total rejection of his interlocutors’ knowledge when they are unable to answer the question can be regarded as a strong evidence for it. Socrates’ elenctic method and his rejection of others’ knowledge in the early dialogues, which all end aporetically with no one accepted as knower and nothing as knowledge, prevent us from finding any positive evidence for this. We have to be content, therefore, of negative evidences which, I think, can be found wherever Socrates rejects his interlocutors’ knowledge when they are not able to give an acceptable answer to his 'what is X?' question. 2. Bipolar Epistemology Socrates’ rejection of his interlocutors’ knowledge has another epistemological principle as its basis. Let me call this principle Bipolar Epistemology' (BE): BE There is no third way besides knowledge and Ignorance. -/- BE says that about every object of knowledge there are only two subjective statuses: knowledge and Ignorance. Socrates’ disavowal, however, says nothing but that he is ignorant of knowledge of X because he does not know what X is. This means that BE is presupposed here. Socrates’ elenchus and his rejection of interlocutors’ having any kind of knowledge are the necessary results of the fact that he does not let any third way besides knowledge and ignorance. The first Socrates never let anyone partly know X or have a true opinion about it, as he would not let anyone know anything about X when he did not know what X is. -/- 3. Bipolar Ontology The principle of BE in first Socrates’ epistemology is parallel to another principle in his ontology. Plato’s bipolar distinction between being and not being is as strict and perfect as his distinction between knowledge and ignorance. This principle I shall call the principle of 'Bipolar Ontology' (BO): BO Being is and not being is not. BO is apparently the same with the well-known Parmenidean Principle of being and not being (cf. Diels-Kranz (DK) Fr. 2.2-5). Euthydemus’ statement against the possibility of false knowledge can be good evidence for this principle: -/- The things which are not surely do not exist (τὰ δὲ μὴ ὄντα … ἄλλο τι ἢ οὐκ ἔστιν). (Euthydemus 284b3-4) -/- He continues (b4-5): -/- There is nowhere for not being to be there (οὖν οὐδαμοῦ τά γε μὴ ὄντα ὄντα ἐστίν). -/- That BE does not let true opinion as a third option besides knowledge and ignorance seems to be related to BO’s rejecting a third option besides being and not being, which is itself the basis of the impossibility of false belief. Socrates’ elaborate discussion of the problem of false belief in Theatetus that leads to a more decisive discussion and finally to some solutions in Sophist can make our consideration of BO for the first group of dialogues authentive. -/- 4. &5. Split Knowledge and Split Being The fourth principle I shall call the principle of 'Split Knowledge' (SK): -/- SK Knowledge of X is separated from any other knowledge (of anything else) as if the whole knowledge is split to various parts. -/- This Principle is hinted and criticized as Socrates’ way of treating with knowledge in Hippias Major: -/- But Socrates, you do not contemplate the entireties of things, nor do people you have used to talk with (τὰ μὲν ὅλα τῶν πραγμάτων οὐ σκοπεῖς, οὐδ᾽ ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). (301b2-4) -/- Contrary to Rankin who regards the passage as 'antilogical, almost eristic in tone rather than presenting a serious philosophy of being' (1983, 54), I think it can be taken as serious. Hippias criticizes Sorcates that he does not contemplate (σκοπεῖς) the entireties of things (ὅλα τῶν πραγμάτων), a critique which Socrates is not its only subject but all those whom Socrates accustomed to talk with (ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). This last phrase, I think, extends this critic beyond this dialogue to other Socratic dialogues. Hippias’ use of the perfect tense of the verb ἔθω (to be accustomed) is a good evidence of this extension. We can get, thus, these ἐκεῖνοι as Socrates’ interlocutors in his other dialogues that hints that this criticism has the epistemological groundings of the previous dialogues as its subject. What ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι points to is that Hippias does not have in mind Socrates’ way of treating things only in this dialogue, but he is also criticizing Socrates’ way throughout his dialogues. At 301b4-5, Socrates and his interlocutors’ way of beholding things is described as such: -/- You people knock (κρούετε) at the fine and each of the beings (ἕκαστον τῶν ὄντων) by taking each being cut up in pieces (κατατέμνοντες) in words (ἐν τοῖς λόγοις). This leads us to our next principle that is parallel to, and the ontological side of, SK, the principle of 'Split Being'(SB): -/- SB Everything (being) is separated from any other thing as if the whole being is split to many beings. -/- Socrates and his interlocutors and thus, as we saw, the Socratic dialogues are accused to regard everything as it is separated from all other things. This separation is en tois logois that, I think, can reasonably be taken as saying that Socratic dialogues (it refers of course to the dialogues before Hippias Major) cut up all things which have the same name/definition from all other things and try to understand them separately, without considering other things that are not in their logos. They, for example in Hippias Major, are cutting up to kalon and try to understand what it and all others inside this logos are by separating it from all other things. This is directed straightly against Socratic question and the way Socratic dialogues follow to find its answer, every time separating one logos. As Meyer (1995, 85) points out, every question 'presupposes that the X in question in a logos is something' and 'every answer to every question aims at unity' (84). The critique of Hippias Major is, therefore, at the same time a critique of SK and SB. It is also a critique of KWX because it is only based on KWX that Socratic dialogues could search for the answer of 'what is X' question supposing that knowing what X is is enough for the knowledge of X. SK and KWX are absolutely interdependent. What Socrates and all his previous interlocutors have neglected in Socratic dialogues, Hippias says, was 'continuous bodies of being' (διανεκῆ σώματα τῆς οὐσίας) (301b6). Either this theory actually belongs to the historical Hippias as it is being said or not, it is strictly criticizing SB. We have the same phrase with changing sūma to logos some lines later at 301e3-4: διανεκεῖ λόγῳ τῆς οὐσίας. Although this theory that can be observed as both an ontological and an epistemological theory is rejected by Socrates (301cff.), it is still against first Socrates’ onto-epistemological principles and might let us look at what is rejected as Socratic prineple. -/- 6. Knowledge is of Being The sixth principle that I think is presupposed by the first Socrates, is the 'Knowledge of Being' Principle (KB): -/- KB Knowledge is of Being. -/- This principle is obviously the source of the problem of false knowledge, a very important problem throughout Plato’s philosophy. We face this problem maybe for the first time in Euthydemus. In less than 20 Stephanus’ pages, 276-295, we are encountered with different interwoven problems about knowledge , all grounded in the problem of false opinion. Having challenged the obvious possibility of telling lies at 283e, at 284 Euthydemus discusses it saying that the man who speaks is speaking about 'one of those things that are (ἓν μὴν κἀκεῖνό γ᾽ ἐστὶν τῶν ὄντων)' (284a3) and thus speaks what is (λέγων τὸ ὄν) (a5). He must necessarily be saying truth when he is speaking what is because he who speaks what is (τὸ ὄν) and the things that are (τὰ ὄντα) speaks truth (τἀληθῆ λέγει) (a5-6). This is based on Parmenidean principle of the impossibility of being of not being which Euthydemus restates (284b3-4) and we mentioned discussing BO principle above. The things that are not are nowhere (οὐδαμοῦ) and there is no possibility for anyone to do (πράξειεν) anything with them because they must be made as being before anything else can be done, which is impossible (b5-7). The words, then, are of things that exist (εἰσὶν ἑκάστῳ τῶν ὄντων λόγοι) (285e9) and as they are (ὡς ἔστιν) (e10). The result is that no one can speak of things as they are not. It is this impossibility of false speach that is extended to thinking (δοξάζειν) at 286d1 and leads to the impossibility of false opinion (ψευδής … δόξα) (286d4). The general conclusion is asserted at 287a extending this impossibility to actions and making any kind of mistake. Not only knowledge is of being but speech, thought and action are of being simply because of the fact that nothing can be of not being. -/- B. First Socrates’ Principles in the Middle Period Dialogues Out of what were presupposed or criticized mostly in five dialogues, Euthyphro, Euthydemus, Hippias Major, Laches and Charmides, we tried to draw the first Socrates’ principles. Our inquiry here is directed to find out the fate of these principles in the three dialogues of the middle period, Meno, Phaedo and Republic. To do this, first we ought to check the situation of Socratic circle in these dialogues. The Socratic circle that was predominant in the early dialogues, does not look like a circle here anymore though they certainly have some features in common. Meno, Phaedo and Republic II-X are not committed to the principles of the circle and the whole circle in disrupted in them. The difference of the two Socrateses towards acquiring knowledge is obvious. The Socrates of Meno, Phaedo and Republic is evidently more self-confident that he can get to some truths during his arguments as he does. They are in their first appearance, as almost all other dialogues, committed to Socrates’ disavowal. All of them try to keep the shape of the Socratikoi Logoi genre, which is committed to the historical Socrates’ way of discussion; a dramatic personage who is to challenge his interlocutors, ask them and refuse the answers. Nevertheless, the fact is that what we have in common between two groups of dialogues is mostly a dramatic structure. Whereas the first group’s arguments are based on Socrates’ disavowal and lead to no positive results, the second group is decisively going to achieve some positive results. The aim of the first Socrates was to show others that they are ignorant of what they thought they knew. The new Socrates of Meno, on the opposite, makes so much efforts to show that the slave boy has within himself true opinions (ἀληθεῖς δόξαι) about the things that he does not know (οἶδε) (85c6-7). Despite his lack of knowledge, he has true opinions nevertheless. The way from these true opinions to knowledge, as Socrates states, is not so long. These true opinions are now like a dream but 'can become knowledge of the same things not less accurate than anyone’s' (οὐδενὸς ἧττον ἀκριβῶς ἐπιστήσεται περὶ τούτων) (c11-d1), if they be repeated by asking the same questions. The most outstanding text regarding Socrates’ disavowal is Meno 98b where he explicitly claims knowledge: -/- And indeed I also speak as (ὡς) one who does not know (εἰδὼς) but is guessing (εἰκάζων). However, [about the fact] that true opinion and knowledge are different, I do not altogether expect (δοκῶ) myself to be guessing (εἰκάζειν), but if I say about anything that I know (εἰδέναι) -which about few things I say- this is one of the things that I know (οἶδα). (98b1-5) This passage is very significant about Plato’s disavowal of knowledge. There can hardly be found, I think, anywhere else in Plato’s corpus where Socrates speaks about his knowledge of something as such. He says first that he speaks as someone who does not know. This ὡς οὐκ εἰδὼς λέγω comparing with what he used to say in the first group, οὐκ οἶδα, has this added ὡς. Socrates does not claim strongly anymore that he does not know anything but speaks only as someone who does not know. He needs this ὡς not only because he is going to accept that he does know some, though few, things immediately after this sentence, but also because he needs his previous disavowal to be loosened from Meno on. He does not merely say here that he knows something. It is then different from the examples mentioned before which could be taken as idiomatic or at least not emphatic. Socrates’ remarkable emphasis on distinguishing εἰδέναι from εἰκάζειν departs it from all other passages where he says only he knows something. Moreover, he claims definitely that he has knowledge about few (ὀλίγα) things. From the early to the middle dialogues, Socrates’ attitude to knowledge has totally renewed its face. He brings forth a new concept, true opinion, and he does not speak of knowledge as he used to before; the rough, perfect and unachievable knowledge of the first group has turned to something more smooth, realistic and achievable. Comparing with the early dialogues that did not set out from the first to reach positive results, the middle ones are extraordinarily and surprisingly positive and hence destroy the basis of the Socratic circle. The questions and answers are purposely directed to some specific new theories; most of them are not directly related to the topics or the main questions of the dialogues. They are suggested when Socrates draws the attention of the interlocutor away from the main question because of the necessity of another discussion. Even if the main question remains unanswered, we have still many positive theories, prominently of metaphysical type. These theories are so abundant and dominant in these dialogues, especially Phaedo and Republic, that one might think that they may appear to be arbitrarily sandwiched in there. This helps dialogues to keep their original Socratic structure while they are suggesting new theories. Hence, the Socratic question of 'what is X?', though is still used to launch the discussion, is loosened and is forgotten for most part of the dialogues. Meno that has first a differently formulated question, 'can virtue be taught?', leads finally to the Socratic question of 'What is virtue?'. Phaedo is dedicated to the demonstration of the immortality of soul and the life after death without having a central Socratic question. The case of Republic is more complicated. The first book, on the one hand, has all the criteria of a Socratic circle: its 'what is justice?' question, Socrates’ strong disavowal (e.g. 337d-e), his rejection of all answers and coming back to the first point without finding out any answer. This Book, considered alone, is a perfect Socratic dialogue, as many scholars regard it as early and separated from other books. The books II-X are, on the other hand, far from implementing a Socratic circle. They have still the 'what is justice?' question as their incentive leading question, but they are, in most of the positive doctrines and methods that encompass the main parts, ignoring the question. Even these books that, I believe, are the farthest discussions from the Socratic circle are so cautious not to break the Socratic structure of the dialogue as long as it is possible. What is changed is not the structure of the dialogue but the ontological and epistemological grounds based on which new theories are suggested. -/- 1. Knowledge of the Good We can clearly see in the second group of dialogues that the KWX principle loses the place it had before in our first group. It is not, of course, rejected, but still we cannot say that it has the same situation. KWX that was based on Socratic question, as we discussed before, was the leading principle of the first Socrates’ epistemology and of the highest position. Other epistemological principles, SK directly and BE indirectly, were relying on Socratic question and therefore on KWX. Such a position does not belong to KWX from Meno on. What makes it different in the second Socrates is another principle that is needed it not only as its complementary principle but also as what is more fundamental. Plato, then, does not reject KWX in this period, but, it seems, he transcends to another more basic principle; a principle we shall call the principle of 'Knowledge of the Good' (KG): -/- KG Knowledge of X requires knowledge of the Good. -/- Whereas all the dialogues of our first group are free from any discuscon about KG, it bears a very important role in the second group so as becomes the superior principle of knowledge in Republic. Trying to solve the problem of teachability of virtue, Socrates says that it can be teachable only if it is a kind of knowledge because nothing can be taught to human beings but knowledge (ἐπιστήμην) (Meno 87c2). The dilemma will be, then, whether virtue is knowledge or not (c11-12) and since virtue is good, we can change the question to: whether is there anything good separate from knowledge (εἰ μέν τί ἐστιν ἀγαθὸν καὶ ἄλλο χωριζόμενον ἐπιστήμης) (d4-5). Therefore, the conclusion will be that if there is nothing good which knowledge does not encompass, virtue can be nothing but knowledge (d6-8). What let us discuss KG as an epistemological principle for the second Secrates is the relation he tries to establish between knowledge and the Good which, though is alongside with the mentioned thesis and the idea of virtue as knowledge, goes much deeper inside epistemology asking to regard the Good as the basis of knowledge. The effort of Phaedo cannot succeed in establishing the Good as the criterion of explanation and knowledge since, I think, it needs a far more complicated ontology of Republic where Socrates can finally announce KG. What is said in Republic is totally compatible with Phaedo 99d–e and the metaphor of watching an eclipse of the sun. In spite of the fact that we do not have adequate knowledge of the Idea of the Good, it is necessary for every kind of knowledge: 'If we do not know it, even if we know all other things, it is of no benefit to us without it' (505a6-7). The problem of our not having sufficient knowledge of the Idea of Good is tried to be solved by the same method of Phaedo 99d-e, that is to say, by looking at what is like instead of looking at thing itself (506d8-e4). It is this solution that leads to the comparison of the Good with sun in the allegory of Sun (508b12-13). What the Good is in the intelligible realm corresponds to what the sun is in the visible realm; as sun is not sight, but is its cause and is seen by it (b9-10), the Good is so regarding knowledge. It has, then, the same role for knowledge that the sun has for sight. Socrates draws our attention to the function of sun in our seeing. The eyes can see everything only in the light of the day being unable to see the same things in the gloom of night (508c4-6). Without the sun, our eyes are dimmed and blind as if they do not have clear vision any longer (c6-7). That the Good must have the same role about knowledge based on the analogy means that it must be considered as a required condition of any kind of knowledge: -/- The soul, then, thinks (νόει) in the same way: whenever it focuses on what is shined upon by truth and being, understands (ἐνόησέν), knows (ἔγνω) and apparently possesses understanding (νοῦν ἔχειν). (508d4-6) -/- Socrates does not use agathon in this paragraph and substitutes it with both aletheia and to on. He links them with the Idea of the Good when he is to assert the conclusion of the analogy: -/- That which gives truth to the objects of knowledge and the power of knowing to the knower, you must say, is the Idea of the Good: being the cause of knowledge and truth (αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας) so far as it is known (ὡς γιγνωσκομένης μὲν διανοοῦ). (508e1-4) Knowledge and truth are called goodlike (ἀγαθοειδῆ) since they are not the same as the Good but more honoured (508e6-509a5). KG, which had been implicitly contemplated and searched in Phaedo, is now explicitly being asserted in Republic. As what was quoted clearly proves, this principle is the very one which we can observe as the most fundamental principle of the second Socrates in Republic, corresponding to the role KWX had in the first Socrates. The Form of the Good in Republic, of which Santas speaks as 'the centerpiece of the canonical Platonism of the middle dialogues, the centerpiece of Plato’s metaphysics, epistemology, ethics and …' (1983, 256) much more can be said. Plato’s Cave allegory in Book VIII dedicates a similar role to the Idea of the Good. The Idea of the Good is there as the last thing to be seen in the knowable realm, something so important that its seeing equals to understanding the fact that it is the cause of all that is correct and beautiful (517b). Producing both light and its source in visible realm, it controls and provides truth and understanding in the intelligible realm (517c). -/- 2. Tripartite Epistemology BE is thoroughy rejected in the second Socrates and substituted by its opposite, the principle of 'Tripartite Epistemolgy' (TE): -/- TE Opinion is an epistemological status between knowledge and ignorance. BE of the first Socrates was denying any third way besides knowledge and ignorance which was the foundation of Socratic circle without which Socrates could not reject his interlocutors’ possessing any kind of knowledge. We cannot say, however, that the first Socrates had a third epistemological status in mind but rejected it. Such a status was unacceptable for him so that one can say that he would reject any kind of such status if suggested. There were only two possibilities about knowledge: either one knows something or he does not know it. TE, thus, was not the first Socrates’ discovery and, I think it is not the second Socrates’discovery. All we can see in our second group of dialouges is that he uses this principle as an already demonstrated one. Having examined the slave boy in Meno for the prupose of showing the working of recollection, it truns out that he has some opinions in him while he still does not know. Without trying to prove it, Socrates takes this as the distinction between knowledge and opinion: -/- So, he who does not know (οὐκ εἰδότι) about what he does not know (περὶ ὧν ἂν μὴ εἰδῇ) has within himself true opinions (ἀληθεῖς δόξαι) about the same things he did not know (περὶ τούτων ὧν οὐκ οἶδε) (85c6-7). -/- The same distinction is set between ὀρθὴν δόξαν and ἐπιστήμην at 97b5-6 ff. (also cf. 97b1-2: ὀρθῶς μὲν δοξάζων … ἐπιστάμενος). He connects then their difference to the myth of Daedalus, the statue that would run away and escape. So are true opinions, not willing to remain long in mind and thus not worthy until one ties them down by αἰτίας λογισμῷ (98a3-4). Socrates says that this tying down is anamnesis. We face, in Phaedo, the same relation is settled between knowledge as the process of being tied down and getting the capability to give an account, on the one hand, and anamnesis, on the other hand. When a man knows, he must be able to give an account of what he knows (Phaedo 76b5-6) and since not all people are able to give such an account, those who recollect, recollect what once they learned (76c4). Although the distinction between knowledge and opinion is not explicitly used in Phaedo, referring to the parallel link between knowledge plus account and anamnesis in Phaedo and Meno, one can say that those who cannot recollect are not able to give account and, thus, are in a state of opinion. What is said at Phaedo 84a, though not yet a definite distinction between knowledge and opinion, makes a distinction between their objects so as we can agree that it is presupposed. The soul of the philosopher, Socrates says, follows reason, stays with it forever and contemplates the divine, which is not the object of opinoin (ἀδόξαστον) (84a8, cf. Meno 98b2-5). The distinction of knowledge and belief in Republic has a significant difference with what we discussed in Meno and Phaedo since the distinction of Meno was based on anamnesis and thus more an epistemological distinction. Even in Phaedo that we do not have any elaborate discussion about the distinction, the only hint to the matter at 76 is bound to the theory of anamnesis. In addition to the relation of the distinction with this theory, there is another evidence that does not permit us to consider the distinction as an ontological distinction. Let’s see Meno 85c6-7: -/- So, he who does not know about what he does not know has within himself true opinions about the same things he did not know (τῷ οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ ἔνεισιν ἀληθεῖς δόξαι περὶ τούτων ὧν οὐκ οἶδε). (85c6-7) -/- This last sentence persists that the objects of knowledge and true opinion are the same. What Socrates is to say here is that whereas he does not know X he has true opinion about the same X. I think Socrates’ sentence that the slave boy οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ and his restatement of it by saying περὶ τούτων ὧν οὐκ οἶδε is because he wants to emphasize that the slave boy who does not know, has true opinion about the same thing. Socrates could say this just with using τούτων and there would be no necessity to bring περὶ ὧν ἂν μὴ εἰδῇ for οὐκ εἰδότι if he did not want to emphasize. -/- 3. Tripartite Ontology The distinction between knowledge and true opinion in Republic, on other side, has nothing to do with recollection, but is based on an ontological principle, 'Tripartite Ontology' (TO): -/- TO There are things that both are and are not. -/- This principle I confine, among our three dialogues of the second group, to Republic not extended to Meno and Phaedo, is obviously the opposite of BO. Speaking about the lovers of sights and sounds in the fifth book, Socrates distinguishes them from philosophers because their thought is unable to understand the nature of beautiful itself besides beautiful things (476a6-8) and hence they can only have opinions. The philosopher who, on the contrary, believes in beautiful itself and can distinguish it from beautiful things (476c9-d3), has knowledge because he knows, contrasting others who have opinion because they only opine (d5-6). Since those whose knowledge were degraded as opinion will complain about Socrates’ such calling their thought, he provides them the following argument (476e7-477b1): -/- - Does the person who knows, knows (γιγνώσκει) something (τὶ) or nothing (οὐδέν)? - He knows something (τί). - Something that is (ὂν) or is not (οὐκ ὄν)? - Something that is (ὂν) for how could something that is not be known (πῶς γὰρ ἂν μὴ ὄν γέ τι γνωσθείη)? - Then we have an adequate grasp of this: No matter how many ways we examine it, what completely is (παντελῶς ὂν) is completely knowable (παντελῶς γνωστόν) and what is in no way (μὴ ὂν δὲ μηδαμῇ) is in every way unknowable (πάντῃ ἄγνωστον). - A most adequate one. - Good. Now, if anything is such as to be and also not to be (ὡς εἶναί τε καὶ μὴ εἶναι), won’t it be intermediate (μεταξὺ) between what purely is (εἰλικρινῶς ὄντος) and what in no way is (μηδαμῇ ὄντος)? - Yes, it’s intermediate. - Then as knowledge (γνῶσις) is set over what is (τῷ ὄντι), while ignorance (ἀγνωσία) is of necessity set over what is not (μὴ ὄντι) mustn’t we find an intermediate between ignorance (ἀγνοίας) and knowledge (ἐπιστήμης) to be set over the intermediate, if there is such a thing? -/- From the third status of being we must reach to the third status of knowledge. The simple reading of this text can be an existential reading, taking the "is" of the mentioned sentences as existence. The problem is that when it is said that there is something that both is and is not reading "is" existentially, it sounds too bizarre to be acceptable. It cannot easily be understandable to have something as both existent and non-existent at the same time. This problem arose so many debates and led many scholars to reject the existential reading of "is" and suggest some other readings like predicative or veridical readings. I think though Plato’s complicated ontology of Republic cannot be correctly understood by a simple existential reading, this "is" cannot be free from existential sense of being and, thus, cannot be reduced to just a predicative or veridical sense of being. -/- 4. Bound Knowledges In addition to KG, the Good is also the basis of another principle in the second Socrates, namely the principle of 'Bound Knowledge' (BK): -/- BK Knowledge of everything is bound to the knowledge of the Good. -/- We distinguished BK from KG because we want to insist, in BK, on what had not been insisted upon in KG, that is, the binding role that the Good plays in the second Socrates, contrasting the absence of such a role in the first Socrates. Socrates remembers, in Phaedo, his wonderful keen on natural philosophers' wisdom when he was young. The origin of this enthusiasm was Socrates’ hope to know the cause of everything as they used to claim. When he was searching the matters of his interest on their basis, Socrates says, he became convinced he can get no acceptable answer from them and found himself blind even to the things he thought he knew before. One day he hears Anaxagoras’ theory that 'it is Mind that arranges and is the cause of everything (ὡς ἄρα νοῦς ἐστιν ὁ διακοσμῶν τε καὶ πάντων αἴτιος)' (Phd. 97c1-2 cf. DK, Fr.15.8-9, 11-12, 12-14) and thinks that he can finally find what he has always expected, i.e. something which can explain all things. What I intend to show here is that what makes Socrates hopeful is that Anaxagoras’ theory tries 1) to explain all things by one thing and 2) this explanation is understood by Socrates as if it is based on the concept of the Good. That Socrates was searching for one explanation for all things can be proved even from what he has been expecting from natural philosophers. The case is, nonetheless, more clearly asserted when he speaks about Anaxagoras’ theory. In addition to διακοσμῶν τε καὶ πάντων αἴτιος of 97c2 mentioned above, we have τὸ τὸν νοῦν εἶναι πάντων αἴτιον (c3-4) and τόν γε νοῦν κοσμοῦντα πάντα κοσμεῖν (c4-5) all emphasizing on the cause of all things (πάντα) which can clearly prove that one of the reasons which caused Socrates to embrace it delightfully was its claim to provide the cause of all things by one thing. Another reason was that Anaxagoras’ Mind, at least in Socrates’ view, was attempting to explain everything by the concept of the Good. This connection between Mind and Good belongs more to the essential relation they have in Socrates’ thinking than Anaxagoras’ theory because there are almost nothing about such a relation in Anaxagoras. The reason for Socrates’ reading can be that Mind is substantially compatible with Socrates’ idea of the relation between good and knowledge. Both the thesis 'no one does wrong willingly' and the theory of virtue as knowledge we pointed to above are evidences of this essential relation. Nobody who knows that something is bad can choose or do it as bad. The reason, when it is reason, that means when it is as it should be, when it is wise or when it knows, works only based on good-choosing. In this context, when Socrates hears that Mind is considered as the cause of everything, it sounds to him like this: good should be regarded as the basis of the explanation of all things. We see him, thus, passing from the former to the latter without any proof. This is done in the second sentence after introducing Mind: -/- I thought that if this were so, the arranging Mind would arrange all things and put each thing in the way that was Best (ὅπῃ ἂν βέλτιστα ἔχῃ). If one then wished to find the cause of each thing by which it either perishes or exists, one needs to find what is the best way (βέλτιστον αὐτῷ ἐστιν) for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is the most excellent (ἄριστον) and best (βέλτιστον). The same man must inevitably also know what is worse (χεῖρον), for that is part of the same knowledge. (97c4-d5) This passage is a good evidence of Socrates’ leap from Anaxagoras’ Mind to his own concept of the Good that can explain why Socrates found Anaxagoras theory after his own heart (97d7). Mind is welcomed because of its capability for explanation on the basis of good to 'explain why it is so of necessity, saying which is better (ἄμεινον), and that it was better (ἄμεινον) to be so' (97e1-3). What Socrates thought he had found in Anaxagoras can indicate what he had been expecting from natural scientists before. Socrates could not be satisfied with their explanations because they were unable to explain how it is the best for everything to be as it is. It can probably be said, then, that it was the lack of the unifying Good in their explanation that had disappointed him. We must insist that we are discussing what Socrates thought that Anaxagoras’ theory of Mind should have been, not about Anaxagoras’ actual way of using Mind. Phaedo 97c-98b, is not about what Socrates found in Anaxagoras but what he thought he could find in it. On the contrary, it should also be noted that it was not this that was dashed at 98b, but Anaxagoras’ actual way of using Mind. It was Anaxagoras’ fault not to find out how to use such an excellent thesis (98b8-c2, cf. 98e-99b). Socrates gives an example to show how not believing in 'good' as the basis of explanation makes people be wanderers between different unreal explanations of a thing. His words δέον συνδεῖν (binding that binds together) as a description for the Good we chose as the name of BK principle: They do not believe that the truly good and binding binds and holds them together (ὡς ἀληθῶς τὸ ἀγαθὸν καὶ δέον συνδεῖν καὶ συνέχειν οὐδὲν οἴονται). (99c5-6) -/- Having in mind Plato’s well-known analogy of the sun and the Good at Republic 508-509, we can dare to say that his warning of the danger of seeing the truth directly like one watching an eclipse of the sun in Phaedo (99d-e) is more about the difficulty of so-called good-based explanation than its insufficiency, a difficulty which is precisely confirmed in Republic (504e-505a, 506d-e). Moreover, BK is asserted in a more explicit way in the Republic, where the Good is considered not only as a condition for the knowledge of X, as was noted above discussing KG, but also as what binds all the objects of knowledge and also the soul in its knowing them. At Republic VI, 508e1-3, when Socrates says that the Form of the Good 'gives truth to the things known and the power to know to the knower (τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν)', he wants to set the Good at the highest point of his epistemological structure by which all the elements of this structure are bound. This binding aspect of the Good is by no means a simple binding of all knowledges or all the objects of knowledge, but the most complicated kind of binding as it is expected from the author of the Republic. The kind of unity the Good gives to the different knowledges of different things is comparable with the unity which each Form gives to its participants in Republic: as all the participants of a Form are united by referring to the ideas, all different kinds of knowledge are united by referring to the Good. If we observe Aristotle's assertion that for Plato and the believers of Forms, the causative relation of the One with the Forms is the same as that of the Forms with particulars (e.g. Metaphysics 988a10-11, 988b4), that is to say the One is the essence (e.g., ibid, 988a10-11: τοῦ τί ἐστὶν, 988b4-6: τὸ τί ἢν εἶναί) of the Forms besides his statement that for them One is the Good (e.g., ibid, 988b11-13) the relation between the Good and unity may become more understandable. Since the quiddity of the Good (τί ποτ᾽ ἐστὶ τἀγαθὸν) is more than discussion (506d8-e2), we cannot await Socrates to tell us how this binding role is played. All we can expect is to hear from him an analogy by which this unifying role is envisaged, the sun. The kind of unity that the Good gives to the knowledge and its objects in the intelligible realm is comparable to the unity that the sun gives to the sight and its objects in the visible realm (508b-c). The allegory of Line (Republic VI, 509d-511), like that of the Sun, tries to bind all various kinds of knowledges. The hierarchical model of the Line which encompasses all kinds of knowledge from imagination to understanding can clearly be considered as Plato’s effort to bind all kinds of knowledges by a certain unhypothetical principle. The method of hypothesis starts, in the first subsection of the intelligible realm, with a hypothesis that is not directed firstly to a principle but a conclusion (510b4-6). It proceeds, in the other subsection, to a 'principle which is not a hypothesis' (b7) and is called the 'unhypothetical principle of all things' (ἀνυποθέτου ἐπὶ τὴν τοῦ παντὸς ἀρχὴν) (511b6-7). This παντὸς must refer not only to the objects of the intelligible realm but to the sensible objects as well. Plato does posit, therefore, an epistemological principle for all things, a principle that all things are, epistemologically, bound and, thus, unified by. -/- 5. Bound Beings The ontological aspect of BK we shall call the principle of 'Bound Beings' (BB): -/- BB Being of all things are bound by the Good. -/- We saw in our principle of Split Being (SB) how the first Socrates was criticized because of his approach to split being and separate each thing from other things. The principle of Bound Beings intends to make the things more related, a duty which is done again by the Good. In the allegory of Sun, there are two paragraphs that evidently and deliberately extend the binding role of the Good to the ontological scene: -/- You will say that the sun not only makes the visible things have the ability of being seen but also coming to be, growth and nourishment. (509b2-4) -/- This clearly intends to remind the ontological role the sun plays in bringing to being all the sensible things in order to display how its counterpart has the same role in the intelligible realm (b6-10): -/- Not only the objects of knowledge (γιγνωσκομένοις) owe their being known (γιγνώσκεσθαι) to the Good, but also their existence (τὸ εἶναί) and their being (οὐσίαν) are due to it, though the Good is not being but superior to it in rank and power. That the Good is here represented as responsible for being of things in addition to their being known means, in my opinion, that Plato wants to posit BB in addition to BK. The allegory of Cave at the very beginning of the seventh Book (514aff.) can be taken as another evidence. The role of the Good, one might say, is confined to the intelligible realm because it is asserted that the role the Good plays in this realm is corresponding to that of the sun in the visible realm. The fact that Plato wants to observe the Good also as the ontological cause of the sensible things is obvious from his saying, in the allegory of Cave, that the Form of the Good 'produces light and its source (τὸν τούτου κύριον) [i.e. the sun] in the visible realm' (517c3). We can conclude, then, that the ontological function of the Good is not confined to the intelligible realm in which it is the lord and provides truth and understanding (c3-4) because it is also responsible to produce τὸν κύριον of light. 6. Proportionality of Being and Knowledge Insofaras BE and BO principles of the first Socrates gave way to TE and TO principles of the second Socrates, we cannot expect him to preserve KB in the same way as it was in the first Socrates. The new tripartite ontology and epistemology necessitates some modifications in KB which results in the principle of 'Proportionality of Being and Knowledge' (PBK): -/- PBK To every class of being there is a proportionate category of knowledge. -/- This principle, of course, does not entail the refutation of KB and thus is not kind of rejecting PBK but only a more complicated version of it. Based on PBK, we can still agree that knowledge is of being (KB) but the issue is that since none of the concepts of knowledge and being in the second Socrates are as simple as they were for the first Socrates, we need a more complicated principle for their relation here. Although from Meno 97a where the distinction of knowledge and true opinion is drawn out in the second group of the dialogues, we can expect a new relation, it is articulated in its most complete way in Republic and specifically in the allegory of Line. All the beings are divided there hierarchically to four classes, to each of them belongs a class of knowledge: imagination to images, belief to the sensible things (more correctly: the things of which they[in previous class] were images (ᾧ τοῦτο ἔοικεν)), thought to mathematical objects (?) and understanding to the Forms and the first principle. The degree of clarity that each of the classes of knowledge shares in (σαφηνείας ἡγησάμενος μετέχειν) is proportionate to the degree that its object shares in truth (ἀληθείας μετέχει). (511e2-4) -/- Conclusion From the six onto-epistemilogical principles of the first Socrates, four principles turn to their opposite in the middle period dialogues. While bipolar epistemology and ontology of the early dialogues give place to tripartite epistemology in the middle period dialogues and tripartite ontology in Republic, the split knowledge and being of the first Socrates are inclined to be substituted by bound knowledges and bound beings in the second Socrates and specifically in Republic. Not all our system of principles in this article is necessarily determinative. Either they are rightly formulated or not, our result would not be vulnerable if we accept that 1) making the distinction of knowledge and belief, 2) accepting the being of not being and 3) trying to bind both being and knowledge by the concept of the Good happens only in middle period dialogues, having been absent in the early ones. These are the favourite results all those somehow arbitrary and even oversimplified principles were to illustrate; that there is kind of a development in the epistemological as well as the ontological grounds of Plato’s philosophy. -/- Notes . (shrink)

The short exposition of the triplet model of concepts and some definitions connected with it are given. In this model any concept may be depicted as having three characteristics: a base, a representing part and the linkage between them. The paper introduces the fuzzification of concepts in terms of the triplet model.

Abstract. Boltzmann brains (BBs) are minds which randomly appear as a result of thermodynamic or quantum fluctuations. In this article, the question of if we are BBs, and the observational consequences if so, is explored. To address this problem, a typology of BBs is created, and the evidence is compared with the Simulation Argument. Based on this comparison, we conclude that while the existence of a “normal” BB is either unlikely or irrelevant, BBs with some ordering may have observable consequences. (...) There are two types of such ordered BBs: Boltzmannian typewriters (including Boltzmannian simulations), and chains of observer moments. Notably, the existence or non-existence of BBs may have practical applications for measuring the size of the universe, achieving immortality, or even manipulating the observed probability of events. -/- Disclaimer and trigger warning: some people have emotional breakdowns when thinking about topics described in the article, especially the “flux universe”. However, everything eventually adds up to normality. (shrink)

Nowadays, many semiconductors such as silicon are used in a wide range of nanoelectronic devices. However, due to the range of thermal changes and its extremely high speed, nano diamond is only compared to gold nanoparticles, which is the second best nano semiconductor in the world. Nano graphite and graphene nano strips are electrically conductive due to cloud scattering. Active nano diamond particles with such features, especially electronic ones, can be the foundation of completely new types of powerful nano (...) electronic devices. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by (...) a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

The n-th PowerSet is used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. (...) Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. This first volume collects original research and applications from different perspectives covering different areas of neutrosophic studies, such as decision-making, neutroalgebra, neutro metric, and some theoretical papers. (shrink)

In De Anima II 5, 417a21-b16, Aristotle makes a number of distinctions between types of transitions, affections, and alterations. The objective of this paper is to sort out the relationships between these distinctions by means of determining which of the distinguished types of change can be coextensive and which cannot, and which can overlap and which cannot. From the results of this analysis, an interpretation of 417a21-b16 is then constructed that differs from previous interpretations in certain important respects, (...) chief among which is its characterization of transitions from first potentiality to first actuality, e.g., learning, not as `ordinary', but rather as acquisitions of natural dispositions or faculties. (shrink)

// tl;dr A Proposition is a Way of Thinking // -/- This chapter is about type-theoretic approaches to propositional content. Type-theoretic approaches to propositional content originate with Hintikka, Stalnaker, and Lewis, and involve treating attitude environments (e.g. "Nate thinks") as universal quantifiers over domains of "doxastic possibilities" -- ways things could be, given what the subject thinks. -/- This chapter introduces and motivates a line of a type-theoretic theorizing about content that is an outgrowth of the recent literature on epistemic (...) modality, according to which contentful thought is broadly "informational" in its nature and import. The general idea here is that an object of thought is not a way *the world* could be, but rather a way *one's perspective* could be (with respect to a relevant representational question). I will spend the middle part of this chapter motivating and developing a version of this strategy that is, I’ll argue, well-suited to explaining clear phenomena concerning the attribution of perspectival attitudes -- in particular, attitudes towards loosely information-sensitive propositions -- with which extant approaches struggle. My overarching goal here will be to motivate a distinctive version of the "informational" approach -- the "Flexible Types" approach, which is based on the theory proposed in Charlow (2020). According to the Flexible Types approach, propositional attitude verbs are quantifiers over sets of possibilities, but a possibility is a type-flexible notion -- sometimes a possible world, sometimes a perspective, sometimes a set of possible worlds, sometimes a set of perspectives. -/- After introducing the Flexible Types approach, this chapter circles back to more traditional concerns for the analysis of propositions as types of possibilities -- Frege's Puzzle and the problem of Logical Omniscience. Here too the Flexible Types approach bears fruit. Although there are certainly significant differences -- I note some in the concluding section -- the gist of this theory is Hinitkkan or Lewisian in spirit (if not quite in letter). We can make progress on addressing the challenges for the analysis of propositional content in terms of types of possibilities, through empirically driven refinement of our notion of what kind of thing a "doxastic possibility" is. (shrink)

The article contains a critical analysis of Wittgenstein’s theory of logical symbolism. According to an influential interpretation, Wittgenstein presented in the Tractatus a new method of solving paradoxes. This method seems a simple and effective alternative to Russell’s type theory. Wittgenstein’s theory of logical symbolism is based on the requirement of clear notation and the context principle: the type of a symbol only “shows” itself in the way we use the signs of our language. The function sign φ(φx) does not (...) express any paradox, because the syntactic rules for its use, written in clear notation, should “show” us that φ(φx) = ψ(φx). Many researchers (Davant, Ishiguro, Mounce, Ruffino, Friedlander, Jolley, Livingston, Ladov, et al.) follow this interpretation. However, the difficulty of such a view on Wittgenstein’s theory of logical symbolism is that there hides the fallacy of petitio principii. Indeed, in examples of a functional sign of the form φ(φx), we are interested not only in the question of whether the functions φ are different symbols, but also in how this functional sign φ(φx) itself excludes the symbolization of the same object by different ways. This interpretation is contrasted with the idea that Wittgenstein’s theory of logical symbolism is in fact a modified analogue of Russell’s simple theory of types. The reciprocality principle becomes the core of Wittgenstein’s theory: the combinatorial potential of the “prototype” of a functional sign is identical to the combinatorial potential of the “prototype” of an argument. According to Wittgenstein, only describing the combinatorial potential of linguistic expressions (symbols) can vanish the illusion of paradoxes. The function cannot be its argument, because the function sign φ(φx) already contains the “prototype” of its argument, “showing” us that φ(φx) = φx. The correctness of this interpretation does not exclude the possibility that the differences between Russell and Wittgenstein are in fact nothing more than façon de parler. (shrink)

Implementing an algorithm on part of our causally-interconnected physical environment requires three choices that are typically considered arbitrary, i.e. no single option is innately privileged without invoking an external observer perspective. First, how to delineate one set of local causal relationships from the environment. Second, within this delineation, which inputs and outputs to designate for attention. Third, what meaning to assign to particular states of the designated inputs and outputs. Having explained these types of arbitrariness, we assess their relevance (...) for algorithms from various computational theories of mind (CTM) seeking to account for phenomenal consciousness. Some CTM accounts can survive some of these arbitrariness challenges, but eventually each one examined faces a trilemma. Each is under pressure to dilute at least one of three important CTM desiderata: its causal relevance, its substrate neutrality, or its assignment discrimination (e.g. ability to avoid near-panpsychism). However, unlike previous research, we suggest the debate cannot be fully settled at the level of principle. Certain complex CTM algorithms may be salvageable, albeit not the algorithms specified to date. The paper specifies three areas of investigative work, as well as further theoretical avenues of research, which computationalists may wish to explore to escape the trilemma. (shrink)

Discusses conceptions of freedom displayed in Tacitus' Agricola. Tacitus seems to have had a clear-cut conceptual grid in which the German defectors, the Usipi, mirror the futile demonstrations of freedom by senators seeking a "ambitious death." The British provincials, including Calgacus and his followers, correspond to the ordinary Roman people and their leadership. It is in the army that a form of non-debasing hierarchy for the common benefit can be conceived, as long as the army and their leader is in (...) the field. Problems arise when the military meets the civilian sphere. (shrink)

This paper is going to deal with water absorption in different types of wood such as: pine, oak, beech, and fir. The amount of water absorbed by these types of wood is known as water absorption and it is determined using the material's initial state and after their immersion in water. The major goal of this study is to explain the effects of water absorption in hardwood materials and to demonstrate the changes that will take place in them (...) over the course of 48 hours. Water can be absorbed by wood in a variety of ways, as a liquid, or as an atmospheric vapor. Despite the fact that wood can absorb other liquids and gases, water is the most important. Because of its hygroscopicity, wood, whether as part of a living tree or as a material, always contains moisture. The experiment will be focused on the selection of different types of wood (most popular in the Albanian context), analyzing their water absorption and moisture level. The wooden samples will be submerged in water for 24 and 48 hours in order to obtain the appropriate results. Their moisture level and water level due to capillarity will be analyzed too. The purpose of the study is to follow the behavior of wooden frames in different environments. (shrink)

A long-standing puzzle for moral philosophers and psychologists alike is the concept of psychopathy, a personality disorder marked by tendencies to defy moral norms despite cognitive knowledge about right and wrong. Previously, discussions of the moral deficits of psychopathy have focused on willingness to harm and cheat others as well as reasoning about rule-based transgressions. Yet recent research in moral psychology has begun to more clearly define the domains of morality, en- compassing issues of harm, fairness, loyalty, authority, and spiritual (...) purity. Clinical descriptions and theories of psychopathy suggest that deficits may exist primarily in the areas of harm and fairness, although quantitative evidence is scarce. Within a broad sample of participants, we found that scores on a measure of psychopathy predicted sharply lower scores on the harm and fairness subscales of a measure of moral concern, but showed no relationship with authority, and very small relationships with ingroup and purity. On a measure of willingness to violate moral standards for money, psychopathy scores predicted greater willingness to violate moral concerns of any type. Results are further explored via potential mediators and analyses of the two factors of psychopathy. (shrink)

Although being widely considered as only a Western tradition, individualism is not absent in traditional Chinese philosophy and culture. In some of the classic Chinese philosophic works such as Zhuangzi, we can clearly identify some elements which can be appropriately attributed to “individualism”, such as the awareness of individual “self” as an independent and unique existence, advocating individual freedom and liberty, emphasizing on the value and dignity of individual life, favoring individuals’ autonomy and privacy, pursuing unconstrained development in personality and (...) spirituality. However, due to its particular pre-Qin social cultural background and its unique Daoist philosophic origin, this kind of individualism in Zhuangzi has its own unique characteristics, which has made it distinguishable from the variety of other individualist thoughts emerged in different times and places in the West. Zhuangzi has a dynamic and open view on individual or “self”, he does not consider individuals as fixed and interchangeable “atoms” but as dynamic, changing and unique beings, he set the unlimited and indefinable Dao as the only and ultimate source for individuals to conform to, thus to release individual mind into an realm of infinite openness and freedom. Zhuangzian individualism is “inward” rather than “outward”, which means while concentrating on individuals’ freedom of spirit and innate nature, it cares less about individuals’ outside material interests and rights in social reality, and does not encourage competition and rivalry among individuals. The special type of individualism in Zhuangzi has a profound influence on Chinese culture, providing a spiritual space for the development of individuality and personality in ancient China. It also provides an alternative understanding of individual as an existence. (shrink)

Philosophers, psychologists, economists and other social scientists continue to debate the nature of human well-being. We argue that this debate centers around five main conceptualizations of well-being: hedonic well-being, life satisfaction, desire fulfillment, eudaimonia, and non-eudaimonic objective-list well-being. Each type of well-being is conceptually different, but are they empirically distinguishable? To address this question, we first developed and validated a measure of desire fulfillment, as no measure existed, and then examined associations between this new measure and several other well-being measures. (...) In addition, we explored associations among all five types of well-being. We found high correlations among all measures of well-being, but generally correlations did not approach unity, even when correcting for unreliability. Furthermore, correlations between well-being and related constructs (e.g., demographics, personality) depended on the type of well-being measured. We conclude that empirical findings based on one type of well-being measure may not generalize to all types of well-being. (shrink)

This paper presents information about the moisture content and temperature level of brick walls in Tirana, Albania. The buildings whose walls have been studied were built in two different eras, throughout the twentieth century, and in more recent times. Given that during the second half of the twentieth century, Albania has been isolated from most of Europe and the West, and consequently the new architectural ideologies of the time, have not had the proper implementation there, the paper focuses on the (...) characteristic types of bricks used in Albania, the functions for which they are used, and their effectiveness in achieving comfort (thermal, moisture content control) during the two time periods mentioned above. Depending on the functions bricks perform in the walls studied in this paper, the walls are separated into two main groups: Walls in which bricks have structural role (red silicate brick walls, white silicate brick walls) and walls in which bricks do not have structural role (concrete block walls, holed brick walls). For all the types of bricks mentioned above, indoor moisture content and temperature measurements have been performed in all four cardinal directions. For the walls in which the bricks have a structural function, moisture measurements have been performed in all the facades of the buildings, because moisture in the bricks of these types of buildings, being a very important factor, directly affects the structural performance of the elements. The aim of the paper is to show the differences in moisture and temperature levels of the walls of these buildings, depending on the engineering and architectural techniques used during the building process, the use of insulation, and the masonry composition. (shrink)

The study aimed to know the relationship between the nature of the work and the type of communication among the Employees in the Palestinian universities. A comparative study between Al-Azhar University and Al-Aqsa University. The researchers used the analytical descriptive method through a questionnaire that is randomly distributed among the employees of Al-Azhar and Al-Aqsa universities in Gaza Strip. The study was conducted on a sample of (176) administrative employees from the surveyed universities. The response rate was (85.79%). The study (...) reached a number of results, the most important of which is that there is a high degree of satisfaction with the nature of work prevailing in the Palestinian universities in Gaza Strip from the point of view of the administrative staff, where the percentage was (68.15%). There is an Mean level of communication from the point of view of administrative staff, with a percentage of (67.50%). There is a direct correlation between the nature of the work and the prevailing pattern of communication. There is an absence of differences between the sample according to the gender variable in their perception of the nature of work and the prevailing pattern of communication. There is an absence of differences in the perception of Employees nature of work and the pattern of communication prevailing depending on the variables (age, years of service, job level, and university). There are statistically significant differences between Al-Azhar University and Al-Aqsa University in favor of Al-Azhar University. The study reached a number of recommendations, the most important of which is that the interest of the management of the Palestinian universities in Gaza Strip in general, and Al-Aqsa and Al-Azhar Universities in particular should be provided with a good nature of work and communication. There is a need for continuing the management of universities to pay attention and continuous improvement of the performance of employees. There is an importance of solving the problems of Employees and giving them the opportunity to contribute to solving their own problems. Staff rotation should be used periodically and the need to strengthen the democratic leadership style and empower university Employees. (shrink)

This study aims to identify various meanings of the expression (name) “dignity”, with particular emphasis on the meanings of this expression as it appears in the text of the Constitution of the Republic of Poland. The meaning of the name “dignity” is the concept of dignity; in turn, the different concepts of dignity encompass dignity of particular types. Twelve different meanings of the expression “dignity” are indicated – twelve different concepts of dignity, and thus twelve types of dignity. (...) Half of them are meanings (concepts) that recognize dignity as something belonging to a human being as a subject of law. They were considered in the essay Godność jako właściwość osoby. Typy godności – propozycja systematyzacji [Dignity as a Quality of Person – a Proposed Systematisation]. This group of meanings includes three concepts of dignity which recognize dignity as something constitutive of being a person: (1) inherent dignity of the person, (2) dignity established by qualities specific to a thinking being, and (3) dignity as a historically emergent social status of all human beings. The second group of meanings, treating dignity as something with which the human being (the person) is endowed, includes concepts which encompass (4) personal dignity (honour and good reputation), (5) dignity as moral excellence, and (6) dignity as appropriateness of attitude or behaviour. -/- Dignity as an attribute of collective entities and dignity as an institutionally grounded attribute are a subject of this paper. The Constitution of the Republic of Poland speaks of (1) the dignity of the Nation, (2) the dignity of office or function, and (3) public dignity. The expression “the dignity of the Nation” can be understood in four different ways: (i) analogously to the understanding of dignity of the person, (ii) of personal dignity, (iii) of dignity as moral excellence, and (iv) of dignity as appropriateness of attitude or behaviour. The expression “dignity” when designating something institutionally grounded can designate (4) the dignity of social roles, (5) the dignity of a profession, and – specifically to the Polish language – (6) dignity meaning a surname. -/- The author argues that it is unacceptable to ascribe different concepts of dignity to the expression “dignity” appearing in a specific legal provision. (shrink)

"Dignity as a Quality of Person: Types of Dignity – a Proposed Systematisation" This study aims to identify various meanings of the expression (name) “dignity”, with particular emphasis on the meanings of the expression as it appears in the text of the Constitution of the Republic of Poland. The meaning of the name “dignity” is the concept of dignity; in turn, the concept of dignity encompasses dignity of particular types. Twelve different meanings of the expression “dignity” are indicated (...) – twelve different concepts of dignity, and thus twelve types of dignity. Half of them are meanings (concepts) that recognize dignity as something belonging to a human being as a subject of law, and this essay is devoted to this group of meanings. This group of meanings includes three concepts of dignity which encompass dignity as something constitutive of being a person: (1) inherent dignity of the person, (2) dignity established by qualities specific to a thinking being, and (3) dignity as a historically emergent social status of all human beings. Only the first of these three concepts of dignity is adequate to the interpretation of the preamble and art. 30 of the Polish Constitution. The second group of meanings, treating dignity as something with which the human being is endowed, includes concepts which encompass (4) personal dignity (honour and good reputation), (5) dignity as moral excellence, and (6) dignity as appropriateness of attitude or behaviour. The other half of the meanings take dignity as something that belongs to something. These meanings will be considered in the forthcoming essay Godność jako cecha podmiotów zbiorowych i godność jako cecha ugruntowana instytucjonalnie. Typy godności – propozycja systematyzacji [Dignity as an Attribute of Collective Entities and Dignity as an Institutionally Grounded Attribute: Types of Dignity – a Proposed Systematisation]. The Constitution of the Republic of Poland speaks of (1) the dignity of the Nation, (2) the dignity of office or function, and (3) public dignity. The expression “dignity” when designating something belonging to something can also designate (4) the dignity of social status based on belonging to a social group, (5) the dignity of a profession, and – specifically to the Polish language – (6) dignity meaning a surname. The author argues that it is unacceptable to ascribe different concepts of dignity to the expression “dignity” appearing in a specific legal provision. STRESZCZENIE Opracowanie zmierza do identyfikacji różnych znaczeń wyrażenia (nazwy) „godność”, ze szczególnym uwzględnieniem znaczeń tego wyrażenia występującego w tekście Konstytucji RP. Znaczeniem nazwy „godność” jest pojęcie godności; z kolei pojęcie godności ujmuje samą godność danego typu. Wskazanych zostaje dwanaście różnych znaczeń wyrażenia „godność” – dwanaście różnych pojęć godności, zatem i dwanaście jej typów. Połowa z nich to znaczenia (pojęcia), które ujmują godność jako coś przynależnego człowiekowi jako podmiotowi i tym znaczeniom (i odpowiadającym im typom godności) poświęcone jest niniejsze opracowanie. W tej grupie znaczeń odróżnione zostają trzy pojęcia godności, które ujmują godność jako coś konstytutywnego dla bycia osobą – (1) przyrodzoną i niezbywalną godność osobową, (2) godność opartą na obserwowalnych i zmiennych cechach specyficznych dla istoty rozumnej i (3) godność opartą na historycznie ukształtowanym statusie społecznym przypisanym wszystkim ludziom. Jedynie pierwsze z tych pojęć jest adekwatne do interpretacji preambuły i art. 30 Konstytucji RP. W drugiej grupie znaczeń ujmujących godność jako coś przysługującego człowiekowi są pojęcia ujmujące godność jako cechę osoby – (4) godność osobistą (cześć i dobre imię), (5) godność osobowościową (poziom moralny) oraz (6) godność jako dyspozycja do stosownego sposobu bycia. Druga połowa znaczeń ujmuje godność jako coś przynależnego czemuś lub jako coś o charakterze konwencjonalnym, instytucjonalnym. Te znaczenia będą omawiane w kolejnym opracowaniu Godność jako cecha podmiotów zbiorowych lub cecha ugruntowana instytucjonalnie. Typy godności – Propozycja systematyzacji – Część 2. Konstytucja RP mówi o (1) godności Narodu, (2) godności urzędu lub funkcji, oraz o (3) godności publicznej (godnościach publicznych. Wyrażenie „godność” jako desygnujące coś przynależnego czemuś może także desygnować (4) godność statusu społecznego opartego na przynależności do jakiejś grupy społecznej, (5) godność zawodu oraz – co specyficzne dla języka polskiego – (6) godność jako nazwisko. Autor argumentuje, że niedopuszczalne jest przypisywanie wyrażeniu „dignity” występującym w danym przepisie prawnym, różnych pojęć godności. (shrink)

I briefly compare and contrast the philosophy of Confucius as written in the I Ching and Lao Tzu's philosophy presented in the Tao Te Ching.

How do people reason about their opponent in turn-taking games? Often, people do not make the decisions that game theory would prescribe. We present a logic that can play a key role in understanding how people make their decisions, by delineating all plausible reasoning strategies in a systematic manner. This in turn makes it possible to construct a corresponding set of computational models in a cognitive architecture. These models can be run and fitted to the participants’ data in terms of (...) decisions, response times, and answers to questions. We validate these claims on the basis of an earlier game-theoretic experiment about the turn-taking game “Marble Drop with Surprising Opponent”, in which the opponent often starts with a seemingly irrational move. We explore two ways of segregating the participants into reasonable “player types”. The first way is based on latent class analysis, which divides the players into three classes according to their first decisions in the game: Random players, Learners, and Expected players, who make decisions consistent with forward induction. The second way is based on participants’ answers to a question about their opponent, classified according to levels of theory of mind: zero-order, first-order and second-order. It turns out that increasing levels of decisions and theory of mind both correspond to increasing success as measured by monetary awards and increasing decision times. Next, we use the logical language to express different kinds of strategies that people apply when reasoning about their opponent and making decisions in turn-taking games, as well as the ‘reasoning types’ reflected in their behavior. Then, we translate the logical formulas into computational cognitive models in the PRIMs architecture. Finally, we run two of the resulting models, corresponding to the strategy of only being interested in one’s own payoff and to the myopic strategy, in which one can only look ahead to a limited number of nodes. It turns out that the participant data fit to the own-payoff strategy, not the myopic one. The article closes the circle from experiments via logic and cognitive modelling back to predictions about new experiments. (shrink)

The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three of which hinge on (...) intricacies of provability logic and its arithmetical interpretations. To check whether Égré’s solutions are satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack and we propose some refinements of them. This article aims to describe to what extent the knower paradox can be solved using provability logic and to what extent the solutions proposed in the literature satisfy Haack’s criteria. Finally, the article offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox and its solutions. (shrink)