Reductionists about knowledge-wh hold that "s knows-wh" (e.g. "John knows who stole his car") is reducible to "there is a proposition p such that s knows that p, and p answers the indirect question of the wh-clause." Anti-reductionists hold that "s knows-wh" is reducible to "s knows that p, as the true answer to the indirect question of the wh-clause." I argue that both of these positions are defective. I then offer a new analysis of knowledge-wh as a special kind (...) of de re knowledge. (shrink)

This paper raises some questions about the formalization of sentences containing ‘if’ or similar expressions. In particular, it focuses on three kinds of sentences that resemble conditionals in some respects but exhibit distinctive logical features that deserve separate consideration: whether-or-not sentences, biscuit conditionals, and concessive conditionals. As will be suggested, the examples discussed show in different ways that an adequate formalization of a sentence must take into account the content expressed by the sentence. This upshot is arguably (...) what one should expect on the view that logical form is determined by truth conditions. (shrink)

This article examines the various Liar paradoxes and their near kin, Grelling’s paradox and Gödel’s Incompleteness Theorem with its self-referential Gödel sentence. It finds the family of paradoxes to be generated by circular definition–whether of statements, predicates, or sentences–a manoeuvre that generates pseudo-statements afflicted with the Liar syndrome: semantic vacuity, semantic incoherence, and predicative catalepsy. Such statements, e.g., the self-referential Liar statement, are meaningless, and hence fail to say anything, a point that invalidates the reasoning on which the (...) various paradoxes rest. The seeming plausibility of the paradoxes is due to the fact that often the sentence used to make the pseudo-statement is ambiguous in that it may also be used to make a genuine statement about the pseudo-statement. Hence, if a formal system is to avoid ambiguity and consequent paradox and contradiction, it must distinguish between the two statements the sentence may be used to make. Gödel’s Theorem presents a further complication in that the self-reference involved is sentential rather than statemental. Nevertheless, on the intended interpretation of the system as a formalization of arithmetic, the self-referential Gödel sentence can only be an ambiguous statement, one that is both a pseudo-statement and its genuine double. Consequently, the conclusions commonly drawn from Gödel’s theorem must be deemed unwarranted. Arithmetic might well be formalized in a proper system that either excludes circular definition or introduces disambiguators. (shrink)

Proposition are the material of our reasoning. Proposition are the basic building blocks of the world/thought. Proposition have intense relation with the world. World is a series of atomic facts and these facts are valued by the proposition although sentences explain the world of reality but can’t have any truth values, only proposition have truth values to describe the world in terms of assertions. Propositions are truth value bearers, the only quality of proposition is truth & falsity, that they (...) are either true or false. Proposition mirrors the world and explains how world is arranged in an orderly manner. It scans the world(object) and are composed of atomic facts experienced and can be analyzed into propositions. Propositions are the basic units of logic. The truth (affirm) and falsity (nego) are the qualities of the propositions and universality (generality) and Particularity are the quantities of the propositions. There are propositions which are neither true nor false, they are called Pseudo-Propositions and their quality are ipso-facto i.e meaningless. Propositions are used in computers with the modifications brought by the modern logicians in the form of statements or logical sentences. The truth table of the logical gates and binary operations (1,s or 0,s are due to the revolution of the modern logic or mathematical logic. It is a fact that proposition cannot change the word but it shows the relation between the object and of the word. Objectives: The objectives of this research is to explore the importance and need of propositions in logic. It also shows the analysis of propositions and how a philosopher thoughts in terms of propositions or concepts. In this research problem it is shown that propositions had been described in many ways by most of the philosophers and logicians from Aristotle to contemporary philosophers. It also analysis the contribution of the philosophers towards proposition and its relation to the world of reality. This research also describes the definition and nature of proposition. (shrink)

Popper's account of refutation is the linchpin of his famous view that the method of science is the method of conjecture and refutation. This thesis critically examines his account of refutation, and in particular the practice he deprecates as avoiding a refutation. I try to explain how he comes to hold the views that he does about these matters; how he seeks to make them plausible; how he has influenced others to accept his mistakes, and how some of the ideas (...) or responses to Popper of such people are thus similarly mistaken. I draw some distinctions necessary to the provision of an adequate account of the so-called practice of avoiding a refutation, and try to rid the debate about this practice of at least one red herring. I analyse one case of 'avoiding' a refutation in detail to show how the rationality of scientific practice eludes both Popper and many of his commentators. Popper's skepticism about contingent knowledge prevents him from providing an acceptable account of contingent refutation, and so his method is really the method of conjecture and conjecture. He cannot do without the concepts of knowledge and refutation, however, if his account of science is to be plausible or persuasive, and so he equivocates between, amongst other things, refutation as disproof and refutation as the weaker notion of discorroboration. I criticise David Stove's account of this matter, in particular to show how he misses this point. An additional advantage Popper would secure from this equivocation is that if refutations were mere discorroborations they would be easier to achieve, and hence more common in science, than is the case. On Popper's weak notion of refutation, it would be possible to refute true theories since corroboration does not entail truth. There are two other related doctrines Popper holds about refutation which, if accepted, make some refutations seem easier to obtain than is the case. I call these doctrines 'Strong Popperian Falsificationism' (SPF) and 'Weak Popperian Falsificationism' (WPF). SPF is the false doctrine that if a prediction from some theory is refuted then that theory is refuted. Popper does not always endorse SPF. In particular, when confronted with a counterexample to it, he retreats to WPF, which is the false doctrine that if a prediction from some theory is refuted then that theory is prima facie refuted. WPF , or even SPF, can seem plausible if one has in mind predictions derived from theories in strong or conclusive tests of those theories, which I suggest Popper characteristically does. v Popper is disposed to describe any such case of predictive failure which does not lead to the refutation of the theory concerned as one in which that refutation has been avoided. To reinforce his portrayal of the refutation, or the attempted refutation, of major scientific theories as the rational core of scientific practice, Popper treats the so-called practice of avoiding a refutation as untypical of science, and much so-called avoidance he dismisses as unscientific or pseudo-scientific. I argue that his notion of avoiding a refutation is incoherent. Popper is further driven to believe that such avoidance is possible, however, because he conflates sentences with propositions and propositions with propositional beliefs. Also, he wishes to avoid being saddled with the relativisim that is a consequence of his weak account of refutation as discorroboration. Popper believes that ad hoc hypotheses are the most important of the unscientific means of avoiding a refutation. I argue that his account of such hypotheses is also incoherent, and that several hypotheses thought to be ad hoc in his sense are not. Such hypotheses appear to be so largely because of Popper's use of rhetoric and partly because these hypotheses are unacceptable for other reasons. I conclude that to know that a hypothesis is ad hoc in Popper's sense does not illuminate scientific practice. Popper has also attempted to explicate ad hocness in terms of some undesirable, or allegedly undesirable, properties of hypotheses or the explanations they would provide. The first such property is circularity, which is undesirable; the second such property is reduction in empirical content, which is not. In the former case I argue that non-circularity is clearly preferable to non-ad hocness as a criterion for a satisfactory explanation or explanans, as the case may be, and in the latter case that Popper is barking up the wrong tree. Some cases of so-called avoidance are obviously not unscientific. The discovery of Neptune from a prediction based on the reasonable belief that there were residual perturbations in the motion of Uranus is an important case in point, and one that is much discussed in the literature. The manifest failure of astronomers to account for Uranus's motion did not lead to the refutation of Newton's law of gravitiation, yet significant scientific progress obviously did result. Retreating to WPF, Popper claims that Newton's law was prima facie refuted. In general, astronomers have never shared this view, and they are correct in not doing so. I argue that the law of gravitation would have been prima facie refuted only if there had been good reason at the time to believe as false what is true, namely, that an unknown trans-Uranian planet was the cause of those Uranian residuals. Knowledge of the trans-Uranian region was then so slight that it was merely a convenient assumption, one which there was little reason to believe was false, that the known influences on Uranus's motion were the only such influences. I conclude that in believing vi or supposing that it was this assumption that was false, rather than the law of gravitation, Leverrier and Adams, the co-predictors of Neptune, were acting rationally and intelligently. Popper's commentators offer a variety of accounts of the alleged practice of avoiding a refutation, and of this case in particular. I analyse a sample of their accounts to show how common is the acceptance of some of Popper's basic mistakes, even amongst those who claim to reject his falsificationism, and to display the effects on their accounts of this acceptance of his mistakes. Many commentators recognize that anomalies are typically dealt with by changes in the boundary conditions or in other of the auxiliary propositions employed. Where many still go wrong, however, is in retaining the presupposition of WPF which encouraged Popper to hold the contradictory view about anomalies in the first place. Thus Imre Lakatos and others, for example, have developed a 'siege mentality' about major scientific theories; they see them as under continual threat of refutation from anomalies, and so come to believe that dogmatism is essential in science if such theories are to survive as they do. I examine various such doomed attempts to reconcile Popper with the history of science. It is a common failure in this literature to conflate or to fail to see the need to distinguish a belief from a supposition, and an epistemic reason from a pragmatic reason. I argue that only if one does draw these distinctions can one give an adequate account of how anomalies are rationally dealt with in science. The other important strand in Popper's thinking about 'avoidance' of refutation which has seriously misled some of his commentators is his unfounded belief in the dangers of ad hoc hypotheses. I examine the accounts that a sample of such commentators provide of the trans-Uranian planet hypotheses of Leverrier and Adams. These commentators imply or assert what Popper only hints at, namely, that there is something fishy about this hypothesis. I provide a further defence of the rationality of entertaining this hypothesis at the time. I conclude with a few remarks about Popper's dilemma in respect of scientific practice and his long standing emphasis on refutations. (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This (...) result also generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

We present a game mechanic called pseudo-visibility for games inhabited by non-player characters (NPCs) driven by reinforcement learning (RL). NPCs are incentivized to pretend they cannot see pseudo-visible players: the training environment simulates an NPC to determine how the NPC would act if the pseudo-visible player were invisible, and penalizes the NPC for acting differently. NPCs are thereby trained to selectively ignore pseudo-visible players, except when they judge that the reaction penalty is an acceptable tradeoff (e.g., (...) a guard might accept the penalty in order to protect a treasure because losing the treasure would hurt even more). We describe an RL agent transformation which allows RL agents that would not otherwise do so to perform some limited self-reflection to learn the training environments in question. (shrink)

In his Exhortation to Philosophy (Protrepticus), the Neoplatonic philosopher Iamblichus famously preserves material culled from lost works of ancient philosophy, including dialogues of Aristotle. He also preserves a work entitled On Wisdom and ascribed to the Pythagorean philosopher Archytas of Tarentum, who was a friend and challenger of Plato. The text On Wisdom is a later Hellenistic production, probably written in the 1st century BCE, but it presents an important piece in the puzzle of reconstructing Pythagoreanism for the Hellenistic and (...) Post-Hellenistic periods. On Wisdom provides ps-Archytas' views on the nature, pursuit, and purposes of philosophy, as well as the division of the parts of knowledge. This article presents the first complete modern translation into English and analysis of this work, whilst also explaining the precise ways in which its first critic, Iamblichus, appropriates its content to Neoplatonic theories. (shrink)

Alors que le débat sur le caractère scientifique ou pseudo-scientifique de l’agriculture biodynamique occupe régulièrement le débat public, l’histoire et la philosophie des sciences ne semblent que très peu s’être emparées de ce sujet. La thèse défendue ici est double : tout d’abord, si l’agriculture biodynamique rencontre un relatif succès aujourd’hui, cela tient sans doute au fait que son théoricien, R. Steiner, a été un des premiers à critiquer le paradigme qui domine l’agronomie, ou en tout cas l’agriculture, depuis (...) plus d’un siècle. Cette critique semble d’ailleurs se maintenir dans ses motifs tout au long du XXe siècle, jusqu’à une certaine critique contemporaine de l’agro-industrie et de ses conséquences désastreuses sur l’environnement. Or, et c’est la seconde thèse défendue ici, cette critique semble méconnaître voire occulter la réalité des débats internes qui ont traversé l’agronomie au cours du XXe siècle et qui continuent de l’agiter aujourd’hui : l’agronomie système a ainsi par exemple intégré dans ses objets des éléments de l’agriculture biodynamique. Selon nous, le problème principal est que l’agronomie est souvent abordée selon une approche externaliste, qui doit impérativement être complétée par une approche internaliste afin tout d’abord de distinguer ce qui relève de la science et ce qui relève du mysticisme, et ensuite de saisir toute la richesse historique et épistémologique de l’agronomie. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

In the last forty years Dummett, Hanks, Künne, and Bobzien have claimed that when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question [Satzfrage] was not a thought [Gedanke] ((Dummett 1981: 307–308); (Hanks 2007: 142–143); (Künne 2010: 427–429); (Bobzien 2021: 163–164)). Recently, Textor has claimed that when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question was not a question [Frage] (Textor 2021: 227 fn.2). I think it is possible that (...) when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question was a question and a thought. To show that this possibility should not be overlooked, I have written a dialogue in which Frege responds to Dummett, Hanks, Künne, Bobzien, and Textor. -/- Bobzien seems to think that when Frege wrote ‘Die Verneinung’, he thought that the sense of a sentence-question was not a question (Bobzien 2021: 163–165). I think it is possible that when Frege wrote ‘Die Verneinung’, he thought that the sense of a sentence-question was a question and a thought. Hence, I have also written the dialogue to show that this possibility should not be overlooked either. (shrink)

This paper discusses continuity between ancient Pythagoreanism and the pseudo-Pythagorean writings, which began to appear after the end of the Pythagorean school ca. 350 BC. Relying on a combination of temporal, formal and substantial criteria, I divide Pseudopythagorica into three categories: 1) early Hellenistic writings ascribed to Pythagoras and his family members; 2) philosophical treatises written mostly, yet not exclusively, in pseudo-Doric from the turn of the first century BC under the names of real or fictional Pythagoreans; 3) (...) writings attributed to Pythagoras and his relatives that continued to appear in the late Hellenistic and Imperial periods. I will argue that all three categories of pseudepigrapha contain astonishingly little that is authentically Pythagorean. (shrink)

The ability to communicate in a specific language like Chinese typically indicates that the speaker understands the language. A counterexample to this belief is John Searle’s Chinese room experiment. It has been shown in this experiment that in certain circumstances we can communicate with a Chinese speaker without intuitively acknowledging that the Chinese language is understood in the conversation. In the present paper, we aim to present another counterexample showing that, in certain circumstances, we can communicate using a specific language (...) by converting its words to those of our natural language, and understand what is expressed using the language without understanding it. Using a specific conversion process introduced in the present paper, symbols and even sounds of a language like the Chinese language lose their original function and act as a tool to express one’s natural language. To better understand this, imagine the English language has another writing or phonological system in addition to its current writing system. (shrink)

In this paper Timothy Williamson’s argument that the knowledge norm of assertion is the best explanation of the unassertability of Morrean sentences is challenged and an alternative account of the norm of assertion is defended.

This study aimed to determine the levels of pre-service teachers' nature of science (NOS) knowledge, assess their pseudo-scientific beliefs, and examine the relationship between aspects of their NOS knowledge and these beliefs. It also aimed to determine whether NOS knowledge and pseudo-scientific beliefs depended on the discipline and gender. A survey method was conducted in this study. Data were collected from 215 pre-service teachers who are being educated in different fields in a state university. Two different five-point Likert (...) scales were applied. Scale 1, which hasthree factors, measured pseudo-scientific beliefs, while Scale 2, which has seven factors, measured NOS knowledge. As a result, preservice teachers' NOS knowledge was found to be inadequate and their pseudoscientific beliefs were excessive. All factors of Scale 1 were positively correlated with each other, and they were correlated with some components of NOS knowledge. Significant differences were found between disciplines in the analysis of the factors of Scale 2; however, no significant differences were found between genders. (shrink)

This paper replies to Himmelreich's ‘The Paraphrase Argument Against Collective Actions’ [2017], which presents three putative counterexamples to the multiple agents analysis of plural action sentences. The paper shows that the argument from the first example, the discursive dilemma, fails because it relies crucially on a simplification of the target analysis, and that the others don't bear on the question because they turn out on examination to be about individual rather than group action sentences.

Is all explanations causal explanation? Puzzles about barometer readings "explain" storms and shadow lengths "explaining" flagpole heights make it attractive to think so. Wesley Salmon (1984) has endorsed this causal thesis. One way to test this thesis is to assess the explanatory import of pseudo-processes. I do so by discussing the concept of heritability, which measures a pseudo-process, and one role it played in the theory of natural selection: explaining response to selection. This will show, not just that (...) heritability has heuristic or predictive utility, but that it can be explanatory. Possible responses to this case are also discussed. (shrink)

In his recent "Thomas vs. Thomas: A New Approach to Nagel's Bat Argument", Yujin Nagasawa interprets Thomas Nagel as making a certain argument against physicalism and objects that this argument transgresses a principle, laid down by Thomas Aquinas, according to which inability to perform a pseudo-task does not count against an omnipotence claim. Taking Nagasawa's interpretation of Nagel for granted, I distinguish different kinds of omnipotence claims and different kinds of pseudo-tasks, and on that basis show that Nagasawa's (...) criticism of Nagel is unsuccessful. I also show how his reflections do nonetheless point to a limitation of the approach he means to criticize. (shrink)

This paper shows that Russell’s theory of descriptions gives the wrong se-mantics for definite descriptions occurring in questions and imperatives. Depending on how that theory is applied, it either assigns nonsense to per-fectly meaningful questions and assertions or it assigns meanings that di-verge from the actual semantics of such sentences, even after all pragmatic and contextual variables are allowed for. Given that Russell’s theory is wrong for questions and assertions, it must be wrong for assertoric state-ments; for the semantics (...) of ‘the phi’ obviously doesn’t vary depending on whether it occurs in a question or an assertion or a command. (shrink)

This paper examines the practice of using predictive systems to lengthen the prison sentences of convicted persons when the systems forecast a higher likelihood of re-offense or re-arrest. There has been much critical discussion of technologies used for sentencing, including questions of bias and opacity. However, there hasn’t been a discussion of whether this use of predictive systems makes sense in the first place. We argue that it does not by showing that there is no plausible theory of punishment (...) that supports it. (shrink)

Based on the notion of a trope, this paper gives a novel analysis of identificational sentences such as 'this is Mary','this is a beautiful woman', 'this looks like Mary', or 'this is the same lump of clay, but not the same statue as that'.

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

ABSTRACT In order to explore what it means to pursue philosophical investigations for theological reasons, this paper argues that Ludwig Wittgenstein continues and corrects Pseudo-Denys’ project in The Divine Names. I first argue that The Divine Names should be interpreted as attempting to render human thought transparent to the divine by relativizing our concepts. The success of this project is compromised because the concept of ‘unity’ is not relativized. I then develop the claim that Wittgenstein does relativize unity in (...) a similar way and for similar religious reasons to Pseudo-Denys. As such, he can be read as continuing and correcting the Pseudo-Dionysian project. I conclude by reflecting on several of this argument’s implications for the relationship between philosophy and Christian systematic theology. (shrink)

In Tractatus, Wittgenstein held that there are null sentences – prominently including logical truths and the truths of mathematics. He says that such sentences are without sense (sinnlos), that they say nothing; he also denies that they are nonsensical (unsinning). Surely it is what a sentence says which is true or false. So if a sentence says nothing, how can it be true or false? The paper discusses the issue.

I discuss what I call practical Moore sentences: sentences like ‘You must close your door, but I don’t know whether you will’, which combine an order together with an avowal of agnosticism about whether the order will be obeyed. I show that practical Moore sentences are generally infelicitous. But this infelicity is surprising: it seems like there should be nothing wrong with giving someone an order while acknowledging that you do not know whether it will obeyed. I (...) suggest that this infelicity points to a striking psychological fact, with potentially broad ramifications concerning the structure of norms of speech acts: namely, when giving an order, we must act as if we believe we will be obeyed. (shrink)

The influential proposal that the analytical component of a theory is captured by its ‘Carnap sentence’ is critically scrutinized. A counterexample which makes the suggestion problematic is presented.

This study proposes a framework by which grammatically and syntactically sound sentences are classified through the perceptual measurement in noise of multilinguals and monolinguals, using an objective measure called SPERI and an interpretivist measure called SPIn, with results evaluated using Shortlist models and the BLINCS model. Hereby filling a knowledge gap on the perception of sentences that combine in varying levels of contextual meaning, linguistic load and cognitive load, this study used sentence clustering methods to find limitations of (...) the proposed framework in determining an absolute and accurate prediction of performance between sentences in the proposed different categories, with factors such as sentence predictability and word frequency taking precedence. There were unintended findings including a relationship between the number of languages spoken and performance, proficiency in other languages decreasing performance despite being an English Native, and how mistakes by multilinguals were more semantically and phonetically influenced than monolinguals. (shrink)

Argues that John of Salisbury's Institutio Traiani is a pseudo-classical forgery. 34: "In my opinion this framework within which John presents his opinions is a pseudo-classical invention of his own, and an invention which in its combination of clerical and classical features is characteristic of the author.".

In this paper I discuss the Newman problem in the context of contemporary epistemic structural realism (ESR). I formulate Newman’s objection in terms that apply to today’s ESR and then evaluate a defence of ESR based on Carnap’s use of Ramsey sentences and Hilbert’s ε-operator. I show that this defence improves the situation by allowing a formal stipulation of non-structural constraints. However, it fails short of achieving object individuation in the context of satisfying the Ramsified form of a theory. (...) Thus, while limiting the scope of Newman’s argument, Carnap sentences do not fully solve the problem. (shrink)

In this paper, I challenge a familiar argument -- a composite of arguments in the literature -- for the view that “Why be moral?” is a pseudo-question. I do so by refuting a component of that argument, a component that is not only crucial to the argument but important in its own right. That component concerns the status of moral reasons in replies to “Why be moral?”; consequently, this paper concerns reasons and rationality no less than it concerns morality. (...) The work I devote to those topics shows not only that the argument I address is unsound, but that the conclusion of that argument is false. “Why be moral?” is no pseudo-question. (shrink)

The paper provides to give a minimal contribution about a typical argumentation scheme which called "ad hominem". Especially, this mode of conduct a dialogue and arguing towards an opponent has been revisited by not long past approaches on Argumentation Theory with the aim to re-legitimate it in logical context and re-consider its consequences in terms of validity, consistence and alethic thinking. Ad hominem argument is part of rational discussion and informs audience about the coherence between speaker and his favored thesis.

The main objective of this paper is to present a reinterpretation of Karl Popper’'s position on the methodological and sociopolitical views of Karl Marx. In spite of the weaknesses of the Popper’'s critique of the achievements of Marx, special attention will be focused on the explanation of contradictions within the epistemological position of the former. This will be of great importance in the context of the analysis of Marx’s historicism, and will also help undermine the coherence view of the founder (...) of falsi
cationism. Additionally, this newly developed perspective will serve as a starting point for evaluation of Marx’s intellectual output, as well as conceptions that refer to him. (shrink)

In his early philosophy as well as in his middle period, Wittgenstein holds a purely syntactic view of logic and mathematics. However, his syntactic foundation of logic and mathematics is opposed to the axiomatic approach of modern mathematical logic. The object of Wittgenstein’s approach is not the representation of mathematical properties within a logical axiomatic system, but their representation by a symbolism that identifies the properties in question by its syntactic features. It rests on his distinction of descriptions and operations; (...) its aim is to reduce mathematics to operations. This paper illustrates Wittgenstein’s approach by examining his discussion of irrational numbers. (shrink)

A suprise may occur if we use a similar strategy to the Liar's paradox to mathematically formalize "This sentence does not contain the symbol X".

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are (...) discussed. Moreover, the relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)

Proposition and sentence are two separate entities indicating their specific purposes, definitions and problems. A proposition is a logical entity. A proposition asserts that something is or not the case, any proposition may be affirmed or denied, all proportions are either true (1’s) or false (0’s). All proportions are sentences but all sentences are not propositions. Propositions are factual contains three terms: subject, predicate and copula and are always in indicative or declarative mood. While sentence is a grammatical (...) entity, a unit of language that expresses a complete thought; a sentence may express a proposition, but is distinct from the proposition it may be used to express: categories, declarative sentences, exclamatory, imperative and interrogative sentences. Not all sentences are propositions, propositions express sentence. Sentence is a proposition only in condition when it bears truth values i.e. true or false. We use English sentences governed by imprecise rule to state the precise rules of proposition. In logic we use sentence as logical entity having propositional function but grammatical sentences are different from logical sentences while the former are having only two divisions namely subject and predicate and may express wishes, orders, surprise or facts and also have multiple subjects and predicates and the latter must be in a propositional form which states quantity of the subject and the quality of the proposition and multiple subjects and multiple predicate make the proposition multiple. (shrink)

Contrary to nouns and verbs that either do not include a co-positing of parts, including nouns and some verbs, or if they are, their parts do not significate separately, a sentence (λόγος) is a ‘significant portion of speech by co-positing, its parts signify something separately, though not as a positive or negative judgment but as utterance.’ (OI ., I, 4, 16b26-28). Therefore, every utterance in language that i) includes parts, ii) its signification is based on the co-positing of its parts, (...) iii) each of its parts is separately significant but iv) the signification of its parts is the signification of an utterance and not a judgment, is a sentence. This definition distinguishes a sentence from: a) Nouns: because they do not have parts; b) Verbs: because they either do not have parts or if they have, their parts do not significate separately; c) Those co-positings of words whose significance is not based on their co-positing. Thus a co-positing like ‘wall tree house’ is not a sentence because it has no significance on the basis of its co-positing; d) Those co-positings that the signification of at least some of their parts is the signification of judgments. Thus, ‘Socrates is from Athens and is a philosopher’ is not a sentence because at least one of its parts, e.g. ‘Socrates is from Athens’ signifies a judgment. Those sentences that either of truth or falsity belongs to them are propositions (ἀπόφανσις or λόγος ἀπόφαντικὸς). (OI., I, 4, 17a2-3) It is this and only this kind of sentence that is the subject of study in philosophy. (OI., I, 4, 17a5-7) The primary forms of a proposition are, firstly, an affirmation (κατάφασις) and then a negation (ἀπόφασις). (OI., I, 4, 17a8-9) To have an affirmation or a denial and, thus, a proposition, what firstly is necessary is a verb or the tense of a verb (OI, I, 4, 17a9-12; I, 10, 19b12-13; OI, I, 4, 16b28-30) and a noun (OI, I, 10, 19b10-12). Aristotle draws a contrast between single and plural proposition: a) Single proposition: a proposition that ‘indicate a single fact, or the conjunction of the parts of which results in unity.’ (OI., I, 5, 17a15-16) b) Plural propositions: a proposition that ‘are separate and many in number, which indicate many facts, or whose parts have no conjunction.’ (OI., I, 5, 17a16-17) He also differentiates between simple and composite propositions (OI, I, 5, 17a20-22): a) Simple proposition: ‘that which asserts or denies something of something’; b) Composite propositions: ‘that which is compounded of simple propositions.’ A simple (ἁπλῆ) proposition is a statement about the belonging or not belonging of something (OI, I, 5, 17a22-24). Affirmation and denial are indeed kinds of simple proposition, one affirming the belonging and the other not belonging. An affirmation or denial may be single or non-single. A single affirmation or denial ‘signifies some one fact about some one subject. This singularity is destroyed neither by the universality of subject nor by the universal character of the statement. The only thing that destroys this singularity is that one part signifies more than one thing, which makes the proposition more than one proposition (OI, I, 8, 18a13-27). In other words, neither ‘predication of one thing of many subjects’ nor ‘many things of the same subject’ results in a unitary proposition. (OI., II, 11, 20b13-16) There is also another cause that might destroy the unity of predicate and thus the unity of proposition, namely when one of the parts of the predicate is implicit in the other. Thus, e.g. animal-man does not form a unity because the notion ‘animal’ is implicit in ‘man.’ (OI., II, 11, 21a16-18) The following are characteristics of propositions: 1. That about which an affirmation signifies something is a noun, whether definite or indefinite. (OI., I, 10, 19b5-12) Moreover, there can be no affirmation or denial without a verb. (OI., I, 10, 19b12-19) Therefore, a proposition must involve at least a noun and a verb. 2. Contrary propositions: since both belonging and not belonging of something to something is possible, we are able to make a negative proposition out of an affirmative one and vice versa. (OI., I, 5, 17a26-31) Therefore, ‘every affirmation has an opposite denial’ and vice versa. (OI., I, 6, 17a31-33) The contradictory of each proposition is made by changing the positivity or negativity of the verb ‘to be’ to its opposite but not by changing the subject to its opposite. Thus, the contradictory of ‘man is white’ is ‘man is not white’ and not ‘not-man is white.’ (OI., II, 11, 21a38-b5) What happens in the mentioned wrong form of contradictory propositions is that they change the subject while the denial must be the contrary of the affirmation about the same subject. (cf. OI., II, 14, 24b1-6) This is made plain in propositions involving a verb other than ‘to be’. What must be changed in these propositions is the verb and not the noun or the subject. Thus, the contradictory of ‘Socrates runs’ is ‘Socrates does not run’ and not ‘not-Socrates runs.’ 3. Conversion possible: ‘Out of conversion (μετατιθεμένου) of the name and the verb, the same affirmation and denial is generated. (OI., I, 10, 20b10-12) In other words, the two affirmations or denials ‘signify the same thing.’ (OI, I, 10, 20b1-2) . (shrink)

They say that argumentative writing skills are best learned through writing argumentative essays. I say that while this is excellent practice for argumentative writing, an important exercise to practice structuring such essays and build critical thinking skills simultaneously is what I call the four-sentence paper. The exercise has the template They say..., I say..., one might object..., I reply... One might object that the assignment oversimplifies argumentative writing, stifles creativity, promotes an adversarial attitude, or that students can’t consider objections well (...) anyway. I reply that a simplified form of argumentative writing is fine for beginners, especially since the template is ubiquitous in philosophy; that any assignment template has room for creativity; that considering objections is consistent with good manners; and that despite some pitfalls of trying to defend a thesis and consider objections, students are capable of considering objections well with proper instruction and practice. (shrink)

Serious actualists take it that all properties are existence entailing. I present a simple puzzle about sentence tokens which seems to show that serious actualism is false. I then consider the most promising response to the puzzle. This is the idea that the serious actualist should take ordinary property-talk to contain an implicit existential presupposition. I argue that this approach does not work: it fails to generalise appropriately to all sentence types and tokens. In particular, it fails to capture the (...) right distinctions we ought to make between what I call _typographical sentence types_—an interesting and previously undiscussed class of fine-grained sentence types which are partially individuated by their typography, or how they look when written out. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of (...) being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

In this article, I seek to answer the following cluster of questions: What would a characteristically African, and specifically relational, conception of a criminal trial’s final end look like? What would the Afro-relational approach prescribe for sentencing? Would its implications for this matter forcefully rival the kinds of penalties that judges in South Africa and similar jurisdictions typically mete out? After pointing out how the southern African ethic of ubuntu is well understood as a relational ethic, I draw out of (...) it a certain conception of reconciliation that I advance as a strong candidate for being the proper final end of a criminal trial. I argue that, far from requiring forgiveness, seeking reconciliation can provide strong reason to punish offenders. Specifically, a reconciliatory sentence is one that roughly has offenders reform their characters and compensate their victims in ways the offenders find burdensome, thereby disavowing the crime and tending to foster cooperation and mutual aid. I argue that this novel account of punishment is a prima facie attractive alternative to more familiar retributive and deterrence rationales, and that it entails that widespread practices such as imprisonment and mandatory minimum sentences are unjust. (shrink)

The polis, as a gathering of various citizens, may be threatened by discord and finally may collapse because of the stasis, the internal conflict between different groups of people with diverging interests. This scheme is tackled by Plato in Gorgias, and more thoroughly in the Republic. Both dialogues were a source of inspiration for the pseudo-Pythagorean writings which flourished between the second half of the 4th century B.C. and the Hellenistic period. Among them, the treaties attributed to Kleinias, Metopus, (...) Theages, Lysis and Hippodamus frequently use the concept of stasis and pleonexia to describe how a city may be governed and what kind of danger may appear if the citizens’ behavior is not controlled. In general, these treaties adapt the vision of Plato concerning conflict to some Pythagorean images and teachings. By mingling both influences, they blur the frontier between Platonism and Pythagoreanism and create a genre of intertwined literature which may be qualified as bricolage, according to Lévi-Strauss’s concept. These philosophical texts use a range of material mostly traced back to the Hellenistic period, but also some fragments related to the conception of conflicts and violence in early Pythagoreanism. (shrink)

The purpose of this paper is to communicate - as a proposal - a general method of assigning a 'truthmaker' to any 1st order sentence in each of its models. The respective construct is derived from the standard model theoretic (recursive) satisfaction definition for 1st order languages and is a conservative extension thereof. The heuristics of the proposal (which has been somewhat idiosyncratic from the current point of view) and some more technical detail of the construction may be found in (...) my article on part I of Spinoza's 'ethica, ordine geometrico demonstrata', which is the context within which I elaborated the assignment. But this context need not be repeated here, the presentation of the truthmaker assignment will be comprehensible to anybody with solid basic knowledge in 1st order model theory, anything used is standard and no advanced techniques are required. (shrink)

Legal theorists have characterized physical evidence of brain dysfunction as a double-edged sword, wherein the very quality that reduces the defendant’s responsibility for his transgression could simultaneously increase motivations to punish him by virtue of his apparently increased dangerousness. However, empirical evidence of this pattern has been elusive, perhaps owing to a heavy reliance on singular measures that fail to distinguish between plural, often competing internal motivations for punishment. The present study employed a test of the theorized double-edge pattern using (...) a novel approach designed to separate such motivations. We asked a large sample of participants (N = 330) to render criminal sentencing judgments under varying conditions of the defendant’s mental health status (Healthy, Neurobiological Disorder, Psychological Disorder) and the disorder’s treatability (Treatable, Untreatable). As predicted, neurobiological evidence simultaneously elicited shorter prison sentences (i.e., mitigating) and longer terms of involuntary hospitalization (i.e., aggravating) than equivalent psychological evidence. However, these effects were not well explained by motivations to restore treatable defendants to health or to protect society from dangerous persons but instead by deontological motivations pertaining to the defendant’s level of deservingness and possible obligation to provide medical care. This is the first study of its kind to quantitatively demonstrate the paradoxical effect of neuroscientific trial evidence and raises implications for how such evidence is presented and evaluated. (shrink)

We take an argument of Gödel's from his ground‐breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: "the sentence G says about itself that it is not provable, and G is indeed not provable; therefore, G is true".

Semanticists face substitution challenges even outside of contexts commonly recognized as opaque. Jennifer M. Saul has drawn attention to pairs of simple sentences - her term for sentences lacking a that-clause operator - of which the following are typical: -/- (1) Clark Kent went into the phone booth, and Superman came out. (1*) Clark Kent went into the phone booth, and Clark Kent came out. -/- (2) Superman is more successful with women than Clark Kent. (2*) Superman is (...) more successful with women than Superman. -/- She challenges us to explain why the upper and lower sentences in each pair differ, or at least appear to differ, in their truth-values and hence truth-conditions. This appearance of substitution failure is inherently puzzling. Moreover, it is taken by Saul to generate a dilemma for anyone hostile to direct reference accounts of that-clause constructions. Direct reference theorists regard the appearance of substitution failure in that-clause contexts as mere appearance, to be dealt with pragmatically rather than semantically. -/- Critics of such accounts need to say something about simple-sentence cases. If they choose to allow that intuitions of substitution failure can be over-ridden and explained away pragmatically in simple-sentence cases but not in that-clause cases, they lay themselves open to the charge of operating a double standard. But if they do not choose this option, they must offer a semantic explanation of apparent substitution failure in simple-sentence cases - no easy task, it turns out. Other respondents to Saul's challenge have sought to provide elaborate semantic treatments. In contrast, this paper proposes a far simpler pragmatic explanation of intuitions of substitution failure in simple sentences, an explanation that deploys no more resources than are to be found in Grice's 'Logic and Conversation'. Ironically, this proposal turns out to be incompatible with a direct reference perspective. So if it is, as I maintain, the most plausible treatment of simple-sentence cases available, Saul's initial thought gets turned around 180 degrees: the phenomenon she has drawn attention to ends up representing a challenge to supporters of direct reference theories. (shrink)

We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a property F, and A does in fact have the property F; therefore A is true. We then examine an argument of this form in the informal introduction of Gödel’s classic (1931) and examine some auxiliary premises which might have been at work in that context. Philosophically significant as it may be, that particular (...) informal argument plays no rôle in Gödel’s technical results. Going deeper into the issue and investigating truth conditions of Gödelian sentences (i.e., those sentences which are provably equivalent to their own unprovability) will provide us with insights regarding the philosophical debate on the truth of Gödelian sentences of systems—a debate which goes back to Dummett (1963). (shrink)