A familiar question is whether psychological egoism (suitably supplemented with plausible further premises) entails ethical egoism. This paper considers this question, treating it much more thoroughly than do any previous treatments. For instance, it discusses all of the most common understandings of ethical and psychological egoism. It further discusses many strategies and arguments relevant to the question addressed. Although this procedure creates complexity, it has value. It forestalls the suspicion, aroused by so many treatments of this subject, that the results (...) stem largely from leaving stones unturned – for instance, from ignoring many natural argumentative strategies and many familiar understandings of the views discussed. The paper’s conclusion is that psychological egoism (suitably supplemented …) does not entail ethical egoism. (shrink)

What exactly is reasoning? While debate on this question is ongoing, most philosophers seem to agree on at least the following: reasoning is a mental process operating on contents, which consists in adopting or revising some of your attitudes in light of others. In this paper, I argue that this characterisation is mistaken: there is no single mental phenomenon that satisfies both of these conditions. Instead, I characterise two distinct mental phenomena, which I call ‘deducing’, on the one hand, and (...) ‘reasoning’ or ‘inference’ on the other, to play each of these roles. Recognising this division of labour is essential to developing a better understanding of our rational economy. (shrink)

In The Matter of Consciousness, in the course of his extended discussion and defense of Frank Jackson’s famous knowledge argument, Torin Alter dismisses some objections on the grounds that they are cases of cheating. Though some opponents of the knowledge argument offer various scenarios in which Mary might come to know what seeing red is like while still in the room, Alter argues that the proposed scenarios are irrelevant. In his view, the Mary case is offered to defend the claim (...) that phenomenal facts cannot be a priori deduced from physical facts. Thus, a proposed scenario constitutes an objection to the knowledge argument only if it presents a case in which Mary’s learning inside the room comes about via a priori deduction from physical facts. Call this the deducibility standard. In what follows, I’ll explore a series of relevant cases in an effort to clarify this standard. Doing so enables us to better understand how cheating should be assessed in this context and thereby also to get clearer on the argumentative dialectic surrounding the Mary case. (shrink)

Demonstrating Information Theory of Aging's robustness and practicality through deductive reasoning. Potentially anti-aging vaccines will automatically mass produce. Information Theory of Aging is the most robust and practical out of current theories explaining human age. Aging is a disease best explained as information loss. Damage theory does not account for damage’s possible necessity towards human personal growth. A cellular error is difficult to define, thus, error theory also lacks veracity. When is an error actually an adaptive mutation? When is damage (...) actually adaptive mutation? Plus, information theory of aging is uniquely accessible to computer assistance. Unfortunately, death may be inevitable, a sequel to this essay, to hopefully map the afterlife, will be Critical Rationalist Parapsychology. (shrink)

Here we discuss about the following results: 1.

Abstract Introduction Logically valid deductive arguments are clear examples of abstract recursive computational proce‐ dures on propositions or on probabilities. However, it is not known if the cortical time‐consuming inferential pro‐ cesses in which logical arguments are eventually realized in the brain are in fact physically different from other kinds of inferential processes. Methods In order to determine whether an electrical EEG discernible pattern of logical deduction exists or not, a new experimental paradigm is proposed contrasting logically valid and invalid (...) inferences with exactly the same content (same premises and same relational variables) and distinct logical complexity (propositional truth‐functional operators). Electroencephalographic signals from 19 subjects (24.2 ± 3.3 years) were acquired in a two‐condition para‐ digm (100 trials for each condition). After the initial general analysis, a trial‐by‐trial approach in beta‐2 band allowed to uncover not only evoked but also phase asynchronous activity between trials. Results showed that (i) deductive inferences with the same content evoked the same response pattern in logically valid and invalid conditions, (ii) mean response time in logically valid inferences is 61.54% higher, (iii) logically valid inferences are subjected to an early (400 ms) and a late reprocessing (600 ms) verified by two distinct beta‐2 activa‐ tions (p‐value < 0,01, Wilcoxon signed rank test). Conclusion We found evidence of a subtle but measurable electrical trait of logical validity. Results put forward the hypothesis that some logically valid deductions are recursive or computational cortical events. Keywords Beta‐2 band, Evoked potentials, Induced potentials, Deductive inference, Logical validity, Cortical bases of logical reasoning. (shrink)

This article surveys different forms of emergence, distinguishing them from each other by means of their relationship to deducibility conceived as Kimian functional reduction.

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)

Our standard model-theoretic definition of logical consequence is originally based on Alfred Tarski’s (1936) semantic definition, which, in turn, is based on Rudolf Carnap’s (1934) similar definition. In recent literature, Tarski’s definition is described as a conceptual analysis of the intuitive ‘everyday’ concept of consequence or as an explication of it, but the use of these terms is loose and largely unaccounted for. I argue that the definition is not an analysis but an explication, in the Carnapian sense: the replacement (...) of the inexact everyday concept with an exact one. Some everyday intuitions were thus brought into a precise form, others were ignored and forgotten. How exactly did the concept of logical consequence change in this process? I suggest that we could find some of the forgotten intuitions in Bernard Bolzano’s (1837) definition of ‘deducibility’, which is traditionally viewed as the main precursor of Tarski’s definition from a time before formalized languages. It turns out that Bolzano’s definition is subject to just the kind of natural features—paradoxicality of everyday language, Platonism about propositions, and dependence on the external world—that Tarski sought to tame by constructing an artificial concept for the special needs of mathematical logic. (shrink)

The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak systems there are at least two (...) approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility. (shrink)

I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: -/- (1) There is a qualitative difference between knowledge and non-knowledge. (2) Knowledge is valuable in a way that non-knowledge is not. (3) Subjects in Gettier cases do not have knowledge. (4) If S knows that P, P is part of S’s evidence. (5) If S knows (...) that P, ~P is epistemically impossible for S. (6) If S knows that P, S can rationally act as if P. (7) If S knows that P, S can rationally stop inquiring whether P. (8) If S knows each of {P1, P2, … Pn}, and competently deduces Q from these propositions, S knows that Q. -/- I then argue that the skeptical costs of this thesis are outweighed by its explanatory power. (shrink)

Recent research has identified a tension between the Safety principle that knowledge is belief without risk of error, and the Closure principle that knowledge is preserved by competent deduction. Timothy Williamson reconciles Safety and Closure by proposing that when an agent deduces a conclusion from some premises, the agent’s method for believing the conclusion includes their method for believing each premise. We argue that this theory is untenable because it implies problematically easy epistemic access to one’s methods. Several possible solutions (...) are explored and rejected. (shrink)

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...) one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

I systematically defend a novel account of the grounds for identity and distinctness facts: they are all uniquely zero‐grounded. First, this Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying the Null Account would be an excellent candidate for being the identity relation. Second, a plenitudinist view of relations suggests that there is such a relation. To flesh out this plenitudinist view I sketch a novel framework for expressing real definitions, use this framework (...) to give a definition of identity, and show how the central features of the identity relation can be deduced from this definition. (shrink)

This research explores how a person with whom information has been shared and, importantly, an artificial intelligence (AI) system used to deduce information from the shared data contribute to making the disclosure context private. The study posits that private contexts are constituted by the interactions of individuals in the social context of intersubjectivity based on trust. Hence, to make the context private, the person who is the trustee (i.e., with whom information has been shared) must fulfil trust norms. According to (...) the commitment account of trustworthiness, a person is trustworthy only if they satisfy the norm of competence. It is argued that a person using an AI system to answer a question is competent only if they are ex post justified in believing what has been delivered by the AI system. A person’s belief is justified in the doxastic sense only if the AI system is accurate. This feature of AI’s performance affects a person’s competence and, as a result, trustworthiness. The effect of AI on trust as an essential component of making the context private, and thus on privacy, means an AI system also impacts privacy. Therefore, a private context is constituted when the individual with whom the information is shared fulfils the competence norm and the AI system used for analysing the information is sufficiently accurate to adhere to this norm. The result of this research emphasises the significance of the relationship between individuals involved in information-sharing and how an AI system used for analysing that information impacts the relationship regarding making the context private, as well as how it impacts privacy. The findings of this research have significant implications for improving or ameliorating privacy regulations in light of trust. (shrink)

Several recent commentators argue that Thomas Hobbes’s account of the nature of science is conventionalist. Engaging in scientific practice on a conventionalist account is more a matter of making sure one connects one term to another properly rather than checking one’s claims, e.g., by experiment. In this paper, I argue that the conventionalist interpretation of Hobbesian science accords neither with Hobbes’s theoretical account in De corpore and Leviathan nor with Hobbes’s scientific practice in De homine and elsewhere. Closely tied to (...) the conventionalist interpretation is the deductivist interpretation, on which it is claimed that Hobbes believed sciences such as optics are deduced from geometry. I argue that Hobbesian science places simplest conceptions as the foundation for geometry and the sciences in which we use geometry, which provides strong evidence against both the conventionalist and deductivist interpretations. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

In this paper I defend an intermediate position between the ‘bare mathematical results’ view and the ‘transmission’ view of mathematical explanations of physical phenomena (MEPPs). I argue that, in MEPPs, it is not enough to deduce the explanandum from the generalizations cited in the explanans. Rather, we must add information regarding why those generalizations obtain. However, I also argue that it is not necessary to provide explanatory proofs of the mathematical theorems that represent those generalizations. I illustrate this with the (...) bridges of Königsberg case. -/- . (shrink)

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral (...) and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov's intuitionistic fuzzy set. Some neutrosophic concepts have been investigated by Salama et al. [61-70]. Forwarding the study of neutrosophic sets, this book consists of seven chapters, targeting to:  generalize the previous studies in [1-59], and[91-94] so to define the neutrosopic crisp set and neutrosophic set concepts;  discuss their main properties; A. A. Salama & Florentin Smarandache  introduce and study some concepts of neutrosophic crisp and neutrosophic topological spaces and deduce their properties;  deduce many types of functions and give the relationships between different neutrosophic topological spaces, which helps to build new properties of neutrosophic topological spaces;  stress once more the importance of Neutrosophic Ideal as a nontrivial extension of neutrosophic set and neutrosophic logic [71, 72, 73, 74];  propose applications on computer sciences by using neutrosophic sets. (shrink)

Our present day knowledge in the area of medicine in Ancient Egypt has been severally sourced from medical papyri several of which have been deduced and analyzed by different scholars. For educational purposes it is always imperative to consult different literature or sources in the teaching of ancient Egypt and medicine in particular. To avoid subjectivity the author has found the need to re-engage the efforts made by several scholars in adducing evidences from medical papyri. In the quest to re-engage (...) the efforts of earlier writers and commentaries on the medical papyri, we are afforded the opportunity to be informed about the need to ask further questions to enable us to construct or reconstruct both past and modern views on ancient Egyptian medical knowledge. It is this vocation the author sought to pursue in the interim, through a preliminary review, to highlight, comment and reinvigorate in the reader or researcher the need for a continuous engagement of some pertinent documentary sources on Ancient Egyptian medical knowledge for educational and research purposes. The study is based on qualitative review of published literature. The selection of those articles as sources was based on the focus of the review, in order to purposively select and comment on articles that were published based either on information from a medical papyrus or focused on medical specialization among the ancient Egyptians as well as ancient Egyptian knowledge on diseases and medicine. It was found that the Egyptians developed relatively sophisticated medical practices covering significant medical fields such as herbal medicine, gynecology and obstetrics, anatomy and physiology, mummification and even the preliminary form of surgery. These practices, perhaps, were developed as remedies for the prevailing diseases and the accidents that might have occurred during the construction of their giant pyramids. It must be stated that they were not without flaws. Also, the key issues raised from these literatures are but a few among the Egyptian medical corpus across the academic and publishing world. It should therefore afford researchers, students and readers the opportunity to continue the educational dialogue on the medical practices of the Ancient Egyptians. (shrink)

The most successful science on the Aristotelian model was geometry in the style of Euclid. As advocated in the Posterior Analytics, Euclid’s Elements laid out geometry as a structure of theorems deduced from definitions and axioms that were evident to reason. However, geometry deals with the category of quantity, whereas Aristotelian definitions are paradigmatically in the category of substance. This chapter argues that definitions in the category of quantity have fulfilled well the Aristotelian ideal of stating the essence of ‘what (...) a thing is’, in such a way as to support a superstructure of demonstrations about that thing. Euclid’s definition of circle is a prime example: it is philosophically satisfying and from the first theorem of the Elements proved itself very productive of theorems. As this chapter demonstrates, the definition of ratio was more difficult. Euclid stands at the end of a long search for a definition of ratio, one of the most central notions of mathematics, that is both philosophically satisfying and mathematically productive. The search was not wholly successful. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...) epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

[If you find this article interesting, let me mention another of my articles, “On Deducing Ethical Egoism from Psychological Egoism” (Theoria, 2023), which in many ways is a more thorough treatment of the topic. But it’s not an expanded version of this one. For instance, each article addresses arguments not addressed in the other.] Philosophers generally reject the view that psychological egoism (suitably supplemented with further premises) entails ethical egoism. Their rejections are generally unsatisfying. Some are too brief to win (...) confidence; others employ an uncharitable statement of psychological egoism. This is unfortunate, for the view that psychological egoism entails ethical egoism is philosophically significant (and not without proponents). Although it ultimately deserves rejection, it warrants better treatment than it typically receives. I thus examine it in some detail. Among other things, I carefully consider some original, sophisticated attempts to establish it, having first taken care to produce proper formulations of ethical and psychological egoism. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...) attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

The Transcendental Reading of the Tractatus argues that Wittgenstein endorses, under the notion of ‘metaphysical subject’, the existence of a willing subject as a transcendental condition of ethics and representation. Tejedor aims to reject this reading resorting to three criticisms. The notion of ‘willing subject’ does not appear explicitly in, nor can it be deduced from, the Tractatus, the metaphysical subject and the willing subject are not synonymous or analogous notions and, finally, Wittgenstein abandons the notion of ‘willing subject’ at (...) the end of the Notebooks. The aim of this article is twofold. Firstly, it analyzes the critique introduced by Tejedor and presents three problems that demonstrate that Tejedor’s critique cannot adequately reject the Transcendental Reading. Secondly, it sets forth an alternative reading of the Tractatus that overcomes the issues that stem from the Transcendental Reading. This alternative reading conceives the metaphysical subject as an ethical subject and a willing subject. Additionally, it advances an alternative account of the transcendental character of ethics that does not defend the existence of a transcendental subject understood as a condition of ethics and representation in the Tractatus. (shrink)

Even if our justified beliefs are closed under known entailment, there may still be instances of transmission failure. Transmission failure occurs when P entails Q, but a subject cannot acquire a justified belief that Q by deducing it from P. Paradigm cases of transmission failure involve inferences from mundane beliefs (e.g., that the wall in front of you is red) to the denials of skeptical hypotheses relative to those beliefs (e.g., that the wall in front of you is not white (...) and lit by red lights). According to the Bayesian explanation, transmission failure occurs when (i) the subject’s belief that P is based on E, and (ii) P(Q|E) P(Q). No modifications of the Bayesian explanation are capable of accommodating such cases, so the explanation must be rejected as inadequate. Alternative explanations employing simple subjunctive conditionals are fully capable of capturing all of the paradigm cases, as well as those missed by the Bayesian explanation. (shrink)

Putting all of his faith in the power of abstract reason, Parmenides argues in his poem that genuine knowledge can only involve being, and that non-being is literally unspeakable and unthinkable. Using only the premise that "what is" is and what "is not" is not, he proceeds to deduce the nature of reality. The reality he arrives at bears no resemblance at all to the world we experience around us through our senses. -/- When starting out on a rational inquiry, (...) according to Parmenides, there are only two logically coherent possibilities: either you begin your inquiry with the premise that the subject of your inquiry exists or you begin with the premise that it does not exist. (shrink)

I reconstruct Kant's derivation of the Categorical Imperative (CI) as an argument that deduces what the voice of conscience must say from how it must sound - that is, from the authority that is metaphorically attributed to conscience in the form of a resounding voice. The idea of imagining the CI as the voice of conscience comes from Freud; and the present reconstruction is part of a larger project that aims to reconcile Kant's moral psychology with Freud's theory of moral (...) development. As I reconstruct it, Kant's argument yields an imperative commanding us to act for reasons whose validity we can consistently will to be common knowledge among all agents. Universalizing a maxim thus turns out to consist in willing, not that there be some universally quantified rule of conduct, but rather that a principle of practical reasoning be common knowledge - as a principle of reasoning ought to be. (shrink)

How is moral knowledge possible? This paper defends the anti-Humean thesis that we can acquire moral knowledge by deduction from wholly non-moral premises. According to Hume’s Law, as it has become known, we cannot deduce an ‘ought’ from an ‘is’, since it is “altogether inconceivable how this new relation can be a deduction from others, which are entirely different from it” (Hume, 1739, 3.1.1). This paper explores the prospects for a deductive theory of moral knowledge that rejects Hume’s Law.

The contrast between the strategies of research employed in reductionism and holism masks a radical contradiction between two different scientific philosophies. We concentrate in particular on an analysis of the key philosophical issues which give structure to holistic thought. A first (non-exhaustive) analysis of the philosophical tradition will dwell upon: a) the theory of emergence: each level of organisation is characterised by properties whose laws cannot be deduced from the laws of the inferior levels of organisation (Engels, Morgan); b) clarification (...) of the relations between the “whole” and the “parts” (Woodger, Needham); c) the ontological or epistemological nature of the emergent properties; are they a phenomenological reality or solely an artefact of the state of our knowledge? (Pepper, Henle, Hempel and Oppenheim); d) the proposition of the holistic theoretical and methodological model ( Novikoff, Feibleman). I then go on to examine the differences that exist between the reductionist and the holistic approaches at various levels of analysis: that is to say, the differences which affect their ontologies, methodologies and epistemologies respectively. I attempt to understand the spirit of a holistic approach to ecology by analyzing the major work of E.P. Odum Fundamentals of ecology (1953, 1959, 1971). I set forward what might be meant by the “holistic approach”, which is implicated in all the different levels of organisation at which the problem of “complexity” is debated. Ecology presents itself as an “holistic science” and Odum’s book offers a vision of the world which dates far back in the history of philosophy. By looking at the three different editions of this fundamental text on ecology, we may become aware of the evolution of Odum’s thought. In fact, only in the third and last edition is there a conscious appropriation of the holistic approach (by using the theoretical models of Feibleman who, for his part, refers to Novikoff). However, even when formally referring to the theory of emergence (that is to say the ontological nucleus of every holistic approach), Odum’s systemic analysis presents the same logical errors, which push him back into the reductionist domain. Above all, in his examination of the main concepts of “population”, “community” and “ecosystem”, there is a misunderstanding of the profound difference between “collective properties” and “emergent properties”. Moreover, the cybernetic models of Odum’s systemic analysis (introduced into ecology by Margalef), allowed him to vastly oversimplify his methodological task: in fact, neither how many levels nor which levels of organization are fundamental for the study of each individual level is clearly marked. Finally, Odum analyses the ecosystem as composed of energetic flux and cycles of matter, referring to the trophic-dynamic vision of Lindeman. That is to say, in my opinion, he juxtaposes a reductionistic methodology and epistemology to an holistic ontology. (shrink)

This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...) the model-theoretic concepts, based on those in [7], that guide the rest of this paper. Section 3 presents Natural Deduction systems IK and CK, formalizations of intuitionistic and classical one-step versions of K. In these systems, occurrences of step-markers allow deductions to display deductive structure that is covered over in familiar “no step” proof-theoretic systems for such logics. Box and Diamond are governed by Introduction and Elimination rules; the familiar K rule and Necessitation are derived (i.e. admissible) rules. CK will be the result of adding the 0-version of the Rule of Excluded Middle to the rules which generate IK. Note: IK is the result of merely dropping that rule from those generating CK, without addition of further rules or axioms (as was needed in [7]). These proof-theoretic systems yield intuitionistic and classical consequence relations by the obvious definition. Section 4 provides some examples of what can be deduced in IK. Section 5 defines some proof-theoretic concepts that are used in Section 6 to prove the soundness of the consequence relation for IK (relative to the class of models defined in Section 2.) Section 7 proves its completeness (relative to that class). Section 8 extends these results to the consequence relation for CK. (Looking ahead: Part 2 will investigate one-step proof-theoretic systems formalizing intuitionistic and classical one-step versions of some familiar logics stronger than K.). (shrink)

The chapter distinguishes between a weak and a strong form of ontological naturalism. Strong ontological naturalism is the view that all truths can be deduced, at least in principle, from truths about physical entities at the lowest level of organization, for example, truths about the elementary particles and forces. Weak ontological naturalism is the view that only physical properties can be causally efficacious. Strong ontological naturalism entails weak ontological naturalism but not vice versa. I then argue that the existence of (...) a truth property is consistent with weak ontological naturalism, as truth is not causally efficacious. After considering several prominent theories of truth, I argue that the only theories of truth that are consistent with strong ontological naturalism are deflationary doctrines that deny that there is a substantial truth property but these theories are not suitable adjoints to strong naturalism, as folks with strong naturalist inclinations normally want to posit the existence of substantial natural properties. Yet if the truth property itself is insubstantial, so are claims about the existence of substantial natural properties. I conclude by arguing that the result that there cannot be a naturalistic theory of truth is unsurprising, as there are independent reasons for thinking that the basic semantic notions must be treated an irreducible, primitive properties. (shrink)

Instability occurs when the very fact of choosing one particular possible option rather than another affects the expected values of those possible options. In decision theory: An act is stable iff given that it is actually performed, its expected utility is maximal. When there is no stable choice available, the resulting instability can seem to pose a dilemma of practical rationality. A structurally very similar kind of instability, which occurs in cases of anti-expertise, can likewise seem to create dilemmas of (...) epistemic rationality. One possible line of response to such cases of instability, suggested by both Jeffrey (1983) and Sorensen (1987), is to insist that a rational agent can simply refuse to accept that such instability applies to herself in the first place. According to this line of thought it can be rational for a subject to discount even very strong empirical evidence that the anti-expertise condition obtains. I present a new variety of anti-expertise condition where no particular empirical stage-setting is required, since the subject can deduce a priori that an anti-expertise condition obtains. This kind of anti-expertise case is therefore not amenable to the line of response that Jeffrey and Sorensen recommend. (shrink)

Madness can be understood as something sealed off from the intelligible human world, a way of being that has been detached and isolated from the essential elements of normative society. It can represent all that is contrary to what is rational, what is normal and even, what is human. By following this line of thinking, madness cannot be penetrated by the outside nor does it have an established internal structure, and yet it can be used to construct and form its (...) opposite—the rational, normal human. Human rationality then becomes something that can be fully deduced, explained, and understood, and anything that contains mystery or ambiguity can be relegated to the realm of madness.These are the common definitions of... (shrink)

Kant has often been criticized for his morality destroying happiness. I argue against this common misconception and focus the analysis on the idea that happiness, although not a primary motive for moral action, is still grounded in morality. Thus, happiness can be deduced from morality. Furthermore, I highlight the ontological difference between morality and happiness, both in their transcendental dimensions and in the narrower and broader senses of Kantian morality, by demonstrating that happiness can only be comprehended within the moral (...) framework. I will clarify that happiness is not seen as antithetical to morality, but rather as a potential and necessary future perspective, achievable through moral action and the formation of a community. This indicates that Kant’s moral philosophy is diverse, accommodating eudaimonism alongside his doctrine of duty. (shrink)

I begin with an exposition of the two main variants of the Prosentential Theory of Truth (PT), those of Dorothy Grover et al. and Robert Brandom. Three main types of criticisms are then put forward: (1) material criticisms to the effect that (PT) does not adequately explain the linguistic data, (2) an objection to the effect that no variant of (PT) gives a properly unified account of the various occurrences of "true" in English, and, most importantly, (3) a charge that (...) the comparison with proforms is explanatorily idle. The last objection is that, given a complete semantic account of pronouns, proadjectives, antecedents, etc., together with a complete (PT), the essential semantic character of "true" could be deduced, but then, the idleness of the comparison with pronouns would be apparent. It turns out that objections (2) and (3) are related in the following way: the prosentential terminology is held to conceal the lack of unity in (PT), by describing the different data in the same terms ("proform", "antecedent", etc.). But this, I argue, is only a way of truly describing, rather than explaining, the data, these being certain relations of equivalence and consequence between sentences. I consider a language for which (PT) would be not only true, but also explanatory, but note that this language is very different from English. I end by showing that Robert Brandom's case that "is true" is not a predicate fails, and that his motivation for saying so is based on fallacious reasoning (namely, Boghossian's argument against deflationism). (shrink)

This paper is dedicated to the relationship between ordinary moral thought and ethical theory in Sidgwick’s The Methods of Ethics. I suggest that different contents of ordinary moral thought play different roles and are lent different philosophical weight in Sidgwick’s arguments. I start by showing how Sidgwick appeals to certain features of ordinary moral thought, deduced from moral language and experience, both in criticising rival metaethical positions and in establishing his own claims. I then turn to the notion of common-sense (...) morality. After clarifying what Sidgwick means by this expression, I argue that common-sense morality has neither probative value in Sidgwick’s argument for the utilitarian principle nor independent validity, and that its authority is ultimately motivated on utilitarian grounds. Pointing out how different contents of ordinary moral thought play different argumentative roles in the foundation and defence of Sidgwick’s utilitarianism enables to ac- count more comprehensively for Sidgwick’s arguments and moral methodology and provides with a more articulated account of the dialectic between his utilitarian theory and ordinary moral thought. (shrink)

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven. -/- .

Quine's argument for a naturalized epistemology is routinely perceived as an argument from despair: traditional epistemology must be abandoned because all attempts to deduce our scientific theories from sense experience have failed. In this paper, I will show that this picture is historically inaccurate and that Quine's argument against first philosophy is considerably stronger and subtler than the standard conception suggests. For Quine, the first philosopher's quest for foundations is inherently incoherent; the very idea of a self-sufficient sense datum language (...) is a mistake, there is no science-independent perspective from which to validate science. I will argue that a great deal of the confusion surrounding Quine's argument is prompted by certain phrases in his seminal ‘Epistemology Naturalized’. Scrutinizing Quine's work both before and after the latter paper provides a better key to understanding his remarkable views about the epistemological relation between theory and evidence. (shrink)

The aim of the Analytic of Concepts is to derive and deduce a set of pure concepts of the understanding, the categories, which play a central role in Kant’s explanation of the possibility of synthetic a priori cognition and judgment. This chapter is structured around two questions. First, what is a pure concept of the understanding? Second, what is involved in a deduction of a pure concept of the understanding? In answering the first, we focus on how the categories differ (...) from the pure forms of sensibility and examine whether they are known only to be the pure forms of human thinking or rather the forms of discursive cognition as such. In answering the second, we draw a distinction between the application and the exemplification of the categories and use it to identify different ways of understanding Kant’s project in the Transcendental Deduction of the Categories. These questions connect because the answer to the first determines how we should understand the kind of entitlement which is to be established in the Deduction. (shrink)

Facticity and the Fate of Reason After Kant is the first history of the concept of facticity. G. Anthony Bruno argues that this concept’s coining, transmission, and repurposing by post-Kantian thinkers leaves a lasting divide concerning the question of whether a science of intelligibility can tolerate brute facts. In the phenomenological tradition, ‘facticity’ denotes undeducibly brute conditions of intelligibility such as sociality, mortality, and temporality. This suggests an affirmative answer to the post-Kantian question. However, the term’s original use in the (...) German idealist tradition is associated with a negative answer: a science of intelligibility must eliminate bruteness in order to be systematic, as Fichte says, or presuppositionless, as Hegel says. Moreover, eliminating bruteness requires a new logic for deducing conditions of intelligibility from reason’s self-contradictions, a dialectical logic that Fichte invents and Hegel develops. In response to the German idealists, Heidegger argues that dialectic ineluctably presupposes brute facts of lived experience, whose interpretation requires a hermeneutics of facticity. The untold history of the concept of facticity thus contains the deepest parting of the ways after Kant, one in which reason is fated to transform from the hand that holds the world to the thrown activity of being-in-the-world. Facticity and the Fate of Reason After Kant explores this transformation while confronting our inheritance of the still-pressing post-Kantian question. (shrink)

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict it (...) to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction. (shrink)

This paper takes issue with an influential interpretationist argument for physicalism about intentionality based on the possibility of radical interpretation. The interpretationist defends the physicalist thesis that the intentional truths supervene on the physical truths by arguing that it is possible for a radical interpreter, who knows all of the physical truths, to work out the intentional truths about what an arbitrary agent believes, desires, and means without recourse to any further empirical information. One of the most compelling arguments for (...) the possibility of radical interpretation, associated most closely with David Lewis and Donald Davidson, gives a central role to decision theoretic representation theorems, which demonstrate that if an agent’s preferences satisfy certain constraints, it is possible to deduce probability and utility functions that represent her beliefs and desires. We argue that an interpretationist who wants to rely on existing representation theorems in defence of the possibility of radical interpretation faces a trilemma, each horn of which is incompatible with the possibility of radical interpretation. (shrink)

Within much contemporary social ontology there is a particular methodology at work. This methodology takes as a starting point two or more asocial or atomic individuals. These individuals are taken to be perfectly functional agents, though outside of all social relations. Following this, combinations of these individuals are considered, to deduce what constitutes a social group. Here I will argue that theories which rely on this methodology are always circular, so long as they purport to describe the formation of all (...) social groups, as they must always presuppose a pre-existing collectivity. Such methodology also produces various distortions in our theories, such as voluntarism. I focus on the workings of Plural Subject Theory as laid out by Margaret Gilbert in On Social Facts. I show that the formation of a plural subject always requires communication, and that communication always requires a pre-existing collectivity. i examine the elements within Plural Subject Theory which protect gilbert from these accusations of circularity, and argue against them. I finalise by suggesting that what Plural Subject Theory, and social ontology in general, requires as a theoretical starting point is not atomic individuals and their combinations, but rather combinations of already socialised or embedded individuals. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

Accounting for the epistemic contribution of deduction has been a pervasive problem for logicians interested in deduction, such as, among others, Jakko Hintikka. The problem arises because the conclusion validly deduced from a set of premises is said to be “contained” in that set; because of this containment relation, the conclusion would be known from the moment the premises are known. Assuming this, it is problematic to explain how we can gain knowledge by deducing a logical consequence implied by a (...) set of known premises. To address this problem, we offer an alternative account of the epistemic contribution of deduction as the process required to deduce a conclusion or a theorem, understanding such a process not only in terms of the number of steps in the derivation but also, more importantly, in terms of the reason for or justification for every step. That is, we do not know a proposition unless we have a justification or proof of that proposition. With this goal in mind, we develop a justification logic system which exhibits the epistemic contribution of a deductive derivation as the resulting justified formula. (shrink)

From the comparison of time in inertial frames, possible types of transformations between inertial frames are deduced. This elementary deduction directly relates the properties of time with the type of transformations. When all inertial frames measure the same time (time is absolute), the transformations are Galilean. When each inertial frame has its own time, different from the times of other inertial frames (time is not invariant) the transformations are Lorentz-like with the same positive parameter k. The parameter k is the (...) supremum of possible velocities in an inertial frame, the same for all inertial frames. Einstein's postulate about the invariance of the speed of light says more: there is a uniform motion with the supremum k, which is exactly the motion of light in a vacuum. At the end of the article, attempts to reduce the special theory of relativity to the principle of relativity are criticized. (shrink)

The view that the fetus' potential for human consciousness confers upon it the right to life has been widely criticised on the basis that the notion of potentiality is so vague as to be meaningless, and on the basis that actual rights cannot be deduced from the mere potential for personhood. It has also been criticised, although less commonly, on the basis that it is not the potential to assume consciousness, but rather the potential to resume consciousness which is morally (...) significant, and on the basis that the fetus does not really possess the potential for consciousness. In response, I argue that these criticisms are mistaken and that the potential for human consciousness is a sufficient condition not simply of potential, but actual, personhood. Since it possesses this potential from the moment of conception, the fetus should be considered an actual person from the moment of its conception. (shrink)