Charles Sanders Peirce famously claimed that ‘The opinion which is fated to be ultimately agreed to by all who investigate is what we mean by the truth’ (W3: 273). Christopher Hookway has argued for a highly distinctive interpretation of this claim in terms of speech-acts and the normative commitments we incur in performing them. So-construed, Peirce’s conception of truth is difficult to compare with standard theories of the concept, which tend to focus instead upon some property or feature that is (...) shared by all and only true propositions, and with whether or not that property is substantive or metaphysically significant. This paper examines Hookway’s interpretation of Peirce’s conception of truth in an effort to clarify its position in logical space. It then raises some difficulties for the way Hookway tries to accommodate Peirce’s remarks about the special status of assertion and belief in science. (shrink)

In his influential book Truth, Paul Horwich deploys a philosophical method focused on linguistic usage, that is, on the function(s) the concept of truth serves in actual discourse. In doing so Horwich eschews abstract metaphysics, arguing that metaphysical or ontological conceptions of truth rest on basic misconceptions. From this description, one might reasonably expect Horwich's book to have drawn inspiration from, or even embodied philosophical pragmatism of some kind. Unfortunately Horwich relies upon Russell's tired caricature of pragmatism about truth (''p' (...) is true if and only if it is useful to believe p' (Ibid., p. 34, p. 47)), and as a result underestimates the challenge it poses to Minimalism. This paper develops a pragmatist critique of minimalism that focuses on the seemingly central, plausibly constitutive role played by the concept of truth in the speech-act of assertion. The critique suggests that Horwich's Minimalism does not and cannot accomplish its stated goal of explaining all of the facts involving truth. Indeed, the kind of thorough-going deflationism sought by Horwich and others (including pragmatist sympathizer Bob Brandom) is incompatible with an adequate account of assertion, and perhaps other concepts (like belief, judgement and inquiry) as well. (shrink)

Scholarly processes play a pivotal role in discovering, challenging, improving, advancing, synthesizing, codifying, and disseminating knowledge. Since the 17th Century, both the quality and quantity of knowledge that scholarship has produced has increased tremendously, granting academic research a pivotal role in ensuring material and social progress. Artificial Intelligence (AI) is poised to enable a new leap in the creation of scholarly content. New forms of engagement with AI systems, such as collaborations with large language models like GPT-3, offer affordances that (...) will change the nature of both the scholarly process and the artifacts it produces. (shrink)

Recently, several authors have utilized the notion of dependence to respond to the traditional argument for the incompatibility of freedom and divine foreknowledge. However, proponents of this response have not always been so clear in specifying where the incompatibility argument goes wrong, which has led to some unfounded objections to the response. We remedy this dialectical confusion by clarifying both the dependence response itself and its interaction with the standard incompatibility argument. Once these clarifications are made, it becomes clear both (...) (1.) that the dependence response does not beg the question against the proponent of the incompatibility argument and (2.) that the dependence response advances the dialectic whether it is developed as a version of Ockhamism or as a version of multiple-pasts compatibilism. (shrink)

This paper explores the philosophy of tertiary civic education in Hong Kong. It does not only investigate the role of tertiary education that can play in civic education, but also explores the way to achieve the aim of integrating liberal democratic citizenship and collective national identity in the context of persistent conflicts between two different identity politics in Hong Kong: politics of assimilation and politics of difference. As Hong Kong is part of China and is inevitably getting closer cooperation with (...) the mainland in the future, I argue that Hong Kong citizenship should affirm its own distinctiveness while also identifying with Chinese nationality. Thus, tertiary civic education should foster a trans-cultural political vision so that the two different horizons can be synthesized and the political framework and identity can be transformed in order to reduce conflicts between the two peoples. (shrink)

The goal of this paper is to sketch an account of Kant’s signature metaphysical doctrine (transcendental idealism) that (a) has no supporters – as far as I am aware – in the contemporary literature, and (b) draws its primary motivation (as interpretation) from considerations regarding our practical situation and needs as agents. -/- The consideration I focus on here is that people not only have mental and moral features, but they also appear to us – in our daily experience – (...) to have such features: “[w]e can perceive virtue in our experience (Wir können in der Erfahrung wohl Tugend wahrnehmen)” (24: 906). The same presumably goes for vice: When I see you casually torturing a cat, you appear to me to be brown-haired, wearing jeans, moving your arms, laughing, and so on, but you also appear to me to be vicious and cruel. Your character shines through in your actions. I can then make a defeasible inference from those appearances to the moral reality. -/- Such appearances and inferences play a central role in our practices of praise, blame, forgiveness, and punishment. An interpretation of transcendental idealism that gives primacy to the practical will thus seek to analyze the concepts of experience, acquaintance, and appearance/phenomenon in a capacious-enough way that they can apply to mental and moral features too. If successful, such an interpretation would have a clear practical advantage over those that leave us merely conjecturing from experiences of bodies, gestures, and secondary qualities to moral features that do not appear, or even to the non-appearing features of a distinct set of things. (shrink)

A review of Personhood, Ethics, and Animal Cognition: Situating Animals in Hare’s Two-Level Utilitarianism, by Gary E. Varner. New York, NY: Oxford University Press, 2012. Pp. xv + 336. H/b £40.23. and The Philosophy of Animal Minds, edited by Robert W. Lurz. New York, NY: Cambridge University Press, 2009. Pp. 320. P/b £20.21.

On Russell's and Quine's "naturalism".

This is Part 2 of a four part paper, intended as an introduction to the key concepts and issues of time directionality for physicists and philosophers. It redresses some fundamental confusions in the subject. These need to be corrected in introductory courses for physics and philosophy of physics students. Here we analyze the quantum mechanical time reversal operator and the reversal of the deterministic Schrodinger equation. It is argued that quantum mechanics is anti-symmetric w.r.t. time reversal in its deterministic laws. (...) This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric (reversible), and that we must adopt the anti-unitary operator (T*) instead of the unitary time reversal operator (T) for time reversal in quantum mechanics. This is widely claimed as settled scientific fact, and large metaphysical conclusions about the symmetry of time are drawn from it. But it is an error. (shrink)

A review of A.W. Moore's book on Kantian themes in religion and ethics. -/- .

Review of Roger Gibson, ed., The Cambridge Companion to Quine.

Scrutiny (1932-1953) was one of the most important critical reviews of the last century. Its editors and contributors included F. R. Leavis, Q. D. Leavis, Denys Thompson, L. C. Knights, D. W. Harding, W. H. Mellers, H. A. Mason, among others. In recasting Scrutiny’s critique of mass culture by way of Alisdair MacIntyre’s After Virtue (1981), I hope to show that the Scrutiny project not only dramatizes the conflicts internal to what MacIntyre calls emotivist culture, but provides a new way (...) of looking at the group’s relation to the culture industry, its purported elitism, and its deep ties with a communitarian rather than socialist politics. (shrink)

Social scientists use many different methods, and there are often substantial disagreements about which method is appropriate for a given research question. In response to this uncertainty about the relative merits of different methods, W. E. B. Du Bois advocated for and applied “methodological triangulation”. This is to use multiple methods simultaneously in the belief that, where one is uncertain about the reliability of any given method, if multiple methods yield the same answer that answer is confirmed more strongly than (...) it could have been by any single method. Against this, methodological purists believe that one should choose a single appropriate method and stick with it. Using tools from voting theory, we show Du Boisian methodological triangulation to be more likely to yield the correct answer than purism, assuming the scientist is subject to some degree of diffidence about the relative merits of the various methods. This holds even when in fact only one of the methods is appropriate for the given research question. (shrink)

Roger Gibson offers a defence of W.V.O. Quine’s conception of ethics as “methodologically infirm” against Owen Flanagan’s criticism. Gibson argues that Flanagan’s critique of Quinean ethics is misdirected, and that he (Flanagan) fails to establish that ethics and science (natural science) are on a methodological par. In this essay, we argue that there may actually be some sort of overemphasis in Flanagan’s argument, given its inclination to see Quine’s holism as rejecting any form of correspondence theory, yet, pace Gibson (as (...) well as Quine), this does not suggest that ethics is “methodologically infirm” in comparison with natural science. Rather, we argue that the comparative attempt between ethics and natural science is mistaken, because the two disciplines are necessarily different in goals, tasks and methods. (shrink)

This study identified and characterised Wittgenstein’s socialised epistemology. It examined some arguments against Wittgenstein’s socialised epistemology. It also assessed the strength of Wittgenstein’s socialised epistemology in light of the arguments against it. This was with a view to redirecting epistemology from its endless attempts in refuting radical skepticism to providing a solid ground for knowledge in Wittgenstein’s notion of “forms of life”. The study made use of both primary and secondary sources of data. The primary source comprised a close reading (...) of Plato’s “Theatetus”, Roderick Chisholm’s Theory of Knowledge, D.W. Hamlyn’s The Theory of Knowledge, Ludwig Wittgenstein’s The Blue and Brown Books, Ludwig Wittgenstein’s Philosophical Investigation, and Ludwig Wittgenstein’s On Certainty. The Secondary source included books, journal articles and the Internet. The data collected were subjected to conceptual analysis and philosophical argumentation. The results showed that Wittgenstein’s epistemology was a rejection of the orthodox epistemology, which assumed a representational relationship between words and objects in providing valid basis for knowledge. The study discovered that Wittgenstein treated knowledge as a product of epistemic community. It found out that in spite of its shortcomings Wittgenstein’s epistemology remained a plausible alternative approach to orthodox epistemology. It also discovered that contrary to the criticisms against Wittgenstein’s socialised epistemology, there were numerous merits that made it worth adopting as an approach to the problems of knowledge. The study concluded that rather than endlessly seeking to refute radical skepticism, epistemologists should be contented with knowledge as provided by the form of life embedded in an epistemic community. It also concluded that it was in this form of life that the nature of knowledge could be properly understood and attained as a socialised phenomenon. (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...) that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

A satisfactory theory of linguistic communication must explain how it is that, through the interpersonal exchange of auditory, visual, and tactile stimuli, the communicative preconditions for the acquisition of testimonial knowledge regularly come to be satisfied. Without an account of knowledge-yielding communication this success condition for linguistic theorizing is left opaque, and we are left with an incomplete understanding of testimony, and communication more generally, as a source of knowledge. This paper argues that knowledge-yielding communication should be modelled on knowledge (...) itself. It is argued that knowledge-yielding communication occurs iff interlocutors coordinate on truth values in a non-lucky and non-deviant way. This account is able to do significant explanatory work: it sheds light on the nature of referential communication, and it allows us to capture, in an informative way, the sense in which interlocutors must entertain similar propositions in order to communicate successfully. (shrink)

In this paper I argue that the enkratic principle in its classic formulation may not be a requirement of rationality. The investigation of whether it is leads to some important methodological insights into the study of rationality. I also consider the possibility that we should consider rational requirements as a subset of a broader category of agential requirements.

Kant holds that in order to have knowledge of an object, a subject must be able to “prove” that the object is really possible—i.e., prove that there is neither logical inconsistency nor “real repugnance” between its properties. This is (usually) easy to do with respect to empirical objects, but (usually) impossible to do with respect to particular things-in-themselves. In the first section of the paper I argue that an important predecessor of Kant’s account of our ignorance of real possibility can (...) be found in Locke’s Essay Concerning Human Understanding. In the middle sections I discuss the way in which our inability to prove the real possibility of things-in-themselves motivates Kant’s famous prohibition on certain kinds of knowledge-claims about them. In the final section I examine Hegel’s attempts to dissolve this problem of real repugnance and thereby remove an inherited obstacle to speculative knowledge of the supersensible. -/- . (shrink)

Empirical work has lately confirmed what many philosophers have taken to be true: people are ‘biased toward the future’. All else being equal, we usually prefer to have positive experiences in the future, and negative experiences in the past. According to one hypothesis, the temporal metaphysics hypothesis, future-bias is explained either by our beliefs about temporal metaphysics—the temporal belief hypothesis—or alternatively by our temporal phenomenology—the temporal phenomenology hypothesis. We empirically investigate a particular version of the temporal belief hypothesis according to (...) which future-bias is explained by the belief that time robustly passes. Our results do not match the apparent predictions of this hypothesis, and so provide evidence against it. But we also find that people give more future-biased responses when asked to simulate a belief in robust passage. We take this to suggest that the phenomenology that attends simulation of that belief may be partially responsible for future-bias, and we examine the implications of these results for debates about the rationality of future-bias. (shrink)

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)

Empirical evidence suggests that a majority of people believe that time robustly passes, and that many also report that it seems to them, in experience, as though time robustly passes. Non-dynamists deny that time robustly passes, and many contemporary non-dynamists—deflationists—even deny that it seems to us as though time robustly passes. Non-dynamists, then, face the dual challenge of explaining why people have such beliefs and make such reports about their experiences. Several philosophers have suggested the stable-self explanation, according to which (...) what partly explains one or both of the explananda is that people believe themselves to have a stable persisting self which is imagined either as moving through time, or as being stationary, with time moving around it. This paper empirically investigates this explanation. We found, however, no evidential support for the stable-self explanation, leaving the non-dynamist but also, we will argue, the dynamist, with an extant explanatory challenge. (shrink)

This is a discussion of the state of discussion on pragmatic reasons for belief.

This essay considers Kant’s theory of modality in light of a debate in contemporary modal metaphysics and modal logic concerning the Barcan formulas. The comparison provides a new and fruitful perspective on Kant’s complex and sometimes confusing claims about possibility and necessity. Two central Kantian principles provide the starting point for the comparison: that the possible must be grounded in the actual and that existence is not a real predicate. Both are shown to be intimately connected to the Barcan formulas, (...) and Kant’s views on what he distinguishes as three different kinds of modality are then considered in light of this connection. (shrink)

This is a theoretical treatment of the term "Sha Zhu Pan" (杀猪盘) in Chinese, which translates to “Pig-Butchering” in English. The article critically examines the propagation and validation of "Pig Butchering," an animal metaphor, and its implications for the dehumanisation of victims of online fraud across various discourses. The study provides background information about this type of fraud before investigating its theoretical foundations and linking its emergence to the dehumanisation of fraud victims. The analysis highlights the disparity between academic literature, (...) subjected to rigorous peer-review processes, and sensationalised narratives prevalent in the media. While academic works subject "pig butchering" to critical scrutiny and refrain from endorsing derogatory terms to depict fraud victims, numerous media outlets employ this term uncritically, further worsening the predicament of these victims. "Pig butchering" is firmly rooted in the concept of dehumanisation, and this article underscores how language moulds perceptions of fraud and behaviour, extending to the development of preventive strategies. The role of law enforcement agencies in generating and disseminating materials is also a central theme, emphasising their responsibility as trusted sources of information. We suggest that these agencies should adopt non-victim shaming language to encourage victims to report crimes and alleviate the stigma attached to victimisation. Additionally, the article offers valuable cross-cultural insights by comparing metaphors from Chinese and Nigerian contexts. This comparative analysis enriches our comprehension of the global dimensions of online fraud and its cultural diversities, highlighting the substantial impact of language on perceptions and behaviours. We advocate for a departure from victim-blaming tendencies perpetuated by select media outlets, urging a more compassionate and accurate portrayal of those affected by online fraud. We, therefore, call for a more empathetic and accurate portrayal of individuals affected by online fraud, aligning with the broader objective of promoting understanding and support for these victims. (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)

This paper argues that underlying social biases are able to affect the processes underlying linguistic interpretation. The result is a series of harms systematically inflicted on marginalised speakers. It is also argued that the role of biases and stereotypes in interpretation complicates Miranda Fricker's proposed solution to epistemic injustice.

The fallacy fallacy is either the misdiagnosis of fallacy or the supposition that the conclusion of a fallacy must be a falsehood. This paper explores the relevance of these and related errors of reasoning for the appraisal of arguments, especially within virtue theories of argumentation. In particular, the fallacy fallacy exemplifies the Owl of Minerva problem, whereby tools devised to understand a norm make possible new ways of violating the norm. Fallacies are such tools and so are vices. Hence a (...) similar problem arises with argumentative vices. Fortunately, both instances of the problem have a common remedy. (shrink)

An important advance in normativity research over the last decade is an increased understanding of the distinction, and difference, between normativity and rationality. Normativity concerns or picks out a broad set of concepts that have in common that they are, put loosely, guiding. For example, consider two commonly used normative concepts: that of a normative reason and that of ought. To have a normative reason to perform some action is for there to be something that counts in favour of performing (...) that action. Likewise with ought, when there is sufficient evidence for something, one ought to believe it (at least under normal circumstances). Not all guidance need be directed towards a specific state or a specific action. Subject to the requirements of normativity, too, are relations. It is commonly believed, for example, that we ought not to hold contradictory beliefs.1 At least some of the requirements that concern relations amongst an agent’s mental states are, or seem, distinctive. Agents who fail to satisfy these requirements are considered, at least to some degree, irrational. On many current views, being irrational is distinct in some way from not being how one ought to be; rationality is a concept distinct from normativity. Much of the literature on this topic over the last decade stems from attempts to capture the characteristic features of the requirements of rationality. Two influential views in particular did much to set the agenda. The first of these two was put forward John Broome.2 His view, the particulars of which I shall discuss in more detail below, is that the requirements of rationality could be expressed using a normative relation, which he calls a ‘normative requirement’. Normative requirements are conditionals governed by an all-thingsconsidered ought. In the case of rationality, the conditional is made up entirely of mental states.. (shrink)

Virtue theories of argumentation (VTA) emphasize the roles arguers play in the conduct and evaluation of arguments, and lay particular stress on arguers’ acquired dispositions of character, that is, virtues and vices. The inspiration for VTA lies in virtue epistemology and virtue ethics, the latter being a modern revival of Aristotle’s ethics. Aristotle is also, of course, the father of Western logic and argumentation. This paper asks to what degree Aristotle may thereby be claimed as a forefather by VTA.

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...) is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

David Lewis—famously—never tasted vegemite. Did he have any knowledge of what it's like to taste vegemite? Most say 'no'; I say 'yes'. I argue that knowledge of what it’s like varies along a spectrum from more exact to more approximate, and that phenomenal concepts vary along a spectrum in how precisely they characterize what it’s like to undergo their target experiences. This degreed picture contrasts with the standard all-or-nothing picture, where phenomenal concepts and phenomenal knowledge lack any such degreed structure. (...) I motivate the degreed picture by appeal to (1) limits in epistemic abilities such as recognition, imagination, and inference, and (2) the semantics of ‘knows what it’s like’ expressions. I argue that approximate phenomenal knowledge cannot be explained merely via determinable or vague phenomenal concepts. I develop a framework for systematizing approximate knowledge of phenomenal character. And I explain how my view challenges some standard assumptions about the acquisition conditions, requirements for mastery, and referential mechanisms of phenomenal concepts. (shrink)

After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...) involving the distinction between characterizing a system and axiomatizing the truths of a system. (shrink)

Disagreements that resist rational resolution, often termed “deep disagreements”, have been the focus of much work in epistemology and informal logic. In this paper, I argue that they also deserve the attention of philosophers of mathematics. I link the question of whether there can be deep disagreements in mathematics to a more familiar debate over whether there can be revolutions in mathematics. I propose an affirmative answer to both questions, using the controversy over Shinichi Mochizuki’s work on the abc conjecture (...) as a potential example of both phenomena. I conclude by investigating the prospects for the resolution of mathematical deep disagreements in virtue-theoretic approaches to informal logic and mathematical practice. (shrink)

Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...) many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology. (shrink)

In this chapter, I present and explore various arguments for skepticism that are related to memory. My focus will be on the aspects of the arguments that are unique to memory, which are not shared, for example, by the more often explored skeptical arguments related to perception. -/- Here are some interesting upshots. First, a particular problem for justifiably concluding that one's memory is reliable is that any reasoning in favor of this conclusion will either result in epistemically circularity or (...) not be sufficient to justify the conclusion. Second, since many beliefs stored in memory do not appear to be based on evidence, it might also appear to follow that they are not justified. Third, although many stored memory beliefs are not based on stored memory experiences in the same way that perceptual beliefs are based on perceptual experiences, skeptical scenarios loom just as problematically for memory beliefs as they do for perceptual beliefs. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

I argue that assertoric content functions as a means for us to track the responsibilities undertaken by communicators, and that distinctively assertoric commitments are distinguished by being generated directly in virtue of the words the speaker uses. This raises two questions: (a) Why are speakers responsible for the content thus generated? (b) Why is it important for us to distinguish between commitments in terms of their manner of generation? I answer the first question by developing a novel responsibility based metasemantics. (...) I answer the second by reference to the conflicting pressures governing the resources we have available for appraising speech. (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)

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)

A famous mathematical theorem says that the sum of an infinite series of numbers can depend on the order in which those numbers occur. Suppose we interpret the numbers in such a series as representing instances of some physical quantity, such as the weights of a collection of items. The mathematics seems to lead to the result that the weight of a collection of items can depend on the order in which those items are weighed. But that is very hard (...) to believe. A puzzle then arises: How do we interpret the metaphysical significance of this mathematical theorem? I first argue that prior solutions to the puzzle lead to implausible consequences. Then I develop my own solution, where the basic idea is that the weight of a collection of items is equal to the limit of the weights of its finite subcollections contained within ever-expanding regions of space. I show how my solution is intuitively plausible and philosophically motivated, how it reveals an underexplored line of metaphysical inquiry about quantities and locations, and how it elucidates some classic puzzles concerning supertasks. (shrink)

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

How is it that a speaker _S_ can at once make it obvious to an audience _A_ that she intends to communicate some proposition _p_, and yet at the same time retain plausible deniability with respect to this intention? The answer is that _S_ can bring it about that _A_ has a high justified credence that ‘_S_ intended _p_’ without putting _A_ in a position to know that ‘_S_ intended _p_’. In order to achieve this _S_ has to exploit a (...) sense in which communication can be lottery-like. After defending this view of deniability I argue that it compares favorably to a rival account recently developed by Dinges and Zakkou (Mind, https://doi.org/10.1093/mind/fzac056, 2023 ). (shrink)

Is a human more conscious than an octopus? In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is for a (...) degreed property to count as degrees of consciousness, and (4) applies the analysis to various theories of consciousness. I argue that whether consciousness comes in degrees ultimately depends on which theory of consciousness turns out to be correct. But I also argue that most theories of consciousness entail that consciousness comes in degrees. (shrink)

A number of `no-proposition' approaches to the liar paradox find themselves implicitly committed to a moderate disquotational principle: the principle that if an utterance of the sentence `$P$' says anything at all, it says that $P$ (with suitable restrictions). I show that this principle alone is responsible for the revenge paradoxes that plague this view. I instead propose a view in which there are several closely related language-world relations playing the `semantic expressing' role, none of which is more central to (...) semantic theorizing than any other. I use this thesis about language and the negative result about disquotation to motivate the view that people do say things with utterances of paradoxical sentences, although they do not say the proposition you'd always expect, as articulated with a disquotational principle. (shrink)

One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...) the premises. The complementarity and interrelation of premise-conclusion arguments and premise-conclusion-mediation arguments resonate throughout the rest of the paper which articulates the conceptual structure found in logic from Aristotle to Tarski. This 1972 paper can be seen as anticipating Corcoran’s signature work: the more widely read 1989 paper, Argumentations and Logic, Argumentation 3, 17–43. MR91b:03006. The 1972 paper was translated into Portuguese. The 1989 paper was translated into Spanish, Portuguese, and Persian. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)