JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would (...) be surprised to find out that in normal first-order logic existential import is quite common: some universals “Everything that is S is P” —actually quite a few—imply their corresponding existentials “Something that is S is P”. Anyway, perhaps contrary to its title, this paper is not a cataloging of surprises in logic but rather about the mistakes that did or might have or might still lead people to think that there are no surprises in logic. The paper cataloging of surprises in logic is on our “to-do” list. -/- ► JOHN CORCORAN AND WILIAM FRANK, Surprises in logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] There are many surprises in logic. Peirce gave us a few. Russell gave Frege one. Löwenheim gave Zermelo one. Gödel gave some to Hilbert. Tarski gave us several. When we get a surprise, we are often delighted, puzzled, or skeptical. Sometimes we feel or say “Nice!”, “Wow, I didn’t know that!”, “Is that so?”, or the like. Every surprise belongs to someone. There are no disembodied surprises. Saying there are surprises in logic means that logicians experience surprises doing logic—not that among logical propositions some are intrinsically or objectively “surprising”. The expression “That isn’t surprising” often denigrates logical results. Logicians often aim for surprises. In fact, [1] argues that logic’s potential for surprises helps motivate its study and, indeed, helps justify logic’s existence as a discipline. Besides big surprises that change logicians’ perspectives, the logician’s daily life brings little surprises, e.g. that Gödel’s induction axiom alone implies Robinson’s axiom. Sometimes wild guesses succeed. Sometimes promising ideas fail. Perhaps one of the least surprising things about logic is that it is full of surprises. Against the above is Wittgenstein’s surprising conclusion : “Hence there can never be surprises in logic”. This paper unearths basic mistakes in [2] that might help to explain how Wittgenstein arrived at his false conclusion and why he never caught it. The mistakes include: unawareness that surprise is personal, confusing logicians having certainty with propositions having logical necessity, confusing definitions with criteria, and thinking that facts demonstrate truths. People demonstrate truths using their deductive know-how and their knowledge of facts: facts per se are epistemically inert. [1] JOHN CORCORAN, Hidden consequence and hidden independence. This Bulletin, vol.16, p. 443. [2] LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus, Kegan Paul, London, 1921. -/-. (shrink)

Charles S. Peirce (1839-1914) made relevant contributions to deductive logic, but he was primarily interested in the logic of science, and more especially in what he called 'abduction' (as opposed to deduction and induction), which is the process whereby hypotheses are generated in order to explain the surprising facts. Indeed, Peirce considered abduction to be at the heart not only of scientific research, but of all ordinary human activities. Nevertheless, in spite of Peirce's work and writings in the (...) field of methodology of research, scarce attention has been paid to the logic of discovery over the last hundred years, despite an impressive development not only of scientific research but also of logic. -/- Having this in mind, the exposition is divided into five parts: 1) a brief presentation of Peirce, focusing on his work as a professional scientist; 2) an exposition of the classification of inferences by the young Peirce: deduction, induction and hypothesis; 3) a sketch of the notion of abduction in the mature Peirce; 4) an exposition of the logic of surprise; and finally, by way of conclusion, 5) a discussion of this peculiar ability of guessing understood as a rational instinct. -/- . (shrink)

This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...) numbers satisfying “not odd but not not-prime”. The mistake is thinking that every two logically-equivalent false universal propositions have the same counterexamples. Only false universal propositions have counterexamples. A counterexample for “every two logically-equivalent false universal propositions have the same counterexamples” is two logically-equivalent false universal propositions not having the same counterexamples. The following counterexample arose naturally in my sophomore deductive logic course in a discussion of inner and outer converses. “Every even number precedes every odd number” is counterexemplified only by even numbers, whereas its equivalent “Every odd number is preceded by every even number” is counterexemplified only by odd numbers. Please let me know if you see this mistake in print. Also let me know if you have seen these points discussed before. I learned them in my own course: talk about learning by teaching! (shrink)

This paper investigates the metaphysics in higher-order counterfactual logic. I establish the necessity of identity and distinctness and show that the logic is committed to vacuism, which entails that all counteridenticals are true. I prove the Barcan, Converse Barcan, Being Constraint and Necessitism. I then show how to derive the Identity of Indiscernibles in counterfactual logic. I study a form of maximalist ontology which has been claimed to be so expansive as to be inconsistent. I show that (...) it is equivalent to the collapse of the counterfactual into the material conditional---which is itself equivalent to the modal logic TRIV. TRIV is consistent, from which it follows that maximalism is, surprisingly, consistent. I close by arguing that stating the limit assumption requires a higher-order logic. (shrink)

Knowledge is good, ignorance is bad. So it seems, anyway. But in this dissertation, I argue that some ignorance is epistemically valuable. Sometimes, we should suspend judgment even though by believing we would achieve knowledge. In this apology for ignorance (ignorance, that is, of a certain kind), I defend the following four theses: 1) Sometimes, we should continue inquiry in ignorance, even though we are in a position to know the answer, in order to achieve more than mere knowledge (e.g. (...) understanding) while minimizing the effects of confirmation bias. 2) It’s false that we should believe every proposition such that we are guaranteed to be right about it (and even such that we are guaranteed to know it) if we believe it. 3) Being in a position to know is the norm of assertion: importantly, this does not require belief or (thereby) knowledge, and so proper assertion can survive speaker-ignorance. 4) It can be permissible and conversationally useful to tell audiences things that it is logically impossible for them to come to know: Proper assertion can survive (necessary) audience-side ignorance. Cumulatively, this project suggests that, properly understood, ignorance has an important role to play in the good epistemic life. (shrink)

If the import of a book can be assessed by the problem it takes on, how that problem unfolds, and the extent of the problem’s fruitfulness for further exploration and experimentation, then Duffy has produced a text worthy of much close attention. Duffy constructs an encounter between Deleuze’s creation of a concept of difference in Difference and Repetition (DR) and Deleuze’s reading of Spinoza in Expressionism in Philosophy: Spinoza (EP). It is surprising that such an encounter has not already been (...) explored, at least not to this extent and in this much detail. Since the two works were written simultaneously, as Deleuze’s primary and secondary dissertations, it is to be expected that there is much to learn from their interaction. Duffy proceeds by explicating, in terms of the differential calculus, a logic of what Deleuze in DR calls different/ciation, and then maps this onto Deleuze’s account of modal expression in EP. (shrink)

Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as (...) he called them, ‘logical forms’. This portion of logic he called ‘philosophical logic’. Russell asserted that ... some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure. (p. 53) Perhaps no one still endorses quite this grand a view of the role of logic and the investigation of logical form in philosophy. But talk of logical form retains a central role in analytic philosophy. Given its widespread use in philosophy and linguistics, it is rather surprising that the concept of logical form has not received more attention by philosophers than it has. The concern of this paper is to say something about what talk of logical form comes to, in a tradition that stretches back to (and arguably beyond) Russell’s use of that expression. This will not be exactly Russell’s conception. For we do not endorse Russell’s view that propositions are the bearers of logical form, or that appeal to propositions adds anything to our understanding of what talk of logical form comes to. But we will be concerned to provide an account responsive to the interests expressed by Russell in the above quotations, though one clarified of extraneous elements, and expressed precisely. For this purpose, it is important to note that the concern expressed by Russell in the above passages, as the surrounding text makes clear, is a concern not just with logic conceived narrowly as the study of logical terms, but with propositional form more generally, which includes, e.g., such features as those that correspond to the number of argument places in a propositional function, and the categories of objects which propositional.... (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much (...) of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

What makes a valid argument valid? Generally speaking, in a valid argument, if the premisses are true, then the conclusion must necessarily also be true. But on its own, this doesn’t tell us all that much. What is truth? And what is necessity? In what follows, I consider answers to these questions proposed by the fourteenth century logician John Buridan († ca. 1358). My central claim is that Buridan’s logic is downstream from his metaphysics. Accordingly, I treat his metaphysical (...) discussions as the key to his logic. As has been often noted, Buridan’s metaphysics are radically anti-realist about universals, though I think the depth and scope of his anti-realism has at times been papered over. Buridan constructs his logic on an amazingly spartan ontology, and this accomplishment is overdue for reconsideration. To the foregoing questions: truth is a feature of propositions, and of propositions only—not of proposition-like states of affairs, or anything like that. It is a function of the reference or supposition (suppositio) of their terms, which depends on predication in a propositional context. And necessary truth is grounded in causation: a predication is necessary if it cannot be falsified by any power, natural or supernatural, without ii annihilating what its terms stand for. “Socrates is a human”, for instance, can only be falsified by annihilating Socrates, and so it is a necessary truth. -/- These considerations provide an ample theoretical basis for a thorough examination of Buridan’s modal logic. This is what the thesis culminates with. In the final chapter, I set forth some novel and surprising findings, chief of which is this: Buridan’s modal syntax and semantics are nothing like Kripke’s—and indeed are incompatible with them. This has significant implications not only for modal logic and metaphysics, but for how we think about medieval logic and philosophy more generally. -/- Throughout the thesis, I advocate a methodology of emphasising the differences, rather than the similarities, between past and present thought. Buridan is wildly unlike what we’re used to, and we should let him speak for himself. (shrink)

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called (...) SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal characterisations of the surprise notion, (...) crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

Augment the propositional language with two modal operators: □ and ■. Define ⧫ to be the dual of ■, i.e. ⧫=¬■¬. Whenever (X) is of the form φ → ψ, let (X⧫) be φ→⧫ψ . (X⧫) can be thought of as the modally qualified counterpart of (X)—for instance, under the metaphysical interpretation of ⧫, where (X) says φ implies ψ, (X⧫) says φ implies possibly ψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (...) (X⧫) to imply (X)—so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy. (shrink)

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of (...) the Bible, and analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation. Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques. Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning. In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic. (shrink)

Anti-exceptionalism about logic is the doctrine that logic does not require its own epistemology, for its methods are continuous with those of science. Although most recently urged by Williamson, the idea goes back at least to Lakatos, who wanted to adapt Popper's falsicationism and extend it not only to mathematics but to logic as well. But one needs to be careful here to distinguish the empirical from the a posteriori. Lakatos coined the term 'quasi-empirical' `for the counterinstances (...) to putative mathematical and logical theses. Mathematics and logic may both be a posteriori, but it does not follow that they are empirical. Indeed, as Williamson has demonstrated, what counts as empirical knowledge, and the role of experience in acquiring knowledge, are both unclear. Moreover, knowledge, even of necessary truths, is fallible. Nonetheless, logical consequence holds in virtue of the meaning of the logical terms, just as consequence in general holds in virtue of the meanings of the concepts involved; and so logic is both analytic and necessary. In this respect, it is exceptional. But its methodologyand its epistemology are the same as those of mathematics and science in being fallibilist, and counterexamples to seemingly analytic truths are as likely as those in any scientic endeavour. What is needed is a new account of the evidential basis of knowledge, one which is, perhaps surprisingly, found in Aristotle. (shrink)

Iffication, Preiffication, Qualiffication, Reiffication, and Deiffication. -/- Roughly, iffication is the speech-act in which—by appending a suitable if-clause—the speaker qualifies a previous statement. The clause following if is called the qualiffication. In many cases, the intention is to retract part of the previous statement—called the preiffication. I can retract part of “I will buy three” by appending “if I have money”. This initial study focuses on logical relations among propositional contents of speech-acts—not their full conversational implicatures, which will be treated (...) elsewhere. The modified statement—called the iffication—is never stronger than the preiffication. A degenerate iffication is one logically equivalent to its preiffication. There are limiting cases of degenerate iffications. In one, the qualiffication is tautological, as “I will buy three if three is three”. In another, the negation of the qualiffication implies the preiffication, as “I will buy three if I will not buy three”. Reiffication is iffication of an iffication. “I will buy three if I have money” is reifficated by appending “if there are three left”. Deiffication is the speech-act in which—by appending a suitable and-clause—the effect of an iffication is cancelled so that the result implies the preiffication. “I will buy three if I have money” is deifficated by appending “and I have money”. All further examples come from standard (one-sorted, tenseless, non-modal) first-order arithmetic. All theorems are about first-order arithmetic propositions. An easy theorem, hinted above, is that an iffication is degenerate if and only if the negation of the qualiffication implies the preiffication. The iffication of a conjunction using one of the conjuncts as qualiffication need not imply the other conjunct: “Two is an even square if two is square” does not imply “Two is even”. END OF PRINTED ABSTRACT. -/- Some find that the last statement provides a surprise in logic. https://www.academia.edu/s/a5a4386b75?source=link Acknowledgements: Robert Barnes, William Frank, Amanda Hicks, David Hitchcock, Leonard Jacuzzo, Edward Keenan, Mary Mulhern, Frango Nabrasa, and Roberto Torretti. (shrink)

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the (...) philosophy of language, logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

Contemporary discussions of expressivism in metaethics tend to run together two quite different antidescriptivist views, and only one of them is subject to the objection about compositional semantics pressed most recently by Schroeder (following Dreier, Unwinn, Hale, Geach and others). Here I distinguish the two versions of expressivism and then go on to suggest that those sympathetic to the second sort of expressivism might improve their account of normative vocabulary and the way it figures in reasoning by making what may (...) seem like a somewhat surprising comparison between normative vocabulary and logical vocabulary. I argue that this comparison brings into view the initial steps towards a third antidescriptivist view in metaethics, which we may see as a pragmatist improvement on the second version of expressivism. (shrink)

The distinction between the contexts of discovery and justification, this distinction dear to the projects of logical empiricism, was, as is well known, introduced in precisely those terms by Hans Reichenbach in his Experience and Prediction (Reichenbach 1938). Thus, while the idea behind the distinction has a long history before Reichenbach, this text from 1938 plays a salient role in how the distinction became canonical in the work of philosophers of science in the mid twentieth century. The new contextualist history (...) of philosophy that has arisen in recent years invites us into an investigation of the nuances of philosophical distinctions and their roles in shaping the development of disciplines. Logical empiricism played a key role in the historical development of philosophy of science and this contextualist history has revealed a much richer set of projects in logical empiricism than the potted histories had allowed. Many stories have been told about the contexts of justification and discovery; few of those stories have paid more than passing attention to the larger projects in epistemology and meta-epistemology that Reichenbach was pursuing when he drew the distinction. This brief essay will seek partially to rectify that lack in, I hope, a somewhat surprising way. I shall stress the connection between this canonical distinction and some other epistemological and social terms that loom large in Reichenbach’s text, arguing that the social relevance of scientific philosophy for Reichenbach cannot be set aside in understanding his use of the DJ distinction. My point is, therefore, historical and reflexive. If we attend to the larger significance of the project in scientific philosophy that Reichenbach was advancing, we can see more clearly why the DJ distinction was introduced and rethink the significance of questioning the distinction. (shrink)

ABSTRACT The logic of humor has been acknowledged as an essential dimension of every joke. However, what is the logic of jokes, exactly? The modern theories of humor maintain that jokes are characterized by their own logic, dubbed “pseudo,” “playful,” or “local,” which has been the object of frequent criticisms. This article intends to address the limitations of the current perspectives on the logic of jokes by proposing a rhetorical approach to humorous texts. Building on the (...) traditional development of Aristotle’s almost neglected view of jokes as surprising enthymemes, the former are analyzed as rhetorical arguments. Like enthymemes, jokes are characterized by natural inferences that can be represented as topics, and quasi-formalized in argumentation theory as argumentation schemes. Like rhetorical arguments, jokes express a reason in support of different types of conclusions and proceed from distinct kinds of reasoning and semantic relations. (shrink)

I try to read Aristotle's Poetics and Rhetoric as if they were an integral part of the Organon instead of separate works as they were sorted by Andronicus of Rhodes. The results are quite surprising. First, poetics and rhetoric, considered as sciences of speech, were much more intimately related to Aristotle's analytical logic than it is generally acknowledged by prominent interpreters. I maintain that Dialectics (the Topics) operated as a bridge leading from these two sciences to analytical logic; (...) that the types of speech encompassed by the four respective sciences did not only form a ladder, ascending from the more loose forms of persuasion to the more rigorous ones, but that there was between them a whole net of cross-currents and implications that were too much obvious for Aristotle to remain unaware of them, notwithstanding the fact that he doesn’t describe them anywhere. I maintain, in short, there was an unified science of persuasive speech, whose principles were implicitly intertwined in the fabric of Aristotle's Organon. By means of a comparative study of the works consecrated by Aristotle to poetics, rhetoric, dialectics and analytics, these principles could be unearthed and accurately expressed. I called them the theory of the four discourses. (shrink)

ABSTRACTHegel's Phenomenology of Spirit provides a fascinating picture of individual minds caught up in “recognitive” relations so as to constitute a realm—“spirit”—which, while necessarily embedded in nature, is not reducible to it. In this essay I suggest a contemporary path for developing Hegel's suggestive ideas in a way that broadly conforms to the demands of his own system, such that one moves from logic to a philosophy of mind. Hence I draw on Hegel's “subjective logic”, understood in the (...) light of modern modal logic, in an attempt to model the way minds might be thought as connected by way of shared intentional contents. Here, we should not be surprised at some of the parallels that emerge between the approaches of Hegel and the modal logician Arthur Prior, as Prior had testified to the influence of his teacher, John N. Findlay, who himself had strong Hegelian leanings. In the final section, Robert Stalnaker's version of possible-world semantics is suggested as a framework within which Hegel's recognitive account of the mind might be understood. (shrink)

The author’s aim in this quirky monograph is not to reconstruct all that can be surmised about Stoic logic in the first two centuries A.D. of the Roman empire, but rather to concentrate on the three Stoic authors whose extant texts contain remarks on logic. These imperial Stoics, Seneca, Epictetus, and Marcus Aurelius, are known for their emphasis on ethics and not for their contributions in either logic or physics. So it comes as some surprise that Barnes (...) can find much to say about what these philosophers thought about logic. As Barnes presents it (defying chronology), “Marcus introduces the comedy; Seneca features in the second act; and Epictetus is the hero” (ix). (shrink)

Is behavioral integration (i.e., which occurs when a subjects assertion that p matches her non-verbal behavior) a necessary feature of belief in folk psychology? Our data from nearly 6,000 people across twenty-six samples, spanning twenty-two countries suggests that it is not. Given the surprising cross-cultural robustness of our findings, we suggest that the types of evidence for the ascription of a belief are, at least in some circumstances, lexicographically ordered: assertions are first taken into account, and when an agent sincerely (...) asserts that p, non-linguistic behavioral evidence is disregarded. In light of this, we take ourselves to have discovered a universal principle governing the ascription of beliefs in folk psychology. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper (...) is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

Commentators have not said much regarding Berkeley and Stoicism. Even when they do, they generally limit their remarks to Berkeley’s Siris (1744) where he invokes characteristically Stoic themes about the World Soul, “seminal reasons,” and the animating fire of the universe. The Stoic heritage of other Berkeleian doctrines (e.g., about mind or the semiotic character of nature) is seldom recognized, and when it is, little is made of it in explaining his other doctrines (e.g., immaterialism). None of this is surprising, (...) considering how Stoics are considered arch-materialists and determinists. My aim is to suggest that our understanding of Berkeley’s philosophy is improved significantly by acknowledging its underlying Stoic character. I argue that Berkeley proposes not only a semantic ontology based on assumptions of Stoic logic but also a doctrine in which perceptions or ideas are intelligible precisely because they are always embedded in the propositions of a discourse or language. (shrink)

Once upon a time, some thought that indicative conditionals could be effectively analyzed as material conditionals. Later on, an alternative theoretical construct has prevailed and received wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following critical remarks recently ap- peared in the literature, we suggest that evidential support—rather than conditional probability alone—is key to understand indicative conditionals. There have been motivated concerns that a theory of evidential conditionals (unlike their more tra- ditional counterparts) cannot generate (...) a sufficiently interesting logical system. Here, we will describe results dispelling these worries. Happily, and perhaps surprisingly, appropriate technical variations of Ernst Adams’s classical approach allow for the construction of a logic of evidential conditionals with distinctive fea- tures, which is also well-behaved and reasonably strong. (shrink)

Neopragmatism has been accused of having ‘an experience problem’. This paper begins by outlining Hume's understanding of perception according to which ideas are copies of impressions thought to constitute a direct confrontation with reality. This understanding is contrasted with Peirce's theory of perception according to which percepts give rise to perceptual judgments which do not copy but index the percept (just as a weather-cock indicates the direction of the wind). Percept and perceptual judgment thereby mutually inform and correct one another, (...) as the perceiver develops mental habits of interpreting their surroundings, so that, in this theory of perception, as Peirce puts it: “[n]othing at all…is absolutely confrontitional”. Paul Redding has argued that Hegel’s “idealist understanding of logical form” ran deeper than Kant’s in recognising that Mind is essentially embodied and located, and therefore perspectival. Peirce’s understanding arguably dives deeper still in distributing across the space of reasons (and thus Being) not just Mind’s characteristic features of embodiedness and locatedness, but also its infinite corrigibility. (shrink)

This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the (...) formal sciences. We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later. (shrink)

In this paper we discuss three examples of the appropriation of Kuhn’s ideas in philosophy of science. First we deal with classical logical empiricism. Perhaps somewhat surprisingly, the arch-logical empiricist Carnap considered Kuhn’s socio-historical account as a useful complementation, and not as a threat of the philosophy of science of logical empiricism. As a second example we consider the attempt of the so-called struc- turalist philosophy of science to provide a “rational reconstruction” of Kuhn’s approach. Finally, we will deal with (...) Friedman’s proposal to apply Kuhn’s ideas to the formulation of a modernized, historically enlightened Kantian approach that is based on the concept of a non-apodictic constitutive and historically moving a priori. (shrink)

Many epistemologists hold that an agent can come to justifiably believe that p is true by seeing that it appears that p is true, without having any antecedent reason to believe that visual impressions are generally reliable. Certain reliabilists think this, at least if the agent’s vision is generally reliable. And it is a central tenet of dogmatism (as described by Pryor (2000) and Pryor (2004)) that this is possible. Against these positions it has been argued (e.g. by Cohen (2005) (...) and White (2006)) that this violates some principles from probabilistic learning theory. To see the problem, let’s note what the dogmatist thinks we can learn by paying attention to how things appear. (The reliabilist says the same things, but we’ll focus on the dogmatist.) Suppose an agent receives an appearance that p, and comes to believe that p. Letting Ap be the proposition that it appears to the agent that p, and → be the material implication, we can say that the agent learns that p, and hence is in a position to infer Ap → p, once they receive the evidence Ap.1 This is surprising, because we can prove the following. (shrink)

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

Recently, there has been a shift away from traditional truth-conditional accounts of meaning towards non-truth-conditional ones, e.g., expressivism, relativism and certain forms of dynamic semantics. Fueling this trend is some puzzling behavior of modal discourse. One particularly surprising manifestation of such behavior is the alleged failure of some of the most entrenched classical rules of inference; viz., modus ponens and modus tollens. These revisionary, non-truth-conditional accounts tout these failures, and the alleged tension between the behavior of modal vocabulary and classical (...) logic, as data in support of their departure from tradition, since the revisionary semantics invalidate some of these patterns. I, instead, offer a semantics for modality with the resources to accommodate the puzzling data while preserving classical logic, thus affirming the tradition that modals express ordinary truth-conditional content. My account shows that the real lesson of the apparent counterexamples is not the one the critics draw, but rather one they missed: namely, that there are linguistic mechanisms, reflected in the logical form, that affect the interpretation of modal language in a context in a systematic and precise way, which have to be captured by any adequate semantic account of the interaction between discourse context and modal vocabulary. The semantic theory I develop specifies these mechanisms and captures precisely how they affect the interpretation of modals in a context, and do so in a way that both explains the appearance of the putative counterexamples and preserves classical logic. (shrink)

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

The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical (...) sciences without seemingly begging the question. Appeals to rational intuition and analyticity in order to account for logical knowledge are symptomatic of these commitments to the apriority and basicness of logical evidence. This chapter argues that these historically prevalent accounts of logical evidence are mistaken, and that if we take logical practice seriously we fi nd that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas. (shrink)

Before commenting on the book, I offer comments on Wittgenstein and Searle and the logical structure of rationality. The essays here are mostly already published during the last decade (though some have been updated), along with one unpublished item, and nothing here will come as a surprise to those who have kept up with his work. Like W, he is regarded as the best standup philosopher of his time and his written work is solid as a rock and groundbreaking throughout. (...) However, his failure to take the later W seriously enough leads to some mistakes and confusions. Just a few examples: on p7 he twice notes that our certainty about basic facts is due to the overwhelming weight of reason supporting our claims, but W showed definitively in ‘On Certainty’ that there is no possibility of doubting the true-only axiomatic structure of our System 1 perceptions, memories and thoughts, since it is itself the basis for judgment and cannot itself be judged. In the first sentence on p8 he tells us that certainty is revisable, but this kind of ‘certainty’, which we might call Certainty2, is the result of extending our axiomatic and nonrevisable certainty (Certainty1) via experience and is utterly different as it is propositional (true or false). This is of course a classic example of the “battle against the bewitchment of our intelligence by language” which W demonstrated over and over again. One word- two (or many) distinct uses. -/- His last chapter “The Unity of the Proposition” (previously unpublished) would also benefit greatly from reading W’s “On Certainty” or DMS’s two books on OC (see my reviews) as they make clear the difference between true only sentences describing S1 and true or false propositions describing S2. This strikes me as a far superior approach to S’s taking S1 perceptions as propositional since they only become T or F after one begins thinking about them in S2. However, his point that propositions permit statements of actual or potential truth and falsity, of past and future and fantasy, and thus provide a huge advance over pre or protolinguistic society, is cogent. As he states it “A proposition is anything at all that can determine a condition of satisfaction…and a condition of satisfaction… is that such and such is the case.” Or, one needs to add, that might be or might have been or might be imagined to be the case. -/- Overall, PNC is a good summary of the many substantial advances over Wittgenstein resulting from S’s half century of work, but in my view, W still is unequaled once you grasp what he is saying. Ideally, they should be read together: Searle for the clear coherent prose and generalizations, illustrated with W’s perspicacious examples and brilliant aphorisms. If I were much younger I would write a book doing exactly that. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities. He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}. This is no surprise (...) with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components. (shrink)

This short work presents a popular fringe theory as a source of case studies for use in teaching informal logic in an introductory course. It puts forward ancient astronaut theory as the candidate source, together with a characterization of why it fits the bill. The televised material associated with that theory is well suited to being used as case studies given that they are easy to follow, contain a surprising number of arguments and fallacies, and keep students reliably engaged. (...) The paper includes an overview of the forms of argumentation and fallacies that these cases may be used to teach, along with a sketch of how to best implement them in the classroom. (shrink)

Change is the fundamental idea of evolution. Explaining the extraordinary biological change we see written in the history of genomes and fossil beds is the primary occupation of the evolutionary biologist. Yet it is a surprising fact that for the majority of evolutionary research, we have rarely studied how evolution typically unfolds in nature, in changing ecological environments, over space and time. While ecology played a major role in the eventual acceptance of the population genetic viewpoint of evolution in the (...) synthetic era (circa 1918-1956), it held a lesser role in the development of evolutionary theory until the 1980s, when we began to systematically study the evolutionary dynamics of natural populations in space and time. As a result, early evolutionary theory was initially constructed in an abstract vacuum that was unrepresentative of evolution in nature. The subtle synthesis between ecology with evolutionary biology (eco-evo synthesis) over the past 40 years has progressed our knowledge of natural selection dynamics as they are found in nature, thus revealing how natural selection varies in strength, direction, form, and, more surprisingly, level of biological organization. Natural selection can no longer be reduced to lower levels of biological organization (i.e., individuals, selfish genes) over shorter timescales but should be expanded to include adaptation at higher levels and over longer timescales. Long-term and/or emergent evolutionary phenomena, such as multilevel selection or evolvability, have thus become tenable concepts within an evolutionary biology that embraces ecology and spatiotemporal change. Evolutionary biology is currently suspended at an intermediate stage of scientific progress that calls for the organization of all the recent knowledge revealed by the eco-evo synthesis into a coherent and unified theoretical framework. This is where philosophers of biology can be of particular use, acting as a bridge between the subdisciplines of biology and inventing new theoretical strategies to organize and accommodate the recent knowledge. Philosophers have recommended transitioning away from outdated philosophies that were originally derived from physics within the philosophical zeitgeist of logical positivism (i.e., monism, reductionism, and monocausation) and toward a distinct philosophy of biology that can capture the natural complexity of multifaceted biological systems within diverse ecosystems—one that embraces the emerging philosophies of pluralism, emergence, and multicausality. Therefore, I see recent advances in ecology, evolutionary biology, and the philosophy of biology as laying the groundwork for another major biological synthesis, what I refer to as the Second Synthesis because, in many respects, it is analogous to the aims and outcomes of the first major biological synthesis (but is notably distinct from the inorganic and contrived progressive movement known as the extended evolutionary synthesis). With the general development of a distinctive philosophy of science, biology has rightfully emerged as an autonomous science. Thus, while the first synthesis legitimized biology, the Second Synthesis autonomized biology and afforded biology its own philosophy, allowing biology to finally realize its full scientific potential. (shrink)

ABSTRACT: A report on the pioneering of a new pedagogy designed to challenge students to use and improve their memory, increase their awareness of logical fallacies and tacitly embedded contradiction(s) and sensitize them to the deeply symbolic nature of thought in all its expressions (math, logos, music, picture and motor skills), as created, by the author, from in situ research at a senior level (ESL) course in Storytelling at one of East Asia’s premiere second languages university, and from teaching children (...) in several university summer programs. -/- As a Visiting Professor of Foreign Languages, I recently had a glorious opportunity to innovate curriculum and teaching techniques in an East Asian university classroom. Under the auspices of teaching senior level thematic courses in English as a Foreign Language, or more specifically, “storytelling,” I was blessed with the opportunity to innovate both on the level of curriculum and pedagogy. -/- But let me backtrack to set up my story from the start. All of this began in a children’s ESL class at a private language institute where I was given some newly formed intermediate level English classes for middle school students on a new campus that had yet to form a library. While waiting for my standard textbooks to arrive I began innovating with one of my own childrens’ stories titled The Tale of the Purple People Eater (a three page mythic story written in the late 90s. Please see appendix). In working with this story, because I envisioned presenting it orally (from memory) at first as a way to introduce students to memory arts exercises, I was compelled to read it over many times, which, to my surprise revealed a troubling feature: it was riddled with contradictions in every paragraph. At any rate, with the middle school aged students I only touched on this feature very briefly and focused more on language acquisition exercises. The tale nevertheless impressed upon me this bizarre aspect of language where a story can appear naturally cogent on the surface, but can also come apart at the seems if taken “literally.” Hence, later while teaching Storytelling in university with a rather dry textbook, I was invited to supplement the class with exercises of my own. Here I was curious to try work shopping the ‘Tale of The Purple People Eater’ with young adults. This involved three stages: 1) Memory work — or engaging with the unpublished story orally; 2) Exploring the contradictory nature of language and thought; 3) Probing the “deeply-symbolic” nature of meaning. -/- Of course, all of these levels have a long history of precedence in our civilization. Memory arts — though defunct now — had been highly developed in the ancient world, not least among bards who performed oral recitations from memory of the entire Illiad and Odyssey. Dialectics — now transmuted into the debate for show and prizes — had a deeper epistemological mission to discover truth and achieve enlightenment (i.e. Socrates, Boethius and St-Augustine). And if it could not be done via contradictory-prone rationality, it would do it by re-attaching or re-membering broken meanings via the sym-bol (“throwing together”), as per our lineage of platonic poets who created a world compelling enough to make us ask where Jesus went during his (underworld journey) three days in the crypt? Or, and, on what terrain did Dante travel? -/- Lets look at all three: Memory work can be very simple: it amounts to an oral recitation of the story in class followed by a homework assignment wherein the students are asked to reproduce the story (in writing) from memory. They can then compare ‘notes’ in class and by working in groups attempt to produce one version per group of the story in question. In this way we invite them to engage with ‘live’ stories as did our oral-history ancestors. Likewise, by writing it down (“for the first time”) they are re-living the act of our first bardic writer(s) who wove together a collection of competing versions of a popular legend to produce a standard. Very primal work! If Plato thought that writing meant the end of memory in his time, imagine what smart phones are doing to memory now. Contradictions too are easy to work with. It suffices to project a written version of the teacher’s story on the classroom screen — no note taking! — and let students have ample time to read it over and over, at first to check with their own memorized version, and later to seek out logical contradictions in the prose. Any way to ‘repair’ the story? Does it lose credibility because of contradictions? Can it be real without being true? Can it be true without being real? Do reality (L. res = matter) and truth (Gk. a-leithea = un-forgetting) etymologically speaking, share the same domain? -/- Further, if below the surface-meaning the story falls apart, its apparent mythical meaning immediately is called into question. This is a good time to ask the students to propose a (deeper) interpretation. On the surface, the obvious meaning of the Tale of the Purple People Eater, a world in which a purple ogre predatorily feasted on the purple race of the United Peoples of Benetton (a multi-racial nation representing every “skin colour of the rainbow”), revolves around racism, and indeed everyone save for one, thought the story was about racism. -/- I, the author, had the challenge of discovering the deeper meaning of my own story. Because it was written inspirationally one morning, the way we might record the memory of a dream from the night before in a journal, I also was ignorant of the story’s meaning. As luck would have it, a few days before I was to give my class feedback on their interpretations, a meditation on the color “purple” led to the book “The Color Purple” which I first heard of from a friend who, in my reply to a question about the book she was reading (in 1985), summarized it succinctly in one sentence about a black woman’s sexual awakening and liberation. I quickly got the book from the university library as well as the film which I viewed several times before my next class. -/- To my utter amazement, after reading the Tale of the Purple People Eater in light of the Color Purple and adjusting the meaning of color in the tale from the color of people’s complexion to the “color of people’s souls” (to commensurate with the film) as depicted in their clothing and other accoutrements (e.g. automobiles) as reflective of the “health of their souls” (white for revolt, purple for majesty, etc…) where the enslaved Celie is surrounded by drab lifeless colors in the beginning of the film in contrast to the liberated woman she has become in the end of the story symbolized by the extraordinary intensity of the purple shawl that bedecks her like an African queen, the tale can be considered, in part, as a kind of back story of the inner evolution of the book’s and film’s protagonist. -/- Many other cross-polenised metaphors come to the fore: Hippocrates in the tale is the mail man in the film; St-Yves anti-ageing gel is a metaphor for remaining in “childhood (sexual) slavery”; the Ex-Thrax vaccine is the spiritual laxative in the form of letters from Africa (from Ex-Lax and Thrace, a “wild place”) that eases Celie out of her yoke; the egg-shaped conference table with the pointy end in the tale is the kitchen table in the last meeting where Celie threatens her husband with the pointy end of the knife in the film… -/- Of course, the students could not be expected to decode the meaning of a story of this nature whose collective unconscious connotations the author himself had to go to great lengths to excavate almost like a detective of the subconscious. What was important here was the shared engagement between mind and narrative and how it acted as a vehicle for 1) re-membering, 2) becoming aware that all language is a metaphorical cover and 3) that the deep symbol and fused metaphor are divided not by external time and space but by external reality (in the Latin sense, res) and internal truth (in the Greek sense, aleithea). Myth then, in its highest meaning is a hybrid form (of these two) of narrative. Hence both parts real and true. (shrink)

In hindsight, it is not surprising that the exegesis of Aristotle’s Sophistici elenchi developed into one of the most substantial parts of the Latin commentary tradition. To make a long story short, in its customary capacity as the art of arts and the science of sciences, medieval logic was primarily concerned with discerning the true from the false in arguments as they occur in natural, ordinary speech as opposed to the more formalised parlance later logicians will resort to. It (...) makes perfect sense, then, that medieval logicians paid special attention to everything that threatens sound reasoning and that prevents us from speaking the truth. Indeed, they were second to none and better than most at exposing and elucidating arguments’ flaws and shortcomings. After all, as John Buridan – faithful to a long and illustrious tradition – aptly put it, «rooting out errors» is logic’s first order of business. As early as the 1140s, Aristotle’s Sophistici elenchi provided the most fertile ground for such keen interest in fallacies; which, in turn, explains etc. This much is uncontroversial or, at any rate, can withstand any amount of scrutiny we care to throw at it. Courtesy – first and foremost – of Sten Ebbesen, whose long-standing interest in medieval writings on bad arguments has turned the Byzantine and Latin aftermath of Aristotle’s Sophistici elenchi into well-charted territory, by all standards. The Anonymus Cantabrigiensis has played no small part in shaping this picture. As a matter of fact, time and again over the last forty years or so, quotes and insights from the anonymous work have kept showing up in Ebbesen’s editions and studies: since he first discovered the commentary in the late 1970s and brought it to the general attention, Ebbesen has routinely drawn on the Anonymus as an early witness of the circulation of Aristotelian logical works and related texts, as a convenient illustration of major trends and distinctive features of the Latin literature on fallacies, and as a sensible interpreter in his own right. (shrink)

In a beautiful recent essay, the philosopher Walter Sinnott-Armstrong explains the reasons for his departure from evangelical Christianity, the religious culture in which he was brought up. Sinnot-Armstrong contrasts the interpretive methods used by good philosophers and fundamentalist believers: Good philosophers face objections and uncertainties. They follow where arguments lead, even when their conclusions are surprising and disturbing. Intellectual honesty is also required of scholars who interpret philosophical texts. If I had distorted Kant’s view to make him reach a conclusion (...) that I preferred, then my philosophy professor would have failed me. The contrast with religious reasoning is stark. My Christian friends seemed happy to hide serious problems in the Bible and in their arguments. They preferred comfort to intellectual honesty. I couldn’t. To what extent can we, historians of philosophy, claim the virtue of intellectual honesty? Speaking frankly, I do not find the practice criticized by Sinnot-Armstrong’s philosophy professor rare or unusual at all. We very frequently distort the views of past philosophers in order to reach the conclusions we prefer. We just call it “Charitable Interpretation.” In this essay, I discuss and criticize the logic behind so-called charitable interpretations in the history of philosophy. This phenomenon is ubiquitous and is not at all restricted to a particular philosophical strand or ideology. Analytic philosophers and post-modernists, Marxists, liberals, secularists, and fundamentalists, we all engage in the very same domestication project. Even more disturbing than the sheer ideological pervasiveness of this phenomenon is the fact that, on many occasions, superb philosophers and historians take part in this fairly childish endeavor. In the first part of this essay, I discuss the general logic of charitable interpretations in the history of philosophy, mostly by addressing discussions in metaphysics and epistemology. In the second part, I focus on the somewhat less noticed use of charitable interpretations in the study of political philosophy, and point out the quintessential role ideology plays in these discussions. In both parts, I concentrate mostly on the interpretation of Spinoza’s thought. I do so not because I have special fondness for Spinoza (“guilty as charged,” I admit), but because Spinoza is such a beast (and may I add, an enchanting beast) and attracts a disproportionate share of the domestication efforts from historians and philosophers of all creeds and persuasions. In the third and final part of the paper, I will begin to outline an alternative methodology, which suggests that past philosophers can be most relevant to our current philosophical discussion, to the extent that they provide us with well-motivated challenges to our common-sense beliefs. Such challenges have the invaluable virtue of being able to undermine our most fundamental and secure beliefs, and force us to engage with the most fundamental questions. What more can we expect from good philosophy? (shrink)

Given its centrality to the intellectual thought processes through which the great structures of logic, nature, and spirit are unfolded it is clear that mediation is vital to the very possibility of Hegel’s encyclopaedic philosophy. Yet Hegel gives little specific explanation of the concept of mediation. Surprisingly, it has been the subject of even less attention by scholars of Hegel. Nevertheless it is casually used in discussions of Hegel and post- Hegelian philosophy as though its meaning were simple and (...) straightforward. In these discussions mediation is the thesis that meanings are not atomic in that the independence of something is inseparable from its relation to something else. Hence being is mediated by nothing, the particular by the universal, the individual by society. But does Hegel ever explain mediation in a way which justifies such use of the concept? The same easy employment of mediation is found in Theodor Adorno whose works are replete with the use of this concept and, indeed, acknowledgements of its Hegelian origin. But the concept of mediation in Adorno’s negative dialectic is operative in an entirely different context from that of Hegel. How, it might be asked, can a concept be so adaptable? I want to argue that mediation is, in fact, an equivocal term which in both Hegel and Adorno covers a variety of entirely different conceptual relations. Furthermore, as propounded by both Hegel and Adorno it lacks the rigour which could allow the particular conclusions which the concept allegedly facilitates. (shrink)

By a reasoned change in logic I mean a change in the logic with which you make inferences that is based on your evidence. An argument sourced in recently published material Kripke lectured on in the 1970s, and dubbed the Adoption Problem by Birman (then Padró) in her 2015 dissertation, challenges the possibility of reasoned changes in logic. I explain why evidentialists should be alarmed by this challenge, and then I go on to dispel it. The Adoption (...) Problem rests on a failure to distinguish between logical principles such as Universal Instantiation and Modus Ponens which might or might not govern your inferences with superficially similar laws which must govern your cognitive architecture. (shrink)

In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no (...) longer play a distinctive role. This account employs a new notion of semantic. (shrink)

Whether mathematical truths are syntactical (as Rudolf Carnap claimed) or empirical (as Mill actually never claimed, though Carnap claimed that he did) might seem merely an academic topic. However, it becomes a practical concern as soon as we consider the role of questions. For if we inquire as to the truth of a mathematical statement, this question must be (in a certain respect) meaningless for Carnap, as its truth or falsity is certain in advance due to its purely syntactical (or (...) formal-semantical) nature. In contrast, for Mill such a question is as valid as any other. These differing views have their consequences for contemporary erotetic logic. (shrink)

Before commenting on the book, I offer comments on Wittgenstein and Searle and the logical structure of rationality. The essays here are mostly already published during the last decade (though some have been updated), along with one unpublished item, and nothing here will come as a surprise to those who have kept up with his work. Like W, he is regarded as the best standup philosopher of his time and his written work is solid as a rock and groundbreaking throughout. (...) However his failure to take the later W seriously enough leads to some mistakes and confusions. Just a few examples: on p7 he twice notes that our certainty about basic facts is due to the overwhelming weight of reason supporting our claims, but W showed definitively in ‘On Certainty’ that there is no possibility of doubting the true-only axiomatic structure of our System 1 perceptions, memories and thoughts, since it is itself the basis for judgment and cannot itself be judged. In the first sentence on p8 he tells us that certainty is revisable, but this kind of ‘certainty’, which we might call Certainty2, is the result of extending our axiomatic and nonrevisable certainty (Certainty1) via experience and is utterly different as it is propositional (true or false). This is of course a classic example of the “battle against the bewitchment of our intelligence by language” which W demonstrated over and over again. One word- two (or many) distinct uses. -/- His last chapter “The Unity of the Proposition” (previously unpublished) would also benefit greatly from reading W’s “On Certainty” or DMS’s two books on OC (see my reviews) as they make clear the difference between true only sentences describing S1 and true or false propositions describing S2. This strikes me as a far superior approach to S’s taking S1 perceptions as propositional since they only become T or F after one begins thinking about them in S2. However, his point that propositions permit statements of actual or potential truth and falsity, of past and future and fantasy, and thus provide a huge advance over pre or protolinguistic society, is cogent. As he states it “A proposition is anything at all that can determine a condition of satisfaction…and a condition of satisfaction… is that such and such is the case.” Or, one needs to add, that might be or might have been or might be imagined to be the case. -/- Overall, PNC is a good summary of the many substantial advances over Wittgenstein resulting from S’s half century of work, but in my view, W still is unequaled once you grasp what he is saying. Ideally they should be read together: Searle for the clear coherent prose and generalizations, illustrated with W’s perspicacious examples and brilliant aphorisms. If I were much younger I would write a book doing exactly that. -/- Those wishing a comprehensive up to date account of Wittgenstein, Searle and their analysis of behavior from the modern two systems view may consult my article The Logical Structure of Philosophy, Psychology, Mind and Language as Revealed in Wittgenstein and Searle (2016). Those interested in all my writings in their most recent versions may download from this site my e-book ‘Philosophy, Human Nature and the Collapse of Civilization Michael Starks (2016)- Articles and Reviews 2006-2016’ by Michael Starks First Ed. 662p (2016). -/- All of my papers and books have now been published in revised versions both in ebooks and in printed books. -/- Talking Monkeys: Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B071HVC7YP. -/- The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle--Articles and Reviews 2006-2016 (2017) https://www.amazon.com/dp/B071P1RP1B. -/- Suicidal Utopian Delusions in the 21st century: Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B0711R5LGX . (shrink)

Avant de commenter le livre, je vous propose des commentaires sur Wittgenstein et Searle et la structure logique de la rationalité. Les essais ici sont pour la plupart déjà publiés au cours de la dernière décennie (bien que certains ont été mis à jour), avec un élément non publié, et rien ici ne viendra comme une surprise pour ceux qui ont suivi son travail. Comme W, il est considéré comme le meilleur philosophe standup de son temps et son travail écrit (...) est solide comme un rocher et révolutionnaire tout au long. Cependant, son incapacité à prendre le W plus tard assez au sérieux conduit à quelques erreurs et confusions. Juste quelques exemples: sur p7, il note deux fois que notre certitude sur les faits de base est due à l’importance écrasante de la raison à l’appui de nos revendications, mais W a montré définitivement dans «Sur la certitude» qu’il n’y a aucune possibilité de douter de la véritable seule structure axiomatique de notre système 1 perceptions, souvenirs et pensées, car il est lui-même la base du jugement et ne peut pas lui-même être jugé. Dans la première phrase sur p8, il nous dit que la certitude est révisable, mais ce genre de «certitude», que nous pourrions appeler Certainty2, est le résultat de l’extension de notre certitude axiomatique et non révisible (Certitude1) par l’expérience et est tout à fait différent car il est proposé (vrai ou faux). C’est bien sûr un exemple classique de la « bataille contre l’envoûtement de notre intelligence par la langue » dont W a démontré maintes et maintes fois. Un mot- deux (ou plusieurs) utilisations distinctes. Son dernier chapitre "L’unité de la proposition" (précédemment inédit) bénéficierait également grandement de la lecture de W "On Certainty" ou les deux livres de DMS sur OC (voir mes commentaires) car ils font clairement la différence entre les phrases vraies seulement décrivant S1 et les propositions vraies ou fausses décrivant S2. Cela me semble comme une approche bien supérieure à S de prendre S1 perceptions comme propositionnelle car ils ne deviennent T ou F après que l’on commence à penser à eux dans S2. Cependant, son point que les propositions permettent des déclarations de vérité réelle ou potentielle et de fausseté, du passé et du futur et de la fantaisie, et donc fournir une énorme avancée sur la société pré ou protolinguistique, est convaincante. Comme il l’affirme : « Une proposition est tout ce qui peut déterminer une condition de satisfaction... et une condition de satisfaction... est que tel ou tel est le cas. Ou, il faut ajouter, qui pourrait être ou aurait pu être ou pourrait être imaginé pour être le cas. Dans l’ensemble, PNC est un bon résumé des nombreuses avancées substantielles sur Wittgenstein résultant du demi-siècle de travail de S, mais à mon avis, W est toujours inégalé une fois que vous saisissez ce qu’il dit. Idéalement, ils devraient être lus ensemble: Searle pour la prose et les généralisations clairement cohérentes, illustrés par les exemples perspicaces de W et les aphorismes brillants. Si j’étais beaucoup plus jeune, j’écrirais un livre faisant exactement cela. Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deuxemssyst peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2019) et autres. (shrink)

“Trends in Logic XVI: Consistency, Contradiction, Paraconsistency, and Reasoning - 40 years of CLE” is being organized by the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (CLEUnicamp) from September 12th to 15th, 2016, with the auspices of the Brazilian Logic Society, Studia Logica and the Polish Academy of Sciences. The conference is intended to celebrate the 40th anniversary of CLE, and is centered around the areas of logic, epistemology, (...) philosophy and history of science, while bringing together scholars in the fields of philosophy, logic, mathematics, computer science and other disciplines who have contributed significantly to what Studia Logica is today and to what CLE has achieved in its four decades of existence. It intends to celebrate CLE’s strong influence in Brazil and Latin America and the tradition of investigating formal methods inspired by, and devoted to, philosophical views, as well as philosophical problems approached by means of formal methods. The title of the event commemorates one of the three main areas of CLE, what has been called the “Brazilian school of paraconsistency”, combining such a pluralist view about logic and reasoning. (shrink)

Contemporary research offers a more compelling account on the complex emotion of envy than the traditional view of envy as simply something bad. This essay explains how Logic-Based Therapy can use this account to coach individuals struggling with negative species of envy. Given that jealousy and envy are often equated, the essay differentiates the two; explains the conditions that make the four species of envy possible; identifies cardinal fallacies associated with negative species of envy; proposes counteractive virtues, and describes (...) ways to help people struggling with negative species of envy acquire these virtues. (shrink)

It has been argued recently that classical theism and Lewisian modal realism are incompatible theses. The most substantial argument to this effect takes the form of a trilemma. It argues that no sense can be made of God’s being a necessary being in the modal realistic picture, on pain of, among other things, modal collapse. The question of this essay is: Is that so? My goal here is to detail the reasons that have been offered in support of this contention (...) and then defend the coherence of theistic modal realism from the trilemma. I call my reply to the argument an “Anselmian-Thomistic” defense, since it appeals to resources from classical medieval philosophy, especially from Anselm and Aquinas. (shrink)