In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc present novel and striking results about meta-inferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of non-classical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a logic which (...) agrees with classical logic on tautologies, inferences, meta-inferences, meta-meta-inferences, meta-meta-...-meta-inferences, but that disagrees with classical logic on n + 1-meta-inferences. They suggest that this shows that classical logic can only be characterized by defining its valid inferences at all orders. In this article, I invoke some simple symmetric generalizations of BPS’s results to show that the problem is worse than they suggest, since in fact there are logics that agree with classical logic on inferential validity to all orders but still intuitively differ from it. I then discuss the relevance of these results for truth theory and the classification problem. (shrink)

I argue that there exists a natural kind social bias that subsumes seemingly heterogenous cases of implicit bias and other forms of social cognition. I explore the implications of this explicated notion of bias for the organization of the mind, theories of consciousness, and the system-dependence of biases.

Carroll’s paradox calls the most fundamental concept of logic, namely the concept of inference, into challenge, and appears to convey that one cannot pass, in any inferences, legitimately from premises to conclusion. So as to get hold of any possible solution out of their writings, the current article puts the paradox under three giant thinkers’ views. Wittgenstein puts forward an “inexpressible” but “showable” modus ponens in all inferences that leads ultimately to the distinction between “rule” and “premise”. Ibn Sīnā recognizes (...) the logical principles as criterion not as matter for which the same exactly holds as the above distinction. Also, Tūsī speaks of the necessity of any syllogism to have an “assistant” and “concomitant” modus ponens that can be considered as the iteration of Wittgenstein’s “inexpressible-but-showable modus ponens” leading as before to the mentioned distinction. As a key solution to Carroll’s paradox, one should make a robust distinction between “rule” and “premise”, and bring inadmissibility to converting the former to the latter. (shrink)

I defend a conception of Logic as normative for the sort of activities in which inferences super-vene, namely, reasoning and arguing. Toulmin’s criticism of formal logic will be our framework to shape the idea that in order to make sense of Logic as normative, we should con-ceive it as a discipline devoted to the layout of arguments, understood as the representations of the semantic, truth relevant, properties of the inferences that we make in arguing and reason-ing.

The uses and interpretation of reductio ad absurdum argumentation in mathematical proof and discovery are examined, illustrated with elementary and progressively sophisticated examples, and explained. Against Arthur Schopenhauer’s objections, reductio reasoning is defended as a method of uncovering new mathematical truths, and not merely of confirming independently grasped mathematical intuitions. The application of reductio argument is contrasted with purely mechanical brute algorithmic inferences as an art requiring skill and intelligent intervention in the choice of hypotheses and attribution of contradictions deduced (...) to a particular assumption in a contradiction’s derivation base within a reductio proof structure. (shrink)

A self-fulfilling fallacy (SFF) is a fallacious argument whose conclusion is that the very fallacy employed is an invalid or otherwise illegitimate inferential procedure. This paper discusses three different ways in which SFF’s might serve to justify their conclusions. SFF’s might have probative value as honest and straightforward arguments, they might serve to justify the premise of a meta-argument or, following a point made by Roy Sorensen, they might provide a non-inferential basis for accepting their conclusion. The paper concludes with (...) an assessment of the relative merits of these proposals. (shrink)

I discuss the conjecture that understanding what is said in an utterance is to be modelled as knowing what is said in that utterance. My main aim is to present a number of alter- native models, as a prophylactic against premature acceptance of the conjecture as the only game in town. I also offer preliminary assessments of each of the models, including the propositional knowledge model, in part by considering their respective capacities to sub-serve the transmission of knowledge through testimony. (...) In each case, the preliminary assessment is unfavourable. I end by very briefly sketching an additional model as an object for future consideration. (shrink)

Gilbert Harman, in Logic and Reasoning (Synthese 60 (1984), 107–127) describes an unsuccessful attempt ... to develop a theory which would give logic a special role in reasoning. Here reasoning is psychological, a procedure for revising one''s beliefs. In the present paper, I construe reasoning sociologically, as a process of linguistic interaction; and show how both reasoning in the psychologistic sense and logic are related to that process.

This is a critical discussion of Part III of Peter Railton's recent book Facts, Values, and Norms: Essays Toward a Morality of Consequence (Cambridge University Press, 2003).

Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.

Substructural solutions to the semantic paradoxes have been broadly discussed in recent years. In particular, according to the non-transitive solution, we have to give up the metarule of Cut, whose role is to guarantee that the consequence relation is transitive. This concession—giving up a meta rule—allows us to maintain the entire consequence relation of classical logic. The non-transitive solution has been generalized in recent works into a hierarchy of logics where classicality is maintained at more and more metainferential levels. All (...) the logics in this hierarchy can accommodate a truth predicate, including the logic at the top of the hierarchy—known as CMω—which presumably maintains classicality at all levels. CMω has so far been accounted for exclusively in model-theoretic terms. Therefore, there remains an open question: how do we account for this logic in proof-theoretic terms? Can there be found a proof system that admits each and every classical principle—at all inferential levels—but nevertheless blocks the derivation of the liar? In the present paper, I solve this problem by providing such a proof system and establishing soundness and completeness results. Yet, I also argue that the outcome is philosophically unsatisfactory. In fact, I’m afraid that in light of my results this metainferential solution to the paradoxes can hardly be called a “solution,” let alone a good one. (shrink)

I give a semantics for a logic with two pairs of doxastic modals and an indicative conditional connective that all nest without restriction. Sentences are evaluated as accepted, rejected, or neither. Certainty is the necessity-like modality of acceptance. Inferences may proceed from premises that are certain, or merely accepted, or a mix of both. This semantic setup yields some striking results. Notably, the existence of inferences that preserve certainty but not acceptance very directly implies both failure of modus ponens for (...) the indicative conditional in the logic of acceptance and failure of the deduction theorem for the material conditional in the logic of certainty. The latter failure dissolves, in the logic of certainty, the much - discussed tension between modus ponens and the law of import-export. (shrink)

This paper aims to advance two claims. First, it aims to show that Hume’s argument against the rationality of induction is sound. However, I claim that the conclusion does not follow merely from the self-defeating attempts to justify the rule of induction, unlike traditional readings of the argument. Rather, the skeptical conclusion must also take into account Hume’s argument that the secret powers that are present in bodies and give rise to sensible qualities are unknowable. The paper’s second aim is (...) to show that Newtonian induction escapes Hume’s secret powers argument, given that it includes a transductive inference, from observable phenomena to the powers present in the ultimate parts of matter. Consequently Hume’s argument against the rationality of induction does not demonstrate the non-rational nature of Newtonian induction. (shrink)

This paper aims to advance two claims. First, it aims to show that Hume's argument against the rationality of induction is sound. However, I claim that the conclusion does not follow merely from the self-defeating attempts to justify the rule of induction, unlike traditional readings of the argument. Rather, the skeptical conclusion must also take into account Hume's argument that the secret powers that are present in bodies and give rise to sensible qualities are unknowable. The paper's second aim is (...) to show that Newtonian induction escapes Hume's secret powers argument, given that it includes a transductive inference, from observable phenomena to the powers present in the ultimate parts of matter. Consequently Hume's argument against the rationality of induction does not demonstrate the non-rational nature of Newtonian induction. (shrink)

One notable line of argument for epistemic relativism appeals to considerations to do with non-neutrality: in certain dialectical contexts—take for instance the famous dispute between Galileo and Cardinal Bellarmine concerning geocentrism—it seems as though a lack of suitably neutral epistemic standards that either side could appeal to in order to resolve their first-order dispute is itself—as Rorty influentially thought—evidence for epistemic relativism. In this essay, my aim is first to present a more charitable reformulation of this line of reasoning, one (...) that is framed not merely in terms of the availability of epistemic norms that are suitably neutral between interlocutors, but in terms of the availability of what I call Archimedean metanorms. Once this more charitable line of argument is developed, I show how, even though it avoids problems that face ‘non-neutrality’ versions of the argument, it nonetheless runs into various other problems that appear ultimately intractable and, further, that the strategy in question gives us no decisive reason to draw the relativist’s conclusion rather than the Pyrrhonian sceptic’s. (shrink)

It has recently been argued that inference essentially involves the thinker taking his premises to support his conclusion and drawing his conclusion because of this fact. However, this Taking Condition has also been criticized: If taking is interpreted as believing, it seems to lead to a vicious regress and to overintellectualize the act of inferring. In this paper, I examine and reject various attempts to salvage the Taking Condition, either by interpreting inferring as a kind of rule-following, or by finding (...) an innocuous role for the taking-belief. Finally, I propose an alternative account of taking, according to which it is not a separate belief, but rather an aspect of the attitude of believing: Believing that p implies not only taking p to be true and taking oneself to believe that p, but also taking one's reasons q to support p, when the belief in question is held on account of an inference. (shrink)

I argue that realism about reasons is incompatible with the possibility of reasoning with reasons, because realists are committed to the claim that we are aware of reasons by way of ordinary belief...

A very natural view about perceptual knowledge is articulated, one on which perceptual knowledge is closely related to perceptual discrimination, and which fits well with a relevant alternatives account of knowledge. It is shown that this kind of proposal faces a problem, and various options for resolving this difficulty are explored. In light of this discussion, a two-tiered relevant alternatives account of perceptual knowledge is offered which avoids the closure problem. It is further shown how this proposal can: accommodate our (...) intuitions about perceptual knowledge and perceptual discrimination in terms of the notion of primary relevance, give an account of how alternatives can be rationally excluded without appeal to perceptual discrimination in terms of the notion of secondary relevance, and deal with the problem posed by inverted Gettier cases, and hence explain what it means to rationally exclude alternatives which are of secondary relevance. (shrink)

Identifying the missing or unstated premisses of arguments is important, because their logical quality depends on them. Textbook authors regard enthymematic syllogisms (e.g., "Elvis is a man, so Elvis is mortal") as having an unstated premiss - the major premiss (e.g., "All men are mortal"). They are said to be such because these syllogisms become formally valid when the major premiss is added (i.e., it is a gap-filler). I argue that unstated major premises are not gap-fillers: they support a part (...) of the argument that is already given implicitly - the inference claim ("If the premisses are true then the conclusion is true"). As such, their logical status is the same as that of an unstated proposition that supports the minor premiss, which is not part of the argument. Therefore, the so-called "major premiss" is not an unstated premiss of the enthymeme. (shrink)

Continuing the conversation between Achilles and the tortoise begun by Carroll, this paper proves that, in a supertask context, there are free actions (in general, contingent states of affairs) that can be predicted by means of purely logical reasons.

Suppose q is some proposition, and let P(q) = v0 (1) be the proposition that the probability of q is v0.1 How can one know that (1) is true? One cannot know it for sure, for all that may be asserted is a further probabilistic statement like P(P(q) = v0) = v1, (2) which states that the probability that (1) is true is v1. But the claim (2) is also subject to some further statement of an even higher probability: P(P(P(q) (...) = v0) = v1) = v2, (3) and so on. Thus, an infinite regress emerges of probabilities of probabilities, and the question arises as to whether this regress is vicious or harmless. Radical probabilists would like to claim that it is harmless, but Nicholas Rescher (2010), in his scholarly and very stimulating Infinite Regress: The Theory and History of Varieties of Change, argues that it is vicious. He believes that an infinite hierarchy of probabilities makes it impossible to know anything about the probability of the original proposition q: unless some claims are going to be categorically validated and not just adjudged probabilistically, the radically probabilistic epistemology envisioned here is going to be beyond the prospect of implementation. . . . If you can indeed be certain of nothing, then how can you be sure of your probability assessments. If all you ever have is a nonterminatingly regressive claim of the format . . . the probability is .9 that (the probability is .9 that (the probability of q is .9)) then in the face of such a regress, you would know effectively nothing about the condition of q. After all, without a categorically established factual basis of some sort, there is no way of assessing probabilities. But if these requisites themselves are never categorical but only probabilistic, then we are propelled into a vitiating regress of presuppositions. (shrink)

Epistemology has recently witnessed a number of efforts to rehabilitate rationalism, to defend the existence and importance of a priori knowledge or warrant construed as the product of rational insight or apprehension (Bealer 1987; Bigelow 1992; BonJour 1992, 1998; Burge 1998; Butchvarov 1970; Katz 1998; Plantinga 1993). This effort has sometimes been coupled with an attack on naturalistic epistemology, especially in BonJour 1994 and Katz 1998. Such coupling is not surprising, because naturalistic epistemology is often associated with thoroughgoing empiricism and (...) the rejection of the a priori. In this paper, however, I shall present a conception of naturalistic epistemology that is entirely compatible with a priori justification or knowledge. The resulting conception, I claim, gives us a better appreciation of the respective merits of the rational and the empirical, as well as a better understanding of how moderate epistemological naturalism comports, at least in principle, with moderate rationalism. This paper defends moderate rationalism; but it does not defend everything rationalists have often wanted, only what it is reasonable to grant them. (shrink)

This article examines two empirical research traditions—experimental economics and the social identity approach in social psychology—that may be seen as attempts to falsify and verify the theory of collective intentionality, respectively. The article argues that both approaches fail to settle the issue. However, this is not necessarily due to the alleged immaturity of the social sciences but, possibly, to the philosophical nature of intentionality and intentional action. The article shows how broadly Davidsonian action theory, including Hacking’s notion of the looping (...) effect of the human sciences, can be developed into an argument for the view that there is no theory-independent true nature of intentional action. If the Davidsonian line of thought is correct, the theory of collective intentionality is, in a sense, true if we accept the theory. Key Words: collective intentionality • experimental economics • social identity theory • Donald Davidson • Ian Hacking • constructivism • action • agency • philosophy of the social sciences. (shrink)

The last half of this century witnessed a proliferation of competing and complimentary theories of argumentation, initiated by the methodological shift from the "product" to the "process" of argument. This paper considers the effect of that shift by c omparing the different logical and epistemic status various theories assign to the standards of argument analysis and evaluation. In view of such differences, I argue that the systematic study of argumentation must clearly demarcate the normative and emp irical study of argumentation (...) with sensitivity to both the limit and significance of each. (shrink)