Is it possible to give a justification of our own practice of deductive inference? The purpose of this paper is to explain what such a justification might consist in and what its purpose could be. On the conception that we are going to pursue, to give a justification for a deductive practice means to explain in terms of an intuitively satisfactory notion of validity why the inferences that conform to the practice coincide with the valid ones. That is, a justification (...) should provide an analysis of the notion of validity and show that the inferences that conform to the practice are just the ones that are valid. Moreover, a complete justification should also explain the purpose, or point, of our inferential practice. We are first going to discuss the objection that any justification of our deductive practice must use deduction and therefore be circular. Then we will consider a particular model of justificatory explanation, building on Georg Kreisel’s concept of informal rigour. Finally, in the main part of the paper, we will discuss three ideas for defining the notion of validity: (i) the classical conception according to which the notion of (bivalent) truth is taken as basic and validity is defined in terms of the preservation of truth; (ii) the constructivist idea of starting instead with the notion of (a canonical) proof (or verification) and define validity in terms of this notion; (iii) the idea of taking the notions of rational acceptance and rejection as given and define an argument to be valid just in case it is irrational to simultaneously accept its premises and reject its conclusion (or conclusions, if we allow for multiple conclusions). Building on work by Dana Scott, we show that the last conception may be viewed as being, in a certain sense, equivalent to the first one. Finally, we discuss the so-called paradox of inference and the informativeness of deductive arguments. (shrink)

What is the relationship between logic and thought? One view is that logic merely describes how people think. But this view – called 'psychologism' – cannot be quite right. Logic cannot describe how people reason, because although people can reason well, they can also reason badly. The obvious response is to say that logic does not describe how people do think, but rather prescribes how they ought to think. If logic describes how people ought to reason, then if the premises (...) of a logical argument imply the conclusion of that argument and you believe the premises, then you ought to believe the conclusion. According to classical logic the premise, 'grass is green' implies the conclusion, 'the sky is blue or the sky is not blue', but it seems absurd to say that because I believe that grass is green, I ought to believe that the sky is blue or the sky is not blue. What has gone wrong here? Should the principle, 'if the premises imply the conclusion and you believe the premises, then you ought to believe the conclusion' be changed? If so, perhaps it would be more correct to say, 'if the premises imply the conclusion and you believe the premises, then you have reason to believe the conclusion'. Or is classical logic to blame? Are we mistaken in thinking that 'grass is green' implies 'the sky is blue or the sky is not blue'? I examine a number of arguments that relate to this question. I argue that classical logic deserves a philosophy of logic that does not imply that classical logic is not proper logic. (shrink)

Responding to the paradox of inference and the related problems in philosophy of logic, this paper argues for the necessity of distinguishing between two different objects of justification: logica utens and logica docens. Then, equipped with Peirce’s critical common-sensist conception of logica utens and his classification of sciences, I propose a diagnosis of and a solution to the problem of justification of logic. I argue that this alternative approach successfully avoids circularity in which most attempts in philosophy of logic have (...) been inescapably trapped. I also anticipate and respond to possible objections to taking a Peircean turn in justifying logic. (shrink)

A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by means (...) of harmony. I argue that such a control is possible and desirable. Moreover, it is best achieved by global tests of harmony. (shrink)

This paper examines the conceptions of logic from Leibniz, Hume, Kant, Frege, Wittgenstein and Ayer, and regards the six philosophers as the representatives of logical exceptionalism. From their standpoints, this paper refines the tenets of logical exceptionalism as follows: logic is exceptional to all other sciences because of four reasons: (i) logic is formal, neutral to any domain and any entities, and general; (ii) logical truths are made true by the meanings of logical constants they contain or by logicians' rational (...) insight to consequence relations; (iii) logical truths are analytical, a prior and necessary, so not‐revisable; and (iv) logical laws are normative for how to correctly think. However, logical exceptionalism has encountered difficult open problems: What are logical constants? How to justify basic laws of logic? How are logical laws accessible to us? How to explain the reasonability of rival logics and select from them? How to explain the universal applicability of logical laws? How to explain the normativity of logical laws for correct thinking? This paper concludes that logical anti‐exceptionalism is more hopeful to successfully answer these questions than logical exceptionalism. (shrink)

Although there has been a recent swell of interest in theories of truth that attempt solutions to the liar paradox and the other paradoxes affecting our concept of truth, many of these theories have been criticized for generating new paradoxes, called revenge paradoxes. The criticism is that the theories of truth in question are inadequate because they only work for languages lacking in the resources to generate revenge paradoxes. Theorists facing these objections offer a range of replies, and the matter (...) seems now to be at a standoff. I aim, first, to bolster the revenge objections by considering a relation, internalizability, between languages and theories of truth. A theory of truth is internalizable for a language iff there is an extension of that language in which the theory is expressible and for which the theory provides an accurate and complete assignment of semantic values. There are good reasons to think that acceptable theories of truth are internalizable for any language. With this internalizability requirement in hand, I argue that properly formulated revenge objections are decisive and that the replies to them are inadequate. Second, I show that the internalizability requirement can be met by a certain theory of truth. The central claim of this theory is that truth is an inconsistent concept and should be replaced with a pair of consistent concepts that can then be used to provide a semantics for our truth predicates. This theory is compatible with classical logic, does not give rise to revenge paradoxes of any kind, and satisfies the internalizability requirement. (shrink)

The dissertation examines the nature and epistemic implications of epistemic source circularity. An argument exhibits this type of circularity when at least one of the premises is produced by a belief source the conclusion says is legitimate, e.g. a track record argument for the legitimacy of sense perception that uses premises produced by sense perception. In chapter one I examine this and several other types of circularity, identifying relevant similarities and differences between them. In chapter two I discuss the differences (...) between internalist and externalist analyses of justification. I examine in detail foundationalist and non-foundationalist versions of internalism, and go on to consider how one might characterize externalism: either negatively, by denying particular internalist theses, or positively, in terms of a theory offering different conditions for justification. I discuss the views of reliabilist foundationalists at length. In chapter three I present the internalist objection to externalism that the latter mistakenly permit one to be justified in believing the conclusion of an epistemic source circular inference. I explain the externalists' response that it is not in virtue of their externalism that they permit epistemic source circularity but rather their foundationalism; thus, internalist foundationalists must permit epistemic source circularity as well. I evaluate the positions of several internalists, most of them explicitly foundationalists, and argue that they too cannot avoid permitting epistemic source circularity. In the final chapter I consider whether such circularity is vicious, even though both internalist and externalist foundationalists permit it. I argue that one can sustain an objection to epistemic source circularity by imposing a non-question-begging requirement on justification and explain how respecting this requirement leads one to a non-foundationalist view. I conclude by considering the objection that question-begging leads to a certain arbitrariness in belief formation that should give the foundationalist pause when it comes to determining, at the beginning of inquiry, which beliefs are justified and which are not. The dissertation is primarily concerned with making clear the possible skeptical and non-skeptical positions one can take towards epistemic source circularity. I do not argue for the truth of a particular metaepistemology. (shrink)