Ben Martin

Philosophical accounts of disagreements within logic tend to focus on how logics themselves disagree with one another, such as how their theorems or (meta)inferences diverge, while neglecting the theoretical disagreements that lead to the advocacy of these logics. This has several shortcomings, amongst which it fails to explain why disagreements over the correct logic occur in the first place, as well as overlooking the possibility of substantive logical disagreements amongst those who advocate the same logic. In this paper, we move the debate away from this lawcentrism, highlighting the various ways in which logicians disagree with each other when engaged in theory choice. We propose a framework of logical research programs within which to understand the distinct commitments logicians take on when engaged in theory choice, and show how a range of existent disagreements amongst logicians can be fruitfully understood in terms of disagreements between elements of their respective research programs.

Compared to our appreciation of the epistemology of the sciences and mathematics, we have a relatively poor understanding of the epistemology of logic. This Element highlights three causes of this lack of progress: (i) failure to distinguish between the epistemology of logical theorising and that of good (logical) reasoning; (ii) hesitancy to base epistemology of logic on how logicians actually justify their logics, rather than our own presumptions about logic; and (iii) a presumption that the epistemology of logic must be significantly different to other research areas, such as the recognised sciences. The Element ends by highlighting what can be achieved by avoiding these pitfalls, presenting an account of theory-choice in logic, logical predictivism, motivated by actual logical practice, which suggests that the mechanisms of theory-choice in logic are not that different to those in the recognised sciences.

It is well‐recognized in the sciences that a multitude of nonequivalent models are used by researchers to fulfill a range of goals, even for the same target system, a result known broadly as model pluralism. The possibility of the same form of pluralism occurring in logic, however, has not been adequately considered. This is a surprise, given that both logical pluralism and methodological anti‐exceptionalism about logic (AEL), the view that the methods of theory‐choice in logic are similar to those in the sciences, are now prominent topics. This paper makes the case for four distinct forms of model pluralism in logic, each widely found in the sciences, based upon logical practice. The result is not only interesting in itself but also serves to further support the claims of both methodological AEL and the logic‐as‐modeling view that we should understand the role of logics (at least sometimes) as akin to scientific models.

According to anti-exceptionalism about logic (AEL), logic is not as exceptional in terms of its subject matter and epistemology as has been traditionally thought. In this chapter, we focus our attention on epistemological AEL, the view that logics are justified on the basis of similar mechanisms of theory-choice and sources of evidence as theories in the sciences. In particular, we consider the motivations for rejecting a particularly important traditional property of logic—the foundational status of its laws—based upon empiricist commitments, the nature of logical facts, and logical practice, and then outline those non-foundationalist accounts of logic’s epistemology that result from these motivations, including Quine’s evidential holism, logical abductivism, and logical predictivism.

According to anti‐exceptionalism about logic (AEL), logic is not as exceptional in terms of its subject matter and epistemology as has been conventionally thought. As such, AEL either outright rejects certain traditional properties of logic, such as its formality, apriority, or necessity, or rather proposes that while logic possesses these properties, it does so in a similar way to other research areas. In this second part of a two‐part entry on AEL, we focus on contemporary proposals for Methodological AEL, the view that the mechanisms of theory‐choice in logic are similar to those in the sciences. Firstly, we consider the various contemporary motivations for Methodological AEL and highlight how these motivations need not equally motivate Evidential AEL, the view that the sources of logical evidence are the same as the sources of evidence within the sciences. Secondly, we discuss the two most prominent versions of Methodological AEL in the literature, logical abductivism and predictivism, and end by briefly outlining some of the important challenges presently facing Methodological AEL.

According to some dialetheists, we ought to reject the distinction between object and meta‐languages. Given that dialetheists advocate truth‐value gluts within their object‐language, whether in order to solve the liar paradox or for some other reason, this rejection of the object‐/meta‐language distinction comes with the commitment to use a glutty metatheory. While it has been pointed out that a glutty metatheory brings with it expressive deficiencies, we highlight here another complication arising from the use of a glutty metatheory, this time evidential in nature. According to this countermodel problem, while the thoroughgoing dialetheist who embraces a glutty metatheory can justify their acceptance of a rule of inference's invalidity using countermodels, to justify their renunciation of an unwanted rule they actually require the means to warrant their rejection of the rule's validity—which cannot be supplied by countermodels based on a standard dialetheic semantics. We end by sketching out a possible solution for the thoroughgoing dialetheist using a bilaterialist semantics.

According to anti-exceptionalism about logic (AEL), logic is not as exceptional in terms of its epistemology and subject matter as has been conventionally thought. Whereas logic's epistemology has often been considered distinct from those of the recognised sciences, in virtue of being both non-inferential and a priori, it is in fact neither. Logics are justified on the basis of similar mechanisms of theory-choice as theories in the sciences, and further the sources of evidence which inform these theory choices are (at least) not wholly a priori. In this first part of a two-part entry on AEL, we trace these epistemological elements of AEL back to Quine's naturalism and evidential holism, but then highlight important differences between the motivations and commitments of Quine's version of AEL and those within the contemporary literature. This demonstrates the need to assess contemporary anti-exceptionalist positions on their own merits, rather than treating them as mere reincarnations of Quine's evidential holism.

Philosophers of logic are particularly interested in understanding the aims, epistemology, and methodology of logic. This raises the question of how the philosophy of logic should go about these enquires. According to the practice-based approach, the most reliable method we have to investigate the methodology and epistemology of a research field is by considering in detail the activities of its practitioners. This holds just as true for logic as it does for the recognised empirical and abstract sciences. If we wish to systematically understand the aims and epistemology of logic, we are best placed achieving this by looking at what logicians do, rather than reflecting upon the nature of logic itself. In this entry, we outline the motivations for a practice-based approach towards the philosophy of logic and highlight its advantages over more “top-down” approaches, which attempt to infer conclusions about the nature of logic and its methodology on the basis of traditional assumptions about knowledge, metaphysics, or logic itself. We end by addressing several prominent concerns raised against the practice-based approach.

Among the areas of knowledge that the method of reflective equilibrium (RE) has been applied to is that of logical validity. According to RE in logic, we come to be justified in believing a (deductive) logical theory in virtue of establishing some state of equilibrium between our initial judgements over the validity of specific (natural language) arguments and the logical principles which constitute our logical theory. Unfortunately, however, while relatively popular, RE with regards to logical theorizing is underspecified. In particular, it’s unclear what constitute: (1) the relevant logical “data”, (2) logical theories, so that they can be suitably tested, and (3) the mechanisms under which such theories are tested. Considering the various options for how to interpret the position, we argue that in order to be workable the advocate of RE about logic must embrace what we call an _operationalised_, _wide_ and _communal_ version of RE with a _rich_ understanding of logical theories. Fortunately for the advocate of RE, there is an available account of logic’s epistemology which possesses just these properties, _logical predictivism_. However, equally unfortunately, logical predictivism commits the advocate of RE to certain further claims that they have historically been weary of holding. Consequently, it is unclear whether RE about logic itself is a viable proposal, or rather a similar but distinct epistemology of logic.

Joseph Raz’s _Argument from Authority_ is one of the most famous defences of exclusive positivism in jurisprudence, the position that the existence and content of the law in a society is a wholly social fact, which can be established without the need to engage in moral analysis. According to Raz’s argument, legal systems are _de facto_ practical authorities that, like all _de facto_ authorities, must claim _legitimate_ authority, which itself entails that they must be _capable_ of being an authority. Further, once we properly understand what constitutes practical authority, as captured by Raz’s _service conception_, we realise that the directives of any authority (including the law) must be wholly identifiable without recourse to moral analysis. While the argument has previously been criticised on the grounds that the law does not claim legitimate authority, and further that the service conception of authority itself is inadequate, we argue here that the argument is actually in a worse position than these concerns recognise, for it relies upon the mistaken principle that a sincere belief or claim that _p_ guarantees _p_’s conceptual possibility.

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true. Rather than advocating the truth of certain contradictions, this thesis offers a different challenge to the classical logician. By showing that it can be philosophically coherent to propose that true contradictions are metaphysically possible, the thesis suggests that the classical logician must do more than she currently has to justify her confidence in the impossibility of true contradictions. Simply fighting off the dialetheist’s putative examples of true contradictions at the actual world isn’t enough to justify the classical logician’s conclusion that true contradictions are impossible. To aid the thesis dialectically, we introduce a new position, absolutism, which hypothesises that it’s metaphysically possible for at least one contradiction to be true, contrasting with the dialetheic hypothesis that some contradictions are true in the actual world. We demonstrate that absolutism can be given a philosophically coherent interpretation, an appropriate logic, and that certain criticisms are completely toothless against absolutism. The challenge put to the classical logician is then: On what logical or philosophical grounds can we rule out the metaphysical possibility of true contradictions?

According to Fogelin’s account of deep disagreements, disputes caused by a clash in framework propositions are necessarily rationally irresolvable. Fogelin’s thesis is a claim about real-life, and not purely hypothetical, arguments: there are such disagreements, and they are incapable of rational resolution. Surprisingly then, few attempts have been made to find such disputes in order to test Fogelin’s thesis. This paper aims to rectify that failure. Firstly, it clarifies Fogelin’s concept of deep disagreement and shows there are several different breeds of such disagreements. Thus, to fully assess Fogelin’s thesis, it will be necessary to seek out cases of each breed to evaluate their rational irresolvability. Secondly, it begins this task by looking at a significant debate within the logical literature over the truth of contradictions. We demonstrate that, while the debate exemplifies a breed of deep disagreement, the parties involved can supply one another with rationally compelling reasons.

Considerable attention recently has been paid to anti-exceptionalism about logic, the thesis that logic is more similar to the sciences in important respects than traditionally thought. One of AEL’s prominent claims is that logic’s methodology is similar to that of the recognised sciences, with part of this proposal being that logics provide explanations in some sense. However, insufficient attention has been given to what this proposal amounts to, and the challenges that arise in providing an account of explanations in logic. This paper clarifies these challenges, and shows how the practice-based approach is best placed to meet them.

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 scientific 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 find that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas.

While anti-exceptionalism about logic is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together.

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic, that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation.

Given the plethora of competing logical theories of validity available, it’s understandable that there has been a marked increase in interest in logical epistemology within the literature. If we are to choose between these logical theories, we require a good understanding of the suitable criteria we ought to judge according to. However, so far there’s been a lack of appreciation of how logical practice could support an epistemology of logic. This paper aims to correct that error, by arguing for a practice-based approach to logical epistemology. By looking at the types of evidence logicians actually appeal to in attempting to support their theories, we can provide a more detailed and realistic picture of logical epistemology. To demonstrate the fruitfulness of a practice-based approach, we look to a particular case of logical argumentation—the dialetheist’s arguments based upon the self-referential paradoxes—and show that the evidence appealed to support a particular theory of logical epistemology, logical abductivism.

Rejectivism is one of the most influential embodiments of pragmatism within contemporary philosophy of logic, advancing an explanation of the meaning of a logical notion, negation, in terms of the speech act of denial. This paper offers a challenge to rejectivism by proposing that in virtue of explaining negation in terms of denial, the rejectivist ought to be able to explain the concept of contradiction partially in terms of denial. It is argued that any failure to achieve this constitutes an explanatory failure on the part of rejectivism, and reasons are then provided to doubt that the challenge can be successfully met.

In recent editions of this journal, Jean-Yves Beziau [8] and Marcin Tkaczyk [41] have criticised a prominent dialetheic logic and common arguments for dialetheism, respectively. While Beziau argues that Priest’s logic LP commits the dialetheist to trivialism, the thesis that all propositions are true, Tkaczyk maintains that the arguments traditionally proposed for dialetheism are faulty and ultimately that dialetheism should be rejected as self-refuting. This paper shows that both are mistaken in their contentions. Beziau’s argument conflates truth-in-an-interpretation with truth simpliciter and Tkaczyk misconstrues the substance of dialetheic arguments. In the process of identifying these weaknesses of both arguments, the paper clarifies elements of both dialetheic logics and dialetheism which these discussions demonstrate are still misunderstood within the literature.

This paper first offers a standard modal extension of dialetheic logics that respect the normal semantics for negation and conjunction, in an attempt to adequately model absolutism, the thesis that there are true contradictions at metaphysically possible worlds. It is shown, however, that the modal extension has unsavoury consequences for both absolutism and dialetheism. While the logic commits the absolutist to dialetheism, it commits the dialetheist to the impossibility of the actual world. A new modal logic AV is then proposed which avoids these unsavoury consequences by invalidating the interdefinability rules for the modal operators with the use of two valuation relations. However, while using AV carries no significant cost for the absolutist, the same isn't true for the dialetheist. Although using AV allows her to avoid the consequence that the actual world is an impossible world, it does so only on the condition that the dialetheist admits that she cannot give a dialetheic solution to all self-refe..