Abstract
By playing a crucial role in settling open issues in the philosophical debate about logical consequence, logical evidence has become the holy grail of inquirers investigating the domain of logic. However, despite its indispensable role in this endeavor, logical evidence has retained an aura of mystery. Indeed, there seems to be a great disharmony in conceiving the correct nature and scope of logical evidence among philosophers. In this paper, I examine four widespread conceptions of logical evidence to argue that all should be reconsidered. First, I argue that logical apriorists are more tolerant of logical evidence than empiricists. Second, I argue that evidence for logic should not be read out of natural language. Third, I argue that if logical intuitions are to count as logical evidence, then their evidential content must not be propositional. Finally, I argue that the empiricist proposal of treating experts' judgments as evidence suffers from the same problems as the rationalist conception.
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Notes
In the rest of the article, in discussing correctness, I will assume the conception of logical correctness proposed by Haack (1978, 221).
For the sake of accuracy, in the rest of the paper I will use the term "warrant" to speak about what many epistemologists call by the term "justification." For a discussion on this point, see Burge (2003a, 2003b, 2020); Graham (2012, 2020). Also, by the term "warrant" I will mean doxastic warrant. For a discussion on this point, see Melis (2018); De Toffoli (forthcoming).
Usually, evidence is conceived as having a propositional nature (cf. Davidson, 1990; Williamson, 2000). However, the conception I have adopted above seems to go well beyond this standard view. In my opinion, evidence can also be non-propositional (for a critical discussion, see Sellars, 1956; McDowell, 1994; O'Shea, 2021). This is because I believe that beliefs are not rationally supported only by other propositional states. For instance, in its raw form, perceptual evidence can be considered non-propositional (cf. Burge, 2020, 55–60). Yet, it would be a mistake not to count it as evidence (cf. Alston, 1989; Audi, 1992; Burge, 2003a, 2003b). Moreover, by mirroring this proposal, even supporters of the a priori have argued that a priori warrant can depend on non-propositional evidence (cf. Moretti, 2020; De Toffoli, 2021; BonJour, forthcoming). In section §3 I will present some arguments in favor of the non-propositional conception of evidence.
Although this conception of evidence is broad enough to include non-propositional evidence, the term "considerations" should not imply that arguments à la Wright (2004) or Boghossian (2003) – i.e., arguments concerning the constitutive nature of logical concepts for our rational life – could count as evidence. Although the considerations these authors present might support the belief that, say, P is a valid logical principle, what they actually do is show that some claims can be non-evidentially supported. Therefore, I believe that considerations of this kind should be considered meta-epistemic rather than epistemic. I wish to thank Elia Zardini for raising this issue.
Moreover, since it has often been objected that non-evidentialist approaches may offer at most pragmatic warrant for the claims to which they apply (see especially Graham & Pedersen, 2020), in the remainder of the paper I will focus on evidentialist strategies.
Semanticism is an apriorist thesis that hinges on the distinction between enabling and evidential experiences. While enabling experiences are those necessary to acquire a concept, evidential experiences serve to epistemically support a belief. Since a priori warrant is compatible only with experiences of the former type, then the a priori warrant is a type of epistemic support that does not depend on experience in an evidential manner. Therefore, since the semanticist usually argues that the experiences that are needed to gain linguistic (conceptual) competence are enabling, then in some cases grasping these meanings (contents) is enough to form a warranted belief about certain propositions (usually considered to be analytical).
One of Quine's teachings still present in AEL accounts is the idea that evidence warrants logical theories in a holistic spirit (more on this below). However, moderate views of AEL (cf. Martin & Hjortland, 2022, §3.2) would not follow Quine in saying that all evidence for logic is empirical. On the contrary, many now would admit that evidence for logic is a priori.
At this point someone might object that since Williamson (2013) denies the naturalness of the a priori-a posteriori distinction, he may also deny that there is epistemic overdetermination. To dispel any doubts in this regard, let us proceed carefully by considering two points. First, Williamson does not deny that there are no instances of a priori knowledge. He only denies that the distinction in question is natural (cf. Williamson, 2013, 169). Second, the arguments Williamson proposes against the a priori-a posteriori distinction are based on two crucial assumptions: first, knowledge of modal truths is reducible to knowledge of counterfactuals; second, knowledge of counterfactuals normally requires the use of imagination (an epistemic source that depends on experience in a more than merely enabling, but less than strictly evidential way – cf. fn. 8). Therefore, according to Williamson, since we normally employ a source that does not sit well with the a priori-a posteriori distinction, we should deny the naturalness of this distinction. Now, even granting Williamson his first assumption, can we really say that we normally use only one source of evidence to gain knowledge about the truths that comprise a domain of inquiry? Williamson is not very clear on this point. Still, this assumption remains somewhat controversial. For it is one thing to say that we have isolated a source that does not sit well with the a priori-a posteriori distinction. It is another thing to say that the distinction is not epistemically relevant or natural. Williamson's account thus seems unstable.
Biggs and Wilson (2022, §5) argue that AEL offers an epistemological theory of logic that is conditional in nature. In other words, for AEL advocates, the warrant of a logical theory is a priori only if the inferential method and the evidence are a priori. Although the explanation proposed by these authors is limited to logical abductivism (cf. Priest, 2016; Williamson, 2017), their account easily extends to logical predictivism (cf. Martin & Hjortland, 2021). That is, a logical theory is warranted a priori only if both the hypothetical-deductive method and the evidence are a priori. However, in my view, it follows from this generalization, that logic cannot be a priori warranted for AEL. Let us consider abductivism first. Even assuming that the abductive method is a priori – as Biggs and Wilson have argued elsewhere (see Biggs & Wilson, 2017) – some of the evidence used to carry out this inference is empirical. For example, let us consider the fruitfulness criterion on which abductive inference is (partly) based. The evidence by which we establish that one theory is more fruitful than others is empirical. In other words, only after applying a logic to a scientific theory and deducing its conditional hypotheses can we determine which hypotheses are confirmed. Therefore, some of the evidence on which abduction is based is empirical. A similar argument can be made for the simplicity criterion (cf. Hjortland, 2017, fn. 23). Let us now consider logical predictivism. As before, let us grant that the method is a priori for the sake of argument. Despite this, predictivism is based on expert epistemology (more on this in §4). That is, the evidence from which a theory is constructed and tested is based on experts' judgments (cf. Martin & Hjortland, 2021). However, suppose this evidence is transmitted by testimony from an expert to a predictivist inquirer, as these authors suggest. In that case, the evidence on which the predictivist method is based is empirical, pace Burge (1993).
For example, with due caution, we might say that this is the conception of apriorism that has developed since Plato (see Phaedo – 72a-82a – and the Meno – 82a-85b). For a discussion, see also Casullo (2003, §4) and Dodd & Zardini (forthcoming).
Undoubtedly there is an arbitrary component in the demarcation between E and A since the boundaries of terms such as "empiricism" and "apriorism" are not sharp. However, to admit this is not to admit that a proper distinction cannot be made between the tenets of these views.
This is a desirable result. If S is a logical theory and its claims can be warranted in isolation, this fact would explain why different logical claims often receive different kinds of warrant. For example, it could be argued that modus ponens (MP) – i.e., \(\varphi \to \psi ,\varphi \models \psi\) – is intuitively valid, i.e., non-inferentially, a priori warranted. Alternatively, the rule of contraposition – i.e., \(\varphi \to \psi \models \sim \psi \to \sim \varphi\) – is typically inferentially warranted. However, this latter warrant could be of two kinds: a priori (proof) or a posteriori (testimony/imagination). Similar considerations can be extended beyond the warrant of logical rules. For example, Oms (2019, 196–97), argues with Priest that at least two families of paradoxes (Self-Reference and Sorites) can be treated by grasping the apparent inclosure scheme underlying these paradoxes. Thus, by grasping the pattern underlying these paradoxes in a direct (apparent) way, we could unravel these paradoxes by making the right adjustments to our logical theories.
Now, it could be argued that epistemic overdetermination and epistemic holism presuppose two different conceptions of the structure of warrant. To wit, while overdetermination needs a linear (foundational) structure of warrant to hold, epistemic holism requires a coherentist framework. However, coherentism faces a straightforward challenge in explaining how warrant and truth are linked. For instance, in principle, one can believe a set of false beliefs which are nevertheless coherent. Yet, clearly, one would not be warranted in doing this, for in that case, this warrant would preclude one from having knowledge (cf. Burge, 2020, 39). To solve this problem, advocates of coherentism usually attribute a special role to the claims that stand in the periphery of the belief system, and which are known to be true (cf. Sober, 2000). Specifically, these beliefs are immediately warranted in a way that is independent of the overall coherence of the belief system (cf. Lewis, 1946; Rescher, 1973; BonJour, 1985). Coherentist views that allow this modification can be seen as allowing a moderate version of foundationalism to hold (cf. Olsson, 2021). Still, if claims that are in the belief system can be directly warranted in isolation, then nothing prevents these claims from being overdetermined. Thus, epistemic overdetermination would be consistent within a coherentist framework.
Moreover, the fact that the coherentist must admit independently warranted beliefs amplifies the possibility of these beliefs being a priori warranted. For example, suppose a logical rule is independently warranted as described above (cf. Sober, 1981, 2000, §XI). In this case, since coherentism links the notion of circularity very closely to that of warrant, nothing would rule out the possibility that such a rule could be independently warranted via a rule circular argument. In this way, the logical rule's warrant would count as a priori (cf. fn.14). I want to thank an anonymous referee for making me elaborate on this point.
Some may argue that this principle is overly inclusive, as it could potentially permit the acceptance of unacceptable evidence, such as that which originates from a magical sphere. I believe that this objection can be addressed by considering the following points. Generally, suppose we assume that the warrant of a claim p is at least partially dependent on the quality of the supporting evidence. In that case, the evidence supporting p must be competently produced. It is important to note that this does not necessarily rule out the existence of misleading evidence. However, it is worth acknowledging that the concept of what constitutes good evidence is not rigidly defined and can vary in different circumstances. What qualifies as evidence for p may change depending on the context. For instance, in mathematics, a diagrammatic proof might suffice to establish the truth of p when a more formal proof is unavailable (cf. De Toffoli, 2022). In any case, it appears that for something to be considered evidence (and, by extension, to provide warrant), it must meet the criteria of being good evidence, which implies that it was competently produced. Thus, the reliability of the source generating the evidence play a crucial role in its acceptance (cf. Goldman, 2011, §16.2). Nonetheless, what is considered reliable in one set of circumstances may not hold the same status in another (cf. Graham, 2016). Therefore, if the evidence for p is reliable in the current context, it may not be regarded as reliable in a different context. Consequently, in order to determine which evidence is pertinent for warranting p, it is necessary to consider which epistemic sources are deemed good in those specific circumstances. Failure to do so could lead to making unwarranted epistemic assumptions (cf. Jeshion, 2011, 126-27). I believe this clarification sheds light on the distinction between evidence and data. In this sense, the aforementioned maxim only accommodates evidence for p and does not extend to rhapsodic data. I would like to express my gratitude to an anonymous referee for prompting me to expand on this point.
Beall & Restall (2006) defend the idea that one of the three core features of logic is necessity (the truth of the premises of a logically valid argument necessitates the truth of the conclusion). One way to explain this necessity is through the meaning of logical terms (cf. Martin & Hjortland, 2022, 9). A conclusion follows logically from the premises because of the meaning of the logical terms. This amounts to a kind of metaphysical analyticity. Therefore, if Glanzberg's arguments were sound, language per se could not explain the necessary character of logic.
It is worth specifying that Dicher does not deny that linguistic evidence can serve for logical theorizing. Dicher (2022, 183) assumes that logical theorization involves extracting logical form from natural language. However, as we shall see shortly, he also argues that natural language must be honed to serve as evidence for logic.
McGee's most famous counterexample to MP goes as follows:
‘Opinion polls taken just before the 1980 election showed the Republican Ronald Reagan decisively ahead of the Democrat Jimmy Carter, with the other Republican in the race, John Anderson, a distant third. Those apprised of the poll results believed, with good reason:
[1] If a Republican wins the election, then if it's not Reagan who wins it will be Anderson.
[2] A Republican will win the election.
Yet they did not have reason to believe:
[3] If it's not Reagan who wins, it will be Anderson'. (McGee 1985, 462).
In the same section, Dicher also references a passage from Beall & Restall (2006, 9), in which the authors discuss the type of language that logical theorizing should address. Much like Dicher (2022), as previously noted in fn.18 of this article, Beall & Restall use the concept of logical form to explain how natural language can be constrained. Consequently, it is reasonable to interpret all these authors as proponents of the idea that natural language must be refined to be regarded as logical evidence, and that the key approach is to consider the logical form we aim to derive from it.
These considerations generally pertain to the conditional concept that our logical theories aim to encapsulate. As Zardini (forthcoming, fn.59) reminds us: ‘Frege […] might have been right that the laws of logic are norms of thought […], but he overlooked the fact that norms are there to be broken. The tremendous power of negativity pushes our thought to displace its “boundary stones” to make room for the possibility of entertaining nontrivial hypotheses about their failure. This cognitive ability is manifested in our use of counterlogical conditionals. It should then not be surprising that conditionals do not unrestrictedly obey any principle: arguably, if they did, they could not be vectors of our boundlessly free hypotheses concerning failures of logical principles'.
The idea that logic has a ‘canonical application' in natural language is unusual. Yet, authors such as Priest adopt this unusual sense of this expression (see especially his quotation located at the beginning of §3). In an attempt to understand this use of the expression "canonical application", let us consider the distinction between pure and applied logic. The former differs from the latter in that it is essentially a formal calculus with its adequacy conditions, i.e., non-triviality. We call these adequacy conditions "internal" since they can be shown to hold formally. In contrast, applied logic has "external" adequacy conditions since, in order to be correct, a logic must also take into account the phenomenon one wants to capture with its canonical application. Therefore, following Priest's ideas, the expression "canonical application" refers to the main source of evidence in logic, namely, natural language.
At this point, it could be argued that we should be interested in the second project, since it clearly has greater importance over the others. Eklund (2020, 4), however, argues that there is no reason to think that what is presented in natural language is normatively or ontologically more interesting than what is shown in the other projects (see also Eklund, 2020, 3).
Besides, one point concerning the second project seems particularly worrying for the proponent of the linguistic conception of logical evidence. In his article on the limits of logical abductivism, Hlobil (2020) argues that abductive methodology is not a neutral method for choosing which logical theory is correct. In nuce, he argues that since different logics explain different data, proponents of these logics cannot agree on the evidence to carry out the abductive inference. Hlobil's conclusions raise other important issues. For example, let us consider the debate between monists and logical pluralists. Assume that the linguistic conception applies. In this case, I think comparing these views would be problematic and lead to unpalatable results. First, monism would have no chance of success. Since language clearly shows us that many terms (logical and otherwise) are ambiguous or polysemic, we would have to immediately conclude that more than one logic is correct. Yet, with Glanzberg, we have seen that this is the opposite of what many authors would argue: there is a correct logic in natural language. Second, since we are considering linguistic meaning to explain which notion of logical consequence is correct (cf. fn. 17), we cannot prescind from the various meanings of logical vocabulary. Therefore, if we cannot exclude these meanings, neither can we exclude the different logics that regiment them. Yet it seems that this way of conceiving logical evidence generates meaning-variant pluralism rather than meaning-invariant pluralism (cf. Dicher, 2016; Ferrari & Orlandelli, 2021). That is, as Quine has put it, ‘change of logic, change of subject'. Still, if this were the case, pluralism would be susceptible to the criticism that different logical theories are not discussing the same notion of validity but rather different version of it (cf. Hlobil, 2020, 334). I want to thank an anonymous referee for making me elaborate on this point.
In this section, I consider Chudnoff's account because of its distinctive features and applications to the debate in the epistemology of logic. However, the reader should not think of this discussion merely as an internal critique of this account. Much of the following could apply to other accounts that employ intuitions as epistemic sources. For example, the idea that by merely reflecting on a proposition, one can be warranted to form an intuitive belief can be found in many authors (cf. Bealer 1998; Bengson 2015a; Boghossian & Williamson, 2020; BonJour, 1998; Sosa, 2007). Therefore, if the idea proposed by Chudnoff is widespread in the literature, it is worth considering its effectiveness by taking a closer look.
The referent of the term "form" used in the quotation above is not clarified by Chudnoff. Most likely, by "form", Chudnoff means "logical form". In any case, the examples he uses in his article suggest that he uses this term ambiguously. Indeed, we can distinguish between a use of "logical form" for perfect languages and a use that concerns the deep structure of natural language (cf. Davidson, 1980, 137). Both senses of this term have their limitations (cf. Sainsbury, 2020). In the following, I will remain neutral with respect to this distinction by avoiding further interpretation of Chudnoff's work. For now, it is enough for us to know that awareness of forms is non-propositional evidence since it involves awareness of schemata. I thank an anonymous referee for inviting me to clarify this point.
Some might argue that self-evident claims (logical truths or axioms) are reasons in themselves (cf. Burge, 2003b). Therefore, an advocate of unreflective intuitions might argue that because we are aware of the propositions these claims express, we have a direct warrant for these claim (no reasoning would be necessary). To reply to this objection, we need to keep a couple of things in mind. First, this line of reasoning seems to assume a notion of metaphysical analyticity, a notion widely rejected nowadays (let us remember that, in this account of intuitions, propositions are doing all the heavy lifting; awareness only allows us to see something that is already there, that is, the truth of the proposition). Moreover, it is not clear whether self-evidence and analyticity (metaphysical or epistemological) are co-extensional concepts. Therefore, some may already doubt the effectiveness of this proposal. This latter remark leads us to consider a second aspect (I will set aside for now the issues about the complicated relationship between understanding and intuition – for a discussion, see fn.27). If we were really to turn to the notion of analyticity to save this line of argument, we would have to use an epistemic notion of analyticity: understanding and meaning warrant the belief that p (cf. Teixeira, 2023). Now, the introduction of understanding complicates things a bit. Since it is no longer just the propositional content that warrants the belief that p, but the combination of meaning and understanding, we cannot rule out reasoning (cf. Bengson, 2015b, §4). Therefore, if reasoning cannot be ruled out for warranting beliefs involving self-evident truths, reasoning cannot be ruled out for the case of unreflective intuitions (more on this in §5).
Besides, if we can assume that propositions are conceived of as abstracta by Chudnoff, his internalist account of intuitions fails (cf. Chudnoff 2011, §2), as the mind-and-language independent nature of abstracta clashes with the internalist tenet of considering only the internal features of our psychology to explain warrant (cf. Pollock & Cruz, 1999, 25).
Bengson (2015a, 740) has convincingly argued that understanding is neither necessary nor sufficient to have intuitional warrant. Reason: understanding is not sufficient for intuitions because it is possible to understand that p without having the intuition that p (see the case of the principle of non-contradiction and its negation above; we can understand both claims, but only intuit the principle of non-contradiction). Moreover, understanding is not necessary for intuitions because it is possible to intuit that p without understanding that p. For example, Bengson takes up the case of Weierstrass reported in Frege's posthumous writings. In this case, Frege argued that Weierstrass had correct intuitions about the properties of numbers even though he did not fully understand the concept number.
Specifically, these authors seem to argue that experts' judgments count as evidence regardless of how they form such judgments. For example, if an expert judges that "X is a valid logical principle", then this judgment is part of the evidence by which we can warrant a logical theory. Still, whether this judgment is made from linguistic skills, intuitions, or empirical observations makes no difference in this account. One reason to support this latter precisification stems from these authors failure to explain experts' reliability (competence). Indeed, in both of their articles (Martin & Hjortland 2021, 298; Martin & Hjortland 2022, fn. 25), these authors must assume that experts are reliable (competent) in making (logical) judgements in order to count these judgements as evidence. However, since the reliability of experts' judgments could be easily explained by considering the reliability of the sources they use (or their competence in using these sources), and since Martin & Hjortland fail to do so, it would be natural to interpret their account as ruling out an epistemic role for sources of evidence.
Besides, I would like to point out that this remark was discussed in a private meeting with Ole Hjortland.
My point below is not directly about whether experts' judgments can be considered evidence. I see no major problem in arguing for this claim (except perhaps for the point I will make later about the factiousness of such evidence). The problem I want to emphasize here is that the evidential standards of this AEL proposal undermine the possibility of using experts' judgments to warrant logic. Foreshadowing my strategy a bit, the point is that if we talk about logical evidence, we cannot ignore its sources (cf. fn. 16). Although sources of evidence are not, de facto, evidence for logic, sources play a crucial role in the evidential relations that are instantiated when we warrant a belief (logical or whatever). Indeed, if we were not committed to the sources by which evidence is produced, we could not explain why we rely on experts and their judgments. After all, the fact that logical evidence is what an expert judges to be true is not enough to make a logical judgment a "good piece of evidence" since nothing precludes that such judgment may be incompetently produced. I thank an anonymous referee for inviting me to clarify this point.
Although for authors such as Frege, obviousness is neither necessary nor sufficient for self-evidence, the subsequent literature on this topic has pointed out that it would be fair to say that in most cases obviousness is at least a safe guide to self-evidence (cf. Jeshion, 2001).
The importance of epistemic sources for making judgments was well understood by Frege. Consider the following passage: ‘A sense-impression is not in itself a judgment, but becomes important in that it is the occasion for our making a judgment' (Frege, 1979, 267). In other words, sources of evidence make possible the formation of judgments by enabling the conceptualization of content, that is, by enabling predication (cf. Burge, 2010, 30–8).
Interestingly, in a couple of passages of his work, Frege seems to discuss the role of sources in grasping and judging the basic laws of logic. Take for instance what he writes in a footnote of his 1897 unpublished Logic: ‘I should say that this question is still far from being grasped in all its difficulty. People are usually quite content to smuggle thought in through a back door in the imagination, so that they don't themselves know how it really got in' (Frege, 1897/1979, 145). Although this passage merely represents a note in his discussion of how we grasp thoughts about the basic laws, in the wider context in which this passage is located Frege sticks to his guns and warns us about the irrelevancy and the perils of the psychologistic intrusions. Yet, despite these admonitions, he still seems to conceive the problem of grasping a law ‘as a question in its own right', while remaining convinced that ‘it is not the holding something to be true that concerns us but the laws of truth'.
Moreover, consider a second passage ‘The question why and with what right we acknowledge a law of logic to be true, logic can answer only by reducing it to another law of logic. Where that is not possible, logic can give no answer. If we step away from logic, we may say: we are compelled to make judgments by our own nature and by external circumstances; and if we do so, we cannot reject this law – of Identity, for example; we must acknowledge it unless we wish to reduce our thought to confusion and finally renounce all judgments whatever. I shall neither dispute nor support this view; I shall merely remark that what we have here is not a logical consequence' (Frege, 1884/1968, XVII). In this passage, the question for Frege has changed. As matter of fact, in this second quotation, Frege is not interested anymore in the problem of explaining how thoughts about basic laws can be grasped. Specifically, he is now concerned with knowing whether these could be judged as being true. Even in this case, knowledge of basic laws is problematic for we cannot appeal to logical proof. Although it is difficult to pin down exactly what Frege had really in mind here, one interpretation could be that one could acknowledge these truths via sources other than logic. Again, although the sources he mentions do not pertain to the prerogatives of logic, these are deemed, to some extent, as being relevant for judging something as being true.
For example, in this case, what I have in mind is the evidence Maddy (2007, §3.5) talks about for the case of logic and mathematics. Maddy indeed pays much attention to the logical evidence provided by infants in the preverbal stage of development.
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Acknowledgements
I am indebted to Ole Hjortland and Elia Zardini for many enlightening comments on some of the early versions of this paper. I am indebted to the audience at the Russell 150 conference for making me reconsider some of the arguments in §2 and §3. Finally, I am indebted to two anonymous referees who – I firmly believe – helped me greatly improve this article with their valuable comments.
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Baggio, M. What Logical Evidence Could not be. Philosophia 51, 2559–2587 (2023). https://doi.org/10.1007/s11406-023-00695-0
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DOI: https://doi.org/10.1007/s11406-023-00695-0