In this paper, I take issue with a core commitment of logical conventionalism: that we impose a logic on ourselves by adopting general linguistic conventions governing our use of logical terms, thereby determining the meanings of the logical constants and which of our inferences are valid. Drawing on Kripke’s ‘adoption problem’, I argue that general logical principles cannot be adopted, either explicitly or implicitly. I go on to argue that the meanings of our logical terms, and the validity of our (...) inferences, cannot depend on our adoption of logico-linguistic conventions. (shrink)

In the last 35 years many philosophers have appealed to reference magnetism to explain how it is that we mean what we mean. The idea is that it is a constitutive principle of metasemantics that the interpretation that assigns the more natural meanings is correct, ceteris paribus. Among other things, magnetism has been used to answer the challenges of grue and quus, Quine’s indeterminacy of translation argument, and Putnam’s model-theoretic argument against realism. Critics of magnetism have usually objected to the (...) base notion of naturalness. Here I assume naturalness for the sake of argument, but argue that even still, reference magnetism should be rejected. The supposed force of reference magnetism is arbitrarily weak, and the best explanation of this is that it simply does not exist. (shrink)

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I (...) argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning. -/- (Note for readers: the paper's brief discussion of uniform reflection and omega inconsistency is misleading. The imagined interlocutor's argument makes an assumption about the PA-provability of provability generalizations that, while true for the Godel sentence's instances, is unjustified, in general. This means my position is stronger against this objection than the paper suggests, since omega inconsistent theories are not automatically inconsistent with their uniform reflection principles, you also need to assume the arithmetically true Pi-2 sentences.). (shrink)

Inferences are familiar movements of thought, but despite important recent work on the topic, we do not yet have a fully satisfying theory of inference. Here I provide a functionalist theory of inference. I argue that the functionalist framework allows us the flexibility to meet various demands on a theory of inference that have been proposed (such as that it must explain inferential Moorean phenomena and epistemological ‘taking’). While also allowing us to compare, contrast, adapt, and combine features of extant (...) theories of inference into one unified theory. In fleshing out the inference role, I also criticize the common assumption that inference requires rule-following. (shrink)

In this paper, I argue from a metasemantic principle to the existence of analytic sentences. According to the metasemantic principle, an external feature is relevant to determining which concept one expresses with an expression only if one is disposed to treat this feature as relevant. This entails that if one isn’t disposed to treat external features as relevant to determining which concept one expresses, and one still expresses a given concept, then something other than external features must determine that one (...) does. I argue that, in such cases, what determines that one expresses the concept also puts one in a position to know that certain sentences are true—these sentences are thus analytic relative to this determination basis. Finally, I argue that there are such cases: some sentences are analytic relative to what determines that we express certain key concepts, and these sentences include ones that have always been thought to be the best candidates for being analytic, namely, stipulative truths, and first principles of mathematics. (shrink)

The resemblance is plain to see between Kripke’s Wittgenstein introducing bizarre rules such as _quaddition_ (in illustrating the _sceptical paradox_ against theories of meaning) and Goodman’s introducing the equally bizarre _grue_ (in generating the _new riddle of induction_). But the two sorts of bizarre cases also differ in interesting respects. For those familiar with Goodman’s case, this similarity sparks a strong temptation to enlist to the meaning sceptic’s cause key elements of Goodman’s new riddle, which are missing from Kripke’s case. (...) In this essay, I characterize a natural way of doing just this, which targets dispositionalist solutions to the sceptical paradox. I also show that, despite initial appearances, this new objection to dispositionalism (the symmetry problem) is not nearly as worrisome as originally thought. The solution offered on behalf of semantic dispositionalists does require a trade-off, though, from the severe form of indeterminacy advanced by the meaning sceptic to a much milder thesis. (shrink)

In a trio of recent articles, Johnson and Nado defend a form of metasemantic dispositionalism, arguing for a novel approach to the “error”-problem, based on speakers’ dispositional states under what they call a state of “full information”. In this article, I argue that their brand of dispositionalism fails to solve the “error”-problem, because of what I think of as counterexamples to it. In the final sections, I propose a way to amend the theory to shield it from some of the (...) counterexamples, based on the idea that what determines meaning is not only dispositions to apply words under full information, but also dispositions to evaluate one’s prior usage, under full information. (shrink)

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order PA and Zermelo’s quasi-categoricity (...) theorem for second-order ZFC—these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic. (shrink)

What are Carnap's views on the epistemology of mathematics? Did he believe in a priori justification, and if so, what is his account of it? One might think that such questions are misguided, since in the 1930s Carnap came to reject traditional epistemology as a confused mixture of logic and psychology. But things are not that simple. Drawing on recent work by Richardson and Uebel, I will show that Carnap's mature metaphilosophy leaves room for two distinct notions of a priori (...) justification: one propositional, the other doxastic. The latter is especially interesting since it comes closest to a traditional understanding of a priority. On the other hand, Carnap has little to say about doxastic justification in his writings. This lacuna can be filled by drawing on an unpublished exchange with Irving M. Copi. In it, so I will show, Carnap endorses the view that agents can come to know all mathematical truths a priori. This fact, so I will further argue, can be used to adjudicate a dispute between Ricketts and Friedman about the nature and viability of Carnap's philosophy of mathematics—specifically his reliance on infinitary methods. (shrink)

In virtue of what does a sign have meaning? This is the question raised by Wittgenstein's rule-following considerations. Semantic dispositionalism is a (type of) theory that purports to answer this question. The present paper argues that semantic dispositionalism faces a heretofore unnoticed problem, one that ultimately comes down to its reliance on unanalyzed notions of repeated types of signs. In the context of responding to the rule-following paradox—and offering a putative solution to it—this amounts to simply assuming a solution to (...) the problem in one domain and using it to solve the same problem in another. Given, moreover, the level at which the rule-following paradox undercuts dispositionalism—the level of the notion of a sign's repetition—the objections made to the view also rule out causal/informational theories of meaning as well as communitarian/assertion-theoretic ones as potential solutions to the rule-following paradox. (shrink)

The paper presents teleo-inferentialism, which is a novel meta-semantic theory that combines advantages of teleosemantics and normative inferentialism. Like normative inferentialism, teleo-inferentialism holds that contents are individuated by the norms that govern inferences in which they occur. This allows teleo-inferentialism to account for sophisticated concepts. Like teleosemantics, teleo-inferentialism explains conceptual norms in a naturalistically acceptable way by appeal to the broadly biological well-functioning of our innate capacities. As a test-case for teleo-inferentialism, I discuss how the view handles Kripkenstein-style meaning skepticism.

In metasemantics, semantic dispositionalism is the view that what makes it the case that, given the value of the relevant parameters, a certain linguistic expression refers to what it does are the speakers’ dispositions. In the literature, there is something like a consensus that the fate of dispositionalism hinges on the status of three arguments, first put forward by Saul Kripke ‒ or at least usually ascribed to him. This paper discusses a different, and strangely neglected, anti-dispositionalist argument, which develops (...) some remarks first put forward by Paul Boghossian and Anandi Hattiangadi and revolves around the idea that semantic dispositionalists have no way to justify their privileging certain dispositions, the ones they take to be reference-determining, over all the others. After some background (Section 1) and a first presentation of the argument (Section 2), I discuss three ways a dispositionalist might try to answer it and find them all wanting (Section 3). (shrink)

Kripkenstein’s challenge is usually described as being essentially about the use of a word in new kinds of cases ‒ the old kinds of cases being commonly considered as non-problematic. I show that this way of conceiving the challenge is neither true to Kripke’s intentions nor philosophically defensible: the Kripkean skeptic can question my answering “125” to the question “What is 68 plus 57?” even if that problem is one I have already encountered and answered. I then argue that once (...) the real nature of Kripkenstein’s challenge is properly appreciated, one extremely popular strategy to try to meet it, what usually goes by the name of “semantic dispositionalism”, loses much of its appeal. Along the way, I also explain that Kripkenstein’s challenge is actually two distinct challenges ‒ one concerning the mental state of meaning, or intending, something by a sign and the other concerning the meaning (referentially conceived) of linguistic expressions. (shrink)

Semantic dispositionalism is roughly the view that meaning a certain thing by a word, or possessing a certain concept, consists in being disposed to do something, e.g., infer a certain way. Its main problem is that it seems to have so many and disparate exceptions. People can fail to infer as required due to lack of logical acumen, intoxication, confusion, deviant theories, neural malfunctioning, and so on. I present a theory stating possession conditions of concepts that are counterfactuals, rather than (...) disposition attributions, but which is otherwise similar to inferentialist versions of dispositionalism. I argue that it can handle all the exceptions discussed in the literature without recourse to ceteris paribus clauses. Psychological exceptions are handled by suitably undemanding requirements (unlike that of giving the sum of any two numbers) and by setting the following two preconditions upon someone’s making the inference: that she considers the inference and has no motivating reason against it. The non-psychological exceptions, i.e., cases of neural malfunctioning, are handled by requiring that the counterfactuals be true sufficiently often during the relevant interval. I argue that this accommodates some important intuitions about concept possession, in particular, the intuition that concept possession is vague along a certain dimension. (shrink)

This draft preprint presents a nine step argument for “Connectionist Structuralism” (CS), an account of the ontology of abstract objects that is neither purely nominalist nor purely platonist. CS is a common, often implicit assumption in parts of the artificial intelligence literature, but such discussions have not presented formal accounts of the position or engaged with metaphysical issues that potentially undermine it. By making the position legible and presenting an initial case for it, we hope to support a constructive dialogue (...) between AI researchers and philosophers of metaphysics that helps both sides to refine the position. -/- CS proposes that each abstract object we can draw on in human analysis corresponds to a particular subset of an individual person’s brain structure whose functionality is isomorphic to a subset of the nodes and connections in a suitable connectionist network. In other words, abstract objects are physically realised, but in individual brains, rather than only in the referent objects (pure nominalism) or in metaphysical universals (pure platonism). -/- This paper’s minimum claim is that CS can account for all abstract object predicables regarding sensible properties, such as “is red” or “is a square”. Using evidence from cognitive neuroscience, machine learning, and evolutionary biology, as well as a fully traceable toy example, we describe how CS can support our core cognitive uses of such sensible properties and can account for our core phenomenal experiences of them. In the former, CS provides sufficient albeit imperfect inferential safety, whose limitations are argued to strengthen rather than weaken the case for CS as describing human behaviour. In the latter, four target phenomenal features are accounted for – abstract objects as feeling intangible, non-located, transparent, and unchanging - along with accounts for further phenomena such as semantic refinement, the Stroop effect, synaesthesia, semantic clarity, sensory overload, and satiation. -/- Our minimum claim concerns the day-to-day usage and felt experience of abstract objects, but we suggest also an extended claim in which CS can form the basis of a pragmatic sufficient logic. As such, the initial outline of a response is provided for five common objections to positions that seek to ground abstract objects without reference to metaphysically stand-alone universals: referential opacity; identity of indiscernibles; infinite regression; non-physical concepts; and necessary truths. These outlines lay the foundation for (but do not seek to formally demonstrate) an extended CS account that addresses other abstract objects, including issues relating to their use in mathematics and formal logic. -/- The CS account leads to a four-layer hierarchy of similarity for whether your “red” is the same as mine. Considering both semantic and phenomenal similarity, we conclude that our “reds” are likely non-identical but can be made close enough for practical purposes. Finally, we describe how future work could elaborate CS as a metaphysical project and how confidence in it could be tested through empirical research. (shrink)

Even though he is not very explicit about it, in “Wittgenstein on Rules and Private Language” Kripke discusses two different, albeit related, skeptical theses ‒ the first one in the philosophy of mind, the second one in the philosophy of language. Usually, what Kripke says about one thesis can be easily applied to the other one, too; however, things are not always that simple. In this paper, I discuss the case of the so-called “Normativity Argument” against semantic dispositionalism (which I (...) take to be epistemological in nature) and argue that it is much stronger as an argument in the philosophy of mind than when it is construed as an argument in the philosophy of language. (shrink)

In this paper, I present a game-theoretic solution to the rule-following paradox in terms of what I will call basic constitutive practices. The structure of such a practice P constitutes what it is to take part in P by defining the correctness conditions of our most basic concepts as those actions that lie on the correlated equilibrium of P itself. Accordingly, an agent S meant addition by his use of the term ‘+’ because S is taking part in a basic (...) constitutive practice of adding where quus-like answers are ruled out by not lying on the equilibrium. The resulting picture of language will preserve the objectivity and correctness conditions of meaning, all the while providing room for the community as a whole to make a mistake. I also argue that by accepting the account presented, we have a strong reason to reject the idea that language is rule-governed. (shrink)