Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

Which concepts should we use to think and talk about the world and to do all of the other things that mental and linguistic representation facilitates? This is the guiding question of the field that we call ‘conceptual ethics’. Conceptual ethics is not often discussed as its own systematic branch of normative theory. A case can nevertheless be made that the field is already quite active, with contributions coming in from areas as diverse as fundamental metaphysics and social/political philosophy. In (...) this pair of papers, we try to unify the field, reflecting on its basic nature, structure, and methodology. (shrink)

Which concepts should we use to think and talk about the world, and to do all of the other things that mental and linguistic representation facilitates? This is the guiding question of the field that we call ‘conceptual ethics’. Conceptual ethics is not often discussed as its own systematic branch of normative theory. A case can nevertheless be made that the field is already quite active, with contributions coming in from areas as diverse as fundamental metaphysics and social/political philosophy. In (...) this pair of papers, we try to unify the field, reflecting on its basic nature, structure, and methodology. (shrink)

This chapter aims to provide materials with which to substantiate the claim that, under the appropriate circumstances, the notion of analyticity can help explain how one might have a priori knowledge even in the strong sense. It argues that Implicit Definition, properly understood, is completely independent of any form of irrealism about logic. The chapter defends the thesis of Implicit Definition against Quine's criticisms, and examines the sort of account of the apriority of logic that this doctrine is able to (...) provide. The chapter shows that, against the background of a rejection of indeterminacy, its insolubility cannot be conceded. It also argues that neither a non‐factualism about Frege‐analyticity, nor an error thesis about it, can plausibly fall short of an outright rejection of meaning itself. The chapter shows how the doctrine that appears to offer the most promising account of how we grasp the meanings of the logical constants. (shrink)

In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...) that it provides important insights intoCarnap''s development during this critical period, thetransition from Aufbau to Syntax,especially regarding the nature and motivation ofCarnap''s logicism. Moreover, we show how theAxiomatics influenced Carnap''s student Gödel inreaching the fundamental logical results that soonafterwards undermined Carnap''s project. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

European Journal of Philosophy, Volume 30, Issue 2, Page 578-600, June 2022.

An influential argument against the possibility of truth by linguistic convention holds that while conventions can determine which proposition a given sentence expresses, they (conventions) are powerless to make propositions true or false. This argument has been offered in the literature by Lewy, Yablo, Boghossian, Sider and others. But despite its influence and prima facie plausibility, the argument: (i) equivocates between different senses of “making true”; (ii) mistakenly assumes hyperintensional contexts are intensional; and (iii) relies upon an implausible vision of (...) the way that language works. (shrink)

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...) idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic. (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)

del's appeal to mathematical intuition to ground our grasp of the axioms of set theory, is notorious. I extract from his writings an account of this form of intuition which distinguishes it from the metaphorical platonism of which Gödel is sometimes accused and brings out the similarities between Gödel's views and Dummett's.

This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.

Many commentators now view Quine's ‘Truth by Convention’ as a flawed criticism of Carnap. Gary Ebbs argued recently that Quine never intended Carnap as his target. Quine's criticisms were part of his attempt to work out his own scientific naturalism. I agree that Carnap was not Quine's target but object that Quine's criticisms were wholly internal to his own philosophy. Instead, I argue that C.I. Lewis held the kind of truth‐by‐convention thesis that Quine rejects. This, however, leaves Carnap out of (...) the picture. I then show how Quine came to see the earlier criticisms as also having force against Carnap. (shrink)

Rudolf Carnap’s principle of tolerance states that there is no need to justify the adoption of a logic by philosophical means. Carnap uses the freedom provided by this principle in his philosophy of mathematics: he wants to capture the idea that mathematical truth is a matter of linguistic rules by relying on a strong metalanguage with infinitary inference rules. In this paper, I give a new interpretation of an argument by E. W. Beth, which shows that the principle of tolerance (...) does not suffice to remove all obstacles to the employment of infinitary rules. (shrink)

From 1953 to 1959 Gödel worked on a response to Carnap’s philosophy of mathematics. The drafts display Gödel’s familiarity with Carnap’s position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Gödel’s two principal points, however, will here be defended. Gödel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap’s later views. Carnap’s position, however, had changed significantly in the intervening years, and to (...) a significant extent, this mature position realizes much of what Gödel himself wanted out of a philosophy of mathematics. (shrink)

Do numbers exist? Carnap (1956 [1950]) famously argues that this question can be understood in an “internal” and in an “external” sense, and calls “external” questions “non-cognitive”. Carnap also says that external questions are raised “only by philosophers” (p. 207), which means that, in his view, philosophers raise ”non-cognitive” questions. However, it is not clear how the internal/external distinction and Carnap’s related views about philosophy should be understood. This paper provides a new interpretation. I draw attention to Carnap’s distinction between (...) purely external statements, which are independent from all frameworks, and pragmatic external statements, which concern which framework one should adopt, and argue that the latter express noncognitive mental states. Specifically, I argue that “frameworks” are systems of rules for the assessment of statements, which are utterances of ordinary language sentences. Pragmatic external statements express noncognitive dispositions to follow only certain rules of assessment. For instance, “numbers exist” understood as a pragmatic external statement expresses a noncognitive disposition to use only rules of assessment according to which numbers do exist. Carnap can thereby be understood as proposing a distinctive form of noncognitivism about ontology that is in some respects analogous to norm-expressivism in metaethics. (shrink)

A definition of a property P is impredicative if it quantifies over a domain to which P belongs. Due to influential arguments by Ramsey and Gödel, impredicative mathematics is often thought to possess special metaphysical commitments. It seems that an impredicative definition of a property P does not have the intended meaning unless P already exists, suggesting that the existence of P cannot depend on its explicit definition. Carnap (1937 [1934], p. 164) argues, however, that accepting impredicative definitions amounts to (...) choosing a "form of language" and is free from metaphysical implications. This paper explains this view in its historical context. I discuss the development of Carnap’s thought on the foundations of mathematics from the mid-1920s to the mid-1930s, concluding with an account of Carnap’s (1937 [1934]) non-Platonistic defense of impredicativity. This discussion is also important for understanding Carnap’s influential views on ontology more generally, since Carnap’s (1937 [1934]) view, according to which accepting impredicative definitions amounts to choosing a "form of language", is an early precursor of the view Carnap presents in "Empiricism, Semantics and Ontology" (1956 [1950]), according to which referring to abstract entities amounts to accepting a "linguistic framework". (shrink)

Through detailed and trenchant criticism of standard interpretations of some of the key arguments in analytical philosophy over the last sixty years, this book ...

According to the standard story W. V. Quine ’s criticisms of the idea that logic is true by convention are directed against, and completely undermine, Rudolf Carnap’s idea that the logical truths of a language L are the sentences of L that are true-in- L solely in virtue of the linguistic conventions for L, and Quine himself had no interest in or use for any notion of truth by convention. This paper argues that and are both false. Carnap did not (...) endorse any truth -by- convention theses that are undermined by Quine ’s technical observations. Quine knew this. Quine ’s criticisms of the thesis that logic is true by convention are not directed against a truth -by- convention thesis that Carnap actually held, but are part of Quine ’s own project of articulating the consequences of his scientific naturalism. Quine found that logic is not true by convention in any naturalistically acceptable sense. But he also observed that in set theory and other highly abstract parts of science we sometimes deliberately adopt postulates with no justification other than that they are elegant and convenient. For Quine such postulations constitute a naturalistically acceptable and fallible sort of truth by convention. It is only when an act of adopting a postulate is not indispensible to natural science that Quine sees it as affording truth by convention ‘unalloyed’. A naturalist who accepts Quine ’s notion of truth by convention is therefore not limited to accepting only those postulates that she regards as indispensible to natural science. (shrink)

In constructing semantic theories of normative and evaluative terms, philosophers have commonly deployed a certain type of disagreement -based argument. The premise of the argument observes the possibility of genuine disagreement between users of a certain normative or evaluative term, while the conclusion of the argument is that, however differently those speakers employ the term, they must mean the same thing by it. After all, if they did not, then they would not really disagree. We argue that in many of (...) the cases in which this argument is deployed, the conclusion not only fails to follow from the premises, but is very likely false. Disagreements between speakers who do not mean the same things by their words are common, genuine, and not easily distinguished from ordinary disagreements over the truth of literally expressed content. We make this case by developing the notion of a metalinguistic negotiation, an exchange in which speakers tacitly negotiate the proper deployment of some linguistic expression in a context. Metalinguistic negotiations express disagreements over information that is conveyed pragmatically and about what concepts should be deployed in the context at hand. We argue that neither of these features poses any obstacle to metalinguistic negotiations serving to express genuine, substantive disagreements that can be well worth engaging in. Contrary to what has been widely assumed in the literature, many normative and evaluative disputes—among ordinary speakers and even among philosophers themselves—may be of exactly this type, a conclusion with important consequences for both the subject matter and the methodology of metanormative theory. (shrink)