According to Amie Thomasson's Modal Normativism (MN), knowledge of metaphysical modality is to be explained in terms of a speaker’s mastery of semantic rules, as opposed to one’s epistemic grasp of independent modal facts. In this chapter, I outline (MN)'s account of modal knowledge (§1) and argue that more than semantic mastery is needed for knowledge of metaphysical modality. Specifically (§2), in reasoning aimed at gaining such knowledge, a competent speaker needs to further deploy essentialist principles and information. (...) In response, normativists might contend that a competent speaker will only need to appeal to specific independence counterfactuals, on analogy with quasi-realism about morality. These conditionals fix the meaning of our terms at the actual world, independently of the particular context in which a statement is evaluated. However, I show that this strategy causes several problems for the account (§3). While those problems might perhaps be avoided by endorsing a certain picture of modal metaphysics (Modal Monism), such a picture involves notorious issues that normativists will have to address (§4). It is thus doubtful that (MN) can explain knowledge of metaphysical modality. Still, it may explain some modal knowledge without committing to Modal Monism. As I show (§5), semantic mastery may suffice for gaining knowledge of logical-conceptual modality or analyticity. (shrink)

According to Amie Thomasson’s modal normativism, the function of modal discourse is to convey semantic rules. But what is a "semantic rule"? I raise three worries according to which there is no conception of a semantic rule that can serve the needs of a modal normativist. The first worry focuses on de re and a posteriori necessities. The second worry concerns Thomasson's inferential specification of the meaning of modal terms. The third worry asks about the (...) normative status of semantic rules. (shrink)

Cajetan’s analogy theory is usually evaluated in terms of its fidelity to the teachings of Aquinas. But what if Cajetan was trying to answer questions Aquinas himself did not raise, and so could not help to answer? Cajetan’s De Nominum Analogia can be interpreted as intending to solve a particular semantic problem: to characterize the unity of the analogical concept, so as to defend the possibility of a non-univocal term’s mediating syllogistic reasoning. Aquinas offers various semantic characterizations of (...) analogy, saying it involves, for instance: signification per prius et posterius; or a ratio propria which is only found in one analogate; or diverse modi significandi with a common res significata. Examined in turn, it is clear that none of Aquinas’s rules for analogy solve the semantic problem described. Cajetan thus cannot be reasonably expected to have intended his analogy treatise primarily as an interpretation or systematization of Aquinas’s teaching on analogy. (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)

This paper attempts to answer whether the property of “efficacy” can be attributed to constitutive rules. In particular, according to Di Lucia, I will point out some problems that the “semantic conception of efficacy” has concerning constitutive and regulative rules. Then, the main goal of the paper will be to reflect on the possibility of the efficacy of constitutive rules by means of a complex case that the semantic conception seems to disregard: The case of the cheater. Does (...) the action of the cheater show the inefficacy of constitutive rules? Does she play the game while breaking the rule? Can the semantic conception of efficacy explain this situation, or do we need a more flexible concept of efficacy that takes nomotropism into account? These are some of the questions I will try to answer. (shrink)

We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...) the lexicalized operators are all upward or downward monotone, an observation known as the Monotonicity Universal. We propose a logical explanation of lexical gaps and of the Monotonicity Universal, based on the dynamic behaviour of connectives and quantifiers. We define update potentials for logical operators as procedures to modify the context, under the assumption that an update by \( \phi \) depends on the logical form of \( \phi \) and on the speech act performed: assertion or rejection. We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language. Finally, we show that on this framework the Monotonicity Universal follows from the logical properties of the updates that correspond to each operator. (shrink)

It is often argued that inferential role semantics (IRS) entails semantic holism as long as theorists fail to answer the question about which inferences, among the many, are meaning-constitutive. Since analyticity, as truth in virtue of meaning, is a widely dismissed notion in indicating which inferences determine meaning, it seems that holism follows. Semantic holism is often understood as facing problems with the stability of content and many usual explanations of communication. Thus, we should choose between giving up (...) IRS, to avoid these holistic entailments, and defending holism against this charge, to rescue IRS. I try to pursue the second goal by analyzing certain patterns of counterfactual reasoning. Wilfrid Sellars and Robert Brandom claim that, to defend IRS, content-constitutive inferences are those counterfactually robust. While it is difficult to assess the goodness of such a view, it nonetheless entails that counterfactually non-robust inferences (which I call “modally ruled out inferences”) are not content-constitutive. If this is true, and if we take certain remarks about the grasp of concepts on board, there is a way to restrict the scope of the holism entailed by IRS to the extent of reshaping problems with the stability of content. (shrink)

In the middle of the 20th century, it was a common Wittgenstein-inspired idea in philosophy that for a linguistic expression to have a meaning is for it to be governed by a rule of use. In other words, it was widely believed that meanings are to be identified with use-conditions. However, as things stand, this idea is widely taken to be vague and mysterious, inconsistent with “truth-conditional semantics”, and subject to the Frege-Geach problem. In this paper I reinvigorate the (...) ideas that meaningfulness is a matter of being governed by rules of use and that meanings are best thought of in terms of use-conditions. I will do this by sketching the Rule-Governance view of the nature of linguistic meaningfulness, showing that the view isn’t by itself subject to the two problems, and explain why the idea has had a lasting appeal to philosophers from Strawson to Kaplan and why we should find it continually attractive. (shrink)

Tagging is the phenomenon in which regions of a picture, map, or diagram are annotated with words or other symbols, to provide descriptive information about a depicted object. The interpretive principles that govern tagged images are not well understood, due in part to the difficulty of integrating pictorial and linguistic semantic rules. Rather than directly combining these rules, I propose to use the framework of perspectival feature maps as an intermediary representation of content, in which the outputs of pictorial (...) and linguistic interpretation may be assimilated. The result is a simple and compositional semantics for tagged images. (shrink)

In “Is semantics possible?” Putnam connected two themes: the very possibility of semantics (as opposed to formal model theory) for natural languages and the proper semantic treatment of common nouns. Putnam observed that abstract semantic accounts are modeled on formal languages model theory: the substantial contribution is rules for logical connectives (given outside the models), whereas the lexicon (individual constants and predicates) is treated merely schematically by the models. This schematic treatment may be all that is needed for (...) an account of validity in a formal setting, but it does not help to understand how proper and common nouns function in reality (not in models). Putnam then initiated the empirical study of such nouns to indicate, (i), that the popular Frege-Carnap account of them as (“disguised” compound) predicates is empirically incorrect, and, (ii), that they offer a new paradigm for a naturalistic semantics of natural languages. We take Putnam’s program a couple of steps further. First, we investigate the semantics of common nouns and argue that they refer (to kinds), rather than apply by satisfaction/truth to a designation/denotation. Second, we point to general results about semantics as a theory whose fulcrum is the reference relation rather than satisfaction in models and validity across them. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

In the chapter “Information and Content” of their Impossible Worlds, Berto and Jago provide us with a semantic account of information in deductive reasoning such that we have an explanation for why some, but not all, logical deductions are informative. The framework Berto and Jago choose to make sense of the above-mentioned idea is a semantic interpretation of Sequent Calculus rules of inference for classical logic. I shall argue that although Berto and Jago’s idea and framework are hopeful, (...) their definitions do not capture what is intended. This is so because the definitions are solely based on the logical complexity of an argument and they fail to capture the richness of the non- logical content of that argument. Then I will suggest some amendments to address this problem. Finally, I will extend the application of the definitions to first-order logic. It shall be observed that in some classical deductions, applying contraction may lead to hiding some epistemic impossibilities. This happens when formulae which contribute different propositions to the proof get contracted at the quantified level. (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)

In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of Dummett and (...) his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system (...) with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

Vann McGee has recently argued that Belnap’s criteria constrain the formal rules of classical natural deduction to uniquely determine the semantic values of the propositional logical connectives and quantifiers if the rules are taken to be open-ended, i.e., if they are truth-preserving within any mathematically possible extension of the original language. The main assumption of his argument is that for any class of models there is a mathematically possible language in which there is a sentence true in just those (...) models. I show that this assumption does not hold for the class of models of classical propositional logic. In particular, I show that the existence of non-normal models for negation undermines McGee’s argument. (shrink)

Semantic originalism is a theory of constitutional meaning that aims to disentangle the semantic, legal, and normative strands of debates in constitutional theory about the role of original meaning in constitutional interpretation and construction. This theory affirms four theses: (1) the fixation thesis, (2) the clause meaning thesis, (3) the contribution thesis, and (4) the fidelity thesis. -/- The fixation thesis claims that the semantic content of each constitutional provision is fixed at the time the provision is (...) framed and ratified: subsequent changes in linguistic practice cannot change the semantic content of an utterance. -/- The clause meaning thesis claims that the semantic content is given by the conventional semantic meaning (or original public meaning) of the text with four modifications. The first modification is provided by the publicly available context of constitutional utterance: words and phrases that might be ambiguous in isolation can become clear in light of those circumstances of framing and ratification that could be expected to known to interpreters of the Constitution across time. The second modification is provided by the idea of the division of linguistic labor: some constitutional provisions, such as the natural born citizen clause may be terms of art, the meaning of which are fixed by the usages of experts. The third modification is provided by the idea of constitutional implicature: the constitution may mean things it does not explicitly say. The fourth modification is provided by the idea of constitutional stipulations: the constitution brings into being new terms such as House of Representatives and the meaning of these terms is stipulated by the Constitution itself. -/- The contribution thesis asserts that the semantic content of the Constitution contributes to the law: the most plausible version of the contribution thesis is modest, claiming that the semantic content of the Constitution provides rules of constitutional law, subject to various qualifications. Our constitutional practice provides strong evidence for the modest version of the contribution thesis. -/- The fidelity thesis asserts that we have good reasons to affirm fidelity to constitutional law: virtuous citizens and officials are disposed to act in accord with the Constitution; right acting citizens and officials obey the constitution in normal circumstances; constitutional conformity produces good consequences. Our public political culture affirms the great value of the rule of law. -/- We can summarize semantic originalism as a slogan: The original public meaning of the constitution is the law and for that reason it should be respected and obeyed. The slogan recapitulates each of the claims made by semantic originalism, but it is potentially misleading because it does not clearly distinguish between the semantic claims made by the fixation and clause meaning theses, the legal claim made by the contribution thesis, and the normative claim made by the fidelity thesis. -/- Part I introduces the four theses. Part II is entitled An Opinionated History of Constitutional Originalism, and it provides the context for all that follows. Part III is entitled Semantic Originalism: A Theory of Constitutional Meaning, and it lays out the case for original public meaning as the best nonnormative theory of constitutional content. Part IV is entitled The Normative Implications of Semantic Originalism, and it articulates a variety of normative arguments for originalism. Part V is entitled Conclusion: Semantic Originalism and Living Constitutionalism, and it explores the broad implications of semantic originalism for living constitutionalism and the future of constitutional theory. (shrink)

Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the semantic (...) differences between nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

This paper presents a new reconstruction of Wittgenstein’s famous (and controversial) rule-following arguments. Two are the novel features offered by our reconstruction. In the first place, we propose a shift of the central focus of the discussion, from the general semantics and the philosophy of mind to the philosophy of mathematics and the rejection of the notion of a function. The second new feature is positive: we argue that Wittgenstein offers us a new alternative notion of a rule (...) (to replace the rejected functions), a notion reminiscent of Category Theory’s notion of a morphism. (shrink)

This thesis argues for two main points concerning the philosophy of natural language semantics. Firstly, that the objects of assertion are distinct from the entities appealed to in the compositional rules of natural language semantics. Secondly, natural languages contain context-shifting operators known as "monsters". In fact, it will be shown that these theses are simply two sides of the same coin.

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings of (...) modal operators in terms of rules of inference. (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)

The article contains a critical analysis of the skeptical solution to the rule- following problem. The skeptical solution denies the existence of “superlative” R-facts that would make statements of the form “P means R by ‘+’ ” true. The role of the sources for the meaning of ‘+’ here is played by the patterns of solidarity behavior of members of some community to which P belongs. The correct use of ‘+’ would be one that is approved by the competent (...) majority of this community, and there can be no other sense in which it would be correct or wrong. Boyd’s hypothesis denies the communal character of the ‘+’ meaning. While there are no “superlative” R-facts, there should be C-facts not about the R as the standard that P or its community follows in their practice of using ‘+’, but about whether they do it correctly. The proof of the Boyd hypothesis is based on the example of an imaginary Ω-community, whose agents use a finite set of simple symbols for the needs of their arithmetic: ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’. Each symbol denotes a subset of identical, from the Ω-community point of view, numerical values. The symbol ‘A’ is used, for ex- ample, for a subset of the natural numbers 1, 10, 19, 28, 37, 46, etc.; ‘B’ for 2, 11, 20, 29, 38, 47, etc.; ‘C’ for 3, 12, 21, 30, 39, 48, etc. The Ω-community’s arithmetic uses the only local function ⊕ whose range of values forms a finite set of mathematical propositions {α} that are true. The Ω-community’s arithmetic, like our own, is open to many skeptical challenges. Is there a fact that determines the meaning of ‘⊕’? What do agents do when they calculate with ‘⊕’ (say, solve examples ‘A⊕B = ?’, ‘C⊕E=?’, etc.)? Do they Add, Badd or Dadd? To answer them would require a “superlative” R-fact. For the calculation practice with ‘⊕’, it could be a certain R-fact that determines the only possible order for the sequence of numerals ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’ such that {α} is true. An analysis of the calculation practice using the local arithmetic function ⊕ shows that for it there are no such R-facts that would determine the only correct standard R – even if the agents in the Ω-community were trained in such calculations on a full set of cases for the application of that function. However, for such practice there are C-facts (independent in their existence from R-facts) that make it possible to distinguish between what seems to be right and what is right. The solitary agent P and the Ω-community are in the same position regarding the knowledge of C-facts. The Ω-community’s point of view has no advantage in matters of C-facts knowledge over the solitary agent P’s point of view. The Ω-community arithmetic shows that if a solitary agent P had the suitable knowledge of C-facts about the practice of calculations with ‘⊕’, it would allow him/her to disagree with the not correct answers of other members of the community even when they would constitute an absolute majority. (shrink)

This paper defends the view that common nouns have a dual semantic structure that includes extension-determining and non-extension-determining components. I argue that the non-extension-determining components are part of linguistic meaning because they play a key compositional role in certain constructions, especially in privative noun phrases such as "fake gun" and "counterfeit document". Furthermore, I show that if we modify the compositional interpretation rules in certain simple ways, this dual content account of noun phrase modification can be implemented in a (...) type-driven formal semantic framework. In addition, I also argue against traditional accounts of privative noun phrases which can be paired with the assumption that nouns do not have a dual semantic structure. At the most general level, this paper presents a proposal for how we can begin to integrate a psychologically realistic account of lexical semantics with a linguistically plausible compositional semantic framework. (shrink)

In proof-theoretic semantics, meaning is based on inference. It may be seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , (...) K4, and S4, with □ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between □ and a natural presentation of ♢. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases. (shrink)

In this essay, I seek to demonstrate the interplay of philosophical voices – particularly, that of a platonist voice and a community-agreement-view voice – that drives Wittgenstein’s rule-following dialectic forward; and I argue that each voice succumbs to a particular form of dialectical oscillation that renders its response to the problem of rule-following philosophically inadequate. Finally, I suggest that, by seeing and taking stock of the dilemma in which these responses to the skeptical problem are caught, we can (...) come to appreciate Wittgenstein’s own view of what might constitute a proper a response to the so-called problem of rule-following. This view can be preliminarily characterized by saying that Wittgenstein’s aim is to dissolve the temptation to philosophically rebut the skeptical challenge posed by the rule-following dialectic, an aim he achieves by revealing the semantic emptiness of the apparent sentences that raise the skeptical problem. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg Restall’s (...) bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

In recent work, Williamson has defended a suggestive account of assertion. Williamson claims that the following norm or rule (the knowledge rule) is constitutive of assertion, and individuates it: (KR) One must ((assert p) only if one knows p) Williamson is not directly concerned with the semantics of assertion-markers, although he assumes that his view has implications for such an undertaking; he says: “in natural languages, the default use of declarative sentences is to make assertions” (op. cit., 258). (...) In this paper I will explore Williamson’s view from this perspective, i.e., in the light of issues regarding the semantics of assertion-markers. I will end up propounding a slightly different account, on which, rather than KR, what is constitutive and individuating of assertion is an audience-involving transmission of knowledge rule: (TKR) One must ((assert p) only if one’s audience comes thereby to be in a position to know p) I will argue that TKR, of which KR is an illocutionary consequence (but not the other way around), has all the virtues that Williamson claims for his account and no new defect. (shrink)

One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should not be thought of as describing, in any substantive sense, (...) an abstract realm of eternal mathematical objects, as traditional platonists have thought. In Rules to Infinity, this view, which I call mathematical normativism, is updated with contemporary philosophical tools, and it is argued that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the platonistic idea that there exist abstract mathematical objects that explain such truths. Furthermore, Rules to Infinity defends a particular account of the distinction between scientific explanations that are in some sense distinctively mathematical – those that explain natural phenomena in some uniquely mathematical way – and those that are only standardly mathematical, and it lays out desiderata for any account of this distinction. Normativism is compared with other prominent views in the philosophy of mathematics such as neo-Fregeanism, fictionalism, conventionalism, and structuralism. Rules to Infinity serves as an entry point into debates at the forefront of philosophy of science and mathematics, and it defends novel positions in these debates. (shrink)

Predicativists hold that proper names have predicate-type semantic values. They face an obvious challenge: in many languages names normally occur as, what appear to be, grammatical arguments. The standard version of predicativism answers this challenge by positing an unpronounced determiner in bare occurrences. I argue that this is a mistake. Predicativists should draw a distinction between two kinds of semantic type—underived semantic type and derived semantic type. The predicativist thesis concerns the underived semantic type of (...) proper names and underdetermines a view about the semantic type of bare occurrences. I’ll argue that predicativists should hold that bare names are derived individual-denoting expressions. I end by considering what this result means for the relationship between predicativism and other metalinguistic theories of names. (shrink)

This paper explores how realism is crucial in understanding rule-following. The strategy involves starting from what has been achieved by Wittgenstein and others as regards semantic normativity and then applying it to other areas, including moral deliberation. The result shows that realism in rule-following involves not only the weak claim that rules are independent of the individual rule-follower, as conventions are. It involves also the stronger claim that conventional rules are constrained by non-conventional constraints. These constraints (...) depend neither on the individual nor on the group. They arise from the nature of things. Human rule-followers are constrained first by being material beings, secondly by being living organisms, and thirdly by being rational. (shrink)

ABSTRACT -/- A propositional attitude (PA) is a belief, desire, fear, etc., that x is the case. This dissertation addresses the question of the semantic content of a specific kind of PA-instance: an instance of a belief of the form all Fs are Gs. The belief that all bachelors are sports fans has this form, while the belief that Spain is a country in Eastern Europe do not. Unlike a state of viewing the color of an orange, a belief-instance (...) is semantically contentful because it has reference, a meaning, logical implications, or a truth-value. While the intrinsic semantics view holds that either concepts or abstract objects are the source of content for PAs, the extrinsic semantics view holds that symbols of a mental language provide this content. I argue that a successful theory of intentionality must explain: (1) the truth-preserving causal powers of PAs, (2) the failure of the deductive principle Substitutivity to preserve truth over sentences that ascribe PAs, and (3) the truth-evaluability of PAs. As an internalist version of the extrinsic semantics view, I first evaluate Fodor’s Computational Theory of Mind, which says the semantic ingredients of mental states are symbols governed by rules of a mental syntax. I argue that in order to meet (1), CTM would have to associate the causal patterns of each thought-type with the inferential relations of some proposition – in an arbitrary or question-begging way. I also evaluate Fodor’s causal theory, as an externalist version of the extrinsic semantics view. This view is that lawlike causal relations between mental symbols and objects determine the reference, and thus the truth-value, of a thought. I argue that Brian Loar’s circularity objection refutes the ability of this theory to meet (3); and I endorse the intrinsic semantics perspective. I evaluate Frege’s theory of abstract, mind-external, and intrinsically semantic objects (senses), as an attempt to meet condition (2). I conclude that mind-external universals are the source of the intrinsically semantic features of concepts. Finally, I put forth a theory called ‘Bare Property Intentionality’, which describes the features of intrinsically representative and semantic concepts that connect them to these universals. (shrink)

Recent work in epistemology defends the unorthodox theses that belief is (1) an evidentially weak, and (2) question-sensitive attitude, and (3) that forming beliefs is sometimes a matter of guessing. What motivates these theses are examples of rationally permissible belief-ascriptions that exhibit these traits. The main aim of this paper is to outline a semantic account of categorical and conditional belief-ascriptions that captures the motivating data. We then survey some consequences of the proposed semantics, particularly with respect to the (...) question of whether closure under rules of inference is rationally required for weak, question-sensitive belief. (shrink)

In this paper, an interpretation of "necessity", inspired by a Leibnizian idea and based on the method of dialogical logic, is introduced. The semantic rules corresponding to such an account of necessity are developed, and then some peculiarities, and some potential advantages, of the introduced dialogical explanation, in comparison with the customary explanation offered by the possible worlds semantics, are briefly discussed.

The author considers the model-theoretic character of proofs and disproofs by means of attempted counterexample constructions, distinguishes this proof format from formal derivations, then contrasts two approaches to semantic tableaux proposed by Beth and Lambert-van Fraassen. It is noted that Beth's original approach has not as yet been provided with a precisely formulated rule of closure for detecting tableau sequences terminating in contradiction. To remedy this deficiency, a technique is proposed to clarify tableau operations.

: The Hamblin-Karttunen approach has led to many insights about questions in English. In this article the results of this rule-by-rule tradition are reconsidered from a crosslinguistic perspective. Starting from the type-driven XLS theory developed in Bittner (1994a, b), it is argued that evidence from simple questions (in English, Polish, Lakhota and Warlpiri) leads to certain revisions. The revised XLS theory then immediately generalizes to complex questions — including scope marking (Hindi), questions with quantifiers (English) and multiple wh-questions (...) (English, Hindi, Japanese). Eliminating language- and construction-specific information from the compositional rules, in favor of universal semantic filters, leads to analyses that not only generalize across unrelated languages but are also empirically more accurate, not less. (shrink)

Semantic holists view what one's terms mean as function of all of one's usage. Holists will thus be coherentists about semantic justification: showing that one's usage of a term is semantically justified involves showing how it coheres with the rest of one's usage. Semantic atomists, by contrast, understand semantic justification in a foundationalist fashion. Saul Kripke has, on Wittgenstein's behalf, famously argued for a type of skepticism about meaning and semantic justification. However, Kripke's argument has (...) bite only if one understands semantic justification in foundationalist terms. Consequently, Kripke's arguments lead not to a type of skepticism about meaning, but rather to the conclusion that one should be a coherentist about semantic justification, and thus a holist about semantic facts. (shrink)

Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is shown (...) to account for various phenomena — including scope relations in English and Greenlandic Eskimo, internally headed relative clauses in Lakhota, serial verbs in Yoruba and VP ellipsis in English. (shrink)

This paper considers proof-theoretic semantics for necessity within Dummett's and Prawitz's framework. Inspired by a system of Pfenning's and Davies's, the language of intuitionist logic is extended by a higher order operator which captures a notion of validity. A notion of relative necessary is defined in terms of it, which expresses a necessary connection between the assumptions and the conclusion of a deduction.

Terry Horgan and John Tienson have suggested that connectionism might provide a framework within which to articulate a theory of cognition according to which there are mental representations without rules (RWR) (Horgan and Tienson 1988, 1989, 1991, 1992). In essence, RWR states that cognition involves representations in a language of thought, but that these representations are not manipulated by the sort of rules that have traditionally been posited. In the development of RWR, Horgan and Tienson attempt to forestall a particular (...) line of criticism, theSyntactic Argument, which would show RWR to be inconsistent with connectionism. In essence, the argument claims that the node-level rules of connectionist networks, along with the semantic interpretations assigned to patterns of activation, serve to determine a set of representation-level rules incompatible with the RWR conception of cognition. The present paper argues that the Syntactic Argument can be made to show that RWR is inconsistent with connectionism. (shrink)

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...) completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

Alberto Coffa used the phrase "the Copernican turn in semantics" to denote a revolutionary transformation of philosophical views about the connection between the meanings of words and the acceptability of sentences and arguments containing those words. According to the new conception resulting from the Copernican turn, here called "the Copernican view", rules of use are constitutive of the meanings of words. This view has been linked with two doctrines: (A) the instances of meaning-constitutive rules are analytically and a priori true (...) or valid; (B) to grasp a meaning is to accept its rules. The pros and cons of different versions of the Copernican view, ascribable to Wittgenstein, Carnap, Gentzen, Dummett, Prawitz, Boghossian and other authors, will be weighed. A new version will be proposed, which implies neither (A) nor (B). (shrink)

This paper aims at showing that the generative-semantic framework is not essential to the proposal in H.J. Verkuyl On the Compositional Nature of the Aspects Reidel:Dordrecht 1972. Compositionality can be shown to be neutral as to the then-difference between generative-semantic and the interpretive-semantic branch of transformational grammar.

Possible worlds are commonly seen as an interpretation of modal operators such as "possible" and "necessary". Here, we develop possible world semantics (PWS) which can be expressed in basic set theory and first-order logic, thus offering a reductionist account of modality. Specifically, worlds are understood as complete sets of statements and possible worlds are sets whose statements are consistent with a set of conceptual laws. We introduce the construction calculus (CC), a set of axioms and rules for truth, possibility, worldness (...) and consistency. We show that CC allows to prove fundamental theorems about necessity, possibility, impossibility and contigency, thus demonstrating prima-facie plausibility of PWS. Finally, we discuss the explanatory power of our approach and draw connections between our account and established philosophical conceptions of possible worlds. (shrink)

Taking the semantic values of predicates to be precise properties leaves no room for predicate vagueness. I suggest instead understanding talk of properties as used in semantics as idealized placeholders for the imprecise results of navigating the word/world interface. Basic predications result by applying imprecise informal rules of word use, and it is in the imprecision of these rules that vagueness arises. The idealized property-placeholders then function to separate the messy process of navigating the word/world interface from the exact (...) rules of semantic composition. This scheme applies a methodology of problem separation that is well known in the physical sciences. (shrink)

According to grice, Semantic concepts like meaning and reference should be explicated in terms of the propositional attitudes. In this paper, I argue that grice's program is mistaken in principle. I first motivate a gricean strategy for defining denotation, Or semantic reference, In terms of rules that govern what speakers may refer to with the terms they use. I then express three paradigm gricean theories of denotation and introduce considerations which show that these theories are false.

To avoid difficulties that arise when we appeal to speaker intentions or multiple rules to determine the meaning of indexicals, Cohen (2013) recently defends a conventionalist account of these terms that focuses on their context of tokening. Apart from some tricky cases already discussed in the literature, however, such an account faces a serious difficulty: in many speech acts, multiple apparent tokens are produced – for example when a speaker speaks on a telephone, and her utterance is heard both where (...) she speaks, and at the location of the receiver of the call. The ‘token-contextual’ account seems to imply that in such cases a speaker will simultaneously produce multiple contradictory utterances. Here I argue that to resolve such problems we cannot help but to invoke speaker intentions. However, by appealing to intentions at the level of the metaphysics of semantic tokens, rather than to decide their meaning, the token-contextualist can make this appeal without reintroducing the difficulties associated with intentionalist accounts that she hopes to avoid. The resulting metaphysics of semantic tokens is, interestingly, more complex than we might have expected. -/- . (shrink)