Richard Samuels

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism.

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts.

The concept of innateness has historically exerted an influence in many regions of biology and it continues to play a significant role in cognitive science especially, developmental psychology and linguistics. This chapter provides an overview of some recent efforts to empirically study the innateness concept, both as deployed in folk contexts and among scientists. It considers whether this research really bolsters the standard criticism. The chapter describes research by Paul Griffiths and his collaborators, which seeks to assess whether the folk concept of innateness is a manifestation of the folk biology. It reviews further research, largely due to Josh Knobe and Richard Samuels, on folk innateness judgments. The chapter describes how this research was extended in order to explore the issue of whether scientists’ innateness judgments rely on a distinctly scientific innateness concept, or whether they merely redeploy the folk concept.

There are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Nevertheless, some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is more “legitmate” in virtue of being “more basic” or “more fundamental”. This paper addresses two related issues. First, we review some of these non-egalitarian arguments, lay out a laundry list of different, legitimate, notions of relative priority, and suggest that these arguments plausibly employ different such notions. Secondly, we argue that given a metaphysical-cum-epistemological gloss suggested by Frege’s foundationalist epistomology, the ordinals are plausibly more basic than the cardinals. This is just one orientation to relative priority one could take, however. Ultimately, we subscribe to an egalitarian attitude towards these formal characterizations: they are, in some sense, equally “legitimate”.

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of _which number_ is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of _notation_. The purpose of this article is to explore the relationship between the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects.

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects.

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting.

In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.

According to the Rationality Constraint, our concept of belief imposes limits on how much irrationality is compatible with having beliefs at all. We argue that empirical evidence of human irrationality from the psychology of reasoning and the psychopathology of delusion undermines only the most demanding versions of the Rationality Constraint, which require perfect rationality as a condition for having beliefs. The empirical evidence poses no threat to more relaxed versions of the Rationality Constraint, which only require only minimal rationality. Nevertheless, we raise problems for all versions of the Rationality Constraint by appealing to more extreme forms of irrationality that are continuous with actual cases of human irrationality. In particular, we argue that there are conceivable cases of “mad belief” in which populations of Lewisian madmen have beliefs that are not even minimally rational. This undermines Lewis’s claim that our ordinary concept of belief is a theoretical concept that is implicitly defined by its role in folk psychology. We argue that introspection gives us a phenomenal concept of belief that cannot be analyzed by applying Lewis’s semantics for theoretical terms.

Emotion development research centrally concerns capacities to produce emotions and to think about them. We distinguish these enterprises and consider a novel account of how they might be related. On one recent account, the capacity to have emotions of various kinds comes by way of the acquisition of emotion concepts. This account relies on a constructionist theory of emotions and an embodied theory of emotion concepts. We explicate these elements, then raise a challenge for the approach. It appears to be incompatible with various familiar ways in which cognitions about one’s own emotions can come apart from episodes of emotion.

A core commitment of Bob Hale and Crispin Wright’s neologicism is their invocation of Frege’s Constraint—roughly, the requirement that the core empirical applications for a class of numbers be “built directly into” their formal characterization. According to these neologicists, if legitimate, Frege’s Constraint adjudicates in favor of their preferred foundation—Hume’s Principle—and against alternatives, such as the Dedekind–Peano axioms. In this paper, we consider a recent argument for legitimating Frege’s Constraint due to Hale, according to which the primary empirical application of the naturals is transitive counting, or answering ‘how many’-questions using numerals. We make two claims regarding Hale’s argument. First, it fails to legitimate Frege’s Constraint in virtue of resting on unsupported and highly contentious assumptions. Secondly, even if sound, Hale’s argument would vindicate a version of Frege’s Constraint which fails to adjudicate in favor of Hume’s Principle over alternative characterizations of the naturals.

This volume gathers together leading philosophers of science and cognitive scientists from around the world to provide one of the first book-length studies of this important and emerging field. Specific topics considered include learning and the nature of scientific knowledge, the cognitive consequences of exposure to explanations, climate change, and mechanistic reasoning and abstraction. Chapters explore how experimental methods can be applied to questions about the nature of science and show how to fruitfully theorize about the nature and role of science with well-grounded empirical research. Advances in Experimental Philosophy of Science presents a new direction in the philosophical exploration of science and paves a path for those who might seek to pursue research in experimental philosophy of science.

One of the more distinctive features of Bob Hale and Crispin Wright’s neologicism about arithmetic is their invocation of Frege’s Constraint – roughly, the requirement that the core empirical applications for a class of numbers be “built directly into” their formal characterization. In particular, they maintain that, if adopted, Frege’s Constraint adjudicates in favor of their preferred foundation – Hume’s Principle – and against alternatives, such as the Dedekind-Peano axioms. In what follows we establish two main claims. First, we show that, if sound, Hale and Wright’s arguments for Frege’s Constraint at most establish a version on which the relevant application of the naturals is transitive counting – roughly, the counting procedure by which numerals are used to answer “how many”-questions. Second, we show that this version of Frege’s Constraint fails to adjudicate in favor of Hume’s Principle. If this is the version of Frege’s Constraint that a foundation for arithmetic must respect, then Hume’s Principle no more – and no less – meets the requirement than the Dedekind-Peano axioms do.

There are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is ‘more basic’ or ‘more fundamental’ than the others. This paper addresses two related issues. First, we review some of these non-egalitarian arguments, lay out a laundry list of different, legitimate, notions of relative priority, and suggest that these arguments plausibly employ different such notions. Secondly, we argue that given a metaphysical-cum-epistemological gloss suggested by Frege's foundationalist epistemology, the ordinals are plausibly more basic than the cardinals. This is just one orientation to relative priority one could take, however. Ultimately, we subscribe to an egalitarian attitude towards these formal characterizations: they are, in some sense, equally ‘legitimate’.

This dissertation focuses on the massive modularity hypothesis defended by evolutionary psychologists---the hypothesis that the human mind is composed largely or perhaps even entirely of special purpose information processing organs or "modulees" that have been shaped by natural selection to handle the sorts of recurrent information processing problems that confronted our hunter-gatherer forebears. ;In discussing MMH, I have three central goals. First, I aim to clarify the hypothesis and develop theoretically useful notions of "module" and "domain-specificity" that can play the roles required of them by evolutionary psychology. Second, I aim to evaluate the plausibility MMH in the light of the broad range of arguments that have been developed and defended in the literature. I argue that all the main, general arguments both for and against MMH are unsatisfactory. Moreover, I suggest that if the case for MMH is to be made, it will only result from the successive accumulation of specific, empirical evidence for the existence of particular modules. ;Finally, I address a range of issues that arise from evolutionary psychological approaches to reasoning and rationality. Much of what evolutionary psychologists have said about human reasoning is in response to a widely discussed "pessimistic" interpretation that has been developed and defended by Kahneman, Tversky and their followers. According to this view, human beings are prone to systematic deviations from appropriate norms of rationality because they lack the underlying competence to handle a wide array of reasoning tasks. Evolutionary psychologists appear to reject this pessimistic interpretation in favor of the view that we possess a wide range of reasoning modules that employ rational rules of inference. I argue, however, that there is no genuine disagreement between evolutionary psychologists and their opponents over the extent to which human beings are rational. I also discuss the distinction between competence efforts and performance efforts. Although this distinction has played a central role in recent discussions of human rationality, I argue that if MMH is true, then we face insurmountable problems in trying to draw the performance error/competence error distinction

In his recent John Locke Lectures – published as Between Saying and Doing – Brandom extends and refines his views on the nature of language and philosophy by developing a position that he calls Analytic Pragmatism. Although Brandom’s project bears on an extraordinarily rich array of different philosophical issues, we focus here on the contention that certain vocabularies have a privileged status within our linguistic practices, and that when adequately understood, the practices in which these vocabularies figure can help furnish us with an account of semantic intentionality. Brandom’s claim is that such vocabularies are privileged because they are a species of what he calls universal LX vocabulary –roughly, vocabulary whose mastery is implicit in any linguistic practice whatsoever. We show that, contrary to Brandom’s claim, logical vocabulary per se fails to satisfy the conditions that must be met for something to count as universal LX vocabulary. Further, we show that exactly analogous considerations undermine his claim that modal vocabulary is universal LX. If our arguments are sound, then, contrary to what Brandom maintains, intentionality cannot be explicated as a “pragmatically mediated semantic phenomenon”, at any rate not of the sort that he proposes.

In this paper I defend the classical computational account of reasoning against a range of highly influential objections, sometimes called relevance problems. Such problems are closely associated with the frame problem in artificial intelligence and, to a first approximation, concern the issue of how humans are able to determine which of a range of representations are relevant to the performance of a given cognitive task. Though many critics maintain that the nature and existence of such problems provide grounds for rejecting classical computationalism, I show that this is not so. Some of these putative problems are a cause for concern only on highly implausible assumptions about the extent of our cognitive capacities, whilst others are a cause for concern only on similarly implausible views about the commitments of classical computationalism. Finally, some versions of the relevance problem are not really objections but hard research issues that any satisfactory account of cognition needs to address. I conclude by considering the diagnostic issue of why accounts of cognition in general—and classical computational accounts, in particular—have faired so poorly in addressing such research issues.Keywords: Computationalism; Frame problem; Relevance