A discussion of views first presented by this author and Edward Zalta in 1995 in the paper “Naturalized Platonism vs. Platonized Naturalism”. That paper presents an application of Zalta’s “object theory” to the ontology of mathematics, and claims that there is a plenitude of abstract objects, all the creatures of distinct mathematical theories. After a summary of the position, two questions concerning the view are singled out for discussion: just how many mathematical objects there are by our account, and the nature of the properties we use to characterize abstract objects. The difference between the authors in more recent developments of the view are also discussed.

Jim Brown (1991, viii) says that platonism, in mathematics involves the following: 1. mathematical objects exist independently of us; 2. mathematical objects are abstract; 3. we learn about mathematical objects by the faculty of intuition. The same is being claimed by Jerrold Katz (1981, 1998) in his platonistic approach to linguistics. We can take the object of linguistic analysis to be concrete physical sounds as held by nominalists, or we can assume that the object of linguistic study are psychological or mental states which presents the conceptualism or psychologism of Chomsky and that language is an abstract object as held by platonists or realists and urged by Jerrold Katz hinlself.I want to explicate Katz’s proposal which is based on Kant’s conception of pure intuition and give arguments why I find it implausible. I also present doubts that linguists use intuitive evidence only. I conclude with some arguments against the a prioricity of intuitive judgements in general which is also relevant for Jim Brown’s platonistic beliefs.

In his Realism, Mathematics, and Modality, Hartry Field attempted to revitalize the epistemological case against mathematical platontism by challenging mathematical platonists to explain how we could be epistemically reliable with regard to the abstract objects of mathematics. Field suggested that the seeming impossibility of providing such an explanation tends to undermine belief in the existence of abstract mathematical objects regardless of whatever reason we have for believing in their existence. After more than two decades, Field’s explanatory challenge remains among the best available motivations for mathematical nominalism. This paper argues that Field’s explanatory challenge misidentifies the central epistemological problem facing mathematical platonism. Contrary to Field’s suggestion, inexplicability of epistemic reliability does not act as an epistemic defeater. The failure to explain our epistemic reliability with respect to the existence and properties of abstract mathematical objects is simply one aspect of a broader failure to establish that we are epistemically reliable with respect to abstract mathematical objects in the first place. Ultimately, it is this broader failure that is the source of mathematical platonism’s real epistemological problems.

The aim of this paper is to point to the analogy between mathematical and physical thought experiments, and even more widely between the epistemic paths in both domains. Having accepted platonism as the underlying ontology as long as the platonistic path in asserting the possibility of gaining knowledge of abstract, mind-independent and causally inert objects, my widely taken goal is to show that there is no need to insist on the uniformity of picture and monopoly of certain epistemic paths in the epistemic descriptive context. And secondly, to show the analogy with the ways we come to know the truths of (natural) sciences.

Recent debates about thought experiments have focused on a perceived epistemological problem: how do thought experiments manage to provide knowledge when they yield no new empirical data? A bold answer to this question is provided by James Robert Brown’s platonisrn, according to which a certain class of thought experiments allow a sort of intellectual perception of laws of nature, understood as relations between universals. I suggest that there are three main problems with platonism. First, it is restricted to a very small class of thought experiments; hence, it largely fails to address the general epistemological problem. Second, it is not quite clear what it is supposed to explain. Third, its explanatory value in any case seems dubious, since the mechanisms it postulates (i) appear to raise issues more ditficult than what they would explain, and (ii) seem to obviate the very need for conducting thought experiments. I also argue that it fails to give an accurate account of Brown’s flagship example, Galileo’s thought experiment on falling bodies. In conclusion, I suggest that although platonism about thought experiments is an exciting thesis, it is at present unconvincing.

Noam Chomsky’s well-known claim that linguistics is a “branch of cognitive psychology” has generated a great deal of dissent—not from linguists or psychologists, but from philosophers. Jerrold Katz, Scott Soames, Michael Devitt, and Kim Sterelny have presented a number of arguments, intended to show that this Chomskian hypothesis is incorrect. On both sides of this debate, two distinct issues are often conflated: (1) the ontological status of language and (2) the relation between psychology and linguistics. The ontological issue is, I will argue, not the relevant issue in the debate. Even if this Chomskian position on the ontology of language is false, linguistics may still be a subfield of psychology if the relevant methods in linguistic theory construction are psychological. Two options are open to the philosopher who denies Chomskian conceptualism: linguistic nominalism or linguistic platonism. The former position holds that syntactic, semantic, and phonological properties are primarily properties, not of mental representations, but rather of public languagesentence tokens; The latter position holds that the linguistic properties are properties of public language sentence types. I will argue that both of these positions are compatible with Chomsky’s claim that linguistics is a branch of psychology, and the arguments that have been given for nominalism and platonism do not establish that linguistics and psychology are distinct disciplines.

Recent years have seen a number of naturalist accounts of mathematics. Philip Kitcher’s version is one of the most important and influential. This paper includes a critical exposition of Kitcher’s views and a discussion of several issues including: mathematical epistemology, practice, history, the nature of applied mathematics. It argues that naturalism is an inadequate account and compares it with mathematical Platonism, to the advantage of the latter.

According to the “Folieism” I have been recently defending, communication is a kind of folie à deux in which speakers and hearers enjoy a stable and innocuous illusion of producing and hearing standard linguistic entities (“SLE”s) that are seldom if ever actually produced. In the present paper, after summarizing the main points of the view, I defend it against efforts of Barber, Devitt and Miščević to rescue SLEs in terms of social, response-dependent proposals. I argue that their underlying error is a failure to appreciate the important shift of the explanatory locus in modern linguistics, from external objects to internal conceptions. I go on to show how (i) pace Devitt, this shift is entirely compatible with there being conventional aspects to language, and also serves to distinguish the ease of natural language from the waggle dance of the bees; and (ii) pace Barber and Smith, it is compatible with an appearance / reality distinction, and with reliance on testimony in epistemology. I conclude with further arguments about why, pace Collins and Matthews, intentionality is a crucial feature of linguistic explanation, even if it is ultimately spelt out largely in terms of computational role.

I suggest that the idea that conversational implicatures express argument can be significant for the notion of communicational responsibility. This underlying argument should be included in the reconstruction of conversational implicatures as a justification for the belief formed by the hearer on the basis of indirect communication. What makes this argument specific is the fact that its only explicit element is the speaker’s utterance taken as its initial premise. In order to reconstruct all the other elements, the hearer has to take into consideration factors such as the context and general knowledge of the shared language and the world. As the reconstruction of conversational implicatures in general, the reconstruction of implicatures as arguments is only potential. It is proposed that we should consider conversational implicatures as reason-giving arguments in which the speaker (arguer) addresses a hearer who does not need to reply. In those cases, the speaker is not trying to convince the hearer to accept his position but is explicitly stating a reason in support of his intended message. I believe that this approach can strengthen the idea of the speaker’s communicational responsibility for an implicated message even in the case when he wants to distance himself from it.

Some central philosophical issues concern the use of mathematics in putatively non-mathematical endeavors. One such endeavor, of course, is philosophy, and the philosophy of mathematics is a key instance of that. The present article provides an idiosyncratic survey of the use of mathematical results to provide support or counter-support to various philosophical programs concerning the foundations of mathematics.

The topic of this paper is the question of in virtue of what first-person thoughts are about what they are about. I focus on a dilemma arising from this question. On the one hand, approaches to answering this question that promise to be satisfying seem doomed to be inconsistent with the seeming truism that first-person thought is always about the thinker of the thought. But on the other hand, ensuring consistency with that truism seems doomed to make any answer to the question unsatisfying. Contrary to a careful and enticing recent effort to both sharpen and escape this dilemma by Daniel Morgan, I will argue that the dilemma remains pressing both for broadly epistemic and broadly causal-acquaintance-based accounts of the aboutness of first-person thought.

The problem of value disagreement and contextualist, relativist and metalinguistic attempts of solving it are laid out. Although the metalinguistic account seems to be on the right track, it is argued that it does not sufficiently explain why and how disagreements about the meaning of evaluative terms are based on and can be decided by appeal to existing social practices. As a remedy, it is argued that original suggestions from Putnam’s “The Meaning of ‘Meaning’” ought to be taken seriously. The resulting dual aspect theory of meaning can explain value disagreement in much the same way as it deals with disagreement about general terms. However, the account goes beyond Putnam’s by not just defending a version of social externalism, but also defending the thesis that the truth conditional meaning of many evaluative terms is not fixed by experts either and instead constantly contested as part of a normal function of language.

In this paper I concentrate on three issues concerning Williamson’s book The Philosophy of Philosophy: the problem of analytic statements being first-order propositions, the issue concerning aposteriority and the concerns related to the semantic vs. metasemantic distinction.

This paper takes up the two main points in John Collins “Note” (2008b), which responds to my paper, “Explanation and Reality in Linguistics” (2008). (1) Appealing to what grammars actually say, the paper argues that they primarily explain the nature of linguistic expressions. (2) The paper responds to Collins’ criticisms of my view that these expressions have many of their properties by convention.

It is commonly assumed that natural languages, construed as sets of sentences, contain denumerably many sentences. One argument for this claim is that the sentences of a language must be recursively enumerable by a grammar, if we are to understand how a speaker-hearer could exhibit unbounded competence in a language. The paper defends this reasoning by articulating and defending a principle that excludes the construction of a sentence non-denumerably many words long.

The first, critical part of the paper summarizes J. R. Brown’s Platonic view of thought experiments (TEs) and raises several questions. One of them concerns the initial, particular judgments in a TE. Since they seem to precede the general insight, Brown’s Platonic intuition, and not to derive from it, the question arises as to the nature of the initial particular judgment. The other question concerns the explanatory status of Brown’s epistemic Platonism. The second, constructive descriptive-explanatory part argues for an alternative, i.e. the view of TE as reasoning in, or with help of, mental models which can accommodate all the relevant data within a non-aprioristic framework (or, at worst, within a minimally “aprioristic”, nativist one). The last part turns to issues of justification and argues that the mental model proposal can account for justification of intuitional judgments and can also support the view of properly functioning intuition as an epistemic virtue, all within a more naturalist framework than the one endorsed by Brown.

This paper argues for a hybrid and alternative theory of names—Socio-historical Causal Descriptivism, which consists of six claims: (1) the referring relation between a name and an object originates from a generalized “initial baptism” of that object. (2) The causal chain of the name N firstly and mainly transmits informative descriptions of N’s bearer. (3) The meaning of N consists of an open-ended collection of informative descriptions of N’s bearer acknowledged by a linguistic community. (4) With respect to practical needs of agents there is s weighted order in the collection of descriptions of N’s bearer. (5) The meaning or even partial meaning of N, together with the background of a discourse, the network of knowledge, speaker’s intention, etc., determines the referent of N. (6) All names have their own referents, including physical individuals, and parasitic, fictional, or intensional objects; there are few names absolutely without reference.

This paper concerns the role of intuitions in mathematics, where intuitions are meant in the Kantian sense, i.e. the “seeing” of mathematical ideas by means of pictures, diagrams, thought experiments, etc.. The main problem discussed here is whether Platonistic argumentation, according to which some pictures can be considered as proofs (or parts of proofs) of some mathematical facts, is convincing and consistent. As a starting point, I discuss James Robert Brown’s recent book Philosophy of Mathematics, in particular, his primarily examples and analogies. I then consider some alternatives and counterarguments, namely John Norton’s opposite view, that intuitions are just pictorially represented logical arguments and are superfluous; and the Kantian transcendental theory of construction in imagination, as it is developed in the works of Marcus Giaquinto and Michael Friedman. Although I support the claim that some intuitions are essential in mathematical justification, I argue that a Platonistic approach to intuitions is partial and one should go further than a Platonist in explaining how some intuitions can deliver new mathematical knowledge.