Philosophy

In his account of ‘double sensation’ Merleau-Ponty contends that we cannot be touched and
touching at the same time. However, Husserl’s account of ‘sensings’ (Empfindnisse) in Ideas II
suggests that one sensation can be apprehended in two different ways. I consider Husserl’s
description of ‘double sensation’ from the perspective of On the Phenomenology of the
Consciousness of Internal Time. I suggest the possibility that, if we take into account the flow of
sensations in non-objectifying intentionality, the double apprehension of one sensation is not
possible. Which means that Merleau-Ponty’s judgment about ‘double sensation,’ although
problematic, accounts better for temporality.

This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerraf ’s dilemma. The account builds upon Georg Kreisel’s work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a Fregean account of the objectivity and our knowledge of abstract objects. It is then argued that the resulting view faces no insurmountable metaphysical or epistemic obstacles.

ABSTRACT. This paper will deal with three questions regarding Carnap’s transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap’s attitude towards truth at the time of writing Syntax? (2) What was Carnap’s position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap’s acceptance of Tarski’s analysis of truth and reference detrimental to his philosophical project? Section 1 of this paper will deal with the first of these questions. Special attention will be paid to identifying what it was that prevented Carnap from defining a truth predicate for descriptive languages in Syntax. Section 2 of this paper will deal with the question of Carnap’s attitude towards reference and ontology in Syntax. It will be shown that the attempt in Syntax to address ontological questions is seriously defective. Section 3 of this paper addresses the last of the questions posed above. It is argued that in the light of what is established in Sections 1 and 2, Carnap could not have retained the position of Syntax with respect to truth and reference.

"Carnap’s position on mathematical truth in The Logical Syntax of
Language has been attacked from two sides: Kreisel argues that it is
formalistic but should not be, and Friedman argues that it is not form-
alistic but needs to be. In this paper I argue that the Carnap of Syntax
does not eliminate our ordinary notion of mathematical truth in favour
of a formal analogue; so Carnap’s notion of mathematical truth is not
formalistic. I further argue that there is no conflict between Carnap’s use
of informal notions and his principle of tolerance; so Carnap’s definition
of mathematical truth need not be formalistic.
"

This paper investigates the relation between Carnap and Quine's views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine's own remarks, and set theory is at least defensibly analytic.

I will begin by looking at the position Carnap held at the time of The Logical Syntax of Language (Syntax hereafter) and consider how his thoughts on the axiom changed over time. The surprising thing is that his position on this axiom changed very little over time. I say that this is surprising because his views on meaning and ontology changed quite radically just after Syntax. The philosophical program of Syntax was predicated on the rejection of meaning (at least as concerns a proper philosophical understanding of what is being claimed). Questions about ontology, especially abstract ontology, are then dismissed as inappropriately asking about the meaning of a term. In contrast to this drastic change in his views on ontology and meaning, Carnap’s discussion of the axiom of infinity after Syntax does not undergo a parallel metamorphosis. As we see in Frost-Arnold’s book, Carnap is still partial to interpreting the axiom of infinity as asserting the existence of infinitely many positions in 1940-41. Of course, the notes Frost-Arnold is dealing with contain many other suggested interpretations of the axiom of infinity, but a variation of the one from Syntax is contained there, and it is also one that Carnap keeps coming back to throughout the 40s and up to the mid 50s.

This paper investigates Gödel's criticism of Carnap's philosophy of mathematics. Gödel produced six drafts of a paper which was prepared for, but not included in, the Schilpp volume on Carnap. Gödel shows he is most familiar with Carnap's position from The Logical Syntax of Language (Syntax), and his arguments are nearly all directed against the position in this work. After looking at Syntax and identifying the problems with the philosophical position defended there, it will be seen that many of Gödel's criticisms are correct. While Gödel's  arguments are not perfect, it will be argued that the problems with them are not those identified in well-known articles by Goldfarb and Ricketts or Awodey and Carus. G\"odel did not, however, intend his arguments to apply exclusively to the position of Syntax, he thought the same arguments, with minor adaptation, apply to Carnap's newer views. It will be shown that this is not the case and that Gödel failed to appreciate how much Carnap's position had changed from the early 1930s to the mid 1950s.

There is much about Carnap's position ontology that remains constant over the course of his career. These include the views that ontological questions are closely tied to the choice of a language, and that they are generally not theoretical in character. On the other hand, there is much about his views on ontology that does change. One of the most significant changes involves his attitude toward truth and reference. At the time of The Logical Syntax of Language (Syntax), Carnap recommended eliminating these concepts, but after Tarski's influence, he came to see these concepts as standing in need of clarification (or explication). To properly understand Carnap's mature position on ontology, it is essential to understand the position that it had emerged from.

Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward and defends a novel interpretation of this paradox, according to which the concept of a unit plays a central role. There is every reason to think the paradox turns on the concept of a unit: after the presentation of the paradox the text of the Parmenides immediately turns to a discussion of units, and the concept of a unit is also central to the Greek conception of a plurality. If this interpretation is correct then the paradox that Zeno presented was the same as one discussed and solved in Frege’s Grundlagen.