Results 1  10
of
10
Church’s Thesis and the Conceptual Analysis of Computability
 Notre Dame Journal of Formal Logic
, 2007
"... ..."
Function and concatenation
 Logical Form and Language
, 2002
"... For any sentence of a natural language, we can ask the following questions: what is its meaning; what is its syntactic structure; and how is its meaning related to its syntactic structure? Attending to these questions, as they apply to sentences that provide evidence for Davidsonian event analyses, ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
For any sentence of a natural language, we can ask the following questions: what is its meaning; what is its syntactic structure; and how is its meaning related to its syntactic structure? Attending to these questions, as they apply to sentences that provide evidence for Davidsonian event analyses, suggests that we reconsider some traditional views about how the syntax of a natural sentence is related to its meaning. Many theorists have held, at least as an idealization, that every phrase–and in particular, every verb phrase–consists of (i) an expression semantically associated with some function, and (ii) an expression semantically associated with some element in the domain of that function. On this view, which makes it comfortable to speak of both verbs and functions as taking arguments, each phrase is semantically associated with the value of the relevant function given the relevant argument(s); the semantic contribution of natural language syntax is functionapplication, as in a Fregean Begriffschrift; and the meaning of a sentence is determined by the meanings of ’s constituents, in the way that the sum of two numbers is determined by those numbers and the addition function. I want to urge a different conception of natural language semantics.
1 Induction and Comparison
"... Frege proved an important result, concerning the relation of arithmetic to secondorder logic, that bears on several issues in linguistics. Frege’s Theorem illustrates the logic of relations like PRECEDES(x, y) and TALLER(x, y), while raising doubts about the idea that we understand sentences like ‘ ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Frege proved an important result, concerning the relation of arithmetic to secondorder logic, that bears on several issues in linguistics. Frege’s Theorem illustrates the logic of relations like PRECEDES(x, y) and TALLER(x, y), while raising doubts about the idea that we understand sentences like ‘Carl is taller than Al ’ in terms of abstracta like heights and numbers. Abstract paraphrase can be useful—as when we say that Carl’s height exceeds Al’s—without reflecting semantic structure. Related points apply to causal relations, and even grammatical relations like DOMINATES(x, y). Perhaps surprisingly, Frege provides the resources needed to recursively characterize labelled expressions without characterizing them as sets. His theorem may also bear on questions about the meaning and acquisition of number words.
BIVALENCE AND THE CHALLENGE OF TRUTHVALUE GAPS
, 2003
"... This thesis is concerned with the challenge truthvalue gaps pose to the principle of bivalence. The central question addressed is: are truthvalue gaps counterexamples to bivalence and is the supposition of counterexamples coherent? My aim is to examine putative cases of truthvalue gaps against an ..."
Abstract
 Add to MetaCart
This thesis is concerned with the challenge truthvalue gaps pose to the principle of bivalence. The central question addressed is: are truthvalue gaps counterexamples to bivalence and is the supposition of counterexamples coherent? My aim is to examine putative cases of truthvalue gaps against an argument by Timothy Williamson, which shows that the supposition of counterexamples to bivalence is contradictory. The upshot of his argument is that either problematic utterances say nothing, or they cannot be neither true nor false. I start by identifying truthbearers: an utterance, for instance, is a truthbearer if it says that something is the case. Truthbearers are evaluable items, with truth and falsityconditions statable in corresponding instances of schemas for truth and falsehood. A genuine case of a truthvalue gap should be an utterance that is neither true nor false but says something to be the case. But it is inconsistent to accept the schemas for truth and falsehood and the existence of genuine cases of truthvalue gaps. Secondly, I expound Williamson’s argument, which explores this inconsistency, and I identify two kinds of strategy to disarm
Are ‘that’clauses singular terms? 1 Are ‘That’Clauses Really Singular Terms?*
"... The received view in the philosophy of language and formal semantics is that 'that'clauses in English are singular terms, and in particular, that the complementizer ‘that ’ is a termforming operator that turns meaningful sentences of the language into complex singular terms. ..."
Abstract
 Add to MetaCart
The received view in the philosophy of language and formal semantics is that 'that'clauses in English are singular terms, and in particular, that the complementizer ‘that ’ is a termforming operator that turns meaningful sentences of the language into complex singular terms.
Spring Term 1999REFERENCE AND ESSENCE
"... Permission is granted to make and distribute verbatim copies of this handbook provided the copyright notice and this permission notice are preserved on all copies. The most recent version of this handbook can be found in zipped portable document format at the following URL: ..."
Abstract
 Add to MetaCart
Permission is granted to make and distribute verbatim copies of this handbook provided the copyright notice and this permission notice are preserved on all copies. The most recent version of this handbook can be found in zipped portable document format at the following URL:
1.1. Fodor’s Background Theory A. Elements of Classical RTM
"... For such a short book (165 pages of text, plus a three page Preface), ..."
Russell’s 1903 – 1905 Anticipation of the Lambda Calculus
 HISTORY AND PHILOSOPHY OF LOGIC, 24 (2003), 15–37
, 2003
"... It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church’s ‘Lambda Calculus ’ for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts writ ..."
Abstract
 Add to MetaCart
It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church’s ‘Lambda Calculus ’ for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903 and 1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the Lambda Calculus. Russell also anticipated Schönfinkel’s Combinatory Logic approach of treating multiargument functions as functions having other functions as value. Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and ‘valueranges’. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the Lambda Calculus.