Online research in philosophy

Truth, falsity, and unity -- Sentences, lists, and collections -- Declarative and other kinds of sentence -- Declarative sentences and propositions -- Sentences, propositions, and truth-values -- Sentences, propositions, and unity -- Unity and complexity -- Reference and supposition -- Reference and signification -- Linguistic idealism and empirical realism -- Russell on truth, falsity, and unity (I) : 1903 -- Russell on truth, falsity, and unity (II) : 1910-13 -- Russell on truth, falsity, and unity (III) : 1918 -- Sense, reference, and propositions -- Russellian propositions, Fregean thoughts, and facts -- The location of propositions -- Proper names, concept-expressions, and definite descriptions -- Concept-expressions and Carnapian intensions -- Carnapian intensions and understanding -- Carnapian intensions and Russellian propositions -- Russellian propositions and functionality -- A revised semantic map -- Sentences as referring expressions -- False propositions at the level of reference -- The world's own language -- Signification and supposition revisited -- Frege and Russell on unity -- Saturatedness and unsaturatedness -- The copula as secundum adiacens and as tertium adiacens -- Frege and the Copula -- The paradox of the concept horse -- Russell on unity and the paradox -- An unsuccessful attempt to avoid the paradox -- The paradox and the level of language -- Reforming Frege's treatment of concept-expressions -- Concepts and functions -- The reformed Frege : refinements and objections -- Frege, Russell, and the anti-fregean strategy -- The anti-fregean strategy : the case of names -- Disquotation and propositional form -- The context principle -- Prabhakara semantics and the related designation theory -- For that is not a word which is not the name of a thing -- The impartial strategy -- Secundum and tertium adiacens, matter and form -- The hierarchy of levels and the syntactic priority thesis -- Fregean and anti-fregean strategies -- The anti-fregean strategy and relations (I) -- Interlude: The subject--predicate distinction -- The anti-fregean strategy and relations (II) -- The reality of relations -- Polyadicity, monadicity, and identity -- The anti-fregean strategy and Montague grammar -- Fregean and anti-fregean strategies : further comparison -- Ramsey on the subject : predicate distinction -- Dummett's attack on the anti-fregean strategy -- Linguistic idealism revisited -- Alternative hierarchies and the context principle -- The linguistic hierarchy and categorial nonsense -- Logical syntax and the context principle -- Proper names, singular terms, and the identity test -- Proper names, Leibniz's law, and the identity of indiscernibles -- The negation asymmetry test -- Dummett's tests for singular termhood -- Discarding the syntactic priority thesis -- Logical predication, logical form, and Bradley's regress -- Names, verbs, and the replacement test -- Analy

Philosophers of language have lavished attention on names and other singular referring expressions. But they have focused primarily on what might be called lexicalsemantic character of names and have largely ignored both what I call the lexicalsyntactic character of names and also what I call the pragmatic significance of the naming relation. Partly as a consequence, explanatory burdens have mistakenly been heaped upon semantics that properly belong elsewhere. This essay takes some steps toward correcting these twin lacunae. When we properly distinguish that which belongs to the lexical-syntactic character of names, from that which belongs to the lexical semantic character of names, from that which rests on the pragmatics of the naming relation, we lay to rest many misbegotten claims about names and their presumed semantic behavior. For example, though many believe that Frege’s puzzle about the possibility of informative identity statements motivates a move away from a referentialist semantics for names, I argue that the very possibility of Frege cases has its source not in facts about the lexical-semantic character of names but in facts about the lexical-syntax of the naming relation. If I am right, Frege cases as such are insufficient to justify the introduction of the distinction between sense and reference. In a similar vein, I offer a new diagnosis of the widely misdiagnosed felt invalidity of the substitution of coreferring names within propositional attitude contexts. That felt invalidity has been taken 1 to justify the conclusion that an embedded referring expression must be playing some semantic role either different from or additional to its customary semantic role of standing for its reference. I argue, to the contrary, that failures of substitutivity have their source not in the peculiar semantic behavior of embedded expressions but entirely in certain pragmatic principles.

Like '&', '=' is no term; it represents no extrasentential property. It marks an atomic, nonpredicative, declarative structure, sentences true solely by codesignation. Identity (its necessity and total reflexivity, its substitution rule, its metaphysical vacuity) is the objectual face of codesignation. The syntax demands pure reference, without predicative import for the asserted fact. 'Twain is Clemens' is about Twain, but nothing is predicated of him. Its informational value is in its 'metailed' semantic content: the fact of codesignation (that 'Twain' names Clemens) that explains what fact it asserts and why it is necessary. Critiques of concepts of rigidity and elimination of singular terms result.

Gottlob Frege maintained that two name-containing identity sentences, represented schematically as a=a and a=b,can both be true in virtue of the same object’s self-identity but nonetheless, puzzlingly, differ in their epistemic profiles. Frege eventually resolved his puzzlement by locating the source of the purported epistemic difference between the identity sentences in a difference in the Sinne, or senses, expressed by the names that the sentences contain. 

Thus, Frege portrayed himself as describing a puzzle that can be posed prior to and independently of any particular theoretical position regarding names, and then resolving that puzzle with his theory of Sinn and Bedeutung. In this paper, I suggest that Frege’s presentation is problematic. If attempt is made to characterize the epistemic status of true identity sentences without appeal to Frege’s theoretical commitments, then what initially seemed puzzling largely dissolves. It turns out that, in order to generate puzzlement, Frege must invoke the theoretical account that he uses the puzzle to establish the purported necessity of. 

Frege’s method of introducing abstract singular terms by transforming an equivalence statement into an identity statement suffers from one major defect: it is haunted by a pervasive indeterminacy of putative reference. In this paper, I. discuss mainly Frege’s introduction of courses-of-values in his magnum opus Grundgesetze der Arithmetik (Volume I, 1893, Volume 11, 1903). More specifically, I want to assesscritically, with respect to course-of-values names, what I call Frege’s indeterminacy problem. In the first part, I sketch the nature of this problem in connection with the introduction of numerical singular terms in his book Die Grundlagen der Arithmetik of 1884. In the second part, I try to shed light on the analogies and differences concerning the introduction of numerical terms on the one hand and of course-of-values terms on the other.

P.T. Geach has maintained (see, e.g., Geach (1967/1968)) that identity (as well as dissimilarity) is always relative to a general term. According to him, the notion of absolute identity has to be abandoned and replaced by a multiplicity of relative identity relations for which Leibniz’s Law – which says that if two objects are identical they have the same properties – does not hold. For Geach relative identity is at least as good as Frege’s cardinality thesis – which he takes to be strictly connected with relative identity – according to which an ascription of cardinality is always relative to a concept which specifies what, in any particular case, counts as a unit. The idea that there is a close connection between relative identity and Frege’s cardinality thesis has been issued again quite recently by Alston and Bennett in (1984). In their opinion, Frege’s cardinality thesis is not only similar to relative identity – as Geach maintains – but it implies it. Moreover, they agree with Geach in claiming that a commitment to Frege’s cardinality thesis forces a parallel commitment to relative identity. Against Geach, Alston and Bennett we will claim that (T1): «Frege’s cardinality thesis is similar to relative identity» is false and that therefore (T2) «Frege’s cardinality thesis implies relative identity» is false as well.

Frege introduced the distinction between sense and reference to account for the information conveyed by identity statements. We can put the point like this: if the meaning of a term is exhausted by what it stands for, then how can 'a =a' and 'a =b' differ in meaning? Yet it seems they do, for someone who understands all the terms involved would not necessarily judge that a =b even though they judged that a =a. It seems that 'a =b' just says something more than the trivial ’a = a' - it seems to contain more information, in some sense of 'information'. So either we have to add something to explain this extra information, or sever the very plausible links between meaning and understanding. This is what some writers have called 'Frege's Puzzle' It is undeniable that there is a phenomenon here to be explained, and it was Frege's insight to see the need for its explanation. But how should we explain it? Frege's idea was to add another semantic notion - Sinn, or Sense -— to account for the information conveyed. Sense is part of the meaning of an expression: it is the 'cognitive value' of the expression, or that ’wherein the mode of presentation is contained' (Frege 1957 p.57). Sense has a role to play in systematically determining the meanings of complex expressions, and ultimately in fixing the contents of judgements. It is the senses of whole sentences — Gedanken or Thoughts - which are candidates for truth and falsehood, and which are thus the objects of our propositional attitudes. Of course, introducing the notion of sense in this way does not, by itself, tell us what sense is. It only imposes a condition on a theory of meaning (and ultimately) belief: that it must account for distinctions in cognitive value or 'mode of presentation' (this is not a trivial thesis —- some philosophers today would deny that an explanation of Frege's Puzzle must occur within semantics or the theory of meaning: see Salmon 1985). In this paper I want to explore one way of meeting this condition for the theory of names in natural language, by examining Kripke's well-known 'Puzzle about Belief' (Kripke 1979)..

Singular-term semantics has been intractable. Frege took the referents of singular terms to be their semantic values. On his account, vacuous terms lacked values. Russell separated the semantics of definite descriptions from the semantics of proper names, which caused truth-values to be composed in two different ways and still left vacuous names without values. Montague gave all noun phrases sets of verb-phrase extensions for values, which created type mismatches when noun phrases were objects and still left vacuous names without values. There is a single type of value for all noun phrases that dissolves the difficulties which have beset singular-term semantics.

In some ways that have been largely ignored, ethnic-group names might be similar to names of other kinds. If they are, for instance, analogous to proper names, then a correct semantic account of the latter could throw some light on how the meaning of ethnic-group names should be construed. Of course, proper names, together with definite descriptions, belong to the class of singular terms, and an influential view on the semantics of such terms was developed, at the turn of the nineteenth century, from discussion of a puzzle about some differences in the cognitive value of certain statements of identity. Clearly, that a = a (e.g., that Mark Twain was Mark Twain) is trivial, and its truth could be known a priori, just by thinking. On the other hand, that a = b (e.g., that Mark Twain was Samuel Clemens) is of course informative and knowable only by empirical investigation. To solve this puzzle, Frege famously proposed that those variations in the cognitive value of statements of identity “can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated.” On his view, although in the above statements of identity, the singular terms, ‘a,’ and, ‘b,’ may designate the same thing, they do so with different senses, or under different modes of presentation of that object. When the puzzling statements involving ‘a’ and ‘b’ are true, they may then be said to have exactly the same reference. But since those singular terms pick out the object of reference differently (i.e., under different senses or modes of presentation), therefore the cognitive value of these statements also varies significantly. On this account, then, the reference of a non-vacuous proper name is secured by the name’s sense, or mode of presentation, which constitutes its semantic content. And given that Fregeans (here under the influence of Russell) cash out that sense as consisting in whatever concept (or cluster of concepts) could be uniquely associated with that name, they might hold, for example, that the property of being the author of Huckleberry Finn, and that of being an American who lived his early life in Hannibal, Missouri, and later became a famous writer, amount to the senses of ‘Mark Twain,’ and ‘Samuel Clemens,’ respectively..

This essay offers a detailed philosophical criticism of Frege’s popular thesis that identity is a relation of names. I consider Frege’s position as articulated both in ‘On Sense and Reference’, and in the Grundgesetze, where he appears to take an objectual view of identity, arguing that in both cases Frege is clearly committed to the proposition that identity is a relation holding between names, on the grounds that two different things can never be identical. A counterexample to Frege’s thesis is considered, and a positive thesis is developed according to which, in contradistinction to the Fregean position, identity is a reflexive, symmetric, and transitive relation holding only between a thing and itself which can be expressed as a relation between names.