Dummett's Backward Road to Frege and to Intuitionism - Tripod

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with Frege’s primitive terms, given as ostensibly referring names, and wish to explain how Frege thinks he proves they do in fact refer, thereby establishing realism of the second kind for abstract objects. So we already know which terms are ostensibly names of identity, negation, and so on. Following Grundgesetze, we limit the objects of concern to truth-values and courses-of-values (the Moon is an object in the preface). We must take truth-values as understood because Frege’s proof procedure, regimentation, cannot be understood if we do not. Thus for objects, the only permutation problem of interest would be for courses-of-values. Here I think we are still in basic agreement. If by “deriving” subsentential references from truth-conditions, Dummett merely means proving that ostensible names refer by ensuring that every statement in which they occur has a determinate truth-value, I agree this is Frege’s project. Frege’s principles of importance here are that every true or false sentence must have a denoting logical subject, and that every such statement can be sliced in different ways into a logical subject or subjects and a logical predicate. But I believe this does not amount to identifying references via truth-conditions. For we already know not only which marks are the ostensible names, but what their ostensible references are. And that is because they were explicated as expressing certain as-yet-unregimented senses. Since each mark “behaves as if it names,” “it is thus assured of a sense” (Frege 1979c: 122). Dummett says the terms are translated, as from metalinguistic German “gleich” to the formal identity sign. This is fine if the explication of the sense is not swept under the rug. The explication would be of “gleich,” whose sense we then transfer to the formal sign. Again, I doubt that regimentation (“derivation”) of reference is internal to the formal language, but it does not matter much for me, since explication is ultimately language-external. Since even Dummett’s project takes the backward road, the problem of sensial underdetermination remains. Dummett writes as if he thinks Grundgesetze vol. 1, § 32 states or implies the forced choice argument. But senses are merely regimented by regimentation. Senses are not proved, derived, or identified via proving the references of the primitive names through regimentation, because 36
only senses can guide us on how to regiment references in the first place. This is just what the second problem of realism is: Given senses, are there references? 5. Are senses objects or functions? The most direct way to derive senses from references would be to show that some senses are references. That would not only kill Russell’s main argument that whenever we try to refer to senses we refer instead to references, but would make the explicit and the implicit “no backward road” theses pointless as well. Dummett’s argument that senses are objects is simple and seemingly convincing. Namely, we can refer to a sense by a name such as “Fermat’s Last Theorem,” or by a definite description such as “the sense of expression ‘A’” (1981: 226–27; see 190; 1981a: 132). But I think it does not follow that senses are objects. In fact, I think that “the sense of expression ‘A’” does not refer to an object. On its face, Frege’s discussion in “On Concept and Object” of the singular definite article as indicating reference to an object is a discussion of references as opposed to senses (1970d: 46–47). He confines his first mention of senses to a note (1970d: 46 n.*), introducing the sense-reference distinction in the main text only after the discussion of objects and the singular definite article (1970d: 47). He then uses that distinction to explicate objects in terms of reference as opposed to sense in the same paragraph (1970d: 48). His main discussion of senses is at the end of the paper (1970d: 54–55). There is nothing here to show that “the sense of expression ‘A’ refers to an object. If anything, his opposition of reference to sense suggests the opposite. Let us turn to “On Sense and Reference.” Frege says, “In order to speak of the sense of an expression ‘A’ one may simply use the phrase ‘the sense of the expression “A”’” (1970f: 59). Now, this is the first sentence of the second of two paragraphs discussing indirect sense and indirect reference 37
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Page 3 and 4: condition for each of its sentences
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Page 31 and 32: Recalling the forced choice argumen
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Page 55 and 56: or tones when we customarily indica
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Page 73 and 74: 176-77). Since senses are entities,
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Dummett's Backward Road to Frege and to Intuitionism - Tripod

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