Dummett's Backward Road to Frege and to Intuitionism - Tripod
Dummett's Backward Road to Frege and to Intuitionism - Tripod Dummett's Backward Road to Frege and to Intuitionism - Tripod
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
- Page 1 and 2: Dummett’s Backward Road to Frege
- Page 3 and 4: condition for each of its sentences
- Page 5 and 6: is to be any other object namable i
- Page 7 and 8: card packs and of figures subject t
- Page 9 and 10: well-defined as mutual and is there
- Page 11 and 12: eferences in a given sentence. The
- Page 13 and 14: always prior to the object-language
- Page 15 and 16: for identifying senses given the tr
- Page 17 and 18: sentences, and we were only suppose
- Page 19 and 20: why he thinks his program will work
- Page 21 and 22: (I waive the possibility of present
- Page 23 and 24: many more languages L** which lack
- Page 25 and 26: often have problems which more subt
- Page 27 and 28: of “On Denoting” in order to se
- Page 29 and 30: in which the reference is given to
- Page 31 and 32: Recalling the forced choice argumen
- Page 33 and 34: If we remain within the realm of se
- Page 35: sometimes he has references more in
- Page 39 and 40: epresents the thought. But Frege ru
- Page 41 and 42: gap needing completion. In language
- Page 43 and 44: objects....” (1981a: 132, my emph
- Page 45 and 46: out of senses. We can do so precise
- Page 47 and 48: Dummett calls the second problem of
- Page 49 and 50: article indicates reference to a co
- Page 51 and 52: has to be drawn between the sense a
- Page 53 and 54: and all the references on another.
- Page 55 and 56: or tones when we customarily indica
- Page 57 and 58: eversing the metaphysical order of
- Page 59 and 60: entities in different categories, w
- Page 61 and 62: (3) convey forces (such as assertio
- Page 63 and 64: We cannot need to be guaranteed to
- Page 65 and 66: It seems, then, that intuitionism c
- Page 67 and 68: 7. Frege (1979j: 271; see 1980c: 37
- Page 69 and 70: not even bothering to check for tha
- Page 71 and 72: third suggestions are principled in
- Page 73 and 74: 176-77). Since senses are entities,
- Page 75 and 76: of imperceptible senses in Grundges
- Page 77 and 78: mathematical functions are themselv
- Page 79 and 80: logical does not matter to this poi
- Page 81 and 82: in the sense in which philosophers
- Page 83 and 84: 17. ———. 1981. “Frege on Id
- Page 85 and 86: ———. 1970b. “Function and C
only senses can guide us on how <strong>to</strong> regiment references in the first place. This is just what the second<br />
problem of realism is: Given senses, are there references?<br />
5. Are senses objects or functions?<br />
The most direct way <strong>to</strong> derive senses from references would be <strong>to</strong> show that some senses are<br />
references. That would not only kill Russell’s main argument that whenever we try <strong>to</strong> refer <strong>to</strong> senses<br />
we refer instead <strong>to</strong> references, but would make the explicit <strong>and</strong> the implicit “no backward road” theses<br />
pointless as well. Dummett’s argument that senses are objects is simple <strong>and</strong> seemingly convincing.<br />
Namely, we can refer <strong>to</strong> a sense by a name such as “Fermat’s Last Theorem,” or by a definite<br />
description such as “the sense of expression ‘A’” (1981: 226–27; see 190; 1981a: 132). But I think it<br />
does not follow that senses are objects. In fact, I think that “the sense of expression ‘A’” does not refer<br />
<strong>to</strong> an object.<br />
On its face, <strong>Frege</strong>’s discussion in “On Concept <strong>and</strong> Object” of the singular definite article as<br />
indicating reference <strong>to</strong> an object is a discussion of references as opposed <strong>to</strong> senses (1970d: 46–47). He<br />
confines his first mention of senses <strong>to</strong> a note (1970d: 46 n.*), introducing the sense-reference<br />
distinction in the main text only after the discussion of objects <strong>and</strong> the singular definite article (1970d:<br />
47). He then uses that distinction <strong>to</strong> explicate objects in terms of reference as opposed <strong>to</strong> sense in the<br />
same paragraph (1970d: 48). His main discussion of senses is at the end of the paper (1970d: 54–55).<br />
There is nothing here <strong>to</strong> show that “the sense of expression ‘A’ refers <strong>to</strong> an object. If anything, his<br />
opposition of reference <strong>to</strong> sense suggests the opposite.<br />
Let us turn <strong>to</strong> “On Sense <strong>and</strong> Reference.” <strong>Frege</strong> says, “In order <strong>to</strong> speak of the sense of an<br />
expression ‘A’ one may simply use the phrase ‘the sense of the expression “A”’” (1970f: 59). Now,<br />
this is the first sentence of the second of two paragraphs discussing indirect sense <strong>and</strong> indirect reference<br />
37
Change language