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
these three Principia senses of “intension.” I doubt even more that he distinguishes the corresponding three Principia senses of “extension.” In his Frege books, he introduces a single notion of extension in terms of both truth-functionality and opacity, blurring senses (1) and (2). The slip from sense (1) to sense (2) is subtle: ...are...extensional: that is, provided that the truth-value of a complex sentence depends only on the truth-values of the constituents....What happens, then, in a case in which a method of sentence-transformation is used which is not extensional: that is, when a sentence is formed which contains an opaque context? (Dummett 1981: 189–90, my emphasis; see 1981a: 155) But he does clearly identify intension in sense (2) in discussing intuitionism (2000: 16–17). For Frege, all sentential contexts, even opaque contexts, are extensional in sense (1). To preserve truth-functionality in opaque contexts, Frege introduces a systematic reference shift from customary references to senses. Thus senses are extensional in sense (1). But senses are intensional in sense (2). That is the whole point of Frege’s explanation of informative identity statements. Namely, different names expressing different senses can refer to the same reference. All senses are intensional in sense (2), while all customary, i.e., direct, references are extensional in sense (2). For any customary reference, there are indefinitely many senses containing modes of presentation of that reference. Insofar as a reference is informatively identifiable indefinitely many times, there are indefinitely many senses through which it can be identified. Thus in general, the relation of a reference to the senses which are ways of identifying it is one-many. Thus it is magical to suppose that starting from any given set of references, i.e., objects and functions, we can work back so as to determine any one sense in particular as the sense expressed by a name of any one of those 10
eferences in a given sentence. The same goes for truth-conditions. For a truth-condition consists of extensional in sense (2) references. It is the extensional in sense (2) references of the subsentential names, in some extensional in sense (2) order, which make a customary statement true or false. We must not beg the question by using descriptions of truth-conditions to identify them prior to the promised derivation of subsentential references and thereby subsentential senses from them. For such descriptions are intensional in sense (2), while the truth-conditions themselves are extensional in sense (2). Truth-conditions do not contain modes of presentation of truth-values. Thoughts do. Truth- conditions are not intensional in sense (2) because they are not ways of presenting or identifying anything. They are presented or identified in different ways by thoughts. I think Dummett would agree with this (1981: 5, 634, 642; 1981a: 252–53). The sixth problem is that Dummett’s program discusses only Frege’s semantic stage of stipulative regimentation, and entirely ignores Frege’s initial semantic stage of explication. How can we convey the senses of primitive names? Is it by stipulation, as I quoted Dummett as saying? No. Stipulation has all the advantage of theft over honest explicative toil, as Russell might say. For Frege, stipulations cannot be made for primitive names except in the sense of stipulated regimentations of reference to ensure logical determinacy. Regimentations can be highly artificial. But if a regimentation of a primitive name which already has a sense is intuitively correct—notably, regimenting the identity-name so that an object is truly said to be identical with itself but not identical with anything else (Grundgesetze vol. 1, § 7)—Frege calls it an analysis (1979f: 210). Frege’s only other stipulations are his definitions. For Frege, all definitions are stipulations which fix sense and reference for the defined names (Grundgesetze vol. 1, § 27; 1979f: 207–8, 210, 211), and as stipulations, they are neither true nor false (1980c: 36; 1971a: 24; 1971: 50–51). Of course, explications are not true or false either. But there is an important sense in which stipulations logically cannot fail, 11
- 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: well-defined as mutual and is there
- 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 and 36: sometimes he has references more in
- Page 37 and 38: only senses can guide us on how to
- 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
eferences in a given sentence.<br />
The same goes for truth-conditions. For a truth-condition consists of extensional in sense (2)<br />
references. It is the extensional in sense (2) references of the subsentential names, in some extensional<br />
in sense (2) order, which make a cus<strong>to</strong>mary statement true or false.<br />
We must not beg the question by using descriptions of truth-conditions <strong>to</strong> identify them prior <strong>to</strong><br />
the promised derivation of subsentential references <strong>and</strong> thereby subsentential senses from them. For<br />
such descriptions are intensional in sense (2), while the truth-conditions themselves are extensional in<br />
sense (2). Truth-conditions do not contain modes of presentation of truth-values. Thoughts do. Truth-<br />
conditions are not intensional in sense (2) because they are not ways of presenting or identifying<br />
anything. They are presented or identified in different ways by thoughts. I think Dummett would agree<br />
with this (1981: 5, 634, 642; 1981a: 252–53).<br />
The sixth problem is that Dummett’s program discusses only <strong>Frege</strong>’s semantic stage of<br />
stipulative regimentation, <strong>and</strong> entirely ignores <strong>Frege</strong>’s initial semantic stage of explication.<br />
How can we convey the senses of primitive names? Is it by stipulation, as I quoted Dummett as<br />
saying? No. Stipulation has all the advantage of theft over honest explicative <strong>to</strong>il, as Russell might say.<br />
For <strong>Frege</strong>, stipulations cannot be made for primitive names except in the sense of stipulated<br />
regimentations of reference <strong>to</strong> ensure logical determinacy. Regimentations can be highly artificial. But<br />
if a regimentation of a primitive name which already has a sense is intuitively correct—notably,<br />
regimenting the identity-name so that an object is truly said <strong>to</strong> be identical with itself but not identical<br />
with anything else (Grundgesetze vol. 1, § 7)—<strong>Frege</strong> calls it an analysis (1979f: 210). <strong>Frege</strong>’s only<br />
other stipulations are his definitions. For <strong>Frege</strong>, all definitions are stipulations which fix sense <strong>and</strong><br />
reference for the defined names (Grundgesetze vol. 1, § 27; 1979f: 207–8, 210, 211), <strong>and</strong> as<br />
stipulations, they are neither true nor false (1980c: 36; 1971a: 24; 1971: 50–51). Of course, explications<br />
are not true or false either. But there is an important sense in which stipulations logically cannot fail,<br />
11
Change language