[Inquiry] Re: Fractured Frege Tales -- Discussion

[Jon Awbrey]

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FFT.  Discussion Note 2

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Thanks, Theresa.  Can I take that as an agreement?

Jon Awbrey

Theresa Calvet wrote:
> 
> Kirsti, Jon, and list:
> 
> Do allow me to cite Michael Dummett, not the first edition and the second
> edition of his work, Frege: Philosophy of Language, but Chapter 12 ("The
> Notions of 'Object' and 'Function') of The Interpretation of Frege's
> Philosophy (Cambridge, Mass., Harvard University Press), 1981; the main
> point of this book is, he writes  in the Preface, "to establish how Frege
> should be understood", p. xiii), and also part of  Frege's article "uber
> Begriff und Gegenstand" ("On Concept and Object") [1892].
> 
> M. Dummett:
>    "On one point it now appears to me that in FPL [Frege: Philosophy of
> Language] I seriously misrepresented what is to be found in Frege's
> writings. On p. 194 of FPL, I spoke of Frege's saying that a relation can
> only be understood as being the referent of some relational expression; and
> on pp. 539-540 I asserted that 'Frege is even more explicit about the
> notion of "concept" - or..., more generally, that of "function"- than that
> of "object", that we can attain to it only via the notion of the
> corresponding type of linguistic expression: there can be no general
> characterization of concepts save that they are things of the kind for
> which one-place first-level predicates stand'. These passages attribute to
> Frege a thesis that I have been unable to find that he ever states. Given
> his conception of truth-values as objects, the terms 'concept' and
> 'relation' do admit of definition: a concept is a function of one argument
> all of whose values are truth-values, and a relation is a similar function
> of two arguments.* (*Grundgesetze, vol.I, paragraphs 3 and 4.) The
> suggestion embodied in the remarks on pp. 194 and 539-540 of FPL, is that
> one can, without circularity, explain what it is for an expression to be a
> proper name, something  I attempted in Chapter 4 of FPL ["Proper Names"];
> armed with this, one can then explain the notion of a predicate and that of
> a functional expression. An object can be specified as something for which a
> proper name could stand, a concept as something for which a predicate could
> stand, and a function as something for which a functional expression could
> stand. These will not, indeed, be definitions (...). Nevertheless, the
> suggestion is that there is a determinate order of explanation: one can
> attain to the general notion of a proper name in advance of having the
> general notion of an object, and to the general notion of a functional
> expression in advance of having the general notion of a function; but one
> cannot acquire the general notion of an object without first acquiring that
> of a proper name, or the general notion of a function without first
> acquiring that of a functional expression.
> 
>    This suggestion cannot be substantiated, as I implied that it could, by
> direct quotation from Frege. On the contrary, in discussing the general
> notion of 'object' or 'function', Frege almost invariably says merely that
> we are dealing with something too simple to admit of definition, so that he
> can only give hints.* (* In Funktion und Begriff [1891], p. 18, and in
> Grundgesetze [1893], vol I, paragraph 2, he says that an object is whatever
> is not a function;
> the main purpose of the remark is to induce the reader to accept that
> truth-values are objects, but it is otherwise of minimal help, since one
> evidently cannot understand what, in general, a function is without first
> understanding what, in general, an object is.) ... What is more important is
> that I have unable to find a passage in which he says expressly that the
> route to an understanding of what is comprised by any fundamental types of
> entity lies through a prior grasp of the corresponding type of linguistic
> expression. I think that I was in error in asserting that he maintained
> this, and have in FPL 2 [second edition of FPL] altered the passages on
> pp.194 and 539-540 accordingly.
> 
>    I still believe, however, that my suggestion was in accord with the
> spirit of Frege's thought. The reason for saying this can be seen from the
> passage on pp. 56-57 of FPL where I discussed the question whether, from a
> Fregean standpoint, it is because we are compelled to regard numbers as
> objects that we accord the status of proper names to numerical terms, or
> whether, conversely, it is because we are compelled to regard numerical
> terms as
> being, in Frege's sense, proper names that we take numbers to be objects. I
> there argued, as against the view expressed by Geach on p. 136 of Three
> Philosophers, and now retracted by him, that the second alternative is not
> only correct in itself, but is the only one consistent with Frege's general
> views; the argument in no way involves attributing to Frege anything that he
> did not say.
> 
>    The argument is essentially this. There is no intelligible enquiry
> whether a given thing is an object, a concept or a function. It is
> fundamental to Frege's philosophy that we cannot entertain any thought about
> a thing unless that thing is given or presented to us in some particular
> manner. The mode of presentation or manner in which it is given to us
> corresponds to the sense of a possible expression which stands for that
> thing. If we have such an expression, we must know whether it is complete,
> 'saturated', or incomplete, 'unsaturated', and, if it is complete, how many
> argument-places it has and which logical types of expression are required to
> fill them. We must know this, because it is an essential part of the
> characterization of the expression in question. But, if we know the logical
> type of the expression, we thereby know the logical type of its referent;
> whether or not that for which the expression stands is an object cannot be
> in question for us.
> [...]
>    The thesis that we can attain to the general notion of a function via,
> and only via, that of a functional expression, namely as the sort of thing
> for which such an expression stands, was not, however, intended to relate to
> a context in which all that was yet known about functional expressions was
> their syntactic characterization. It was assumed, rather, that the
> explanation was given to one who was already familiar with complex proper
> names containing other proper names as constituents, and understood such
> terms; understood them implicitly, that is, in the sense of having a mastery
> of their use, not of being able to give a semantic account of their
> meanings. And that is just how Frege does go about the process of giving
> 'hints' to enable a reader to attain the notion of a function.* (* Funktion
> und Begriff, 'Was ist eine Funktion?' [1904], Grundgesetze, vol 1,
> paragraphs 1 and
> 4 and 'Logik in der Mathematik', N.S. [Nachgelassene Schriften, ed. Hans
> Hermes, Friedrich Kambartel and Friedrich Kaulbach, Hamburg, 1969], pp.
> 254-261, P.W.
> [Posthumous Writings, trans. Peter Long and Roger White with the assistance
> of Raymond Hargreaves, Oxford, 1979], pp.235-242.)" ( The Interpretation of
> Frege's
> Philosophy, pp. 234-235, 241-242).
> 
> G. Frege:
>    "The word 'concept' is used in various ways; its sense is sometimes
> psychological, sometimes logical, and sometimes perhaps a confused mixture
> of both. Since this licence exists, it is natural to restrict it by
> requiring that when once a usage is adopted it shall be maintained. What I
> decided was to keep strictly to a purely logical use; the question whether
> this or that use is more appropriate is one that I should like to leave on
> one side, as of minor importance. Agreement about the mode of expression
> will easily be reached when once it is recognized that there is something
> that deserves a special term.
> [...]
>     ... The concept (as I understand the word) is predicative.* (* It is, in
> fact, the reference of a grammatical predicate.)
>    On the other hand,  a name of an object, a proper name, is quite
> incapable of being used as a grammatical predicate. This admittedly needs
> elucidation, otherwise it might appear false. Surely one can just as well
> assert of a thing that it is Alexander the Great, or is the number four, or
> is the planet Venus, as that it is green or is a mammal? If anybody thinks
> this, he is not distinguishing the usages of the word 'is'. In the last two
> examples it serves as a copula, as a mere verbal sign of predication. (In
> this sense the German word 'ist' can  sometimes be replaced by the mere
> personal suffix: cf. 'dieses Blatt ist gr¨n' ['this grass is green'] and
> 'dieses Blatt gr¨nt' [lit. 'this grass greens'].) We are here saying that
> something falls under a concept, and the grammatical predicate stands for
> this concept. In the first three examples, on the other hand, 'is' is used
> like the 'equals'  sign in arithmetic, to express an equation. [...] In the
> sentence 'The morning star is Venus', we have two proper names, 'morning
> star' and 'Venus', for the same object. In the sentence 'the morning star is
> a planet' we have a proper name, 'the morning star', and a concept-word,
> 'planet'. So far as language goes, no more has happened than that 'Venus'
> has been replaced by 'a planet'; but really the relation has become wholly
> different. An equation is reversible; an object's falling under a concept is
> an irreversible relation. In the sentence 'The morning star is Venus', 'is'
> is obviously not the mere copula; its content is an essential part of the
> predicate, so that the word 'Venus' does not constitute the whole of the
> predicate.* (* Cf. my Grundlagen, paragraph 66, footnote) One might say
> instead: 'the morning star is no other than Venus'; what was previously
> implicit in the single word 'is' is here set forth in four separate words,
> and in 'is no other than' the word 'is' now really is the mere copula. What
> is predicated here is thus not Venus but no other than Venus. These words
> stand for a concept; admittedly only one object falls under this, but such a
> concept must still always be distinguished from the object.* (Cf. my
> Grundlagen, paragraph 51). We have here a word 'Venus' that  can never be a
> proper predicate although it can form part of a predicate. The reference*
> (* Cf. my paper, ¨ber Sinn und Bedeutung, shortly to appear in the
> Zeitschrift f¨r Phil. und phil. Kritik) of this word is thus something than
> can never occur as a concept, but only as an object. [...]
>    [...]
>  ... As I said before, I was not trying to give a definition, but only
> hints; and to this end I appealed to the general feeling for the German
> language. It is here very much to my advantage that there is such good
> accord between the linguistic distinction and the real one.
> [...]
>    When I wrote my Grundlagen der Arithmetik, I had not yet made the
> distinction between sense and reference, and so, under the expression 'a
> possible content of judgement, I was combining what I now designate by the
> distinctive words 'thought' and 'truth-value'. Consequently, I no longer
> entirely approve of the explanation I then gave (op. cit., p. 77, as regards
> its wording; my view is, however, still essentially the same.
>     We may say in brief, taking 'subject' and 'predicate' in the linguistic
> sense: A concept is the reference of a predicate ; an object is something
> that can never be the whole reference of a predicate, but can be the
> reference of a subject. [...]
> [...]
>     Language has means of presenting now one, now another, part of the
> thought as the subject; one of the most familiar is the distinction of
> active and passive forms. It is thus not impossible that one way of
> analyzing a given thought should make it appear as a singular judgement;
> another, as a particular judgement; and a third, as a universal judgement.
> It need not then surprise us that the same sentence may be conceived as an
> assertion about a concept and also as an assertion about an object; only we
> must observe that what is asserted is different. In the sentence 'there is
> at least one square root of 4'  it is impossible to replace the words
> 'square root of 4'  by 'the concept square root of 4; i.e. the assertion
> that suits the concept does not suit the object. Although our sentence does
> not present the concept as a subject, it asserts something about it; it can
> be regarded as expressing the fact that a concept falls under a higher one.*
> (* In my Grundlagen I called such a concept a second-order concept;  in my
> work Funktion und Begriff I called it a second-level concept, as I shall do
> here.) But this does not in any way efface the distinction between object
> and concept. We see to begin with that in the sentence 'there is at least
> one square root of 4'  the predicative nature of the concept is not belied;
> we could say 'there is something that has the property of giving the result
> 4 when multiplied by itself.' Hence what is here asserted about a concept
> can never be asserted about an object; for a proper name can never be a
> predicative expression, though it can be part of one. I do not want to say
> it is false to assert about an object what is here asserted about a concept;
> I want to say it is impossible, senseless, to do so." ('On Concept and
> Object',  Posthumous Writings, pp. 88-94, 99-105, 108-109).
> 
> M. Dummett (cont.):
>    "The thesis [Dummett's thesis "that the only possible route to an
> explanation of Frege's notion of  'object' and 'function' is via that of the
> corresponding types of linguistic expression"] relates to the first,
> informal  introduction of the terms 'object' and 'function', not, as the
> objection that it is circular took it to do, to that part of a systematic
> theory of meaning for a language in which the semantic roles of its
> expressions are specified. A doubt may nevertheless remain. The informal
> explanation relied on the tacit understanding which we already have of the
> meanings of singular terms (proper names) generally and, in particular, of
> complex singular terms. But is not a theory of meaning supposed to make
> explicit what is merely implicitly involved in our everyday understanding of
> our language? With what right, then, may we make use,within that theory of
> meaning, of terms of art which are explained by appeal to our implicit
> understanding? Is that not to leave as still tacit what the theory of
> meaning is committed to rendering explicit?
>    Frege's inclination would probably have been not to treat such an
> objection very seriously. In the first place, the informal explanation does
> much more than merely label the referent of a functional expression a
> 'function', the referent of a predicate  a 'concept', leaving it to our
> tacit
> understanding of such expressions to see what kinds of things their
> referents must be: it makes explicit what, as it were, constitutes the being
> of a function or of a concept. The whole being of a function consists in a
> correlation of arguments to values; the whole being of a concept consists in
> its correlating each object to a truth-value. Because we already know this
> about functions and concepts from the informal explanation, the stipulation
> that a certain expression is to stand for a function and another for a
> concept does not rely on our tacit understanding of functional expressions
> and predicates to give it substance, but makes highly explicit just what the
> semantic role of those expressions is to be. [...].
>    It is more proper, however, to treat the objection more seriously. We saw
> in Chapter 7 ["Frege's Notion of Reference"] what, in general, a semantic
> theory is, that component of a theory of meaning which, for Frege, assumed
> the form of his theory of reference. A theory of meaning must, however,
> comprise more than just a semantic theory, in the strict sense. As well as
> the theory of reference it must comprise also a theory of sense, that is, a
> theory explaining what it is that confers on the expressions of our language
> the significance that they have. If meaning is to be explained in terms of
> understanding, we may say that a theory of sense must explain in what our
> understanding of those expressions, our mastery of their use, consist: in
> any case, it must give the content of our understanding of the words of our
> language, whether or not it needs to go into the question what it is for us
> to possess such an understanding. The theory of reference merely ascribes to
> each word and expression a particular semantic value: the theory of sense
> must explain in virtue of what each word  and expression has the semantic
> value that it has; and that in virtue of which it has the semantic value
> must be something in terms of which a speaker's understanding of it may be
> explained. This, of course, is merely to state what the theory of sense is
> required to do: how it does it will vary greatly according to the underlying
> philosophy of language. If understanding is thought of as a practical
> ability, the capacity to engage in a common practice, then the sense of a
> word will be characterized directly in terms of its use. But, as we saw in
> Chapter 5 ["Meaning and Understanding"], for Frege to grasp a sense is a
> cognitive act, that is to say, to understand an expression is to know
> something: so, for him, sense is to be characterized as a piece of knowledge
> that a speaker has concerning an expression.
>    Since different senses may correspond to the same reference, the
> reference of an expression does not determine its sense. But we may say
> something stronger than that: the theory of reference does not even
> determine uniquely the form that the theory of sense will assume, the sort
> of thing that is to be said to constitute the sense of an expression of a
> given logical type. [...] Nevertheless, the theory of reference greatly
> circumscribes the character of a theory of sense: for it imposes severe
> conditions on what the sense of an expression of each logical type may be
> taken to be. That is because we know in advance what the theory of sense is
> required to do. In the first place, the sense of an expression must
> determine its reference: that is to say, it must be something which, in view
> of how the world is, determines whatever we have taken to be the semantic
> value of the expression. It is precisely for this reason that the theory of
> reference serves as a foundation for the theory of sense, and determines
> within strict limits the form that it can take. Secondly, because sense is
> distinguished from tone, only that may be assigned to the sense of an
> expression which, among the things that go to make up a speaker's mastery of
> its use, is relevant to determining its referent. And, finally, sense must
> be something that relates to the use of an expression by the speakers of the
> language. Since, for Frege, sense is something that is grasped by a speaker,
> his grasp of it constituting his understanding of the expression, ... this
> means that the sense of an expression must be something that a speaker may
> be said to know, at least implicitly, and that each speaker must know
> implicitly if he is to be said to understand the expression. It follows that
> a characterization of the sense of an expression must amount to a complete
> characterization of the piece of knowledge which a speaker may have, and in
> which his understanding of it consists. Thus, for instance, the sense of a
> proper name cannot consist merely in its having a certain object as its
> bearer, since it could never be a complete characterization of what, in
> virtue of his understanding of the name, a speaker knew concerning it to say
> that he knew, of some object, that it was the bearer of the name. [...]
>    The theory of sense must do more than show what, in our understanding of
> an expression, determines it as having the referent it has; it must also
> show in what the association between the expression and its referent
> consist. In the theory of reference, we merely postulate that such an
> association exists, because that is all we need to do in explaining how each
> sentence is determined as true or otherwise in accordance with its
> composition; we can go ahead and introduce the notion of a semantic
> interpretation as consisting simply in an appropriate association of
> schematic letters with suitable semantic values. The theory of sense,
> however, must justify the assumption that there is such an association for
> actual expressions of the language; it therefore cannot take as given the
> general notion of an object, nor even the notions of each of the various
> sorts or categories of objects.* (see p. 76 of FPL for the use here made of
> 'category' and 'sort'.) [...] A full account of the sense of a proper name
> will therefore comprise an explicit account of the procedure of identifying
> an object of the appropriate kind as the bearer of the name, and hence of
> the use of what on p. 232 of FPL are called 'recognition statements', and,
> as underlying this, of what on p. 577 of FPL are called 'statements of
> identification'; it must therefore pay attention to that fundamental level
> of language of which Frege took so little account, in which the use of
> demonstratives play a crucial role. Only by such a means can it be made
> explicit what it is to use an expression as the proper name of an object of
> a given sort; and, in the process, the general notion of 'object' will
> thereby be made fully explicit also, without the need for mere hints or any
> appeal to a prior understanding of the object-language.
>    Thus, as it seems to me, when we have attained a fully adequate theory of
> sense, that theory will itself explain the highly general notions of
> 'object', 'concept' and 'function' which are employed in the theory of
> reference; no appeal will be made, in this explanation, to the notion of
> reference, as in any degree already understood, because the theory will
> itself make manifest what reference is. We are not in that situation;
> we have only sketchy conceptions of how a theory of sense is to be
> constructed." (The Interpretation of Frege's Philosophy, pp. 244-247).
> 
> Theresa Calvet

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