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Gottlob Frege (1848-1925)

A class about his role in the history of linguistics
by

Marc van Oostendorp

on 14 October 2014

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Transcript of Gottlob Frege (1848-1925)

Gottlob Frege (1848-1925)
History of linguistics
2014-2015

Marc van Oostendorp
LUCL, Leiden
Background

With Frege we go back to the tradition of Wilkins etc. rather than of Bopp etc.
Frege was first and foremost a philosopher, mathematician and logician
His ultimate goal was to provide a logical foundation to mathematics.
This led him to think about the 'imperfect' way in which language represents logic.
Begriffsschrift
Focus on notation
Difference between judgement and content
The trouble with ordinary language
The symbols used in the general theory of magnitude fall into two kinds. The first consists of the letters; each letter represents either an
indeterminate number or an indeterminate function. This indeterminateness makes it possible to express by means of the letters the general validity of propositions; e.g. (a+b)c=ac+be. The other kind contains such symbols as + , •, 0, 1, 2; each of these has its own proper meaning. I adopt this fundamental idea of distinguishing two kinds of symbols […] in order to make it generally applicable in the wider domain of pure thought. Accordingly, I divide all the symbols I use into those that can be taken to mean various things and those that have a fully determinate sense.
(Begriffsschrift §1)
Suppose A means 'unlike magnetic poles attract each other'.
Then –A (the content stroke) is the proposition
While |-A is the judgement
A distinction of subject and predicate finds no place in my way of
representing a judgment. In order to justify this, let me observe that there are two ways in which the content of two judgments may differ; it may, or it may not, be the case that all inferences that can be drawn from the first judgment when combined with certain other ones can always also be drawn from the second when combined with the same other judgments. The two propositions ‘the Greeks defeated the Persians at Plataea’ and ‘the Persianswere defeated by the Greeks at Plataea’ differ in the former way; even if aslight difference of sense is discernible, the agreement in sense is preponderant. Now I call the part of the content that is the same in both the conceptual content. Only this has significance for our symbolic language; we need therefore make no distinction between propositions that have the same conceptual content. (Begriffsschrift §3)
Sinn und Bedeutung
Sinn = Sense = the semantic composition of the expression itself
Bedeutung = Reference = what the expression refers to
The evening star is the morning star
We can refer to the same individual in different ways.
Knowing one sense doesn't imply knowing the other.
An expression can have a sense without a reference.
Also sentences have a sense and a reference:
The sense of a sentence (Satz) = the thought (Gedanke)
If we now replace one word of the sentence by another having the same reference, but a different sense, this can have no bearing upon the referenceof the sentence. Yet we can see that in such a case the thought changes; since, e.g., the thought in the sentence ‘The morning star is a body illuminated by the Sun’ differs from that in the sentence ‘The evening staris a body illuminated by the Sun’. Anybody who did not know that the evening star is the morning star might hold the one thought to be true, theother false. The thought, accordingly, cannot be the reference of thesentence, but must rather be considered as the sense. What is the positionnow with regard to the reference?(‘Über Sinn und Bedeutung’ [62])
Why is the thought not enough for us? Because, and to the extent that, we are concerned with its truth value. This is not always the case. In hearing an epic poem, for instance, apart from the euphony of the language we are interested only in the sense of the sentence and the images and feelings thereby aroused. The question of truth would cause us to abandon aesthetic delight for an attitude of scientific investigation. Hence it is a matter of no concern to us whether the name ‘Odysseus’, for instance, has reference, so long as we accept the poem as a work of art. It is the striving for truth that
drives us always to advance from the sense to the reference.
We have seen that the reference of a sentence may always be sought, whenever the reference of its components is involved; and that this is the case when and only when we are inquiring after the truth value. We are therefore driven into accepting the truth value of a sentence as constituting its reference. By the truth value of a sentence I understand thecircumstance that it is true or false. There are no further truth values. For brevity I call the one the True, the other the False. (‘Über Sinn und Bedeutung’ [63])
If now the truth value of a sentence is its reference, then on the one hand all true sentences have the same reference and so, on the other hand, do all false sentences. From this we see that in the reference of the sentence all that is specific is obliterated. (‘Über Sinn und Bedeutung’ [63])
F
T
The reference and sense of a sign are to be distinguished from the
associated idea. If the reference of a sign is an object perceivable by the senses, my idea of it is an internal mental image, arising from memories of sense impressions which I have had, and acts both internal and external, which I have performed. Such an idea is often saturated with feeling; the clarity of its separate parts varies and oscillates. The same sense is not always connected, even in the same man, with the same idea. The idea is subjective: one man’s idea is not that of another. There results, as a matter of course, a variety of differences in the ideas associated with the same sense. A painter, a horseman, and a zoologist will probably connect different ideas with the name ‘Bucephalus’. This constitutes an essential distinction between the idea and the sign’s sense, which may be the common property of many and therefore is not a part or a mode of theindividual mind.(‘Über Sinn und Bedeutung’ [59])
Der Gedanke
Ideas are private
My companion and I are convinced that we both see the same field; but each of us has a particular sense-impression of green. I glimpse a strawberry among the green strawberry leaves. My companion cannot find it, he is colour-blind. The colour-impression he gets from the strawberry is not noticeably different from the one he gets from the leaf. Now does my companion see the green leaf as red, or does he see the red berry as green, or does he see both with one colour which I am not acquainted with at all? These are unanswerable, indeed really nonsensical, questions. For when the word ‘red’ is meant not to state a property of things but to characterize sense-impressions belonging to my consciousness, it is only applicable within the realm of my consciousness. For it is impossible to compare my sense-impression with someone else’s. For that, it would be necessary to bring together in one consciousness a sense-impression belonging to one consciousness and a sense-impression belonging to another consciousness.
In any case it is impossible for us men to compare other people’s ideas with our own. I pick the strawberry, I hold it between my fingers. Now my companion sees it too, this same strawberry; but each of us has his own idea. Nobody else has my idea, but many people can see the same thing. Nobody else has my pain. Someone may have sympathy with me, but still my pain belongs to me and his sympathy to him. He has not got my pain, and I have not got his feeling of sympathy. (‘Der Gedanke’ [15])
Sentences: more than thoughts
An assertoric sentence often contains, over and above a thought and assertion, a third component not covered by the assertion. This is often meant to act on the feelings and mood of the hearer, or to arouse his imagination. Words like ‘regrettably’ and ‘unfortunately’ belong here. Such constituents of sentences are more strongly prominent in poetry, but are seldom wholly absent from prose. […] What are called the humanities are closer to poetry, and are therefore less scientific, than the exact sciences, which are drier in proportion to being more exact; for exact science is directed towards truth and truth alone. […] On the other hand, the constituents of language to which I here want to call attention make the translation of poetry very difficult, indeed make perfect translation almost always impossible, for it is just in what largely makes poetic value that languages most differ. (‘Der Gedanke’ [8–9])
Much in language serves to aid the hearer’s understanding, for instance emphasizing part of a sentence by stress or word order. Here let us bear in mind words like ‘still’ and ‘already’. Someone using the sentence ‘Alfred has still not come’ actually says ‘Alfred has not come’, and at the same time hints but only hints—that Alfred’s arrival is expected. Nobody can say: Since Alfred’s arrival is not expected, the sense of the sentence is false. The way that ‘but’ differs from ‘and’ is that we use it to intimate that whatfollows it contrasts with what was to be expected from what preceded it. Such conversational suggestions make no difference to the thought.(‘Der Gedanke’ [9])
Grasping thoughts
thoughts are neither things in the external world nor ideas. A third realm must be recognized. Anything belonging to this realm has it in common with ideas that it cannot be perceived by the senses, but has it in common with things that it does not need an owner so as to belong to the contents of his consciousness. Thus for example the thought we have expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no owner. It is not true only from the time when it is discovered; just as a planet, even before anyone saw it, was in interaction with other planets. (‘Der Gedanke’ [17–18])
How different a process handing over a hammer is from communicating a thought! The hammer passes from one control to another, it is gripped, it undergoes pressure, and thus its density, the disposition of its parts, is locally changed. There is nothing of all this with a thought. It does not leave the control of the communicator by being communicated, for after all man has no power over it. When a thought is grasped, it at first only brings about changes in the inner world of the one who grasps it; yet it remains untouched in the core of its essence, for the changes it undergoes affect
only inessential properties. (‘Der Gedanke’ [29])
This presentation is based on Chapter 15 ('Frege on sense and reference') of Roy Harris and Talbot J. Taylor. 2005 Landmarks in
Linguistic Thought 1. London and New York: Routledge
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