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13886
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Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
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Full Idea:
Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument.
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From:
report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv
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A reaction:
Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'.
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9845
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We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
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Full Idea:
Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known
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From:
Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66)
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A reaction:
Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher.
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5784
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In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell]
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Full Idea:
We call a belief true when it is belief in a true proposition, ..but it is to propositions that the primary formal meanings of 'truth' and 'falsehood' apply.
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From:
Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV)
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A reaction:
I think this is wrong. A proposition such as 'it is raining' would need a date-and-time stamp to be a candidate for truth, and an indexical statement such as 'I am ill' would need to be asserted by a person. Of course, books can contain unread truths.
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5783
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Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell]
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Full Idea:
The correspondence of proposition and fact grows increasingly complicated as we pass to more complicated types of propositions: existence-propositions, general propositions, disjunctive and hypothetical propositions, and so on.
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From:
Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV)
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A reaction:
An important point. Truth must not just work for 'it is raining', but also for maths, logic, tautologies, laws etc. This is why so many modern philosophers have retreated to deflationary and minimal accounts of truth, which will cover all cases.
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9886
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Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
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Full Idea:
The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity.
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From:
Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19
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A reaction:
We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals.
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9887
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Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
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Full Idea:
Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence.
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From:
report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics
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A reaction:
The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising.
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5780
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The three questions about belief are its contents, its success, and its character [Russell]
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Full Idea:
There are three issues about belief: 1) the content which is believed, 2) the relation of the content to its 'objective' - the fact which makes it true or false, and 3) the element which is belief, as opposed to consideration or doubt or desire.
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From:
Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III)
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A reaction:
The correct answers to the questions (trust me) are that propositions are the contents, the relation aimed at is truth, which is a 'metaphysical ideal' of correspondence to facts, and belief itself is an indefinable feeling. See Hume, Idea 2208.
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22640
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We find satisfaction in consistency of all of our beliefs, perceptions and mental connections [James]
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Full Idea:
We find satisfaction in consistency between the present idea and the entire rest of our mental equipment, including the whole order of our sensations, and that of our intuitions of likeness and difference, and our whole stock previously acquired truths.
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From:
William James (The Pragmatist Account of Truth [1908], 'Fourth')
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A reaction:
I like this, apart from the idea that the criterion of good coherence seems to be subjective 'satisfaction'. We should ask why some large set of beliefs is coherent. I assume nature is coherent, and truth is the best explanation of our coherence about it.
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5778
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If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell]
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Full Idea:
If privacy is the main objection to introspective data, we shall have to include among such data all sensations; a toothache, for example, is essentially private; a dentist may see the bad condition of your tooth, but does not feel your ache.
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From:
Bertrand Russell (On Propositions: What they are, and Meaning [1919], §II)
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A reaction:
Russell was perhaps the first to see why eliminative behaviourism is a non-starter as a theory of mind. Mental states are clearly a cause of behaviour, so they can't be the same thing. We might 'eliminate' mental states by reducing them, though.
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11846
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If we abstract the difference between two houses, they don't become the same house [Frege]
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Full Idea:
If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction...
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From:
Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99)
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A reaction:
Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it.
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5781
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Our important beliefs all, if put into words, take the form of propositions [Russell]
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Full Idea:
The important beliefs, even if they are not the only ones, are those which, if rendered into explicit words, take the form of a proposition.
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From:
Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III)
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A reaction:
This assertion is close to the heart of the twentieth century linking of ontology and epistemology to language. It is open to challenges. Why is non-propositional belief unimportant? Do dogs have important beliefs? Can propositions exist non-verbally?
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5782
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A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell]
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Full Idea:
I shall distinguish a proposition expressed in words as a 'word-proposition', and one consisting of images as an 'image-proposition'.
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From:
Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III)
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A reaction:
This, I think, is good, though it raises the question of what exactly an 'image' is when it is non-visual, as when a dog believes its owner called. This distinction prevents us from regarding all knowledge and ontology as verbal in form.
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