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5651
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Traditional views of truth are tautologies, and truth is empty without a subject [Kierkegaard, by Scruton]
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Full Idea:
Kierkegaard developed the idea of 'truth as subjectivity'; the traditional conceptions of truth - correspondence or coherence - he regarded as equally empty, not because false, but because tautologous; truth ceases to be empty when related to a subject.
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From:
report of Søren Kierkegaard (Either/Or: a fragment of life [1843]) by Roger Scruton - Short History of Modern Philosophy Ch.13
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A reaction:
It strikes me that the correspondence theory of truth also involves a subject. If you become too obsessed with the subject, you lose the concept of truth. You need a concept of the non-subject too. Truth concerns the contents of thought.
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8729
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Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
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Full Idea:
Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
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From:
Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
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A reaction:
There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.
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8763
|
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
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Full Idea:
It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures.
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From:
Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
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A reaction:
The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed.
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8762
|
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
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Full Idea:
Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3.
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From:
Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
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A reaction:
See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them.
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8749
|
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
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Full Idea:
Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names?
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From:
Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1)
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A reaction:
Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up.
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8750
|
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
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Full Idea:
Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences.
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From:
Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2)
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A reaction:
This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare.
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8753
|
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
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Full Idea:
Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle.
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From:
Stewart Shapiro (Thinking About Mathematics [2000], 7.1)
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A reaction:
The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them.
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8731
|
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
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Full Idea:
I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists.
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From:
Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1)
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|
A reaction:
In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football.
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11993
|
Jones may cease to exist without some simple property, but that doesn't make it essential [Kung]
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Full Idea:
If Jones ceases to be a father, or ceases to be over eight years old, he will cease to exist, yet these properties surely do not belong essentially to him.
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From:
Joan Kung (Aristotle on Essence and Explanation [1977], II)
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A reaction:
This seems to correct, though I would doubt whether either of these count as true properties, in the causal sense I prefer. If being 'over 8' is a property, how many 'over n' or 'under m' properties does he have? One for each quantum moment?
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11992
|
Aristotelian essences underlie a thing's existence, explain it, and must belong to it [Kung]
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Full Idea:
Three essentialist claims are labelled 'Aristotelian': the thing would cease to exist without the property; an essential property is explanatory; and it is such that it must belong to everything to which it belongs.
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From:
Joan Kung (Aristotle on Essence and Explanation [1977], Intro)
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A reaction:
She says the second one is indispensable, and that it rules out the third one. My working assumption, like hers, is that the second one is the key part of the game, because Aristotle wanted to explain things.
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22090
|
For me time stands still, and I with it [Kierkegaard, by Carlisle]
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Full Idea:
Time flows, life is a stream, people say, and so on. I do not notice it. Time stands still, and I with it.
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From:
report of Søren Kierkegaard (Either/Or: a fragment of life [1843], I:26) by Clare Carlisle - Kierkegaard: a guide for the perplexed 3
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A reaction:
This is from the spokesman for the aesthetic option in life, which is largely pleasure-seeking. No real choices ever occur.
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5650
|
Reason is just abstractions, so our essence needs a subjective 'leap of faith' [Kierkegaard, by Scruton]
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Full Idea:
For Kierkegaard, reason, which produces only abstractions, negates our individual essence; this essence is subjectivity, and subjectivity exists only in the 'leap of faith', whereby the individual casts in his lot with eternity.
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From:
report of Søren Kierkegaard (Either/Or: a fragment of life [1843]) by Roger Scruton - Short History of Modern Philosophy Ch.13
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A reaction:
Interesting, but this strikes me as a confusion of reason and logic. A logical life would indeed be a sort of death, and need faith as an escape, but a broad view of the rational life includes emotion, imagination and laughter. Blind faith is disaster.
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22095
|
There are aesthetic, ethical and religious subjectivity [Kierkegaard, by Carlisle]
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Full Idea:
Kierkegaard distinguishes three main types of subjectivity: aesthetic, ethical and religious. But are these types of people, or different phases of one person's life?
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From:
report of Søren Kierkegaard (Either/Or: a fragment of life [1843]) by Clare Carlisle - Kierkegaard: a guide for the perplexed 4
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A reaction:
His picture of the religious mode holds no appeal for me. I also can't accept that the aesthetic and the moral are somewho distinct. People may discover they have slipped into one of these modes, but no one chooses them, do they?
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20747
|
What matters is not right choice, but energy, earnestness and pathos in the choosing [Kierkegaard]
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Full Idea:
In making a choice, it is not so much a question of choosing the right way as of the energy, the earnestness, and the pathos with which one chooses.
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From:
Søren Kierkegaard (Either/Or: a fragment of life [1843], p.106), quoted by Kevin Aho - Existentialism: an introduction 2 'Phenomenology'
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A reaction:
I'm struggling to identify with the experience he is describing. I can't imagine a more quintessentially existentialist remark than this. Reference to 'energy' in choosing strikes me as very romantic. Is 'the way not taken' crucial (in 'pathos')?
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