Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Philosophy of Logics' and 'Abstract of 'The Fourfold Root''

unexpand these ideas     |    start again     |     specify just one area for these texts


9 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer]
     Full Idea: The Principle may be stated as 'There is nothing without a reason why it should be rather than not be', which is a generalisation of the assumption which justifies the question 'Why?', which is the mother of all science.
     From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.I)
     A reaction: This faith is the core of philosophy, to be maintained against all defeatists like Wittgenstein and Colin McGinn. Reality must be rational, or we wouldn't be here to think about it. (Maybe!)
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Logical truth seems much less likely to 'correspond to the facts' than factual truth does [Haack]
     Full Idea: It is surely less plausible to suppose that logical truth consists in correspondence to the facts than that 'factual' truth does.
     From: Susan Haack (Philosophy of Logics [1978], 7.6)
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
The same sentence could be true in one language and meaningless in another, so truth is language-relative [Haack]
     Full Idea: The definition of truth will have to be, Tarski argues, relative to a language, for one and the same sentence may be true in one language, and false or meaningless in another.
     From: Susan Haack (Philosophy of Logics [1978], 7.5)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
10. Modality / C. Sources of Modality / 1. Sources of Necessity
All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer]
     Full Idea: Necessity has no meaning other than the irresistible sequence of the effect where the cause is given. All necessity is thus conditioned, and absolute or unconditioned necessity is a contradiction in terms.
     From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.VIII)
     A reaction: I.e. there is only natural necessity, and no such thing as metaphysical necessity. But what about logical necessity(e.g. 2+3=5)? I think there may be metaphysical necessity, but we can't know much about it, and we are over-confident in assessing it.
11. Knowledge Aims / A. Knowledge / 2. Understanding
All understanding is an immediate apprehension of the causal relation [Schopenhauer]
     Full Idea: All understanding is an immediate apprehension of the causal relation.
     From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.IV)
     A reaction: Based, I take it, on Hume. Presumably he means a posteriori understanding, as it hardly fits an understanding of arithmetic. Understanding needs more than just causation. What aspects of causation?
16. Persons / C. Self-Awareness / 2. Knowing the Self
What we know in ourselves is not a knower but a will [Schopenhauer]
     Full Idea: What we know in ourselves is never what knows, but what wills, the will.
     From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.VII)
     A reaction: An interesting slant on Hume's scepticism about personal identity. Hume was hunting for a thing-which-experiences. If he had sought his will, he might have spotted it.
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer]
     Full Idea: The identity of the subject of willing with that of knowing by virtue whereof ...the word 'I' includes and indicates both, is the knot of the world, and hence inexplicable.
     From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], p.211-2), quoted by Christopher Janaway - Schopenhauer 4 'Self'
     A reaction: I'm struggling to see this as a deep mystery. If we look objectively at animals and ask 'what is their brain for?' the answer seems obvious. This may be a case of everything looking mysterious after a philosopher has stared at it for a while.
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer]
     Full Idea: Time may be defined as the possibility of mutually exclusive conditions of the same thing.
     From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.IV)
     A reaction: An off-beat philosophical view of the question. Sounds more like a consequence of time than its essential nature.