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All the ideas for '', 'works' and 'Consciousness, Philosophy and Mathematics'

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7 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

11211	If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
	Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation.
	From: Ian Rumfitt ("Yes" and "No" [2000], II)
	A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11210	Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
	Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table.
	From: Ian Rumfitt ("Yes" and "No" [2000])
	A reaction: This is the standard view which Rumfitt sets out to challenge.

11212	The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
	Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious.
	From: Ian Rumfitt ("Yes" and "No" [2000], III)
	A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism

8728	Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
	Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.
	From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
	A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!

14. Science / B. Scientific Theories / 1. Scientific Theory

22363	You have only begun to do real science when you can express it in numbers [Kelvin]
	Full Idea: When you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.
	From: Lord Kelvin (Wm Thomson) (works [1881]), quoted by Reiss,J/Spreger,J - Scientific Objectivity 4.1
	A reaction: [Popular Lectures 1 p.73] Clearly the writer is a physicist! Astronomers discover objects, geologists discover structures, biologists reveal mechanisms.

19. Language / F. Communication / 3. Denial

11214	We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
	Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
	From: Ian Rumfitt ("Yes" and "No" [2000], IV)
	A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).

27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy

20644	Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]
	Full Idea: The name 'energy', first used by Thomas Young, has come into use after it was raised from a mere formula of mathematical dynamics to become a principle pervading all nature, and guiding every field of science.
	From: Lord Kelvin (Wm Thomson) (works [1881]), quoted by Peter Watson - Convergence 01 'Principle'
	A reaction: [bit compressed] As far as I can see energy behaves exactly as if it were a substance, like water conserved in rainfalls, and yet it isn't a stuff, and seems to result from a process of abstraction. I take it to be one of the biggest mysteries in physics.