Combining Texts

All the ideas for 'Propositional Objects', 'Two Problems of Epistemology' and 'The Foundations of Mathematics'

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6 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

18844	You would cripple mathematics if you denied Excluded Middle [Hilbert]
	Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists.
	From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4
	A reaction: [p.476 in Van Heijenoort]

11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism

18969	How do you distinguish three beliefs from four beliefs or two beliefs? [Quine]
	Full Idea: Suppose I say that I have given up precisely three beliefs since lunch. An over-coarse individuation could reduce the number to two, and an over-fine one could raise it to four.
	From: Willard Quine (Propositional Objects [1965], p.144)
	A reaction: Obviously if you ask how many beliefs I hold, it would be crazy to give a precise answer. But if I search for my cat, I give up my belief that it is in the kitchen, in the lounge and in the bathroom. That's precise enough to be three beliefs, I think.

14. Science / A. Basis of Science / 6. Falsification

18284	Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
	Full Idea: Whereas particular reality statements are in principle completely verifiable or falsifiable, things are different for general reality statements: they can indeed be conclusively falsified, they can acquire a negative truth value, but not a positive one.
	From: Karl Popper (Two Problems of Epistemology [1932], p.256), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 18 'Laws'
	A reaction: This sounds like a logician's approach to science, but I prefer to look at coherence, where very little is actually conclusive, and one tinkers with the theory instead.

19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense

18967	A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine]
	Full Idea: A 'proposition' is the meaning of a sentence. More precisely, since propositions are supposed to be true or false once and for all, it is the meaning of an eternal sentence. More precisely still, it is the 'cognitive' meaning, involving truth, not poetry.
	From: Willard Quine (Propositional Objects [1965], p.139)
	A reaction: Quine defines this in order to attack it. I equate a proposition with a thought, and take a sentence to be an attempt to express a proposition. I have no idea why they are supposed to be 'timeless'. Philosophers have some very odd ideas.

19. Language / D. Propositions / 6. Propositions Critique

18968	The problem with propositions is their individuation. When do two sentences express one proposition? [Quine]
	Full Idea: The trouble with propositions, as cognitive meanings of eternal sentences, is individuation. Given two eternal sentences, themselves visibly different linguistically, it is not sufficiently clear under when to say that they mean the same proposition.
	From: Willard Quine (Propositional Objects [1965], p.140)
	A reaction: If a group of people agree that two sentences mean the same thing, which happens all the time, I don't see what gives Quine the right to have a philosophical moan about some dubious activity called 'individuation'.

27. Natural Reality / C. Space / 3. Points in Space

18970	The concept of a 'point' makes no sense without the idea of absolute position [Quine]
	Full Idea: Unless we are prepared to believe that absolute position makes sense, the very idea of a point as an entity in its own right must be rejected as not merely mysterious but absurd.
	From: Willard Quine (Propositional Objects [1965], p.149)
	A reaction: The fact that without absolute position we can only think of 'points' as relative to a conceptual grid doesn't stop the grid from picking out actual locations in space, as shown by latitude and longitude.