Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'How to Make our Ideas Clear' and 'Mathematics without Numbers'

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8 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth

7661	Truth is the opinion fated to be ultimately agreed by all investigators [Peirce]
	Full Idea: The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real.
	From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.38)
	A reaction: At least this affirms that truth is an ideal about which we dream, and is not confined merely to what we can actually know. But it rules out anything beyond the reach of all investigation, which seems a misconception of truth. What could angels know?

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

8698	Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
	Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
	From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
	A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?

9557	Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
	Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort.
	From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3
	A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world).

10263	Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
	Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
	From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
	A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?

11. Knowledge Aims / A. Knowledge / 2. Understanding

19089	Our whole conception of an object is its possible practical consequences [Peirce]
	Full Idea: Consider what effects, which might conceivably have practical bearings, we conceive the objects of our conceptions to have. Then, our conception of these effects is the whole of our conception of the object.
	From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], EP i.132), quoted by Albert Atkin - Peirce 2 'early'
	A reaction: This is his 1878 version, which was fine-tuned later in life. He seems to have extended his principle to include possibilities, as well as the mere objects. That is, he moved beyond mere nominalism.

11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs

7660	We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce]
	Full Idea: A belief has just three properties: first, it is something that we are aware of; second, it appeases the irritation of doubt; and, third, it involves the establishment in our nature of a rule of action, or, say for short, a habit.
	From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.28)
	A reaction: Peirce probably believed that Bismarck breathed oxygen, but was unaware of his belief, and no one ever dreamed of acting on such a belief, unless Bismarck was gasping for air.

19. Language / A. Nature of Meaning / 5. Meaning as Verification

14906	Non-positivist verificationism says only take a hypothesis seriously if it is scientifically based and testable [Ladyman/Ross on Peirce]
	Full Idea: With Peirce, we endorse a non-positivist version of verificationism - no hypothesis should be taken seriously if apparently beyond our capacity to investigate, and serious metaphysics must concern at least two plausible scientific hypotheses.
	From: comment on Charles Sanders Peirce (How to Make our Ideas Clear [1878]) by J Ladyman / D Ross - Every Thing Must Go 1.3
	A reaction: [compressed] They say this is NOT a theory about meaning, as 'The Big Bang was caused by Elvis' is perfectly meaningful. Verificationism always seems to rule out bold speculation. Don't say 'take string theory seriously', if we can't test it?

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').