Combining Texts

All the ideas for 'Mathematics without Numbers', 'reports' and 'Concepts of supervenience'

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7 ideas

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?

7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience

3536	Supervenient properties must have matching base properties [Kim]
	Full Idea: Each supervenient property necessarily has a coextensive property in the base family.
	From: Jaegwon Kim (Concepts of supervenience [1984], §5)
	A reaction: This is presumably the minimum requirement for a situation of supervenience. How do you decide which property is the 'base' property? Do we just mean that the base causes the other, but not vice versa?

16. Persons / E. Rejecting the Self / 4. Denial of the Self

5517	Individuals don't exist, but are conventional names for sets of elements [Buddha]
	Full Idea: There exists no individual, it is only a conventional name given to a set of elements.
	From: Buddha (Siddhartha Gautama) (reports [c.540 BCE]), quoted by Derek Parfit - The Unimportance of Identity p.295
	A reaction: I take this to arise from an excessively spiritual concept of a human being, which faces Descartes' problem of how to individuate non-physical minds, when they have no clear boundaries. Combine dualism with a bundle theory, and you have Buddhism.

29. Religion / C. Spiritual Disciplines / 3. Buddhism

7600	The Buddha believed the gods would eventually disappear, and Nirvana was much higher [Buddha, by Armstrong,K]
	Full Idea: The Buddha believed implicitly in the gods because they were part of his cultural baggage, but they were involved in the cycle of rebirth, and would eventually disappear; the ultimate reality of Nirvana was higher than the gods.
	From: report of Buddha (Siddhartha Gautama) (reports [c.540 BCE]) by Karen Armstrong - A History of God Ch.1
	A reaction: We might connect this with Plato's Euthyphro question (Ideas 336 and 337), and the relationship between piety and morality on the one hand, and the gods on the other.

7601	Life is suffering, from which only compassion, gentleness, truth and sobriety can save us [Buddha]
	Full Idea: Buddha taught that the only release from 'dukkha' (the meaningless flux of suffering which is human life) is a life of compassion for all living beings, speaking and behaving gently, kindly and accurately, and refraining from all intoxicants.
	From: Buddha (Siddhartha Gautama) (reports [c.540 BCE], Ch.1), quoted by Karen Armstrong - A History of God Ch.1
	A reaction: Christians are inclined to give the impression that Jesus invented the idea of being nice, but it ain't so. The obvious thought is that the Buddha seems to be focusing on the individual, but this is actually a formula for a better community.