Combining Texts

All the ideas for 'Necessary Existents', 'Mathematics without Numbers' and 'Experience First (and reply)'

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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?

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

19542	It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew]
	Full Idea: The proposition that understanding does not involve knowledge is widespread (for example, in discussions of what philosophy aims at), but hardly withstands scrutiny. If you do not know how a jet engine works, you do not understand how it works.
	From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.24)
	A reaction: This seems a bit disingenuous. As in 'Theaetetus', knowing the million parts of a jet engine is not to understand it. More strongly - how could knowledge of an infinity of separate propositional truths amount to understanding on their own?

19543	To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew]
	Full Idea: An essential prerequisite for useful discussion of the relation between knowledge and understanding is systematic explicitness about what is to be known or understood.
	From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.25)
	A reaction: This is better. I say what needs to be known for understanding is the essence of the item under discussion (my PhD thesis!). Obviously understanding needs some knowledge, but I take it that epistemology should be understanding-first. That is the main aim.

11. Knowledge Aims / A. Knowledge / 7. Knowledge First

19541	Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew]
	Full Idea: If we say our cognitive aim is to get knowledge, the opposing views are the naturalistic view that what matters is just true belief (or just 'getting by'), or that there are rival epistemic goods such as understanding and wisdom.
	From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.17)
	A reaction: [compressed summary] I'm a fan of understanding. The accumulation of propositional knowledge would relish knowing the mass of every grain of sand on a beach. If you say the propositions should be 'important', other values are invoked.

19. Language / D. Propositions / 3. Concrete Propositions

19216	Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
	Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist?
	From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions
	A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done?