Combining Philosophers

All the ideas for Speussipus, Geoffrey Hellman and Ramon

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9 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

19369	Lull's combinatorial art would articulate all the basic concepts, then show how they combine [Lull, by Arthur,R]
	Full Idea: Lull proposed a combinatorial art. He wanted to reconcile Islam and Christianity by articulating the basic concepts that their belief systems held in common, and then inventing a device that would allow these concepts to be combined.
	From: report of Ramon (Ars Magna [1305]) by Richard T.W. Arthur - Leibniz 2 Intro
	A reaction: Leibniz's Universal Characteristic was an attempt at continuing Lull's project. Lull's plan rested on Aristotle's categories.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

8921	Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
	Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do.
	From: Geoffrey Hellman (Structuralism [2007], §1)
	A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed.

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?

8922	Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
	Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'.
	From: Geoffrey Hellman (Structuralism [2007], §1)
	A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics.

9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance

594	Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
	Full Idea: Speusippus suggested principles for each substance, including principles for numbers, magnitude and the soul. He thus arrived at no mean list of substances.
	From: report of Speussipus (thirty titles (lost) [c.367 BCE]) by Aristotle - Metaphysics 1028b

28. God / A. Divine Nature / 3. Divine Perfections

19371	Nine principles of God: goodness, greatness, eternity, power, wisdom, will, virtue, truth and glory [Lull, by Arthur,R]
	Full Idea: Lull restricted himself to only nine 'absolute principles' of God: goodness, greatness, eternity, power, wisdom, will, virtue, truth and glory
	From: report of Ramon (Ars Magna [1305]) by Richard T.W. Arthur - Leibniz 2 'Combinatorics'
	A reaction: Leibniz responded that God's perfections are infinite in number, and thus beyond human comprehension. Lull cut them down to nine, because he was designing a sort of conceptual logic that employed them.

28. God / C. Attitudes to God / 5. Atheism

2632	Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]
	Full Idea: Speusippus, following his uncle Plato, held that all things were governed by some kind of animal force, and tried to eradicate from our minds any notion of the gods.
	From: report of Speussipus (thirty titles (lost) [c.367 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.33