Combining Texts

All the ideas for 'Isagoge ('Introduction')', 'Of the Laws of Ecclesiastical Polity' and 'Mathematics without Numbers'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

8 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?

8. Modes of Existence / D. Universals / 1. Universals

15034	Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry]
	Full Idea: I shall beg off talking of a) whether genera and species are real or situated in bare thoughts alone, b) whether as real they are bodies or incorporeals, and c) whether they are separated or in sensibles and have their reality in connection with them.
	From: Porphyry (Isagoge ('Introduction') [c.295], (2))
	A reaction: This passage, picking up on Aristotle, seems to be the original source that grew into the medievel debate about universals. It seems to rather neatly lay out the agenda for the universals debate which is still with us.

25. Social Practice / C. Rights / 1. Basis of Rights

19896	It is not a law if not endorsed by the public [Hooker,R]
	Full Idea: Laws they are not which public approbation hath not made so.
	From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], I s.10), quoted by John Locke - Second Treatise of Government 134 n1
	A reaction: Margaret Thatcher's Poll Tax, rejected by public rebellion, illustrates the point.

25. Social Practice / D. Justice / 2. The Law / b. Rule of law

19891	Rule of law is superior to autonomy, because citizens can see what is expected [Hooker,R]
	Full Idea: Men saw that to live by one man's will became the cause of all men's misery. This contrained them to come unto laws wherein all men might see their duty beforehand, and know the penalties of transgressing them.
	From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], I s.10), quoted by John Locke - Second Treatise of Government 111 n1
	A reaction: One British school has a single rule, that pupils 'shall always treat other people with respect'. Presumably the rulers, as well as the pupils, must decide when this is transgressed. The rule of law may be preferable.

25. Social Practice / D. Justice / 2. The Law / c. Natural law

19897	Human laws must accord with the general laws of Nature [Hooker,R]
	Full Idea: Laws human must be made according to the general laws of Nature.
	From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], III s.9), quoted by John Locke - Second Treatise of Government
	A reaction: The point simply seems to be that they won't get assent from the public if they are not in accord with natural justice. Positivists say you can make any damned law you like.

26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws

17005	Natural things observe certain laws, and things cannot do otherwise if they retain their forms [Hooker,R]
	Full Idea: Things natural …do so necessarily observe their certain laws, that as long as they keep those forms which give them their being they cannot possibly be apt or inclinable to do otherwise than they do.
	From: Richard Hooker (Of the Laws of Ecclesiastical Polity [1593], 1.3.4), quoted by Marc Lange - Laws and Lawmakers 1.2
	A reaction: Cited by some as the beginnings of the idea of 'laws of nature', but it is striking that Hooker says the laws are controlled by 'forms' (which are Aristotelian essences). This is an essentialist view of laws, not a regularity or divine power one.