Combining Texts

All the ideas for 'fragments/reports', 'works' and 'Remarks on the definition and nature of mathematics'

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6 ideas

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

17807	To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
	Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
	A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17806	It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
	Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
	A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17808	Saying mathematics is logic is merely replacing one undefined term by another [Curry]
	Full Idea: To say that mathematics is logic is merely to replace one undefined term by another.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics')

13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention

1556	By nature people are close to one another, but culture drives them apart [Hippias]
	Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature.
	From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8

22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics

20739	Levinas took 'first philosophy' to begin with seeing the vulnerable faces of others [Levinas, by Aho]
	Full Idea: Levinas forwarded a notion of 'ethics as first philosophy' that begins from the concete exposure and openness to 'the face' of the other, an experience of vulnerability and suffering that undercuts our ordinary egoistic and objectifying tendencies.
	From: report of Emmanuel Levinas (works [1956]) by Kevin Aho - Existentialism: an introduction 1 'Existentialism'
	A reaction: Iris Murdoch speaks of seeing a falcon in flight as having a similar effect of diminishing the ego. If the main focus is on potential 'suffering' does this eventually cash out as utilitarianism? I bet not!

24. Political Theory / D. Ideologies / 9. Communism

20445	Levinas says Marxism is the replacement of individualist ethics, by solidarity and sociality [Levinas, by Critchley]
	Full Idea: For Levinas, Marxism is the absorption of the ethical in the socioeconomic, and so it is the disappearance of the face-to-face relation and the privileging of relations of solidarity and anonymous sociality, which he calls 'socialism'.
	From: report of Emmanuel Levinas (works [1956]) by Simon Critchley - Impossible Objects: interviews 1
	A reaction: Startling, if you are not used to this sort of thing. If you are in trouble, I should help you, not because you are you, or a human being, but because you are a member of my group? So what about the Good Samaritan? Or solidarity with humanity? Animals?