9 ideas
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. |
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? |
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') |
13795 | Properties only have identity in the context of their contraries [Elder] |
Full Idea: The very being, the identity, of any property consists at least in part in its contrasting as it does with its own proper contraries. | |
From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.4) | |
A reaction: See Elder for the details of this, but the idea that properties can only be individuated contextually sounds promising. |
13798 | Maybe we should give up the statue [Elder] |
Full Idea: Some contemporary metaphysicians infer that one of the objects must go, namely, the statue. | |
From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 7.2) | |
A reaction: [He cites Zimmerman 1995] This looks like a recipe for creating a vast gulf between philosophers and the rest of the population. If it is right, it makes the true ontology completely useless in understanding our daily lives. |
13797 | The loss of an essential property means the end of an existence [Elder] |
Full Idea: The loss of any essential property must amount to the end of an existence. | |
From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
A reaction: This is orthodoxy for essentialists, and I presume that Aristotle would agree, but I have a problem with the essence of a great athlete, who then grows old. Must we say that they lose their identity-as-an-athlete? |
13794 | Essential properties by nature occur in clusters or packages [Elder] |
Full Idea: Essential properties by nature occur in clusters or packages. | |
From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.2) | |
A reaction: Elder proposes this as his test for the essentialness of a property - his Test of Flanking Uniformities. A nice idea. |
13796 | Essential properties are bound together, and would be lost together [Elder] |
Full Idea: The properties of any essential nature are bound together....[122] so any case in which one of our envisioned familiar objects loses one of its essential properties will be a case in which it loses several. | |
From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
A reaction: This sounds like a fairly good generalisation rather than a necessary truth. Is there a natural selection for properties, so that only the properties which are able to bind to others to form teams are able to survive and flourish? |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |