10 ideas
| 8250 | So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra] |
| Full Idea: Meinong has recently been credited with inspiring 'free logic': a logic without existence assumptions. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by George / Van Evra - The Rise of Modern Logic 8 | |
| A reaction: This would appear to be a bold escape from the quandries concerning the existential implications of quantifiers. I immediately find it very appealing. It seems to spell disaster for the Quinean program of deducing ontology from language. |
| 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') |
| 8719 | There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend] |
| Full Idea: Meinong (and Priest) leave room for impossible objects (like a mountain made entirely of gold), and even contradictory objects (such as a round square). This would have a property, of 'being a contradictory object'. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8 | |
| A reaction: This view is only possible with a rather lax view of properties. Personally I don't take 'being a pencil' to be a property of a pencil. It might be safer to just say that 'round squares' are possible linguistic subjects of predication. |
| 8971 | There are objects of which it is true that there are no such objects [Meinong] |
| Full Idea: There are objects of which it is true that there are no such objects. | |
| From: Alexius Meinong (The Theory of Objects [1904]), quoted by Peter van Inwagen - Existence,Ontological Commitment and Fictions p.131 | |
| A reaction: Van Inwagen say this idea is 'infamous', but Meinong is undergoing a revival, and commitment to non-existent objects may be the best explanation of some ways of talking. |
| 8718 | Meinong says an object need not exist, but must only have properties [Meinong, by Friend] |
| Full Idea: Meinong distinguished between 'existing objects' and 'subsisting objects', and being an object does not imply existence, but only 'having properties'. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8 | |
| A reaction: Meinong is treated as a joke (thanks to Russell), but this is good. "Father Christmas does not exist, but he has a red coat". He'd better have some sort of existy aspect if he is going to have a property. So he's 'an object'. 'Insubstantial'? |
| 7756 | Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan] |
| Full Idea: Meinong insisted (à la Anselm) that any possible object of thought - even a self-contradictory one - has being of a sort even though only a few such things are so lucky as to exist in reality as well. | |
| From: report of Alexius Meinong (The Theory of Objects [1904]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: ['This idea gave Russell fits' says Lycan]. In the English-speaking world this is virtually the only idea for which Meinong is remembered. Russell (Idea 5409) was happy for some things to merely 'subsist' as well as others which could 'exist'. |
| 15781 | The objects of knowledge are far more numerous than objects which exist [Meinong] |
| Full Idea: The totality of what exists, including what has existed and what will exist, is infinitely small in comparison with the totality of Objects of knowledge. | |
| From: Alexius Meinong (The Theory of Objects [1904]), quoted by William Lycan - The Trouble with Possible Worlds 01 | |
| A reaction: This is rather profound, but the word 'object' doesn't help. I would say 'What we know concerns far more than what merely exists'. |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |