8 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') |
| 14794 | Instead of seeking Truth, we should seek belief that is beyond doubt [Peirce] |
| Full Idea: Your problems would be greatly simplified, if, instead of saying that you want to know the Truth, you were simply to say that you want to attain a state of belief unassailable beyond doubt. | |
| From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) | |
| A reaction: This is not the same as saying that belief beyond doubt IS truth. He is merely offering a strategy for scientists to side-step the sort of scepticism raised by Descartes and radical empiricists. |
| 14792 | A 'conception', the rational implication of a word, lies in its bearing upon the conduct of life [Peirce] |
| Full Idea: The present writer framed the theory that a 'conception', that is, the rational purport of a word or other expression, lies exclusively in its conceivable bearing upon the conduct of life. | |
| From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) |
| 14793 | The definition of a concept is just its experimental implications [Peirce] |
| Full Idea: If one can define accurately all the conceivable experimental phenomena which the affirmation or denial of a concept could imply, one will have therein a complete definition of the concept, and there is absolutely nothing more in it. | |
| From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) | |
| A reaction: Strictly, I would have thought you could only affirm or deny a complete proposition, rather than a concept. What should I do with the concept of a 'unicorn'? Note that all theories, such as empiricism or pragmatism, begin with an account of our concepts. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |