8 ideas
18253 | I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege] |
Full Idea: You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities. | |
From: Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
A reaction: Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc. |
18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
Full Idea: With the loss of my Rule V, not only the foundations of arithmetic, but also the sole possible foundations of arithmetic, seem to vanish. | |
From: Gottlob Frege (Letters to Russell [1902], 1902.06.22) | |
A reaction: Obviously he was stressed, but did he really mean that there could be no foundation for arithmetic, suggesting that the subject might vanish into thin air? |
18269 | Logical objects are extensions of concepts, or ranges of values of functions [Frege] |
Full Idea: How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there? | |
From: Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr | |
A reaction: This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology. |
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. |