7 ideas
| 6710 | You can only define a statement that something is 'true' by referring to its functional possibilities [James] |
| Full Idea: Pragmatism insists that statements and beliefs are inertly and statically true only by courtesy: they practically pass for true; but you cannot define what you mean by calling them true without referring to their functional possibilities. | |
| From: William James (The Meaning of the Word "Truth" [1907], p.2) | |
| A reaction: I think this clarifies an objection to pragmatism, because all functional definitions (e.g. of the mind, or of moral behaviour) are preceded by the question of WHY this thing is able to function in this way. What special quality makes this possible? |
| 22305 | If the hypothesis of God is widely successful, it is true [James] |
| Full Idea: On pragmatistic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, it is true. | |
| From: William James (The Meaning of the Word "Truth" [1907], p.299), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 35 'Prag' | |
| A reaction: How you get from 'widely satisfactory' to 'true' is beyond my comprehension. This is dangerous nonsense. This view of truth seems to be a commonplace in American culture. Peirce hurray! James boo! James accepted verification, where possible. |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| Full Idea: Zermelo's paper sets out to show that the standard set-theoretic axioms (what he calls the 'constitutive axioms', thus the ZF axioms minus the axiom of infinity) have an unending sequence of different models, thus that they are non-categorical. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1209 | |
| A reaction: Hallett says later that Zermelo is working with second-order set theory. The addition of an Axiom of Infinity seems to have aimed at addressing the problem, and the complexities of that were pursued by Gödel. |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| Full Idea: Zermelo included Replacement in 1930, after it was noticed that the sequence of power sets was needed, and Replacement gave the ordinal form of the well-ordering theorem, and justification for transfinite recursion. | |
| From: report of Ernst Zermelo (On boundary numbers and domains of sets [1930]) by Penelope Maddy - Believing the Axioms I §1.8 | |
| A reaction: Maddy says that this axiom suits the 'limitation of size' theorists very well, but is not so good for the 'iterative conception'. |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| Full Idea: Two opposite tendencies of thought, the idea of creative advance and of collection and completion (underlying the Kantian 'antinomies') find their symbolic representation and their symbolic reconciliation in the transfinite numbers based on well-ordering. | |
| From: Ernst Zermelo (On boundary numbers and domains of sets [1930], §5) | |
| A reaction: [a bit compressed] It is this sort of idea, from one of the greatest set-theorists, that leads philosophers to think that the philosophy of mathematics may offer solutions to metaphysical problems. As an outsider, I am sceptical. |
| 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. |