9 ideas
| 14779 | I reason in order to avoid disappointment and surprise [Peirce] |
| Full Idea: I do not reason for the sake of my delight in reasoning, but solely to avoid disappointment and surprise. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: Hence Peirce places more emphasis on inductive and abductive reasoning than on deductive reasoning. I have to agree with him. Anyone account of why we reason must have an evolutionary framework. What advantage does reason bestow? It concerns the future. |
| 14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
| Full Idea: Either J and the judgment 'I say that J is true' are the same for all judgments or for none. But if identical, their denials are identical. These are 'J is not true' and 'I do not say that J is true', which are different. No judgment judges itself true. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: If you are going to espouse the Ramseyan redundancy view of truth, you had better make sure you are not guilty of the error which Peirce identifies here. |
| 14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
| Full Idea: It is foolish to study logic unless one is persuaded that one's own reasonings are more or less bad. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], II) |
| 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? |
| 14778 | Facts are hard unmoved things, unaffected by what people may think of them [Peirce] |
| Full Idea: Facts are hard things which do not consist in my thinking so and so, but stand unmoved by whatever you or I or any man or generations of men may opine about them. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: This is my view of facts, with which I am perfectly happy, for all the difficulties involved in individuating facts, and in disentangling them from our own modes of thought and expression. Let us try to establish the facts. |
| 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. |
| 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. |