14 ideas
| 14775 | Numbers are just names devised for counting [Peirce] |
| Full Idea: Numbers are merely a system of names devised by men for the purpose of counting. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
| A reaction: This seems a perfectly plausible view prior to the advent of Cantor, set theory and modern mathematical logic. I suppose the modern reply to this is that Peirce may be right about origin, but that men thereby stumbled on an Aladdin's Cave of riches. |
| 14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
| Full Idea: To say that 'if' there are two persons and each person has two eyes there 'will be' four eyes is not a statement of fact, but a statement about the system of numbers which is our own creation. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
| A reaction: One eye for each arm of the people is certainly a fact. Frege uses this equivalence to build numbers. I think Peirce is wrong. If it is not a fact that these people have four eyes, I don't know what 'four' means. It's being two pairs is also a fact. |
| 12432 | Explanation of necessity must rest on something necessary or something contingent [Hale] |
| Full Idea: The dilemma is that to give the ultimate source of any necessity, we must either appeal to something which could not have been otherwise (i.e. is itself necessary), or advert to something which could have been otherwise (i.e. is itself merely contingent). | |
| From: Bob Hale (The Source of Necessity [2002], p.301) | |
| A reaction: [Hale is summarising Blackburn's view, and going on to disagree with it] Hale looks for a third way, but Blackburn seems to face us with quite a plausible dilemma. |
| 12434 | Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale] |
| Full Idea: We must distinguish between explaining particular necessities and explaining necessity in general; and we ought to distinguish between explaining, in regard to any necessary truth, why it is true, and explaining why it is necessary. | |
| From: Bob Hale (The Source of Necessity [2002], p.308) | |
| A reaction: Useful. The pluralist view I associate with Fine says we can explain types of necessity, but not necessity in general. If we seek truthmakers, there is a special case of what adds the necessity to the truth. |
| 12435 | The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale] |
| Full Idea: My claim is that there are non-transitive explanations of necessities, where what explains is indeed necessary, but what explains the necessity of the explanandum is not the explanation's necessity, but its truth simpliciter. | |
| From: Bob Hale (The Source of Necessity [2002], p.311) | |
| A reaction: The big idea is to avoid a regress of necessities. The actual truths he proposes are essentialist. An interesting proposal. It might depend on how one views essences (as giving identity, or causal power) |
| 12433 | If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale] |
| Full Idea: If the alleged necessity, e,g, 2+2=4, really does depend upon a convention governing the use of the words in which we state it, and the existence of that convention is merely a contingent matter, then it can't after all be necessary. | |
| From: Bob Hale (The Source of Necessity [2002], p.302) | |
| A reaction: [Hale is citing Blackburn for this claim] Hale suggests replies, by keeping truth and meaning separate, and involving laws of logic. Blackburn clearly has a good point. |
| 12436 | Concept-identities explain how we know necessities, not why they are necessary [Hale] |
| Full Idea: It seems to me that identity-relations among concepts have more to do with explaining how we know that vixens are female foxes etc., than with explaining why it is necessary, and, more generally, with explaining why some necessities are knowable a priori. | |
| From: Bob Hale (The Source of Necessity [2002], P.313) | |
| A reaction: Hale rejects the conceptual and conventional accounts of necessity, in favour of the essentialist view. This strikes me as a good suggestion of Hale's, since I agree with him about the essentialism. |
| 14770 | Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce] |
| Full Idea: All positive reasoning is judging the proportion of something in a whole collection by the proportion found in a sample. Hence we can never hope to attain absolute certainty, absolute exactitude, absolute universality. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
| A reaction: This is the basis of Peirce's fallibilism - that all 'positive' reasoning (whatever that it?) is based on statistical induction. I'm all in favour of fallibilism, but find Peirce's claim to be a bit too narrow. He was too mesmerised by physical science. |
| 14774 | Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce] |
| Full Idea: It seems to me there is the most historic proof that innate truths are particularly uncertain and mixed up with error, and therefore a fortiori not without exception. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |
| Full Idea: A truth which rests on the authority of inspiration only is of a somewhat incomprehensible nature; and we can never be sure that we rightly comprehend it. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
| Full Idea: Even if we decide that an idea really is inspired, we cannot be sure, or nearly sure, that the statement is true. We know one of the commandments of the Bible was printed without a 'not' in it. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 14771 | Only reason can establish whether some deliverance of revelation really is inspired [Peirce] |
| Full Idea: We never can be absolutely certain that any given deliverance [of revelation] really is inspired; for that can only be established by reasoning. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 14769 | Only imagination can connect phenomena together in a rational way [Peirce] |
| Full Idea: We can stare stupidly at phenomena; but in the absence of imagination they will not connect themselves together in any rational way. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], I) | |
| A reaction: The importance of this is its connection between imagination and 'rational' understanding. This is an important corrective to a crude traditional picture of the role of imagination. I would connect imagination with counterfactuals and best explanation. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |