9 ideas
| 7661 | Truth is the opinion fated to be ultimately agreed by all investigators [Peirce] |
| Full Idea: The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. | |
| From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.38) | |
| A reaction: At least this affirms that truth is an ideal about which we dream, and is not confined merely to what we can actually know. But it rules out anything beyond the reach of all investigation, which seems a misconception of truth. What could angels know? |
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 19089 | Our whole conception of an object is its possible practical consequences [Peirce] |
| Full Idea: Consider what effects, which might conceivably have practical bearings, we conceive the objects of our conceptions to have. Then, our conception of these effects is the whole of our conception of the object. | |
| From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], EP i.132), quoted by Albert Atkin - Peirce 2 'early' | |
| A reaction: This is his 1878 version, which was fine-tuned later in life. He seems to have extended his principle to include possibilities, as well as the mere objects. That is, he moved beyond mere nominalism. |
| 7660 | We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce] |
| Full Idea: A belief has just three properties: first, it is something that we are aware of; second, it appeases the irritation of doubt; and, third, it involves the establishment in our nature of a rule of action, or, say for short, a habit. | |
| From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.28) | |
| A reaction: Peirce probably believed that Bismarck breathed oxygen, but was unaware of his belief, and no one ever dreamed of acting on such a belief, unless Bismarck was gasping for air. |
| 14906 | Non-positivist verificationism says only take a hypothesis seriously if it is scientifically based and testable [Ladyman/Ross on Peirce] |
| Full Idea: With Peirce, we endorse a non-positivist version of verificationism - no hypothesis should be taken seriously if apparently beyond our capacity to investigate, and serious metaphysics must concern at least two plausible scientific hypotheses. | |
| From: comment on Charles Sanders Peirce (How to Make our Ideas Clear [1878]) by J Ladyman / D Ross - Every Thing Must Go 1.3 | |
| A reaction: [compressed] They say this is NOT a theory about meaning, as 'The Big Bang was caused by Elvis' is perfectly meaningful. Verificationism always seems to rule out bold speculation. Don't say 'take string theory seriously', if we can't test it? |
| 12709 | Motion is not absolute, but consists in relation [Leibniz] |
| Full Idea: In reality motion is not something absolute, but consists in relation. | |
| From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
| A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity. |