12 ideas
| 6627 | Radical pragmatists abandon the notion of truth [Stich, by Lowe] |
| Full Idea: Some radical pragmatists, such as Stich, are ready to abandon the notion of truth. | |
| From: report of Stephen P. Stich (The Fragmentation of Reason [1990]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.3 n18 | |
| A reaction: Such a proposal strikes me as silly (unless the vacuum left by truth can be filled by something better than just the test of whether 'it works'). It currently strikes me that pragmatism has a sane wing (led by Peirce), and a mad wing. |
| 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) |
| 13536 | Skolem did not believe in the existence of uncountable sets [Skolem] |
| Full Idea: Skolem did not believe in the existence of uncountable sets. | |
| From: Thoralf Skolem (works [1920], 5.3) | |
| A reaction: Kit Fine refers somewhere to 'unrepentent Skolemites' who still hold this view. |
| 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) |
| 13795 | Properties only have identity in the context of their contraries [Elder] |
| Full Idea: The very being, the identity, of any property consists at least in part in its contrasting as it does with its own proper contraries. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.4) | |
| A reaction: See Elder for the details of this, but the idea that properties can only be individuated contextually sounds promising. |
| 13798 | Maybe we should give up the statue [Elder] |
| Full Idea: Some contemporary metaphysicians infer that one of the objects must go, namely, the statue. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 7.2) | |
| A reaction: [He cites Zimmerman 1995] This looks like a recipe for creating a vast gulf between philosophers and the rest of the population. If it is right, it makes the true ontology completely useless in understanding our daily lives. |
| 13797 | The loss of an essential property means the end of an existence [Elder] |
| Full Idea: The loss of any essential property must amount to the end of an existence. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
| A reaction: This is orthodoxy for essentialists, and I presume that Aristotle would agree, but I have a problem with the essence of a great athlete, who then grows old. Must we say that they lose their identity-as-an-athlete? |
| 13794 | Essential properties by nature occur in clusters or packages [Elder] |
| Full Idea: Essential properties by nature occur in clusters or packages. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 2.2) | |
| A reaction: Elder proposes this as his test for the essentialness of a property - his Test of Flanking Uniformities. A nice idea. |
| 13796 | Essential properties are bound together, and would be lost together [Elder] |
| Full Idea: The properties of any essential nature are bound together....[122] so any case in which one of our envisioned familiar objects loses one of its essential properties will be a case in which it loses several. | |
| From: Crawford L. Elder (Real Natures and Familiar Objects [2004], 3) | |
| A reaction: This sounds like a fairly good generalisation rather than a necessary truth. Is there a natural selection for properties, so that only the properties which are able to bind to others to form teams are able to survive and flourish? |
| 4765 | Stich accepts eliminativism (labelled 'pragmatism') about rationality and normativity [Stich, by Engel] |
| Full Idea: Stich accepts a form of eliminativism (which he calls 'pragmatism') about rationality and normativity generally. | |
| From: report of Stephen P. Stich (The Fragmentation of Reason [1990]) by Pascal Engel - Truth §5.3 | |
| A reaction: This seems to be the correct position for a Humean empiricist connectionist. Presumably he has some good reasons for eliminating rationality. |