7 ideas
| 16519 | No one can conceive of a possible substance, apart from those which God has created [Arnauld] |
| Full Idea: I am much mistaken if there is anyone who dares to say that he can conceive of a purely possible substance, …for although one talks so much of them, one never conceives them except according to the notion of those which God has created. | |
| From: Antoine Arnauld (Letters to Leibniz [1686], 1686.05.13), quoted by David Wiggins - Sameness and Substance 4.2 | |
| A reaction: This idea cashes out in the 'necessitism' of Tim Williamson, and views on the Barcan formulae in modal logic. |
| 17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
| Full Idea: In 1846 De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated 'universe of discourse'. It replaced Boole's original - and metaphysically a bit suspect - universe of 'all things'. | |
| From: report of Augustus De Morgan (works [1846]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 | |
| A reaction: This not only brings formal logic under control, but also reflects normal talk, because there is always an explicit or implicit domain of discourse when we talk. Of virtually any conversation, you can say what it is 'about'. |
| 10735 | Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach] |
| Full Idea: For an understanding of arithmetic the grasp of an operation's being performed 'so many times' is quite indispensable; and abstraction of a feature from groups of nuts cannot give us this grasp. | |
| From: Peter Geach (Abstraction Reconsidered [1983], p.170) | |
| A reaction: I end up defending the empirical approach to arithmetic because remarks like this are so patently false. Geach seems to think we arrive ready-made in the world, just raring to get on with some counting. He lacks the evolutionary perspective. |
| 10732 | If concepts are just recognitional, then general judgements would be impossible [Geach] |
| Full Idea: If concepts were nothing but recognitional capacities, then it is unintelligible that I can judge that cats eat mice when neither of them are present. | |
| From: Peter Geach (Abstraction Reconsidered [1983], p.164) | |
| A reaction: Having observed the importance of recognition for the abstractionist (Idea 10731), he then seems to assume that there is nothing more to their concepts. Geach fails to grasp levels of abstraction, and cross-reference, and generalisation. |
| 10731 | For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach] |
| Full Idea: For abstractionists, concepts are essentially capacities for recognizing recurrent features of the world. | |
| From: Peter Geach (Abstraction Reconsidered [1983], p.163) | |
| A reaction: Recognition certainly strikes me as central to thought (and revelatory of memory, since we continually recognise what we cannot actually recall). Geach dislikes this view, but I see it as crucial to an evolutionary view of thought. |
| 10733 | The abstractionist cannot explain 'some' and 'not' [Geach] |
| Full Idea: The abstractionist cannot give a logically coherent account of the features that are supposed to be reached by discriminative attention, corresponding to the words 'some' and 'not'. | |
| From: Peter Geach (Abstraction Reconsidered [1983], p.167) | |
| A reaction: I understand 'some' in terms of mereology, because that connects to experience, and 'not' I take to derive more from psychological experience than from the physical world, building on thwarted expectation, which even animals experience. |
| 10734 | Only a judgement can distinguish 'striking' from 'being struck' [Geach] |
| Full Idea: To understand the verb 'to strike' we must see that 'striking' and 'being struck' are different, but necessarily go together in event and thought; only in the context of a judgment can they be distinguished, when we think of both together. | |
| From: Peter Geach (Abstraction Reconsidered [1983], p.168) | |
| A reaction: Geach seems to have a strange notion that judgements are pure events which can precede all experience, and are the only ways we can come to understand experience. He needs to start from animals (or 'brutes', as he still calls them!). |