display all the ideas for this combination of philosophers
5 ideas
| 17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
| Full Idea: The indispensability of arithmetical concepts is evidence that they do in fact accurately represent features of the independent world. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Intro) | |
| A reaction: This seems to me to be by far the best account of the matter. So why is the world so arithmetical? Dunno, mate; ask someone else. |
| 17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
| Full Idea: I propose that arithmetical truths are known through an examination of our own arithmetical concepts; that basic arithmetical concepts map the arithmetical structure of the world; that the map obtains in virtue of our normal sensory apparatus. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Pref) | |
| A reaction: She defends the nice but unusual position that arithmetical knowledge is both a priori and empirical (so that those two notions are not, as usually thought, opposed). I am a big Carrie Jenkins fan. |
| 17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
| Full Idea: A problem for the neo-Fregeans is that it has not proved easy to establish that Hume's Principle is analytic or definitive in the required sense. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.3) | |
| A reaction: It is also asked how we would know the principle, if it is indeed analytic or definitional (Jenkins p.119). |
| 22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter] |
| Full Idea: Gödel's theorem does not refute formalism outright, because the committed formalist need not recognise the metalinguistic notion of truth to which the theorem appeals. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 45 'Log') | |
| A reaction: The theorem was prior to Tarski's account of truth. Potter says Gödel avoided explicit mention of truth because of this problem. In general Gödel showed that there are truths outside the formal system (which is all provable). |
| 22298 | Why is fictional arithmetic applicable to the real world? [Potter] |
| Full Idea: Fictionalists struggle to explain why arithmetic is applicable to the real world in a way that other stories are not. | |
| From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Math') | |
| A reaction: We know why some novels are realistic and others just the opposite. If a novel aimed to 'model' the real world it would be even closer to it. Fictionalists must explain why some fictions are useful. |