display all the ideas for this combination of texts
4 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. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 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). |