17 ideas
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michčle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 23805 | Some explanations offer to explain a mystery by a greater mystery [Schulte] |
| Full Idea: An 'obscurum per obscurius' explanation is explaining something mysterious by something even more mysterious, | |
| From: Peter Schulte (Mental Content [2023], 6) | |
| A reaction: Schulte's example is trying to explain mental content in terms of phenomenal experience. That is, roughly, explaining content by qualia, when the latter is the 'hard problem'. |
| 23792 | Phenomenal and representational character may have links, or even be united [Schulte] |
| Full Idea: Some theorists maintain that all states with representational content or intentionality must have phenomenal character …and we can also ask whether all states with phenomenal character also have representional content. | |
| From: Peter Schulte (Mental Content [2023], 2.4) | |
| A reaction: He mentions that beliefs could involve inner speech. And pains and moods may be phenomenal but lack content. He also asks which determines which. |
| 23795 | Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte] |
| Full Idea: A 'naturalistic' explanation of content excludes primitive mental or normative notions, but allows causation, counterfactual dependence, probabilistic dependence or structural similarity. | |
| From: Peter Schulte (Mental Content [2023], 4) | |
| A reaction: Apart from causation, what is permissible to naturalists (like me) all sounds rather superficial (and thus not very explanatory). I'm sure we can do better than this. How about using non-primitive mental notions? |
| 23804 | Maybe we can explain mental content in terms of phenomenal properties [Schulte] |
| Full Idea: The phenomenal intentionality approach says that the content properties of mental states can be explained in terms of the phenomenal properties of mental states. | |
| From: Peter Schulte (Mental Content [2023], 6) | |
| A reaction: [Searle and Loar are cited] Tends to be 'non-naturalistic'. We might decide that content derives from the phenomenal, but still without saying anything interesting about content. Mathematical content? Universally generalised content? |
| 23806 | Naturalist accounts of representation must match the views of cognitive science [Schulte] |
| Full Idea: Recent naturalisation of content now also has to offer a matching account of representational explanations in cognitive science. | |
| From: Peter Schulte (Mental Content [2023], 08.1) | |
| A reaction: [He cites Cummins, Neander and Shea] This is in addition to the 'status' and 'content' questions of Idea 23796. This seems to be an interesting shift to philosophers working backwards from the theories of empirical science. Few are qualified for this job! |
| 23793 | On the whole, referential content is seen as broad, and sense content as narrow [Schulte] |
| Full Idea: We can say that non-Fregean content [reference] is (virtually) always contrued as broad, while Fregean content [sense] is usually contrued as narrow. | |
| From: Peter Schulte (Mental Content [2023], 3.2) | |
| A reaction: I can't make sense of mental content actually being outside the mind, so I see all content as narrow - but that doesn't mean that externals are irrelevant to it. If I think that is an oak, and it's an elm, the content is oak. |
| 23796 | Naturalists must explain both representation, and what is represented [Schulte] |
| Full Idea: Naturalistic accounts of content ask 1) what makes a state qualify as a representational state?, and 2) what makes a representational state have one specific content rather than another? | |
| From: Peter Schulte (Mental Content [2023], 4) | |
| A reaction: [As often in this collection, the author uses algebraic letters, but I prefer plain English] I would say that the first question looks more amenable to an answer than the second. Do we know the neuronal difference between seeing red and blue? |
| 23802 | Conceptual role semantics says content is determined by cognitive role [Schulte] |
| Full Idea: Conceptual role semantics says the content of a representation is determined by the cognitive role it plays with a system. | |
| From: Peter Schulte (Mental Content [2023], 4.5) | |
| A reaction: Obvious problem: if 'swordfish' is the password, its role is quite different from its content. I've never thought that the role of something tells you anything about what it is. Hearts pump blood, but how do they fulfil that role? |
| 23797 | Cause won't explain content, because one cause can produce several contents [Schulte] |
| Full Idea: A simple causal theory of content has the 'content indeterminacy' problem - that the presence of a cow causes 'a cow is present', but also 'an animal is present' and 'a biological organism is present'. | |
| From: Peter Schulte (Mental Content [2023], 4.1) | |
| A reaction: That only rules out the 'simple' version. We just need to add that the cause (cow experience) is shaped by current knowledge and interests. Someone buying cows and someone terrified of them thereby produce different concepts. |
| 23799 | Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte] |
| Full Idea: The core idea of teleosemantics is that we need to explain how content can be accurate or inaccurate, true or false, realised or unrealised …which must appeal to the distinction between proper functioning and malfunctioning. | |
| From: Peter Schulte (Mental Content [2023], 4.4) | |
| A reaction: My immediate reaction to this is that you don't learn about content by assessing its success. Surely (as with eyesight) you first need to understand what it does, and only then judge its success. …Though success and failure are implicit in function. |
| 23800 | Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte] |
| Full Idea: Teleosemantic theories usually give a causal account of mental functions …where some trait has a particular function if it was selected for that function by a process of natural selection. | |
| From: Peter Schulte (Mental Content [2023], 4.4) | |
| A reaction: This is an idea I like - that something has a specific function if without that function it wouldn't have come into existence (eyes, for example). But presumably the function of a mind is to collect content - which does nothing to explain content! |
| 23798 | Information theories say content is information, such as smoke making fire probable [Schulte] |
| Full Idea: Information theories of content [usually assume that] a column of smoke over there carries the information that fire is over there because it raises the probability of fire being over there. | |
| From: Peter Schulte (Mental Content [2023], 4.2) | |
| A reaction: Theorists usually add further conditions to this basic one. Fred Dretske is the source of this approach. Not promising, in my opinion. Surely the content is just smoke, and fire is one of dozens of possible inferences from it? |
| 18883 | Any equivalence relation among similar things allows the creation of an abstractum [Simons] |
| Full Idea: Whenever we have an equivalence relation among things - such as similarity in a certain respect - we can abstract under the equivalence and consider the abstractum. | |
| From: Peter Simons (Modes of Extension: comment on Fine [2008], p.19) | |
| A reaction: This strikes me as dressing up old-fashioned psychological abstractionism in the respectable clothing of Fregean equivalences (such as 'directions'). We can actually do what Simons wants without the precision of partitioned equivalence classes. |
| 18884 | Abstraction is usually seen as producing universals and numbers, but it can do more [Simons] |
| Full Idea: Abstraction as a cognitive tool has been associated predominantly with the metaphysics of universals and of mathematical objects such as numbers. But it is more widely applicable beyond this standard range. I commend its judicious use. | |
| From: Peter Simons (Modes of Extension: comment on Fine [2008], p.21) | |
| A reaction: Personally I think our view of the world is founded on three psychological principles: abstraction, idealisation and generalisation. You can try to give them rigour, as 'equivalence classes', or 'universal quantifications', if it makes you feel better. |