53 ideas
| 2463 | A standard naturalist view is realist, externalist, and computationalist, and believes in rationality [Fodor] |
| Full Idea: There seems to be an emerging naturalist consensus that is Realist in ontology and epistemology, externalist in semantics, and computationalist in cognitive psychology, which nicely allows us to retain our understanding of ourselves as rational creatures. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) |
| 2435 | Psychology has to include the idea that mental processes are typically truth-preserving [Fodor] |
| Full Idea: A psychology that can't make sense of such facts as that mental processes are typically truth-preserving is ipso facto dead in the water. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §1.3) |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| Full Idea: In intuitionist logic double negation elimination fails. After all, proving that there is no proof that there can't be a proof of S is not the same thing as having a proof of S. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: I do like people like Colyvan who explain things clearly. All of this difficult stuff is understandable, if only someone makes the effort to explain it properly. |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| Full Idea: The intuitionist rejection of double negation elimination undermines the important reductio ad absurdum proof in classical mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) |
| 2442 | Inferences are surely part of the causal structure of the world [Fodor] |
| Full Idea: Inferences are surely part of the causal structure of the world. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §3) |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| Full Idea: The law of excluded middle (for every proposition P, either P or not-P) must be carefully distinguished from its semantic counterpart bivalence, that every proposition is either true or false. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: So excluded middle makes no reference to the actual truth or falsity of P. It merely says P excludes not-P, and vice versa. |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| Full Idea: Löwenheim proved that if a first-order sentence has a model at all, it has a countable model. ...Skolem generalised this result to systems of first-order sentences. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| Full Idea: A set of axioms is said to be 'categorical' if all models of the axioms in question are isomorphic. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2) | |
| A reaction: The best example is the Peano Axioms, which are 'true up to isomorphism'. Set theory axioms are only 'quasi-isomorphic'. |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| Full Idea: Ordinal numbers represent order relations. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.2.3 n17) |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| Full Idea: For intuitionists, all but the smallest, most well-behaved infinities are rejected. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3) | |
| A reaction: The intuitionist idea is to only accept what can be clearly constructed or proved. |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| Full Idea: The problem with infinitesimals is that in some places they behaved like real numbers close to zero but in other places they behaved like zero. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.2) | |
| A reaction: Colyvan gives an example, of differentiating a polynomial. |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| Full Idea: Given Dedekind's reduction of real numbers to sequences of rational numbers, and other known reductions in mathematics, it was tempting to see basic arithmetic as the foundation of mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.1) | |
| A reaction: The reduction is the famous Dedekind 'cut'. Nowadays theorists seem to be more abstract (Category Theory, for example) instead of reductionist. |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| Full Idea: Transfinite inductions are inductive proofs that include an extra step to show that if the statement holds for all cases less than some limit ordinal, the statement also holds for the limit ordinal. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1 n11) |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| Full Idea: Most mathematical proofs, outside of set theory, do not explicitly state the set theory being employed. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.1) |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| Full Idea: Structuralism is able to explain why mathematicians are typically only interested in describing the objects they study up to isomorphism - for that is all there is to describe. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| Full Idea: In re structuralism does not posit anything other than the kinds of structures that are in fact found in the world. ...The problem is that the world may not provide rich enough structures for the mathematics. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2) | |
| A reaction: You can perceive a repeating pattern in the world, without any interest in how far the repetitions extend. |
| 21513 | We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing] |
| Full Idea: I think it is wrong to tie down the advocates of the coherence theory to a precise definition. ...It would be altogether unreasonable to demand that the moral ideal should be exhaustively defined, and the same may be true of the ideal of thought. | |
| From: A.C. Ewing (Idealism: a critical survey [1934], p.231), quoted by Erik J. Olsson - Against Coherence 7.6 | |
| A reaction: I strongly agree. It is not a council of despair. I think the criteria of coherence can be articulated quite well (e.g by Thagard), and the virtues of enquiry can also be quite well specified (e.g. by Zagzebski). Very dissimilar evidence must cohere. |
| 21497 | If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing] |
| Full Idea: Without a detailed account, coherence is reduced to the mere muttering of the word 'coherence', which can be interpreted so as to cover all arguments, but only by making its meaning so wide as to rob it of almost all significance. | |
| From: A.C. Ewing (Idealism: a critical survey [1934], p.246), quoted by Erik J. Olsson - Against Coherence 2.2 | |
| A reaction: I'm a fan of coherence, but it is a placeholder, involving no intrinsic or detailed theory. I just think it points to the reality of how we make judgements, especially practical ones. We can categorise the inputs, and explain the required virtues. |
| 2462 | Control of belief is possible if you know truth conditions and what causes beliefs [Fodor] |
| Full Idea: Premeditated cognitive management is possible if knowing the contents of one's thoughts would tell you what would make them true and what would cause you to have them. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: I love the idea of 'cognitive management'. Since belief is fairly involuntary, I subject myself to the newspapers, books, TV and conversation which will create the style of beliefs to which I aspire. Why? |
| 2454 | We can deliberately cause ourselves to have true thoughts - hence the value of experiments [Fodor] |
| Full Idea: A creature that knows what makes its thoughts true and what would cause it to have them, could therefore cause itself to have true thoughts. …This would explain why experimentation is so close to the heart of our cognitive style. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) |
| 2455 | Interrogation and experiment submit us to having beliefs caused [Fodor] |
| Full Idea: You can put yourself into a situation where you may be caused to believe that P. Putting a question to someone who is in the know is one species of this behaviour, and putting a question to Nature (an experiment) is another. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) |
| 2460 | Participation in an experiment requires agreement about what the outcome will mean [Fodor] |
| Full Idea: To be in the audience for an experiment you have to believe what the experimenter believes about what the outcome would mean, but not necessarily what the outcome will be. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) |
| 2461 | An experiment is a deliberate version of what informal thinking does all the time [Fodor] |
| Full Idea: Experimentation is an occasional and more or less self-conscious exercise in what informal thinking does all the time without thinking about it. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) |
| 2458 | Theories are links in the causal chain between the environment and our beliefs [Fodor] |
| Full Idea: Theories function as links in the causal chains that run from environmental outcomes to the beliefs that they cause the inquirer to have. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| Full Idea: Those who see probabilities as ratios of frequencies can't use Bayes's Theorem if there is no objective prior probability. Those who accept prior probabilities tend to opt for a subjectivist account, where probabilities are degrees of belief. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.8) | |
| A reaction: [compressed] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| Full Idea: Mathematics can demonstrate structural similarities between systems (e.g. missing population periods and the gaps in the rings of Saturn). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) | |
| A reaction: [Colyvan expounds the details of his two examples] It is these sorts of results that get people enthusiastic about the mathematics embedded in nature. A misunderstanding, I think. |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| Full Idea: Mathematics can show that under a broad range of conditions, something initially surprising must occur (e.g. the hexagonal structure of honeycomb). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2) |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| Full Idea: Another style of proof often cited as unexplanatory are brute-force methods such as proof by cases (or proof by exhaustion). | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| Full Idea: One kind of proof that is thought to be unexplanatory is the 'reductio' proof. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
| A reaction: Presumably you generate a contradiction, but are given no indication of why the contradiction has arisen? Tracking back might reveal the source of the problem? Colyvan thinks reductio can be explanatory. |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| Full Idea: It might be argued that any proof by induction is revealing the explanation of the theorem, namely, that it holds by virtue of the structure of the natural numbers. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1) | |
| A reaction: This is because induction characterises the natural numbers, in the Peano Axioms. |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| Full Idea: The proof of the four-colour theorem raises questions about whether a 'proof' that no one understands is a proof. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.6) | |
| A reaction: The point is that the theorem (that you can colour countries on a map with just four colours) was proved with the help of a computer. |
| 2443 | I say psychology is intentional, semantics is informational, and thinking is computation [Fodor] |
| Full Idea: I hold that psychological laws are intentional, that semantics is purely informational, and that thinking is computation (and that it is possible to hold all of these assumptions at once). | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: When he puts it baldly like that, it doesn't sound terribly persuasive. Thinking is 'computation'? Raw experience is irrelevant? What is it 'like' to spot an interesting connection between two propositions or concepts? It's not like adding 7 and 5. |
| 2453 | We are probably the only creatures that can think about our own thoughts [Fodor] |
| Full Idea: I think it is likely that we are the only creatures that can think about the contents of our thoughts. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: I think this is a major idea. If you ask me the traditional question - what is the essential difference between us and other animals? - this is my answer (not language, or reason). We are the metathinkers. |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| Full Idea: One type of generalisation in mathematics extends a system to go beyond what is was originally set up for; another kind involves abstracting away from some details in order to capture similarities between different systems. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.2) |
| 2445 | Semantics v syntax is the interaction problem all over again [Fodor] |
| Full Idea: The question how mental representations could be both semantic, like propositions, and causal, like rocks, trees, and neural firings, is arguably just the interaction problem all over again. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: Interesting way of presenting the problem. If you seem to be confronting the interaction problem, you have probably drifted into a bogus dualist way of thinking. Retreat, and reformulate you questions and conceptual apparatus, till the question vanishes. |
| 2446 | Cartesians consider interaction to be a miracle [Fodor] |
| Full Idea: The Cartesian view is that the interaction problem does arise, but is unsolvable because interaction is miraculous. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: A rather unsympathetic statement of the position. Cartesians might think that God could explain to us how interaction works. Cartesians are not mysterians, I think, but they see no sign of any theory of interaction. |
| 2464 | Type physicalism equates mental kinds with physical kinds [Fodor] |
| Full Idea: Type physicalism is, roughly, the doctrine that psychological kinds are identical to neurological kinds. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], App A n.1) | |
| A reaction: This gets my general support, leaving open the nature of 'kinds'. Presumably the identity is strict, as in 'Hesperus is identical to Phosphorus'. It seems unlikely that if you and I think the 'same' thought, that we have strictly identical brain states. |
| 2447 | Hume has no theory of the co-ordination of the mind [Fodor] |
| Full Idea: What Hume didn't see was that the causal and representational properties of mental symbols have somehow to be coordinated if the coherence of mental life is to be accounted for. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: Certainly the idea that it all somehow becomes magic at the point where the brain represents the world is incoherent - but it is a bit magical. How can the whole of my garden be in my brain? Weird. |
| 2440 | Propositional attitudes are propositions presented in a certain way [Fodor] |
| Full Idea: Propositional attitudes are really three-place relations, between a creature, a proposition, and a mode of presentation (which are sentences of Mentalese). | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §2.II) | |
| A reaction: I'm not sure about 'really'! Why do we need a creature? Isn't 'hoping it will rain' a propositional attitude which some creature may or may not have? Fodor wants it to be physical, but it's abstract? |
| 2450 | Rationality has mental properties - autonomy, productivity, experiment [Fodor] |
| Full Idea: Mentalism isn't gratuitous; you need it to explain rationality. Mental causation buys you behaviours that are unlike reflexes in at least three ways: they're autonomous, they're productive, and they're experimental. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: He makes his three ways sound all-or-nothing, which is (I believe) the single biggest danger when thinking about the mind. "Either you are conscious, or you are not..." |
| 2437 | XYZ (Twin Earth 'water') is an impossibility [Fodor] |
| Full Idea: There isn't any XYZ, and there couldn't be any, and so we don't have to worry about it. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §2.I) | |
| A reaction: Jadeite and Nephrite are real enough, which are virtually indistinguishable variants of jade. You just need Twin Jewellers instead of Twin Earths. We could build them, and employ twins to work there. |
| 2441 | Truth conditions require a broad concept of content [Fodor] |
| Full Idea: We need the idea of broad content to make sense of the fact that thoughts have the truth-conditions that they do. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §2.II) | |
| A reaction: There seems to be (as Dummett points out) a potential circularity here, as you can hardly know the truth-conditions of something if you don't already know its content. |
| 3114 | Concepts aren't linked to stuff; they are what is caused by stuff [Fodor] |
| Full Idea: If the words of 'Swamp Man' (spontaneously created, with concepts) are about XYZ on Twin Earth, it is not because he's causally connected to the stuff, but because XYZ would cause his 'water' tokens (in the absence of H2O). | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], App B) | |
| A reaction: The sight of the Eiffel tower causes my 'France' tokens, so is my word "France" about the Eiffel Tower? What would cause my 'nothing' tokens? |
| 2452 | Knowing the cause of a thought is almost knowing its content [Fodor] |
| Full Idea: If you know the content of a thought, you know quite a lot about what would cause you to have it. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: I'm not sure where this fits into the great jigsaw of the mind, but it strikes me as an acute and important observation. The truth of a thought is not essential to make you have it. Ask Othello. |
| 2432 | Is content basically information, fixed externally? [Fodor] |
| Full Idea: I assume intentional content reduces (in some way) to information. …The content of a thought depends on its external relations; on the way that the thought is related to the world, not the way that it is related to other thoughts. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §1.2) | |
| A reaction: Does this make Fodor a 'weak' functionalist? The 'strong' version would say a thought is merely a location in a flow diagram, but Fodor's 'mentalism' includes a further 'content' in each diagram box. |
| 2438 | In the information view, concepts are potentials for making distinctions [Fodor] |
| Full Idea: Semantics, according to the informational view, is mostly about counterfactuals; what counts for the identity of my concepts is not what I do distinguish but what I could distinguish if I cared to (even using instruments and experts). | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §2.I) | |
| A reaction: We all differ in our discriminations (and awareness of expertise), so our concepts would differ, which is bad news for communication (see Idea 223). The view has some plausibility, though. |
| 2439 | Semantic externalism says the concept 'elm' needs no further beliefs or inferences [Fodor] |
| Full Idea: It is the essence of semantic externalism that there is nothing that you have to believe, there are no inferences that you have to accept, to have the concept 'elm'. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §2.I) | |
| A reaction: [REMINDER: broad content is filed in 18.C.7, under 'Thought' rather than under language. That is because I am a philospher of thought, rather than of language. |
| 2457 | If meaning is information, that establishes the causal link between the state of the world and our beliefs [Fodor] |
| Full Idea: It is the causal connection between the state of the world and the contents of beliefs that the reduction of meaning to information is designed to insure. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: I'm not clear why characterising the contents of a belief in terms of its information has to amount to a 'reduction'. A cup of tea isn't reduced to tea. Connections imply duality. |
| 2451 | To know the content of a thought is to know what would make it true [Fodor] |
| Full Idea: If you know the content of a thought, you thereby know what would make the thought true. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: The truthmaker might by physically impossible, and careful thought might show it to be contradictory - but that wouldn't destroy the meaning. |
| 2433 | For holists no two thoughts are ever quite the same, which destroys faith in meaning [Fodor] |
| Full Idea: If what you are thinking depends on all of what you believe, then nobody ever thinks the same thing twice. …That is why so many semantic holists (Quine, Putnam, Rorty, Churchland, probably Wittgenstein) end up being semantic eliminativists. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §1.2b) | |
| A reaction: If linguistic holism is nonsense, this is easily settled. What I say about breakfast is not changed by reading some Gibbon yesterday. |
| 2436 | It is claimed that reference doesn't fix sense (Jocasta), and sense doesn't fix reference (Twin Earth) [Fodor] |
| Full Idea: The standard view is that Frege cases [knowing Jocasta but not mother] show that reference doesn't determine sense, and Twin cases [knowing water but not H2O] show that sense doesn't determine reference. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §1.3) | |
| A reaction: How about 'references don't contain much information', and 'descriptions may not fix what they are referring to'? Simple really. |
| 2434 | Broad semantics holds that the basic semantic properties are truth and denotation [Fodor] |
| Full Idea: Broad semantic theories generally hold that the basic semantic properties of thoughts are truth and denotation. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §1.2b) | |
| A reaction: I think truth and denotation are the basic semantic properties, but I am dubious about whole-hearted broad semantic theories, so I seem to have gone horribly wrong somewhere. |
| 2459 | Externalist semantics are necessary to connect the contents of beliefs with how the world is [Fodor] |
| Full Idea: You need an externalist semantics to explain why the contents of beliefs should have anything to do with how the world is. | |
| From: Jerry A. Fodor (The Elm and the Expert [1993], §4) | |
| A reaction: Since externalist semantics only emerged in the 1970s, that implies that no previous theory had any notion that language had some connection to how the world is. Eh? |