30 ideas
22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
Full Idea: The circularity in a definition where the property being defined is used in the definition is now known as 'impredicativity'. ...Some cases ('the tallest man in the room') are unproblematic, as they pick him out, and don't conjure him into existence. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Impred') | |
A reaction: [part summary] |
22301 | The Identity Theory says a proposition is true if it coincides with what makes it true [Potter] |
Full Idea: The Identity Theory of truth says a proposition is true just in case it coincides with what makes it true. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 23 'Abs') | |
A reaction: The obvious question is how 'there are trees in the wood' can somehow 'coincide with' or 'be identical to' the situation outside my window. The theory is sort of right, but we will never define the relationship, which is no better than 'corresponds'. |
22324 | It has been unfortunate that externalism about truth is equated with correspondence [Potter] |
Full Idea: There has been an unfortunate tendency in the secondary literature to equate externalism about truth with the correspondence theory. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 65 'Truth') | |
A reaction: Quite helpful to distinguish internalist from externalist theories of truth. It is certainly the case that robust externalist views of truth have unfortunately been discredited merely because the correspondence account is inadequate. |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
Full Idea: A model of a language assigns values to non-logical terms. If a sentence is true in every model, its truth doesn't depend on those non-logical terms. Hence the validity of an argument comes from its logical form. Thus models explain logical validity. | |
From: Vann McGee (Logical Consequence [2014], 4) | |
A reaction: [compressed] Thus you get a rigorous account of logical validity by only allowing the rigorous input of model theory. This is the modern strategy of analytic philosophy. But is 'it's red so it's coloured' logically valid? |
22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
Full Idea: Natural deduction systems generally depend on conditional proof, but for Frege everything is asserted unconditionally. The modern turnstile |- is allowed to have antecedents, and hence to represent inference rather than Frege's judgement sign |---. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 03 'Axioms') | |
A reaction: [compressed] Shockingly, Frege's approach seems more psychological than the modern approach. I would say that the whole point of logic is that it has to be conditional, because the truth of the antecedents is irrelevant. |
22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |
Full Idea: Deductivism is a good account of large parts of mathematics, but stumbles where mathematics is directly applicable to the world. It fails to explain how we detach the antecedent so as to arrive at unconditional conclusions. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Deduc') | |
A reaction: I suppose the reply would be that we have designed deductive structures which fit our understanding of reality - so it is all deductive, but selected pragmatically. |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
Full Idea: Natural language includes connectives that are not truth-functional. In order for 'p because q' to be true, both p and q have to be true, but knowing the simpler sentences are true doesn't determine whether the larger sentence is true. | |
From: Vann McGee (Logical Consequence [2014], 2) |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
Full Idea: To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over. | |
From: Vann McGee (Logical Consequence [2014], 7) | |
A reaction: Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification. |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
Full Idea: We can get a less ontologically perilous presentation of the semantics of the predicate calculus by using sets instead of concepts. | |
From: Vann McGee (Logical Consequence [2014], 4) | |
A reaction: The perilous versions rely on Fregean concepts, and notably Russell's 'concept that does not fall under itself'. The sets, of course, have to be ontologically secure, and so will involve the iterative conception, rather than naive set theory. |
22295 | Modern logical truths are true under all interpretations of the non-logical words [Potter] |
Full Idea: In the modern definition, a 'logical truth' is true under every interpretation of the non-logical words it contains. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 19 'Frege's') | |
A reaction: What if the non-logical words are nonsense, or are used inconsistently ('good'), or ambiguously ('bank'), or vaguely ('bald'), or with unsure reference ('the greatest philosopher' becomes 'Bentham')? What qualifies as an 'interpretation'? |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
Full Idea: Logically valid sentences are a species of analytic sentence, being true not just in virtue of the meanings of their words, but true in virtue of the meanings of their logical words. | |
From: Vann McGee (Logical Consequence [2014], 4) | |
A reaction: A helpful link between logical truths and analytic truths, which had not struck me before. |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
Full Idea: Soundness theorems are seldom very informative, since typically we use informally, in proving the theorem, the very same rules whose soundness we are attempting to establish. | |
From: Vann McGee (Logical Consequence [2014], 5) | |
A reaction: [He cites Quine 1935] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
Full Idea: One of the culminating achievements of Euclidean geometry was categorical axiomatisations, that describe the geometric structure so completely that any two models of the axioms are isomorphic. The axioms are second-order. | |
From: Vann McGee (Logical Consequence [2014], 7) | |
A reaction: [He cites Veblen 1904 and Hilbert 1903] For most mathematicians, categorical axiomatisation is the best you can ever dream of (rather than a single true axiomatisation). |
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. |
22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
Full Idea: The word 'concrete' is often used as the negative of 'abstract', with the slightly odd consequence that desires and hallucinations are thereby classified as concrete. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Numb') | |
A reaction: There is also the even more baffling usage of 'abstract' for the most highly generalised mathematics, leaving lower levels as 'concrete'. I favour the use of 'generalised' wherever possible, rather than 'abstract'. |
22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |
Full Idea: From the successor function we can deduce its ancestral, the 'greater than' relation, which is a strict total ordering of the natural numbers. (Frege did not mention this, but Dedekind worked it out, when expounding definition by recursion). | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Def') | |
A reaction: [compressed] |
22281 | A material conditional cannot capture counterfactual reasoning [Potter] |
Full Idea: What the material conditional most significantly fails to capture is counterfactual reasoning. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 04 'Sem') | |
A reaction: The point is that counterfactuals say 'if P were the case (which it isn't), then Q'. But that means P is false, and in the material conditional everything follows from a falsehood. A reinterpretation of the conditional might embrace counterfactuals. |
22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter] |
Full Idea: Knowledge might result from a reliable and an unreliable process. ...Is something knowledge if you were told it by a drunken schoolteacher? | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 66 'Rel') | |
A reaction: Nice example. The listener must decide which process to rely on. But how do you decide that, if not by assessing the likely truth of what you are being told? It could be a bad teacher who is inspired by drink. |
7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
22273 | Traditionally there are twelve categories of judgement, in groups of three [Potter] |
Full Idea: The traditional categorisation of judgements (until at least 1800) was as universal, particular or singular; as affirmative, negative or infinite; as categorical, hypothetical or disjunctive; or as problematic, assertoric or apodictic. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 02 'Trans') | |
A reaction: Arranging these things in neat groups of three seems to originate with the stoics. Making distinctions like this is very much the job of a philosopher, but arranging them in neat equinumerous groups is intellectual tyranny. |
7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter] |
Full Idea: Frege's mirroring principle (that the structure of thoughts mirrors that of language) has the uncomfortable consequence that since the phrase 'the concept "horse"' is saturated, it cannot refer to something unsaturated, which includes concepts. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 16 'Conc') |
22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter] |
Full Idea: Compositionality is best seen as saying the semantic value of a string is explained by the strings lower down its parsing tree. It is unimportant whether a string is always parsed in terms of its own substrings. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem') | |
A reaction: That is, the analysis must explain the meaning, but the analysis can contain more than the actual ingredients of the sentence (which would be too strict). |
22282 | 'Direct compositonality' says the components wholly explain a sentence meaning [Potter] |
Full Idea: Some authors urge the strong notion of 'direct compositionality', which requires that the content of a sentence be explained in terms of the contents of the component parts of that very sentence. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem') | |
A reaction: The alternative is that meaning is fully explained by an analysis, but that may contain more than the actual components of the sentence. |
22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter] |
Full Idea: The principle of compositionality is more popular among philosophers of logic than of language, because the subtle context-sensitivity or ordinary language makes providing a compositional semantics for it a daunting challenge. | |
From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Lang') | |
A reaction: Logicians love breaking complex entities down into simple atomic parts. Linguistics tries to pin down something much more elusive. |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
Full Idea: If our linguistic conventions entitle us to assert a sentence, they thereby make it true, because of the maxim that 'truth is the norm of assertion'. | |
From: Vann McGee (Logical Consequence [2014], 8) | |
A reaction: You could only really deny that maxim if you had no belief at all in truth, but then you can assert anything you like (with full entitlement). Maybe you can assert anything you like as long as it doesn't upset anyone? Etc. |