26 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'. |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 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. |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects. |
| 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. |
| 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'? |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity. |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique. |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members. |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature. |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], V) |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they). | |
| From: Penelope Maddy (Sets and Numbers [1981], I) | |
| A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way. |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on. | |
| From: Penelope Maddy (Sets and Numbers [1981], IV) | |
| A reaction: [She is citing Benacerraf's arguments] |
| 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. |
| 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. |
| 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. |