46 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'. |
| 12442 | 'Mickey Mouse is a fictional mouse' is true without a truthmaker [Azzouni] |
| Full Idea: 'Mickey Mouse is a fictional mouse' can be taken as true without have any truthmaker. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.3) | |
| A reaction: There might be an equivocation over 'true' here. 'What, really really true that he IS a fictional mouse?' |
| 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. |
| 12439 | Truth is dispensable, by replacing truth claims with the sentence itself [Azzouni] |
| Full Idea: No truth predicate is ever indispensable, because Tarski biconditionals, the equivalences between sentences and explicit truth ascriptions to those sentences, allow us to replace explicit truth ascriptions with the sentences themselves. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.1) | |
| A reaction: Holding a sentence to be true isn't the same as saying that it is true, and it isn't the same as saying the sentence, because one might say it in an ironic tone of voice. |
| 12437 | Truth lets us assent to sentences we can't explicitly exhibit [Azzouni] |
| Full Idea: My take on truth is a fairly deflationary one: The role of the truth predicate is to enable us to assent to sentences we can't explicitly exhibit. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Intro) | |
| A reaction: Clearly this is a role for truth, as in 'I forget what he said, but I know it was true', but it isn't remotely what most people understand by true. We use 'true' about totally explicit sentences all the time. |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 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. |
| 12446 | Names function the same way, even if there is no object [Azzouni] |
| Full Idea: Names function the same way (semantically and grammatically) regardless of whether or not there's an object that they refer to. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.3 n55) | |
| A reaction: I take this to be a fairly clear rebuttal of the 'Fido'-Fido view of names (that the meaning of the name IS the dog), which never seems to quite go away. A name is a peg on which description may be hung, seems a good slogan to me. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 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'? |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976). |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types. |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 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. |
| 12447 | That all existents have causal powers is unknowable; the claim is simply an epistemic one [Azzouni] |
| Full Idea: If the argument isn't that, metaphysically speaking, anything that exists must have causal powers - how on earth would we show that? - rather, the claim is an epistemic one. Any thing we're in a position to know about we must causally interact with. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.4) | |
| A reaction: A very good point. I am attracted to causal power as a criterion for existence, but Azzouni's distinction is vital. Maybe there is just no point in even talking about things which exist but have no causal powers. |
| 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'. |
| 12445 | If fictional objects really don't exist, then they aren't abstract objects [Azzouni] |
| Full Idea: It's robustly part of common sense that fictional objects don't exist in any sense at all, and this means they aren't abstracta either. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.3) | |
| A reaction: Nice. It is so easy to have some philosopher dilute and equivocate over the word 'object' until you find yourself committed to all sorts of daft things as somehow having objectual existence. We can discuss things which don't exist in any way at all. |
| 12449 | Modern metaphysics often derives ontology from the logical forms of sentences [Azzouni] |
| Full Idea: It is widespread in contemporary metaphysics to extract commitments to various types of object on the basis of the logical form of certain sentences. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.7) | |
| A reaction: I'm with Azzouni in thinking that this procedure is a very bad idea. I'm increasingly inclined towards the wild view that people are only ontologically committed to things if they explicitly say that they are so committed. |
| 12440 | If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni] |
| Full Idea: The argument that objectual quantifiers are ontologically committing has the crucial and unnoticed presupposition that the language in which the semantics for the objectual quantifiers is couched (the 'metalanguage') also has quantifiers with commitment. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.3) | |
| A reaction: That is, presumably we find ourselves ontologically committed to the existence of quantifiers, and are also looking at an infinite regress. See Idea 12439. |
| 12438 | In the vernacular there is no unequivocal ontological commitment [Azzouni] |
| Full Idea: There are no linguistic devices, no idioms (not 'there is', not 'exists') that unequivocally indicate ontological commitment in the vernacular. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Intro) | |
| A reaction: This seems right, since people talk in such ways about soap opera, while understanding the ontological situation perfectly well. Presumably Quine is seeking higher standards than the vernacular, if we are doing science. |
| 12441 | We only get ontology from semantics if we have already smuggled it in [Azzouni] |
| Full Idea: A slogan: One can't read ontological commitments from semantic conditions unless one has already smuggled into those semantic conditions the ontology one would like to read off. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.3) | |
| A reaction: The arguments supporting this are subtle, but it's good enough for me, as I never thought anyone was ontologically committed just because they used the vagueries of language to try to say what's going on around here. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 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] |
| 12448 | Things that don't exist don't have any properties [Azzouni] |
| Full Idea: Things that don't exist don't have any properties. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.4) | |
| A reaction: Sounds reasonable! I totally agree, but that is because my notion of properties is sparse and naturalistic. If you identify properties with predicates (which some weird people seem to), then non-existents can have properties like 'absence' or 'nullity'. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 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. |
| 12450 | The periodic table not only defines the elements, but also excludes other possible elements [Azzouni] |
| Full Idea: The periodic table not only governs what elements there can be, with their properties, but also explicitly excludes others sorts of elements, because the elements are individuated by the number of discrete protons in their nuclei. | |
| From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.7) | |
| A reaction: It has to be central to the thesis of scientific essentialism that the possibilities in nature are far more restricted than is normally thought, and this observation illustrates the view nicely. He makes a similar point about subatomic particles. |