43 ideas
| 7893 | Our life is the creation of our mind [Anon (Dham)] |
| Full Idea: What we are today comes from our thoughts of yesterday, and our present thoughts build our life of tomorrow: our life is the creation of our mind. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.1) | |
| A reaction: I may adopt this as a second epigraph for the database. This idea records the subjective view, which now comes up against evolutionary psychology. Maybe philosophy is opposed to science, because it is committed to exploring the subjective view? |
| 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. |
| 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. |
| 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'? |
| 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. |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 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'. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
| 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] |
| 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. |
| 7898 | The world is just the illusion of an appearance [Anon (Dham)] |
| Full Idea: When a man considers this world as a bubble of froth, and as the illusion of an appearance, then the king of death has no power over him. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §13.170) | |
| A reaction: Strictly, of course, this says you can 'consider' things this way. Perhaps we could substitute 'pretends', but the world's great religions don't go in for that sort of thing. Berkeley would be shocked to learn he was approaching Buddhism. |
| 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. |
| 7894 | Hate is conquered by love [Anon (Dham)] |
| Full Idea: Hate is not conquered by hate: hate is conquered by love. This is the law eternal. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.5) | |
| A reaction: [N.B. This thought was not invented by Jesus] The challenge to this view might be the tit-for-tat strategy of game theory, which says that hate is actually conquered by a combination of hate and love, judiciously applied. |
| 7899 | Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)] |
| Full Idea: Since a shower of gold coins could not satisfy craving desires and the end of all pleasure is pain, how could a wise man find satisfaction even in the pleasures of the gods? | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §14.186) | |
| A reaction: I'm never sure how so many ancient thinkers arrived at this implausible view. They seem to think that no one knows when to stop, and that every drink leads to hangover. What is actually wrong with moderate sensible pleasure? |
| 7896 | The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)] |
| Full Idea: The falling of drops of water will in time fill a water-jar. Even so the foolish man becomes full of evil, although he gather it little by little. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.121) | |
| A reaction: This coincides closely with Aristotle's view of moral education. Maybe a wise man can maintain one small vice. Not all slopes are slippery. |
| 7897 | The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)] |
| Full Idea: The falling of drops of water will in time fill a water-jar. Even so the wise man becomes full of good, although he gather it little by little. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.122) | |
| A reaction: Again, this is like Aristotle's proposal of how to educate people in virtue. In my experience, there is no guarantee that small acts of politeness and charity will eventually guarantee goodness of character. Thought is also needed. |
| 7895 | Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)] |
| Full Idea: If on the great journey of life a man cannot find one who is better or at least as good as himself, let him joyfully travel alone: a fool cannot help him on his journey. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §5.61) | |
| A reaction: This is a slightly disturbing aspect of Buddhism, possibly leading to contradiction. It urges friendship and love, but the finest people will have virtually no friends, and solitude is presented as a finer state than friendship. |
| 7900 | Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)] |
| Full Idea: Speak the truth, yield not to anger, give what you can to him who asks: these three steps lead you to the gods | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §17.224) | |
| A reaction: I don't recall either the Old or New Testament, or the Koran, placing great emphasis on speaking the truth. The injunction to give is not so simple. Give to greedy children, to alcoholics, to criminals, to the rich, to fools, to yourself? |