45 ideas
| 5896 | Speak the truth, for this alone deifies man [Pythagoras, by Porphyry] |
| Full Idea: Pythagoras advised above all things to speak the truth, for this alone deifies man. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Porphyry - Life of Pythagoras §41 | |
| A reaction: Idea 4421 (of Nietzsche) stands in contrast to this. I am not quite sure why speaking the truth has such a high value. I am inclined to a minimalist view, which is just that philosophy is an attempt to speak the truth, as fishermen try to catch fish. |
| 3051 | Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius] |
| Full Idea: Pythagoras discovered the numerical relation of sounds on a string. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.1.11 |
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| Full Idea: The tendency to attack forms of expression rather than attempting to appreciate what is actually being said is one of the more unfortunate habits that analytic philosophy inherited from Frege. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], IV) | |
| A reaction: The key to this, I say, is to acknowledge the existence of propositions (in brains). For example, this belief will make teachers more sympathetic to pupils who are struggling to express an idea, and verbal nit-picking becomes totally irrelevant. |
| 18486 | We might define truth as arising from the truth-maker relation [MacBride] |
| Full Idea: We might define truth using the truth-maker relation, albeit in a roundabout way, according to the pattern of saying 'S is true' is equivalent to 'there is something which makes S true'. | |
| From: Fraser MacBride (Truthmakers [2013], 3.3) | |
| A reaction: [MacBride gives it more algebraically, but I prefer English!] You would need to explain 'truth-making' without reference to truth. Horwich objects, reasonably, that ordinary people grasp 'truth' much more clearly than 'truth-making'. Bad idea, I think. |
| 18484 | Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride] |
| Full Idea: For Martin the fatal error of phenomenalists was their inability to supply credible truth-makers for truths about unobserved objects; the same error afflicted Ryle's behaviourism, ...and Prior's Presentism (for past-tensed and future-tensed truths). | |
| From: Fraser MacBride (Truthmakers [2013], 3.1) | |
| A reaction: This seems to be the original motivation for the modern rise of the truthmaker idea. Personally I find 'Napoleon won at Austerlitz' is a perfectly good past-tensed truthmaker which is compatible with presentism. Truth-making is an excellent challenge. |
| 18466 | If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride] |
| Full Idea: If a truthmaker entails its truth, this threatens to over-generate truth-makers for necessary truths - at least if the entailment is classical. It's a feature of this notion that anything whatsoever entails a given necessary truth. | |
| From: Fraser MacBride (Truthmakers [2013], 1.1) | |
| A reaction: This is a good reason to think that the truth-making relation does not consist of logical entailment. |
| 18473 | 'Maximalism' says every truth has an actual truthmaker [MacBride] |
| Full Idea: The principle of 'maximalism' is that for every truth, then there must be something in the world that makes it true. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1) | |
| A reaction: That seems to mean that no truths can be uttered about anything which is not in the world. If I say 'pigs might have flown', that isn't about the modal profile of actual pigs, it is about what might have resulted from that profile. |
| 18481 | Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride] |
| Full Idea: If maximalism is intellectual heir to Russell's logical atomism, then 'optimalism' (the denial that universal and negative statements need truth-makers) is heir to Wittgenstein's version, where only atomic propositions represent states of affairs. | |
| From: Fraser MacBride (Truthmakers [2013], 2.2) | |
| A reaction: Wittgenstein's idea is that you can use the logical connectives to construct all the other universal and negative facts. 'Optimalism' restricts truthmaking to atomic statements. |
| 18483 | The main idea of truth-making is that what a proposition is about is what matters [MacBride] |
| Full Idea: According the Lewis, the kernel of truth in truth-making is the idea that propositions have a subject matter. They are about things, so whether they are true or false depends on how those things stand. | |
| From: Fraser MacBride (Truthmakers [2013], 2.4.1) | |
| A reaction: [Lewis 'Things Qua Truth-makers' 2003] That sounds like the first step in the story, rather than the 'kernel' of the truth-making approach. |
| 18479 | There are different types of truthmakers for different types of negative truth [MacBride] |
| Full Idea: We recognise that what makes it true that there is no oil in this engine is different from what makes it true that there are no dodos left. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
| A reaction: This looks like a local particular negation up against a universal negation. I'm not sure there is a big difference between 'my dodo's gone missing' (like my oil), and 'all the dodos have gone permanently missing'. |
| 18477 | There aren't enough positive states out there to support all the negative truths [MacBride] |
| Full Idea: It's not obvious that there are enough positive states out there to underwrite all the negative truths. Even though it may be true that this liquid is odourless this needn't be because there's something further about it that excludes its being odourless. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
| A reaction: What is the ontological status of all these hypothetical truths? What is the truthmaker for 'a trillion trillion negative truths exist'? What is the status of 'this is not not-red'? |
| 18482 | Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride] |
| Full Idea: Optimalists say that negative truths are 'true by default' (having the opposite truth value of p), and universal truths are too. Universal truths are equivalent to negative existential truths, which are true by default. | |
| From: Fraser MacBride (Truthmakers [2013], 2.2) | |
| A reaction: The background idea is Wittgenstein's, that if p is false, then not-p is true by default, without anyone having to assert the negation. This strikes me as a very promising approach to truthmaking. See Simons 2008. |
| 18474 | Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride] |
| Full Idea: If the sentence 'This sentence has no truth-maker' has a truth-maker, then it must be true. But then what it says must be the case, so it has no truth-maker. Hence by reductio the sentence has no truth-maker. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.1) | |
| A reaction: [Argument proposed by Peter Milne 2005] Rodriguez-Pereyra replies that the sentence is meaningless, so that it can't possibly be true. The Liar sentence is also said to be meaningless. The argument opposes Maximalism. |
| 18485 | Even idealists could accept truthmakers, as mind-dependent [MacBride] |
| Full Idea: Even an idealist could accept that there are truth-makers whilst thinking of them as mind-dependent entities. | |
| From: Fraser MacBride (Truthmakers [2013], 3.1) | |
| A reaction: This undercuts anyone (me, perhaps?) who was hoping to prop up their robust realism with an angry demand to be shown the truthmakers. |
| 18490 | Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride] |
| Full Idea: Maybe the truth-maker panegyrists have misconstrued the logical form of 'makes true'. They have taken it to be a verb like 'x hits y', when really it is akin to the connective '→' or 'because'. | |
| From: Fraser MacBride (Truthmakers [2013], 3.7) | |
| A reaction: [He cites Melia 2005] This isn't any sort of refutation of truth-making, but an offer of how to think of the phenomenon if you reject the big principle. I like truth-making, but resist the 'makes' that brings unthought propositions into existence. |
| 18493 | Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride] |
| Full Idea: When supporters of truth-making talk of 'something' which makes a sentence true, they make the assumption that it is an objectual quantifier in name position. | |
| From: Fraser MacBride (Truthmakers [2013], 3.8) | |
| A reaction: We might say, more concisely, that they are 'reifying' the something. This makes it sound as if Armstrong and Bigelow have made a mistake, but that are simply asserting that this particular quantification is indeed objectual. |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| Full Idea: The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets). | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], IX) | |
| A reaction: This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely! |
| 9984 | We can have a series with identical members [Tait] |
| Full Idea: Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)? | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], VII) | |
| A reaction: The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature? |
| 18489 | Connectives link sentences without linking their meanings [MacBride] |
| Full Idea: The 'connectives' are expressions that link sentences but without expressing a relation that holds between the states of affairs, facts or tropes that these sentences denote. | |
| From: Fraser MacBride (Truthmakers [2013], 3.7) | |
| A reaction: MacBride notes that these contrast with ordinary verbs, which do express meaningful relations. |
| 18476 | 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride] |
| Full Idea: Statements of the form 'a is F' aren't invariably positive ('a is dead'), and nor are statements of the form 'a isn't F' ('a isn't blind') always negative. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4) | |
| A reaction: The point is that the negation may be implicit in the predicate. There are many ways to affirm or deny something, other than by use of the standard syntax. |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| Full Idea: The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true. | |
| From: report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2 | |
| A reaction: This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks. |
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
| A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
| 7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
| Full Idea: For Pythagoreans, one, 1, is not a true number but the 'essence' of number, out of which the number system emerges. | |
| From: report of Pythagoras (reports [c.530 BCE], Ch.8) by Peter Watson - Ideas Ch.8 | |
| A reaction: I think this is right! Counting and numbers only arise once the concept of individuality and identity have arisen. Counting to one is no more than observing the law of identity. 'Two' is the big adventure. |
| 8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
| Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
| A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
| 18480 | Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride] |
| Full Idea: 'To be is to be a truth-maker' has been proposed as a replacement the standard conception of ontological commitment, that to be is to be the value of a variable. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.2) | |
| A reaction: [He cites Ross Cameron 2008] Unconvincing. What does it mean to say that some remote unexperienced bit of the universe 'makes truths'? How many truths? Where do these truths reside when they aren't doing anything useful? |
| 18471 | Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride] |
| Full Idea: The concept of 'grounding' appears to cry out for treatment as a family resemblance concept, a concept whose instances have no more in common than different games do. | |
| From: Fraser MacBride (Truthmakers [2013], 1.6) | |
| A reaction: I like the word 'determinations', though MacBride's point my also apply to that. I take causation to be one species of determination, and truth-making to be another. They form a real family, with no adoptees. |
| 18472 | Which has priority - 'grounding' or 'truth-making'? [MacBride] |
| Full Idea: Some philosophers define 'grounding' in terms of 'truth-making', rather than the other way around. | |
| From: Fraser MacBride (Truthmakers [2013], 1.6) | |
| A reaction: [Cameron exemplifies the first, and Schaffer the second] I would have thought that grounding was in the world, but truth-making required the introduction of propositions about the world by minds, so grounding is prior. Schaffer is right. |
| 18475 | Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride] |
| Full Idea: The logical atomism of Russell admitted some logically complex facts but not others - in contrast to Wittgenstein's version which admitted only atomic facts. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.3) | |
| A reaction: For truthmakers, it looks as if the Wittgenstein version might do a better job (e.g. with negative truths). I quite like the Russell approach, where complex facts underwrite the logical connectives. Disjunctive, negative, conjunctive, hypothetical facts. |
| 21354 | It may be that internal relations like proportion exist, because we directly perceive it [MacBride] |
| Full Idea: Some philosophers maintain that we literally perceive proportions and other internal relations. These relations must exist, otherwise we couldn't perceive them. | |
| From: Fraser MacBride (Relations [2016], 3) | |
| A reaction: [He cites Mulligan 1991, and Hochberg 2013:232] This seems a rather good point. You can't perceive the differing heights of two people, yet fail to perceive that one is taller. You also perceive 'below', which is external. |
| 21353 | Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride] |
| Full Idea: Internal relations are determined either by the mere existence of the things they relate, or by their intrinsic characters, or they supervene on the intrinsic characters of the things they relate. | |
| From: Fraser MacBride (Relations [2016], 3) | |
| A reaction: Suggesting that they 'supervene' doesn't explain anything (and supervenience never explains anything). I vote for the middle one - the intrinsic character. It has to be something about the existence, and not the mere fact of existence. |
| 21352 | 'Multigrade' relations are those lacking a fixed number of relata [MacBride] |
| Full Idea: A 'unigrade' relation R has a definite degree or adicity: R is binary, or ternary....or n-ary (for some unique n). By contrast a relation is 'multigrade' if it fails to be unigrade. Causation appears to be multigrade. | |
| From: Fraser MacBride (Relations [2016], 1) | |
| A reaction: He also cites entailment, which may have any number of premises. |
| 18478 | Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride] |
| Full Idea: It is almost universally acknowledged that Wittgenstein's plan to show all necessity is logical necessity ended in failure - indeed foundered upon the very problem of explaining colour incompatibilities. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
| A reaction: I'm not sure whether you can 'show' that colour incompatibility is some sort of necessity, though intuitively it seems so. I'm thinking that 'necessity' is a unitary concept, with a wide variety of sources generating it. |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| Full Idea: If the sense of a proposition about the abstract domain is given in terms of the corresponding proposition about the (relatively) concrete domain, ..and the truth of the former is founded upon the truth of the latter, then this is 'logical abstraction'. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: The 'relatively' in parentheses allows us to apply his idea to levels of abstraction, and not just to the simple jump up from the concrete. I think Tait's proposal is excellent, rather than purloining 'abstraction' for an internal concept within logic. |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| Full Idea: Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: [compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set. |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
| Full Idea: A different reading of abstraction is that it concerns, not the individuating properties of the elements relative to one another, but rather the individuating properties of the set itself, for example the concept of what is its extension. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], VIII) | |
| A reaction: If the set was 'objects in the room next door', we would not be able to abstract from the objects, but we might get to the idea of things being contain in things, or the concept of an object, or a room. Wrong. That's because they are objects... Hm. |
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| Full Idea: Why should abstraction from two equipollent sets lead to the same set of 'pure units'? | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996]) | |
| A reaction: [Tait is criticising Cantor] This expresses rather better than Frege or Dummett the central problem with the abstractionist view of how numbers are derived from matching groups of objects. |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| Full Idea: If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features. |
| 3053 | Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius] |
| Full Idea: Pythagoras taught that virtue is harmony, and health, and universal good, and God. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.1.19 | |
| A reaction: I like the link with health, because I consider that a bridge over the supposed fact-value gap. Very Pythagorean to think that virtue is harmony. Plato liked that thought. |
| 5244 | For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle] |
| Full Idea: Some even think that what is just is simple reciprocity, as the Pythagoreans maintained, because they defined justice simply as having done to one what one has done to another. | |
| From: report of Pythagoras (reports [c.530 BCE], 28) by Aristotle - Nicomachean Ethics 1132b22 | |
| A reaction: One wonders what Pythagoreans made of slavery. Aristotle argues that officials, for example, have superior rights. The Pythagorean idea makes fairness the central aspect of justice, and that must at least be partly right. |
| 375 | When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato] |
| Full Idea: When our predecessors discovered musical scales, they also discovered similar features in bodily movement, which should also be measured numerically, and called 'tempos' and 'measures'. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Plato - Philebus 17d |
| 638 | Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle] |
| Full Idea: The Pythagoreans offered definitions of a limited range of things on the basis of numbers; examples are timeliness, justice and marriage. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 1078b |
| 553 | Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle] |
| Full Idea: The Pythagoreans thought that the principles of mathematical entities were the principles of all entities. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 985b |
| 554 | Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle] |
| Full Idea: Pythagoreans said that entities existed by imitation of the numbers, whereas Plato said that it was by participation. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 987b |
| 644 | For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle] |
| Full Idea: For Pythagoreans the entire universe is constructed of numbers. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 1080b |
| 7467 | The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson] |
| Full Idea: The modern concept of the immortal soul is a Greek idea, which owes much to Pythagoras. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Peter Watson - Ideas Ch.5 | |
| A reaction: You can see why it caught on - it is a very appealing idea. Watson connects the 'modern' view with the ideas of heaven and hell. Obviously the idea of an afterlife goes a long way back (judging from the contents of ancient graves). |