113 ideas
| 23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
| Full Idea: It is evident that Plato regards true wisdom as something supernatural. | |
| From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.61 | |
| A reaction: Taken literally, I assume this is wrong, but we can empathise with the thought. Wisdom has the feeling of rising above the level of mere knowledge, to achieve the overview I associate with philosophy. |
| 421 | Men who love wisdom must be inquirers into very many things indeed [Heraclitus] |
| Full Idea: Men who love wisdom must be inquirers into very many things indeed. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B035), quoted by Clement - Miscellanies 5.140.5 | |
| A reaction: …which invites the question 'Is there anything that a wisdom-seeker should NOT be interested in?' |
| 3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
| Full Idea: Plato, who mentions nearly all the ancient philosophers, nowhere speaks of Democritus; he wished to burn all of his books, but was persuaded that it was futile. | |
| From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.7.8 |
| 1491 | Everyone has the potential for self-knowledge and sound thinking [Heraclitus] |
| Full Idea: Everyone has the potential for self-knowledge and sound thinking. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B116), quoted by John Stobaeus - Anthology 3.05.06 | |
| A reaction: This is true. When people are labelled as incapable of philosophy (e.g. by Plato), it is just that they are slow developers. |
| 5863 | Reason is eternal, but men are foolish [Heraclitus] |
| Full Idea: Although reason exists forever, men are foolish. | |
| From: Heraclitus (fragments/reports [c.500 BCE]), quoted by Aristotle - The Art of Rhetoric 1407b | |
| A reaction: The despair of all philosophers (e.g. Plato) who think reason is the easiest thing in the world, and stares everyone in the face, and yet people seem to spurn this supreme gift from the gods. They needed the optimism of the career teacher. |
| 16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
| Full Idea: For me, although the enterprise of philosophical analysis is driven by natural language, its goal is not a linguistic analysis of English but rather an expressively strong framework that may at best be seen as a revision of English. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 12) | |
| A reaction: I agree, but the problem is that there are different ideals for the revision, which may be in conflict. Logicians, mathematicians, metaphysicians, scientists, moralists and aestheticians are queueing up to improve in their own way. |
| 414 | Logos is common to all, but most people live as if they have a private understanding [Heraclitus] |
| Full Idea: Although the universal law (logos) is common to all, the majority live as if they had understanding peculiar to themselves. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B002), quoted by Sextus Empiricus - Against the Professors (six books) 7.133.4- | |
| A reaction: Heraclitus mentions 'logos' in just three fragments - this one, and Idea 15660 and Idea 424. |
| 416 | Beautiful harmony comes from things that are in opposition to one another [Heraclitus] |
| Full Idea: That which is in opposition is in concert, and from things that differ comes the beautiful harmony. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B008), quoted by Aristotle - Nicomachean Ethics 1155b04 |
| 425 | A thing can have opposing tensions but be in harmony, like a lyre [Heraclitus] |
| Full Idea: They do not understand how that which differs with itself is in agreement: harmony consists of opposing tensions, like that of the bow and the lyre. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B051), quoted by Hippolytus - Refutation of All Heresies 9.9.2 | |
| A reaction: Like squabbling couples who resent outside intervention. The remark suggests the virtues of 'dialectic', and may get to the heart of what philosophy is. |
| 23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
| Full Idea: Where contradictions appear there is a correlation of contraries, which is relation. If a contradiction is imposed on the intelligence, it is forced to think of a relation to transform the contradiction into a correlation, which draws the soul higher. | |
| From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.70 | |
| A reaction: A much better account of the dialectic than anything I have yet seen in Hegel. For the first time I see some sense in it. A contradiction is not a falsehood, and it must be addressed rather than side-stepped. A kink in the system, that needs ironing. |
| 16292 | An explicit definition enables the elimination of what is defined [Halbach] |
| Full Idea: Explicit definitions allow for a complete elimination of the defined notion (at least in extensional contexts). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: If the context isn't extensional (concerning the things themselves) then we could define one description of it, but be unable to eliminate it under another description. Elimination is no the aim of an Aristotelian definition. Halbach refers to truth. |
| 16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
| Full Idea: Arguments from analogy are to be distrusted: at best they can serve as heuristics. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4) |
| 16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
| Full Idea: Truth-value 'gluts' correspond to a so-called dialethic conception of truth; excluding gluts and admitting only 'gaps' leads to a conception of what is usually called 'partial' truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.2) | |
| A reaction: Talk of 'gaps' and 'gluts' seem to be the neatest way of categorising views of truth. I want a theory with no gaps or gluts. |
| 16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
| Full Idea: Two typed disquotation sentences, truth axioms of TB, suffice for proving that there at least two objects. Hence truth is not a logical notion if one expects logical notions to be ontologically neutral. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) |
| 16324 | Any definition of truth requires a metalanguage [Halbach] |
| Full Idea: It is plain that the distinction between object and metalanguage is required for the definability of truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 11) | |
| A reaction: Halbach's axiomatic approach has given up on definability, and therefore it can seek to abandon the metalanguage and examine 'type-free' theories. |
| 16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
| Full Idea: A common complaint against traditional definitional theories of truth is that it is far from clear that the definiens is not more in need of clarification than the definiendum (that is, the notion of truth). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: He refers to concepts like 'correspondence', 'facts', 'coherence' or 'utility', which are said to be trickier to understand than 'true'. I suspect that philosophers like Halbach confuse 'clear' with 'precise'. Coherence is quite clear, but imprecise. |
| 16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
| Full Idea: If one were wondering whether truth should be considered a legitimate notion at all, a definition might be useful in dispersing doubts about its legitimacy. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
| A reaction: Halbach is proposing to skip definitions, and try to give rules for using 'true' instead, but he doesn't rule out definitions. A definition of 'knowledge' or 'virtue' or 'democracy' might equally give those credibility. |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| Full Idea: In semantic theories (e.g.Tarski's or Kripke's), a definition evades Tarski's Theorem by restricting the possible instances in the schema T[φ]↔φ to sentences of a proper sublanguage of the language formulating the equivalences. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: The schema says if it's true it's affirmable, and if it's affirmable it's true. The Liar Paradox is a key reason for imposing this restriction. |
| 16337 | Disquotational truth theories are short of deductive power [Halbach] |
| Full Idea: The problem of restricted deductive power has haunted disquotational theories of truth (…because they can't prove generalisations). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.5) |
| 16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
| Full Idea: Compositional Truth CT proves the consistency of Peano arithmetic, which is not provable in Peano arithmetic by Gödel's second incompleteness theorem. Hence the theory CT is not conservative over Peano arithmetic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8.6) |
| 16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
| Full Idea: Choosing an axiomatic approach to truth might well be compatible with the view that truth is definable; the definability of truth is just not presupposed at the outset. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: Is it possible that a successful axiomatisation is a successful definition? |
| 16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
| Full Idea: Revision semantics is arguably the main competitor of Kripke's theory of truth among semantic truth theories. …In the former one may hope through revision to arrive at better and better models, ..sorting out unsuitable extensions of the truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 14) | |
| A reaction: Halbach notes later that Kripke's theory (believe it or not) is considerably simpler than revision semantics. |
| 16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
| Full Idea: If the clauses of Tarski's definition of truth are turned into axioms (as Davidson proposed) then a primitive binary predicate symbol for satisfaction is needed, as Tarski defined truth in terms of satisfaction. Standard language has a unary predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.2) |
| 16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
| Full Idea: In the typed Compositional Truth theory CT, it is compositional because the truth of a sentence depends on the semantic values of the constituents of that sentence. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) | |
| A reaction: [axioms on p. 65 of Halbach] |
| 16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
| Full Idea: Often syntactic objects are identified with their numerical codes. …Expressions of a countable formal language can be coded in the natural numbers. This allows a theory of truth to use Peano Arithmetic (with its results) as a base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 2) | |
| A reaction: The numbering system is the famous device invented by Gödel for his great proof of incompleteness. This idea is a key to understanding modern analytic philosophy. It is the bridge which means philosophical theories can be treated mathematically. |
| 16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
| Full Idea: Considering the truth axioms in the absence of a base theory is not very sensible because characteristically truth theoretic reasoning arises from the interplay of the truth axioms with the base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) | |
| A reaction: The base theory usually seems to be either Peano arithmetic or set theory. We might say that introverted thought (e.g. in infants) has little use for truth; it is when you think about the world that truth becomes a worry. |
| 16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
| Full Idea: In the light of incompleteness phenomena, one should not expect a categorical axiomatisation of truth to be feasible, but this should not keep one from studying axiomatic theories of truth (or of arithmetic). | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
| A reaction: This, of course, is because of Gödel's famous results. It is important to be aware in this field that there cannot be a dream of a final theory, so we are just seeing what can be learned about truth. |
| 16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
| Full Idea: A truth theory is 'conservative' if the addition of the truth predicate does not add any new theorems to the base theory. | |
| From: report of Volker Halbach (Axiomatic Theories of Truth [2011], 6 Df 6.6) by PG - Db (ideas) | |
| A reaction: Halbach presents the definition more formally, and this is my attempt at getting it into plain English. Halbach uses Peano Arithmetic as his base theory, but set theory is also sometimes used. |
| 16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
| Full Idea: The truth theory TB (Tarski Biconditional) is all the axioms of Peano Arithmetic, including all instances of the induction schema with the truth predicate, plus all the sentences of the form T[φ] ↔ φ. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
| A reaction: The biconditional formula is the famous 'snow is white' iff snow is white. The truth of the named sentence is equivalent to asserting the sentence. This is a typed theory of truth, and it is conservative over PA. |
| 16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
| Full Idea: I sort theories of truth into the large families of 'typed' and 'type-free'. Roughly, typed theories prohibit a truth predicate's application to sentences with occurrences of that predicate, and one cannot prove the truth of sentences containing 'true'. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], II Intro) | |
| A reaction: The problem sentence the typed theories are terrified of is the Liar Sentence. Typing produces a hierarchy of languages, referring down to the languages below them. |
| 16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
| Full Idea: The Friedman-Sheard truth system FS is based on compositional theory CT. The axioms of FS are obtained by relaxing the type restriction on the CT-axioms, and adding rules inferring sentences from their truth, and vice versa. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15) | |
| A reaction: The rules are called NEC and CONEC by Halbach. The system FSN is FS without the two rules. |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| Full Idea: KF is useful for explicating Peano arithmetic, but it certainly does not come to close to being a theory that contains its own truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 16) | |
| A reaction: Since it is a type-free theory, its main philosophical aspiration was to contain its own truth predicate, so that is bad news (for philosophers). |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| Full Idea: The Kripke-Feferman theory is relatively deductively very strong. In particular, it is much stronger than its competitor FS, which is based on a completely classical notion of truth. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.3) |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| Full Idea: The Kripke-Feferman theory KF is an axiomatisation of the fixed points of an operator, that is, of a Kripkean fixed-point semantics with the Strong Kleene evaluation schema with truth-value gluts. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.1) |
| 16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
| Full Idea: Compositional Truth CT and its variants has desirable generalisations among its logical consequences, so they seem to have ousted purely disquotational theories such as TB in the discussion on deflationism. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |
| 16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
| Full Idea: Some authors have tried to understand the deflationist claim that truth is not a substantial notion as the claim that a satisfactory axiomatisation of truth should be conservative over the base theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |
| 16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
| Full Idea: There are two doctrines at the core of deflationism. The first says truth is a device of disquotation used to express generalisations, and the second says truth is a thin notion that contributes nothing to our knowledge of the world | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 21) |
| 16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
| Full Idea: The main criticism that deflationist theories based on the disquotation sentences or similar axioms have to meet was raised by Tarski: the disquotation sentences do not allow one to prove generalisations. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) |
| 16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
| Full Idea: Deflationists do not hold that truth is completely dispensable. They claim that truth serves the purpose of expressing infinite conjunctions or generalisations. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
| A reaction: It is also of obvious value as a shorthand in ordinary conversation, but rigorous accounts can paraphrase that out. 'What he said is true'. 'Pick out the true sentences from p,q,r and s' seems to mean 'affirm some of them'. What does 'affirm' mean? |
| 16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
| Full Idea: In Strong Kleene logic a disjunction of two sentences is true if at least one disjunct is true, even when the other disjunct lacks a truth value. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 18) | |
| A reaction: This sounds fine to me. 'Either I'm typing this or Homer had blue eyes' comes out true in any sensible system. |
| 16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
| Full Idea: In Weak Kleene Logic, with truth-value gaps, a sentence is neither true nor false if one of its components lacks a truth value. A line of the truth table shows a gap if there is a gap anywhere in the line, and the other lines are classical. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 18) | |
| A reaction: This will presumably apply even if the connective is 'or', so a disjunction won't be true, even if one disjunct is true, when the other disjunct is unknown. 'Either 2+2=4 or Lot's wife was left-handed' sounds true to me. Odd. |
| 16309 | Every attempt at formal rigour uses some set theory [Halbach] |
| Full Idea: Almost any subject with any formal rigour employs some set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4.1) | |
| A reaction: This is partly because mathematics is often seen as founded in set theory, and formal rigour tends to be mathematical in character. |
| 16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
| Full Idea: The costs of giving up classical logic are easily underestimated, …the price being paid in terms of mathematical reasoning. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 16.2) | |
| A reaction: No one cares much about such costs, until you say they are 'mathematical'. Presumably this is a message to Graham Priest and his pals. |
| 1312 | If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus] |
| Full Idea: The remark of Heraclitus that all things are and are not effectively renders all assertions true, and that of Anaxagoras that there is an intermediary between assertion and negation makes all assertions false. | |
| From: comment on Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Metaphysics 1012a | |
| A reaction: Compare Idea 416. Heraclitus is discussing truth-value 'gluts', as in paraconsistent logic, and Anaxagoras is discussing truth-value 'gaps', as in three-valued Kleene logic. |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| Full Idea: A theory is a set of formulae closed under first-order logical consequence. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.1) |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| Full Idea: One cannot just accept that all the theorems of Peano arithmetic are true when one accepts Peano arithmetic as the notion of truth is not available in the language of arithmetic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: This is given as the reason why Kreisel and Levy (1968) introduced 'reflection principles', which allow you to assert whatever has been proved (with no mention of truth). (I think. The waters are closing over my head). |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| Full Idea: If one endorses a theory, so one might argue, one should also take it to be sound. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| Full Idea: Soundness seems to be a notion essentially involving truth. At least I do not know how to fully express the soundness of Peano arithmetic without invoking a truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: I suppose you could use some alternative locution such as 'assertible' or 'cuddly'. Intuitionists seem a bit vague about the truth end of things. |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| Full Idea: Paradoxes that arise from interaction of predicates such as truth, necessity, knowledge, future and past truths have receive little attention. There may be many unknown paradoxes lurking when we develop frameworks with these intensional notions. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2) | |
| A reaction: Nice. This is a wonderful pointer to new research in the analytic tradition, in which formal problems will gradually iron out our metaphysical framework. |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| Full Idea: An essential feature of the liar paradox is the application of the truth predicate to a sentence with a negated occurrence of the truth predicate, though the negation can be avoided by using the conditional. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.3) |
| 16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
| Full Idea: Nonstandard models of Peano arithmetic are models of PA that are not isomorphic to the standard model. Their existence can be established with the compactness theorem or the adequacy theorem of first-order logic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 8.3) |
| 16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
| Full Idea: The global reflection principle ∀x(Sent(x) ∧ Bew[PA](x) → Tx) …seems to be the full statement of the soundness claim for Peano arithmetic, as it expresses that all theorems of Peano arithmetic are true. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: That is, an extra principle must be introduced to express the soundness. PA is, of course, not complete. |
| 16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
| Full Idea: For the reduction of Peano Arithmetic to ZF set theory, usually the set of finite von Neumann ordinals is used to represent the non-negative integers. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 6) | |
| A reaction: Halbach makes it clear that this is just one mode of reduction, relative interpretability. |
| 16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
| Full Idea: While set theory was liberated much earlier from type restrictions, interest in type-free theories of truth only developed more recently. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 4) | |
| A reaction: Tarski's theory of truth involves types (or hierarchies). |
| 16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
| Full Idea: The observation that Peano arithmetic is relatively interpretable in ZF set theory is taken by many philosophers to be a reduction of numbers to sets. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 23) | |
| A reaction: Nice! Being able to express something in a different language is not the same as a reduction. Back to the drawing board. What do you really mean by a reduction? If we model something, we don't 'reduce' it to the model. |
| 14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
| Full Idea: 'Structure' tends to be characterized by Plato as something that is mathematically expressed. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects V.3 iv | |
| A reaction: [Koslicki is drawing on Verity Harte here] |
| 15658 | The hidden harmony is stronger than the visible [Heraclitus] |
| Full Idea: The hidden harmony is stronger (or 'better') than the visible. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B055), quoted by Hippolytus - Refutation of All Heresies 9.9.5 | |
| A reaction: 'An unapparent connection [harmonia] is stronger than an apparent one' is Curd's translation. I'm taking this for essentialism. It is the basic idea of the essentialising child (see Gelman). The hidden explains the apparent. |
| 3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
| Full Idea: When Diogenes told Plato he saw tables and cups, but not 'tableness' and 'cupness', Plato replied that this was because Diogenes had eyes but no intellect. | |
| From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.2.6 |
| 17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
| Full Idea: Plato's theory of Forms allowed him to claim that the sophists and other opponents were trapped in the world of appearance. What they therefore taught was only apparent wisdom and virtue. | |
| From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.118 |
| 20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
| Full Idea: The Platonists, on the basis of purely logical arguments, posit the existence of an indivisible 'triangle in itself'. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 316a15 | |
| A reaction: A helpful confirmation that geometrical figures really are among the Forms (bearing in mind that numbers are not, because they contain one another). What shape is the Form of the triangle? |
| 556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
| Full Idea: If there is the same Form for the Forms and for their participants, then they must have something in common. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a |
| 563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
| Full Idea: We say there is the form of man, horse and health, but nothing else, making the same mistake as those who say that there are gods but that they are in the form of men. They just posit eternal men, and here we are not positing forms but eternal sensibles. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 997b |
| 565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
| Full Idea: The Forms could not be changeless if they were in changing things. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 998a |
| 557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
| Full Idea: A Form is a cause of things only in the way that white mixed with white is a cause. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a |
| 9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
| Full Idea: The greatest discovery in the history of human thought is Plato's discovery of abstract objects. | |
| From: comment on Plato (works [c.375 BCE]) by James Robert Brown - Philosophy of Mathematics Ch. 2 | |
| A reaction: Compare Idea 2860! Given the diametrically opposed views, it is clearly likely that Plato's central view is the most important idea in the history of human thought, even if it is wrong. |
| 13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
| Full Idea: Due to the mathematical nature of structure and the teleological cause underlying the creation of Platonic wholes, these wholes are intelligible, and are in fact the proper objects of science. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3 | |
| A reaction: I like this idea, because it pays attention to the connection between how we conceive objects to be, and how we are able to think about objects. Only examining these two together enables us to grasp metaphysics. |
| 13782 | Everything gives way, and nothing stands fast [Heraclitus] |
| Full Idea: Everything gives way, and nothing stands fast. | |
| From: Heraclitus (fragments/reports [c.500 BCE]), quoted by Plato - Cratylus 402a | |
| A reaction: This is as good a summary of the Heraclitus view of things as any, and Plato appears to present it as a verbatim quotation. |
| 13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
| Full Idea: The 'structure' of an object tends to be characterised by Plato as something that is mathematically expressible. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3 | |
| A reaction: This seems to be pure Pythagoreanism (see Idea 644). Plato is pursuing Pythagoras's research programme, of trying to find mathematics buried in every aspect of reality. |
| 13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
| Full Idea: Plato was less concerned than Aristotle with the project of how to account, in completely general terms, for the source of unity within a mereologically complex object. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.5 | |
| A reaction: Plato seems to have simply asserted that some sort of harmony held things together. Aristotles puts the forms [eidos] within objects, rather than external, so he has to give a fuller account of what is going on in an object. He never managed it! |
| 593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
| Full Idea: Plato's doctrine was that the Forms and mathematicals are two substances and that the third substance is that of perceptible bodies. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Metaphysics 1028b |
| 11853 | A mixed drink separates if it is not stirred [Heraclitus] |
| Full Idea: The mixed drink, of wine, cheese and barley, separates if it is not stirred. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B125) | |
| A reaction: Wiggins quotes this, because it seems to be Heraclitus struggling to decide what sortal his drink falls under. I take it to be a problem of vagueness, since separation and mixing occur along a continuum, like a sorites. |
| 13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
| Full Idea: Plato considers a 'container' model for wholes (which are disjoint from their parts) [Parm 144e3-], and a 'nihilist' model, in which only wholes are mereological atoms, and a 'bare pluralities' view, in which wholes are not really one at all. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: [She cites Verity Harte for this analysis of Plato] The fourth, and best, seems to be that wholes are parts which fall under some unifying force or structure or principle. |
| 11237 | Only universals have essence [Plato, by Politis] |
| Full Idea: Plato argues that only universals have essence. | |
| From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4 |
| 11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
| Full Idea: Plato and Aristotle have a shared general conception of essence: the essence of a thing is what that thing is simply in virtue of itself and in virtue of being the very thing it is. It answers the question 'What is this very thing?' | |
| From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4 |
| 427 | It is not possible to step twice into the same river [Heraclitus] |
| Full Idea: It is not possible to step twice into the same river. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B091), quoted by Plutarch - 24: The E at Delphi 392b10- |
| 11091 | You can bathe in the same river twice, but not in the same river stage [Quine on Heraclitus] |
| Full Idea: You can bathe in the same river twice, but not in the same river stage. | |
| From: comment on Heraclitus (fragments/reports [c.500 BCE]) by Willard Quine - Identity, Ostension, and Hypostasis 1 | |
| A reaction: This seems to make Quine a 'perdurantist', committed to time-slices of objects, rather than whole objects enduring through change. |
| 2064 | If flux is continuous, then lack of change can't be a property, so everything changes in every possible way [Plato on Heraclitus] |
| Full Idea: According to Heracliteans, since things must be changing, and since lack of change can't be a property of anything, then everything is always undergoing change of every kind. | |
| From: comment on Heraclitus (fragments/reports [c.500 BCE], B030) by Plato - Theaetetus 182a |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| Full Idea: Should necessity be treated as a predicate rather than (as in modal logic) as a sentential operator? It is odd to assign different status to necessity and truth, hampering their interaction. That all necessities are true can't be expressed by an operator. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2) | |
| A reaction: [compressed] Halbach and Horsten consistently treat truth as a predicate, but maybe truth is an operator. Making necessity a predicate and not an operator would be a huge upheaval in the world of modal logic. Nice move! |
| 430 | Senses are no use if the soul is corrupt [Heraclitus] |
| Full Idea: The eyes and ears are bad witnesses for men if they have barbarian souls. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B107), quoted by Sextus Empiricus - Against the Mathematicians 7.126 |
| 1500 | When we sleep, reason closes down as the senses do [Heraclitus, by Sext.Empiricus] |
| Full Idea: Since when we sleep the senses are closed, mind is separated from its surroundings and loses the power of memory. When we wake the mind re-contacts the world, and regains the power of reason. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE], A16) by Sextus Empiricus - Against the Professors (six books) 7.130 |
| 417 | Donkeys prefer chaff to gold [Heraclitus] |
| Full Idea: Donkeys prefer chaff to gold. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B009), quoted by Aristotle - Nicomachean Ethics 1176a07 |
| 426 | Sea water is life-giving for fish, but not for people [Heraclitus] |
| Full Idea: Sea-water is the purest and the most polluted: for fish it is drinkable and life-giving; for men, not drinkable and destructive. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B061), quoted by Hippolytus - Refutation of All Heresies 9.10.5 |
| 431 | Health, feeding and rest are only made good by disease, hunger and weariness [Heraclitus] |
| Full Idea: Disease makes health pleasant and good, hunger makes satisfaction good, weariness makes rest good. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B111), quoted by John Stobaeus - Anthology 3.1.178 |
| 17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
| Full Idea: For Plato, an acceptable explanation is one such that there is no possibility of there being the opposite explanation at all, and he thought that only explanations in terms of the Forms, but never physical explanations, could meet this requirement. | |
| From: report of Plato (works [c.375 BCE]) by David-Hillel Ruben - Explaining Explanation Ch 2 | |
| A reaction: [Republic 436c is cited] |
| 1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
| Full Idea: Plato put high on his agenda a project which did not figure in Socrates' programme at all: the hygienic conditioning of the passions. This cannot be an intellectual process, as argument cannot touch them. | |
| From: comment on Plato (works [c.375 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.88 | |
| A reaction: This is the standard traditional view of any thinker who exaggerates the importance and potential of reason in our lives. |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
| Full Idea: Being able to ascribe the same proposition as a belief to persons who do not have a common language seems to be one of the main reasons to employ propositions. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 2) | |
| A reaction: Propositions concern beliefs, as well as sentence meanings. I would want to say that a dog and I could believe the same thing, and that is a non-linguistic reason to believe in propositions. Maybe 'translation' cuts out the proposition middleman? |
| 3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
| Full Idea: Plato is liable to the charge of having been duped by a figure of speech, albeit the most profound of all, the trope of reification. | |
| From: comment on Plato (works [c.375 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.12 | |
| A reaction: That might be a plausible account if his view was ridiculous, but given how many powerful friends Plato has, especially in the philosophy of mathematics, we should assume he was cleverer than that. |
| 429 | To God (though not to humans) all things are beautiful and good and just [Heraclitus] |
| Full Idea: To God, all things are beautiful, good and just; but men have assumed some things to be unjust, others just. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B102), quoted by Porphyry - Notes on Homer Il.4.4 | |
| A reaction: The idea that all things are actually 'just' strikes me as nonsense. I also don't think I can get my head round the idea that everything is actually good and beautiful. Must try harder. |
| 12294 | Good and evil are the same thing [Heraclitus, by Aristotle] |
| Full Idea: Heraclitus said that good and evil are the same thing. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE], 58/102) by Aristotle - Topics 159b32 | |
| A reaction: Heaven knows what he meant by this, though it sounds suspiciously like moral nihilism. Maybe Heraclitus was not a very nice man. Or is the thought a more sophisticated one, in line with Nietzsche's remarks about cultural morality? |
| 7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
| Full Idea: Plato never speaks of the examination of conscience - never! | |
| From: report of Plato (works [c.375 BCE]) by Michel Foucault - On the Genealogy of Ethics p.276 | |
| A reaction: Plato does imply some sort of self-evident direct knowledge about that nature of a healthy soul. Presumably the full-blown concept of conscience is something given from outside, from God. In 'Euthyphro', Plato asserts the primacy of morality (Idea 337). |
| 2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
| Full Idea: Once gods and fate and social expectation were no longer there, Plato felt it necessary to discover ethics inside human nature, not just as ethical knowledge (Socrates' view), but in the structure of the soul. | |
| From: comment on Plato (works [c.375 BCE]) by Bernard Williams - Shame and Necessity II - p.43 | |
| A reaction: anti Charles Taylor |
| 419 | If one does not hope, one will not find the unhoped-for, since nothing leads to it [Heraclitus] |
| Full Idea: If one does not hope, one will not find the unhoped-for, since there is no trail leading to it and no path. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B018), quoted by Clement - Miscellanies 2.17.4 | |
| A reaction: The best remark about hope I have ever encountered. Usually they are empty platitudes. |
| 9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
| Full Idea: Plato's legacy to European thought was a trio of capital letters - the Good, the Beautiful and the True. | |
| From: report of Plato (works [c.375 BCE]) by John Gray - Straw Dogs 2.8 | |
| A reaction: It seems to have been Baumgarten who turned this into a slogan (Idea 8117). Gray says these ideals are lethal, but I identify with them very strongly, and am quite happy to see the good life as an attempt to find the right balance between them. |
| 94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
| Full Idea: Plato says the life of pleasure is more desirable with the addition of intelligence, and if the combination is better, pleasure is not the good. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Nicomachean Ethics 1172b27 | |
| A reaction: It is obvious why we like pleasure, but not why intelligence makes it 'better'. Maybe it is just because we enjoy intelligence? |
| 415 | If happiness is bodily pleasure, then oxen are happy when they have vetch to eat [Heraclitus] |
| Full Idea: If happiness lay in bodily pleasures, we would call oxen happy when they find vetch to eat. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B004), quoted by Albertus Magnus - On Vegetables 6.401 | |
| A reaction: But surely oxen are happy when they find some good vetch? Presumably, though, they are not 'eudaimon'. What is the complete fulfilment of life for an ox? |
| 17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
| Full Idea: Plato came to the conclusion that virtue and happiness consist in the life of philosophy itself. | |
| From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.117 | |
| A reaction: This view is obviously ridiculous, because it largely excludes almost the entire human race, which sees philosophy as a cul-de-sac, even if it is good. But virtue and happiness need some serious thought. |
| 5155 | It is hard to fight against emotion, but harder still to fight against pleasure [Heraclitus] |
| Full Idea: It is hard to fight against emotion, but harder still to fight against pleasure. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B085), quoted by Aristotle - Nicomachean Ethics 1105a08 | |
| A reaction: 'Emotion' is the Greek word 'thumos'. "The only way to get rid of a temptation is to yield to it", said Oscar Wilde. Heraclitus underestimates how very good many modern people are at dieting. |
| 6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
| Full Idea: Two virtues that are ordinarily kept distinct - theoretical and practical wisdom - are joined by Plato; he thinks that neither one can be fully possessed unless it is combined with the other. | |
| From: report of Plato (works [c.375 BCE]) by Richard Kraut - Plato | |
| A reaction: I get the impression that this doctrine comes from Socrates, whose position is widely reported as 'intellectualist'. Aristotle certainly held the opposite view. |
| 433 | For man character is destiny [Heraclitus] |
| Full Idea: For man character is destiny. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B119), quoted by John Stobaeus - Anthology 4.40.23 | |
| A reaction: This is the extreme opposite of Sartre's existentialist claim that we can entirely change ourselves. Personally I am with Heraclitus, though I don't see why our destined character shouldn't be modified (e.g. by education). |
| 2912 | Plato is boring [Nietzsche on Plato] |
| Full Idea: Plato is boring. | |
| From: comment on Plato (works [c.375 BCE]) by Friedrich Nietzsche - Twilight of the Idols 9.2 |
| 422 | The people should fight for the law as if for their city-wall [Heraclitus] |
| Full Idea: The people should fight for the law as if for their city-wall. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B044), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.2 | |
| A reaction: This may be the first recorded assertion of the rule of law, and hence of the separation of powers. We still have plenty of people who reject this principle. |
| 614 | Heraclitus said sometimes everything becomes fire [Heraclitus, by Aristotle] |
| Full Idea: Heraclitus claimed that from time to time everything becomes fire. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Metaphysics 1067a |
| 424 | Reason tells us that all things are one [Heraclitus] |
| Full Idea: When you have listened, not to me but to the law (logos), it is wise to agree that all things are one. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B050), quoted by Hippolytus - Refutation of All Heresies 9.9.1 |
| 5096 | Heraclitus says that at some time everything becomes fire [Heraclitus, by Aristotle] |
| Full Idea: Heraclitus says that at some time everything becomes fire. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Physics 204b37 | |
| A reaction: Modern cosmology says that Heraclitus was right (pretty much). If we say 'energy' instead of 'fire' (which may be what he meant), then he is absolutely spot-on. |
| 17539 | The sayings of Heraclitus are still correct, if we replace 'fire' with 'energy' [Heraclitus, by Heisenberg] |
| Full Idea: If we replace Heraclitus's word 'fire' by the word 'energy' we can almost repeat his statements word for word from our modern point of view. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Werner Heisenberg - Physics and Philosophy 04 | |
| A reaction: My problem has always been that I have no idea what 'energy' is, so I'm none the wiser. |
| 3054 | Heraclitus said fire could be transformed to create the other lower elements [Heraclitus, by Diog. Laertius] |
| Full Idea: Heraclitus taught that fire when densified becomes liquid, and becoming concrete, becomes also water; again, that the water when concrete is turned to earth, and this is the road down. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.1.6 |
| 15660 | Logos is the source of everything, and my theories separate and explain each nature [Heraclitus] |
| Full Idea: All things come into being according to this Law ('logos'), ...and I expound theories (words) and processes (actions) separating each thing according to its nature and explaining how it is made. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B001), quoted by Sextus Empiricus - Against the Mathematicians 7.133 | |
| A reaction: I like the fact that things are separated according to their natures (particulars!), and not that natures are somehow bestowed on individuals. |
| 12269 | All things are in a state of motion [Heraclitus, by Aristotle] |
| Full Idea: All things are in a state of motion. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Topics 104b22 | |
| A reaction: This seems right, I would say. It seems to make a 'process' the fundamental category of ontology, rather than an 'object'. |
| 1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |
| Full Idea: With a single exception (Plato) everyone agrees about time - that it is not generated. Democritus says time is an obvious example of something not generated. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Physics 251b14 |
| 420 | The cosmos is eternal not created, and is an ever-living and changing fire [Heraclitus] |
| Full Idea: This cosmos, which is the same for all, was not created by any one of the gods or of mankind, but it was ever and is and shall be ever-living fire, kindled and quenched in measure. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B030), quoted by Clement - Miscellanies 5.1.103 |
| 1499 | Heraclitus says intelligence draws on divine reason [Heraclitus, by Sext.Empiricus] |
| Full Idea: According to Heraclitus we become intelligent by drawing on divine reason. | |
| From: report of Heraclitus (fragments/reports [c.500 BCE], A16) by Sextus Empiricus - Against the Professors (six books) 7.129 |
| 15659 | Purifying yourself with blood is as crazy as using mud to wash off mud [Heraclitus] |
| Full Idea: They purify themselves by staining themselves with other blood, as if one were to step into mud to wash off mud. But a man would be thought mad if any of his fellow-men should perceive him acting thus. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B005), quoted by Origen - Against Celsus 7.62 |
| 1501 | In their ignorance people pray to statues, which is like talking to a house [Heraclitus] |
| Full Idea: In their ignorance of the true nature of gods and heroes people pray to these statues, which is like someone holding a conversation with a house. | |
| From: Heraclitus (fragments/reports [c.500 BCE], B005), quoted by Anon (Pyth) - Theosophia Tubigensis 68 |