115 ideas
| 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. |
| 20910 | Everything happens necessarily, and for a reason [Democritus] |
| Full Idea: Nothing happens at random, but everything for a reason and as the effect of necessity. | |
| From: Democritus (fragments/reports [c.431 BCE], B002), quoted by Pseudo-Plutarch - On the Doctrine of the Philosophers 1.25.4 | |
| A reaction: [In Aetius 'Stob'] This remark reminds us of the link between necessity and sufficient reason. Do all reasons arise for a reason? |
| 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. |
| 15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
| Full Idea: It is far from clear that a definition of truth can lead to a philosophically satisfactory theory of truth. Tarski's theorem on the undefinability of the truth predicate needs resources beyond those of the language for which it is being defined. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: The idea is that you need a 'metalanguage' for the definition. If I say 'p' is a true sentence in language 'L', I am not making that observation from within language L. The dream is a theory confined to the object language. |
| 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. |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| Full Idea: In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources. |
| 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) |
| 15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
| Full Idea: Axiomatic theories of truth can be presented within very weak logical frameworks which require very few resources, and avoid the need for a strong metalanguage and metatheory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) |
| 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) |
| 15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
| Full Idea: If truth is not explanatory, truth axioms should not allow proof of new theorems not involving the truth predicate. It is hence said that axiomatic truth should be 'conservative' - not implying further sentences beyond what the axioms can prove. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: [compressed] |
| 15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
| Full Idea: The axiomatic approach does not presuppose that truth can be defined. Instead, a formal language is expanded by a new primitive predicate of truth, and axioms for that predicate are then laid down. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Idea 15647 explains why Halbach thinks the definition route is no good. |
| 15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
| Full Idea: If truth can be explicitly defined, it can be eliminated, whereas an axiomatized notion of truth may bring all kinds of commitments. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: The general principle that anything which can be defined can be eliminated (in an abstract theory, presumably, not in nature!) raises interesting questions about how many true theories there are which are all equivalent to one another. |
| 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. |
| 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) |
| 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). |
| 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) |
| 15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
| Full Idea: According to many deflationists, truth serves merely the purpose of expressing infinite conjunctions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: That is, it asserts sentences that are too numerous to express individually. It also seems, on a deflationist view, to serve for anaphoric reference to sentences, such as 'what she just said is true'. |
| 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? |
| 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) |
| 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. |
| 15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
| Full Idea: The consistency of set theory cannot be established without assumptions transcending set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 2.1) |
| 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. |
| 15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
| Full Idea: The reduction of 2nd-order theories (of properties or sets) to axiomatic theories of truth may be conceived as a form of reductive nominalism, replacing existence assumptions (for comprehension axioms) by ontologically innocent truth assumptions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I like this very much, as weeding properties out of logic (without weeding them out of the world). So-called properties in logic are too abundant, so there is a misfit with their role in science. |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
| Full Idea: Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates. |
| 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) |
| 16146 | Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle] |
| Full Idea: Democritus claimed that one substance could not be composed from two nor two from one. …The same will clearly go for number, on the popular assumption that number is a combination of units. Unless two is one, it cannot contain a unit in actuality. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Aristotle - Metaphysics 1039a15 | |
| A reaction: Chrysippus followed this up the first part with the memorable example of Dion and Theon. The problem with the second part is that 2, 3 and 4 are three numbers, so they can count as meta-units. |
| 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). |
| 20901 | True Being only occurs when it is completely full, with atoms and no void [Democritus, by Aristotle] |
| Full Idea: In response to defenders of the One, Democritus says that what is, in the proper sense, is being that is completely full, but that such a being is not one, but that they are unlimited in number and invisible because of the smallness of their masses. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A007) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325a28 | |
| A reaction: Democritus is in a tangle here. He says proper being has no void, having apparently conceded that motion needs void (which he admits is non-existent). So true being only occurs when everything grinds to a halt, which is not now. But Idea 20902. |
| 20902 | Being does not exist more than non-being [Democritus, by Aristotle] |
| Full Idea: They say that being does not exist more than non-being, because neither does the void exist more than the body. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A006) by Aristotle - Metaphysics 0985b09 | |
| A reaction: The claim that Being and Non-Being are the same thing is pretty startling. It seems to be an expedient to get Void into the picture, even though it is taken to be wholly devoid of qualities. |
| 20904 | The non-existent exists as much as the existent, because it has causal powers [Democritus] |
| Full Idea: What exists does not exist at all more than what does not exist, and both are causes in a similar way for the things that come about. | |
| From: Democritus (fragments/reports [c.431 BCE], A008), quoted by Simplicius - On Aristotle's 'Physics' p.28.4-27 | |
| A reaction: [Simplicius actually attributes this to the shadowy Leucippus] You can see the point. If you drive into a pothole, that has considerable causal powers. |
| 20903 | The only distinctions are Configuration (shape), Disposition (order) and Turning (position) [Democritus, by Aristotle] |
| Full Idea: They say that what is differs only by Configuration ([rhusmos], which is the shape), by Disposition ([diathege], which is the order), and by Turning ([tropê], which is the position. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A006) by Aristotle - Metaphysics 0985b16 | |
| A reaction: If you give the shape, structure and position of an object, there is no much more to say. Perhaps mention time. |
| 20893 | Nothing comes from non-existence, or passes into it [Democritus, by Diog. Laertius] |
| Full Idea: Nothing comes into being from what does not exist, nor is it destroyed into what does not exist. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A001) by Diogenes Laertius - Lives of Eminent Philosophers 09.44 | |
| A reaction: [part of a concise summary of Democritus by DL] Probably an intuition about conservation laws, rather than a speculation about the Big Bang. |
| 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. |
| 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. |
| 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. |
| 20896 | It is not possible to know what sort each thing is [Democritus] |
| Full Idea: In reality [eteé] to recognise what sort each thing is, belongs to what is impracticable [aporos]. | |
| From: Democritus (fragments/reports [c.431 BCE], B008), quoted by Sextus Empiricus - Against the Logicians (two books) 7.137 | |
| A reaction: On the whole modern scientists (and the rest of us) shoehorn virtually everything into a specific category. It strikes me as wildly bad metaphysics to say that everything necessarily has its category. |
| 3357 | Democritus denies reality to large objects, because atomic entities can't combine to produce new ones [Benardete,JA on Democritus] |
| Full Idea: Democritus appears to rule out from his austere ontology all so-called emergent entities - even mountains and rivers - on the ground that two or more entities can never combine to produce a new one. | |
| From: comment on Democritus (fragments/reports [c.431 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.24 |
| 598 | Democritus said that substances could never be mixed, so atoms are the substances [Democritus, by Aristotle] |
| Full Idea: Democritus claimed that one substance could not be composed from two nor two from one; for him it is the atoms that are the substances. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Aristotle - Metaphysics 1039a10 |
| 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! |
| 1532 | Sensible qualities can't be real if they appear different to different creatures [Democritus, by Theophrastus] |
| Full Idea: As proof of the fact that sensible qualities have no real existence he points to the fact that they do not appear the same to all creatures. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A135) by Theophrastus - On the Senses 63 |
| 20894 | Man is separated from reality [Democritus] |
| Full Idea: It is necessary to recognise that man by virtue of this criterion is separated from reality. | |
| From: Democritus (fragments/reports [c.431 BCE], B006), quoted by Sextus Empiricus - Against the Logicians (two books) 7.137 | |
| A reaction: I don't know what 'this criterion' is, but it strikes me as quite a good slogan for fans (like myself) of the representative theory of perception. Critics say it is the big objection to the representative theory, but I say 'get over it'. |
| 517 | All evidence comes from senses, so they are indispensable to the mind [Democritus] |
| Full Idea: Mind must never reject the senses, because that is where it gets its evidence, and it would be the mind's downfall. | |
| From: Democritus (fragments/reports [c.431 BCE], B125), quoted by Galen - On Medical Experience 15.8 |
| 20897 | Obscure knowledge belongs to the five senses, and genuine knowledge is the other type [Democritus] |
| Full Idea: There are two forms of knowledge [gnomé], the one genuine, the other obscure. And to the obscure one belongs all of these: sight, hearing, smell, taste, touch. The other is genuine, and is separated from this one. | |
| From: Democritus (fragments/reports [c.431 BCE], B011), quoted by Sextus Empiricus - Against the Logicians (two books) 7.139 | |
| A reaction: [Sextus goes on to make it clear that the 'genuine' one is knowledge acquired by thought]. I take Parmenides to be the first rationalist. It is interesting that Democritus, who devoted his life to finding causal explanations, seems to be a rationalist. |
| 577 | Democritus says there is either no truth, or it is concealed from us [Democritus, by Aristotle] |
| Full Idea: Democritus concludes that either there is no truth or it is concealed from us. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A112) by Aristotle - Metaphysics 1009b12 |
| 20895 | We actually know nothing, and opinions are mere flux [Democritus] |
| Full Idea: Certainly this argument too makes it clear that in reality [eteé] we know nothing about anything, but for each person opinion is a rhythmic afflux [epirhusmié]. | |
| From: Democritus (fragments/reports [c.431 BCE], B007), quoted by Sextus Empiricus - Against the Logicians (two books) 7.137 | |
| A reaction: This seems to pick 'all is flux' up from Heraclitus, and make Democritus (along with aspects of Socrates) the true source of ancient scepticism. |
| 1528 | We in fact know nothing, but we each restructure our reality with beliefs [Democritus] |
| Full Idea: In reality we know nothing about anything, but belief restructures things for each of us. | |
| From: Democritus (fragments/reports [c.431 BCE], B007), quoted by Sextus Empiricus - Against the Professors (six books) 7.136 |
| 492 | It is obviously impossible to understand the reality of each thing [Democritus] |
| Full Idea: It will be obvious that it is impossible to understand how in reality each thing is. | |
| From: Democritus (fragments/reports [c.431 BCE], B008), quoted by Sextus Empiricus - Against the Professors (six books) 7.137 |
| 515 | We know nothing in reality; for truth lies in an abyss [Democritus] |
| Full Idea: We know nothing in reality; for truth lies in an abyss. | |
| From: Democritus (fragments/reports [c.431 BCE], B117), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.72.10 |
| 20892 | Democritus was devoted to discovering causal explanations [Democritus, by Eusebius] |
| Full Idea: Democritus himself, as they say, stated that he would rather discover a single causal explanation [aitiologia] than become the King of the Persians. | |
| From: report of Democritus (fragments/reports [c.431 BCE], B118) by Eusebius - Preparation for the Gospel 14.27.4 | |
| A reaction: Democritus seems to be clearly the father of the physical sciences, because he focused single-mindedly on physical and causal explanations. David Lewis says all explanations are causal. |
| 5882 | Democritus says soul consists of smooth round bodies brought together in accidental collision [Democritus, by Cicero] |
| Full Idea: Since Democritus makes the soul consist of minute smooth round bodies brought together in some sort of accidental collision, let us pass him over. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by M. Tullius Cicero - Tusculan Disputations I.xi.23 | |
| A reaction: If we accept that Democritus thought the collision of atoms 'accidental', then it doesn't sound like a very good theory. What would Cicero say if we replaced 'accidental' with 'naturally selected'? |
| 6034 | Atomists say soul has a rational part in the chest, and a diffused non-rational part [Democritus, by Aetius] |
| Full Idea: Democritus and Epicurus say the soul has two parts, one which is rational and is situated in the chest area, and the other which is non-rational and is spread throughout the entire compound of the body. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Aetius - fragments/reports 4.4.6 | |
| A reaction: The spread part corresponds to such things as feeling fear in the stomach, or excitement throughout the limbs. I can't think what grounds there would be for choosing the chest as the home of reason. I suppose you can hear reason thumping in there.. |
| 20912 | The soul is the same as the mind [Democritus, by Aristotle] |
| Full Idea: Democritus says the soul is the same thing as the mind. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A101) by Aristotle - De Anima 405a10 | |
| A reaction: This is not in contrast to the Christian concept of the soul, but in contrast to the normal view of psuché, which is more like the life that permeates the whole body. Democritus was more in tune than Aristotle with modern thought on this. |
| 20916 | Animals have a share of reason [Democritus, by Porphyry] |
| Full Idea: Democritus recognised that animals have a share of reason. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Porphyry - On Abstinence 3.6.7 | |
| A reaction: Since he considers thinking to be the interaction of atoms in the body, which animals evidently possess, this seems consistent. No one seems to observed animals closely before the 20th century, other than to exploit them. |
| 20914 | The directive centre is located in the whole head [Democritus, by Ps-Plutarch] |
| Full Idea: Democritus says [the directive centre is located] in the whole head. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A105) by Pseudo-Plutarch - On the Doctrine of the Philosophers 4.5.1 | |
| A reaction: The whole head is not quite the brain, but he is getting very warm indeed, and long before anyone else got so close. |
| 6033 | Democritus said everything happens of necessity, by natural motion of atoms [Democritus, by Cicero] |
| Full Idea: Democritus, the founder of atomism, preferred to accept that all things happened by necessity than to tear from the atomic bodies their natural motions. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by M. Tullius Cicero - On Fate ('De fato') §22 | |
| A reaction: This is in opposition to Epicurus, who said that atoms can have a 'swerve', making free will possible. It is suggested that Epicurus was the first to really grasp the problem of free will. Democritus was just stating the (to him) obvious. |
| 5088 | Some say there is a determinate cause for every apparently spontaneous event [Democritus, by Aristotle] |
| Full Idea: Some people (Democritus?) say there is no such thing as a chance event; they claim that there is always a determinate cause for everything which is said to be a chance or a spontaneous event. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Aristotle - Physics 195b37 | |
| A reaction: This is the mutual implication of physicalism and determinism, which strikes me as unavoidable. I say: don't panic about morality because determinism is true. Embrace determinism - it is harmless and true. Its opposite is a nonsense. |
| 21670 | Democritus said atoms only move by their natural motions, which are therefore necessary [Democritus, by Cicero] |
| Full Idea: The author of the atomic theory, Democritus, preferred to accept the view that all events are caused by necessity, rather than to deprive the atoms of their natural motions. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by M. Tullius Cicero - On Fate ('De fato') 10.23 | |
| A reaction: The 'deprivation' would have to be caused by mind, or by the later 'swerve' of Epicurus. |
| 24041 | Democritus says spherical atoms are fire, and constitute the soul [psuche] [Democritus, by Aristotle] |
| Full Idea: Democritus says the soul is a sort of fire. For the shapes and atoms are unlimitied and those that are spherical he says are fire and soul - which are like the motes in the air when sunbeams come through the window. | |
| From: report of Democritus (fragments/reports [c.431 BCE], DK 67-68) by Aristotle - De Anima 403b31 | |
| A reaction: It's hard to see why the spherical atoms should be fire. Maybe because they move together quickly and easily. …At 404a5 Aristotle agrees with me! |
| 20913 | Democritus says the soul is the body, and thinking is thus the mixture of the body [Democritus, by Theophrastus] |
| Full Idea: Democritus explains thinking by the mixture of the body, which is surely in accordance with his reasoning, since he makes the soul the body. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A135) by Theophrastus - On the Senses 58 | |
| A reaction: I agree with Democritus. |
| 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? |
| 1540 | Pleasure and pain guide our choices of good and bad [Democritus] |
| Full Idea: The guides to what is good and bad for people are pleasure and pain. | |
| From: Democritus (fragments/reports [c.431 BCE], B188), quoted by John Stobaeus - Anthology 3.01.46 |
| 495 | Wisdom creates a healthy passion-free soul [Democritus] |
| Full Idea: Medicine heals diseases of the body, wisdom frees the soul from passions. | |
| From: Democritus (fragments/reports [c.431 BCE], B031), quoted by Clement - Pedagogue 1.6.2.1 | |
| A reaction: The interesting concept of a healthy mind seems to have got lost in modern moral philosophy. |
| 1537 | Happiness is identifying and separating the pleasures [Democritus, by Stobaeus] |
| Full Idea: Democritus thinks that happiness consists in the determination and separation of pleasures, and that this is what is both finest and most beneficial for people. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A167) by John Stobaeus - Anthology 2.07.3 | |
| A reaction: A great deal of the strategy and ethics of living consists (if you are lucky) of discriminating among possible pleasures. Philosophers should produce criteria. |
| 20917 | Contentment comes from moderation and proportion in life [Democritus, by Stobaeus] |
| Full Idea: Contentment [euthumia] comes about for human beings from the moderation of enjoyment and proportion [summetria] in life. | |
| From: report of Democritus (fragments/reports [c.431 BCE], B191) by John Stobaeus - Anthology 3.1.210 | |
| A reaction: This is close to Aristotle's doctrine of the Mean. The majority of ethical ideas attributed to Democritus (presumably by the Epicureans) are thought to be spurious. This idea actually sounds rather stoic. |
| 13551 | Democritus says wealth is a burden to the virtuous mind [Democritus, by Seneca] |
| Full Idea: Democritus rejected wealth, regarding it as a burden to the virtuous mind. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Seneca the Younger - On Providence §6 | |
| A reaction: The rival view is that wealth empowers a virtuous person to perform more fine deeds. Democritus seems to have a rather solitary view of virtue. |
| 20899 | Atoms cling together, until a stronger necessity disperses them [Democritus, by Aristotle] |
| Full Idea: Democritus thinks that the substances hold on to one another and remain together for a length of time until some stronger necessity arising from their surroundings shakes and disperses them. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A037) by Aristotle - On Democritus (frag) | |
| A reaction: [quoted in Simplicius, Commentary on Aristotle's On the Heavens] He's not wrong. This seems to provide a mechanism for the Heracltean flux. Ancient critics wanted to know where the 'stronger necessity' came from. |
| 20898 | Atoms are irregular, hooked, concave, convex, and many other shapes [Democritus, by Aristotle] |
| Full Idea: Some substances are irregular, others hook-shaped, other concave, other convex, others provided with innumerable other differences. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A037) by Aristotle - On Democritus (frag) | |
| A reaction: [quoted in Simplicius, Commentary on Aristotle's On the Heavens] 'Substance' here means a fundamental object, which for Democritus is an undividable atom. |
| 20908 | There could be an atom the size of the world [Democritus, by Ps-Plutarch] |
| Full Idea: Democritus say that it is possible that there exists an atom of the size of the world. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A047) by Pseudo-Plutarch - On the Doctrine of the Philosophers 1.12.6 | |
| A reaction: The editor says this may have been a criticism of Democritus - presumably a reductio ad absurdum. But Democritus has no upper limit on the size of an atom. It challenges the imagination to treat such a huge thing as indivisible. |
| 1527 | There must be atoms, to avoid the absurdity of infinite division down to nothing [Democritus, by Aristotle] |
| Full Idea: If everything is infinitely divided, what survives the divisions? Alternatively, division would end at points with no magnitude, in which case bodies are composed of nothing. This is the argument claiming there are atoms of some magnitude. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A048b) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 316a14- |
| 493 | Experiences are merely convention; only atoms and the void are real [Democritus] |
| Full Idea: Sweet exists by convention, bitter by convention, colour by convention; atoms and void alone exist in reality. | |
| From: Democritus (fragments/reports [c.431 BCE], B009), quoted by Sextus Empiricus - Against the Logicians (two books) 7.135 |
| 20909 | The basic atoms are without qualities - which only arise from encounters between atoms [Democritus, by Galen] |
| Full Idea: Democritus and the Epicureans posit that the first element is without quality, possessing by nature neither whiteness, blackness, sweetness or bitterness, warmth or cold. ...It is from the encounter of the atoms that all the sensible qualities come about. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A049) by Galen - On Hippocrates and Plato 1.2 | |
| A reaction: Idea 493 comes in the middle of this summary by Galen. Hence atoms play the role that substrates play in object-based metaphysics. So atoms have the same problem. Is the shape of an atom a quality of an atom. Or are qualities what atoms DO? |
| 1536 | If a cone is horizontally sliced the surfaces can't be equal, so it goes up in steps [Democritus] |
| Full Idea: If a cone is cut parallel to the base are the two new surfaces equal or unequal? If they are unequal, the cone must have gone up in steps. If they are equal then the cone must have been a cylinder, which is absurd. | |
| From: Democritus (fragments/reports [c.431 BCE], B155), quoted by Plutarch - 72: Against Stoics on common Conceptions 1079e1 |
| 17542 | 'Full' and 'Void' secularised Parmenides's Being and Not-being [Democritus, by Heisenberg] |
| Full Idea: In atomism, the antithesis of Being and Not-being of Parmenides is secularised into the antithesis of the 'Full' and the 'Void'. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Werner Heisenberg - Physics and Philosophy 04 |
| 1525 | Atomists say there are only three differences - in shape, arrangement and position [Democritus, by Aristotle] |
| Full Idea: Democritus and Leucippus say that there are only three differences - in shape, arrangement and position. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A006) by Aristotle - Metaphysics 0985b15 |
| 5947 | If only atoms are real and the rest is convention, we wouldn't bother to avoid pain [Democritus, by Diogenes of Oen.] |
| Full Idea: Democritus erred when he said that the atoms alone exist in truth among realities, but everything else is convention; for then, far from discovering the truth, we shall not even be able to live, since we shall avoid neither fire nor wounds. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Diogenes (Oen) - fragments/reports F2 7 | |
| A reaction: The point is that we have to treat pain as a reality, not just as a convention. I suspect that Diogenes is making the same mistake made by modern attackers of 'eliminativism'. It is all about identity and reduction and levels of reality… |
| 13219 | When atoms touch, why don't they coalesce, like water drops? [Aristotle on Democritus] |
| Full Idea: Why, when they come into contact, do they [atoms] not coalesce into one, as drops of water run together when drop touches drop? | |
| From: comment on Democritus (fragments/reports [c.431 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 326a33 | |
| A reaction: Presumably we must think of atoms as having basic ontological unity, rather than as being little globules of 'stuff'. They are more like monads than they are like mud. |
| 1533 | Because appearance is infinitely varied, atomists assume infinitely many shapes of atom [Democritus, by Aristotle] |
| Full Idea: They thought that truth lay in appearances, which they appreciated are contradictory and infinite, so they made the shapes of atoms infinite. Thus the infinite changes in compounds create the infinitely varies appearances. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A009) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 315b9 |
| 23314 | Greeks explained regularity by intellectual design, not by laws [Democritus, by Frede,M] |
| Full Idea: It is clear that Democritus had no idea of laws of nature …for in Greek thought regularity of behaviour is associated with design by an intellect. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Michael Frede - A Free Will Intro | |
| A reaction: Ah. A simple realisation…! Seventeenth century laws of nature offered an explanation of natural order which didn't rely on God. Even though those scientists were all theists. |
| 24059 | Democritus is wrong: in a void we wouldn't see a distant ant in exact detail [Aristotle on Democritus] |
| Full Idea: Democritus did not speak correctly in supposing that if the intermediate space became a void, we would see an ant in exact detail if it were up in the heaven. …If the intermediate space became a void, rather nothing would be seen at all. | |
| From: comment on Democritus (fragments/reports [c.431 BCE]) by Aristotle - De Anima 419a15 | |
| A reaction: Depends what you mean by void, but Aristotle is nearer the truth. Is vision clearer in outer space than in our higher atmosphere? |
| 5101 | Movement is impossible in a void, because nothing can decide the direction of movement [Aristotle on Democritus] |
| Full Idea: Void makes it impossible for anything to move, since in a void there is nowhere for a thing to move to more or less than anywhere else, because the void by definition contains no differentiation. | |
| From: comment on Democritus (fragments/reports [c.431 BCE]) by Aristotle - Physics 214b32 | |
| A reaction: A lovely application of the Principle of Sufficient Reason. However this assumes that the cause of the movement is going to be in the void (telos?), rather than in the body which will move (modern causation?). |
| 20905 | Growth and movement would not exist if there were no void to receive them [Democritus] |
| Full Idea: They say that one argument for void is that otherwise local motion (that is, locomotion and growth) would not exist: for there would not seem to be motion if there were no void, for what is full is incapable of receiving anything. | |
| From: Democritus (fragments/reports [c.431 BCE], A019), quoted by Aristotle - Physics 213b03 | |
| A reaction: The modern concept of a 'field' seems to have removed the possibility of a genuine 'void'. |
| 20911 | There are unlimited worlds of varying sizes, some without life or water [Democritus, by Hippolytus] |
| Full Idea: Democritus says that there exist unlimited worlds and that they are different in magnitude. ...Some worlds are devoid of animals and plants and of all humidity. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A010, A040) by Hippolytus - Refutation of All Heresies 1.12,13.2-4 | |
| A reaction: I'm not clear why Democritus came up with the idea of the Multicosmos. I don't suppose he meant the moon or planets, but another Cosmos. |
| 1535 | Democritus said people imagined gods as the source of what awed or frightened them [Democritus, by Sext.Empiricus] |
| Full Idea: Democritus thought that people imagined gods as responsible for the frightening and awesome things that happen in this world. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A075) by Sextus Empiricus - Against the Professors (six books) 9.24 |
| 20915 | The soul is destroyed with the body [Democritus, by Ps-Plutarch] |
| Full Idea: Democritus says the soul is destructible, and is destroyed together with the whole body. | |
| From: report of Democritus (fragments/reports [c.431 BCE], A109) by Pseudo-Plutarch - On the Doctrine of the Philosophers 4.7.4 | |
| A reaction: This is the only belief possible for Democritus, since everything, including life and soul, is just the confluence of atoms, and they are regularly dispersed. This is the epitome of materialist philosophy. |