116 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. |
224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
From: Plato (Parmenides [c.364 BCE], 135e) |
19917 | Without reason and human help, human life is misery [Spinoza] |
Full Idea: Without mutual help and the cultivation of reason, human beings necessarily live in great misery. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.05) | |
A reaction: A clarion call from a great voice of the Enlightenment. I agree, but in 2017 the rest of western civilization seems to have given up on this ideal. I blame Adorno and Horkheimer. |
232 | Opposites are as unlike as possible [Plato] |
Full Idea: Opposites are as unlike as possible. | |
From: Plato (Parmenides [c.364 BCE], 159a) |
8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
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) |
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) |
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. |
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) |
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. |
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. |
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) |
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. |
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] |
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) |
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. |
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? |
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) |
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) |
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? |
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) |
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. |
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. |
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) |
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. |
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). |
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. |
13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
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. |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
From: Plato (Parmenides [c.364 BCE], 144a) | |
A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
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). |
229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
From: Plato (Parmenides [c.364 BCE], 155d) | |
A reaction: This seems to be rhetorical, rather a precise theory, given that the One is said to be eternal and unchanging. The One is not just what we call 'reality'. |
21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
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. |
221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
From: Plato (Parmenides [c.364 BCE], 134c) | |
A reaction: These seems to thoroughly pre-empt Plato's Theory of Forms a century before he created it. Which shows (as Simone Weil says) that Plato was just part of a long tradition. |
227 | You must always mean the same thing when you utter the same name [Plato] |
Full Idea: You must always mean the same thing when you utter the same name. | |
From: Plato (Parmenides [c.364 BCE], 147d) |
223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
From: Plato (Parmenides [c.364 BCE], 135c) |
210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
From: Plato (Parmenides [c.364 BCE], 130d) |
219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
From: Plato (Parmenides [c.364 BCE], 133c) |
228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
From: Plato (Parmenides [c.364 BCE], 149e) |
211 | If admirable things have Forms, maybe everything else does as well [Plato] |
Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
From: Plato (Parmenides [c.364 BCE], 130d) |
220 | The concept of a master includes the concept of a slave [Plato] |
Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
From: Plato (Parmenides [c.364 BCE], 133e) |
16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
From: Plato (Parmenides [c.364 BCE], 132c) |
212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
From: Plato (Parmenides [c.364 BCE], 131a) |
213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
From: Plato (Parmenides [c.364 BCE], 131b) |
216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
From: Plato (Parmenides [c.364 BCE], 132e) |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
From: Plato (Parmenides [c.364 BCE], 133a) |
217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
From: Plato (Parmenides [c.364 BCE], 133a) |
214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
From: Plato (Parmenides [c.364 BCE], 132a) |
15851 | Parts must belong to a created thing with a distinct form [Plato] |
Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
From: Plato (Parmenides [c.364 BCE], 157d) | |
A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
From: Plato (Parmenides [c.364 BCE], 157c) | |
A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
From: Plato (Parmenides [c.364 BCE], 146b) | |
A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
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! |
19922 | People are only free if they are guided entirely by reason [Spinoza] |
Full Idea: The only genuinely free person is one who lives with his entire mind guided solely by reason. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.10) | |
A reaction: It strikes me as blatantly impossible to be entirely guided by reason. His point is that it is a subservience to reason which is entirely chosen. Why is that different from choosing to be entirely subservient to another person? |
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? |
19935 | Peoples are created by individuals, not by nature, and only distinguished by language and law [Spinoza] |
Full Idea: Nature certainly does not create peoples, individuals do, and individuals are only separated into nations by differences of language, law and morality. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.26) | |
A reaction: Quite wrong, I think. How did languages evolve if there were not already distinct peoples? Do ants and bees only form into colonies by individual choice? All social contract theories seem to make Spinoza's assumption. |
19914 | In nature everything has an absolute right to do anything it is capable of doing [Spinoza] |
Full Idea: Since the universal power of nature is only the power of all individual things together, it follows that each individual thing has the sovereign right to do everything it can do, or the right of each thing extends as far as its determined power extends. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.01) | |
A reaction: A typically ruthless Spinoza idea, very different from the rather ill-founded claims of Locke and Rousseau about the state of nature. |
19915 | Natural rights are determined by desire and power, not by reason [Spinoza] |
Full Idea: Each person's natural right is determined not by sound reason but by desire and power. For it is not the case that all men are naturally determined to behave according to the rules and laws of reason | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.03) | |
A reaction: Locke would have been horrified by this. It looks like hopeless unfounded optimism to claim a natural right to anything. Doomed prey can struggle all it likes, but its right to do so seems irrelevant. Yet we see self-evident injustice all the time. |
7487 | Society exists to extend human awareness [Spinoza, by Watson] |
Full Idea: For Spinoza the purpose of society was the extension of human awareness. | |
From: report of Baruch de Spinoza (Tractatus Theologico-Politicus [1670]) by Peter Watson - Ideas Ch.24 | |
A reaction: I like that. Personally I think human understanding is the best aim our lives can have, but I am inclined to see this in rather individualistic terms (despairing of getting others interested in the project!). |
19943 | The state aims to allow personal development, so its main purpose is freedom [Spinoza] |
Full Idea: It is the purpose of the state ...to allow people's minds and bodies to develop in their own way in security and enjoy the free use of reason ...Therefore the true purpose of the state is in fact freedom. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 20.06) | |
A reaction: The core of Spinoza's political thinking. This strikes me as being as close to communitarianism as to liberalism. |
19930 | Sovereignty must include the power to make people submit to it [Spinoza] |
Full Idea: Either there is no sovereignty nor any right over subjects, or else sovereignty must necessarily extend to everything that might be effective in inducing men to submit to it. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.02) | |
A reaction: In the seventeenth century this usually includes the death penalty. Refusal to submit may be fairly passive and harmless, so the issue must concern duties, rather than rights. Taxes, jury duty, calls to arms. |
19936 | Kings tend to fight wars for glory, rather than for peace and liberty [Spinoza] |
Full Idea: As soon as the kings took control [of the Hebrews] the reason for going to war was no longer peace and liberty but rather glory, | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 18.05) | |
A reaction: As Spinoza was writing, Louis XIV had just invaded Holland, solely in quest of military glory. As soon as a leader like Napoleon discovers they are good at war, I assume that the thrill of glory takes over for them too. |
19937 | Monarchs are always proud, and can't back down [Spinoza] |
Full Idea: Monarchical minds are always proud, and cannot back down without feelings of humiliation. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 18.05) | |
A reaction: This would seem to be a problem in all politicians. As I teacher I found that backing down was sometimes quite a smart move, but you can only do it occasionally. |
19940 | Deposing a monarch is dangerous, because the people are used to royal authority [Spinoza] |
Full Idea: It is dangerous to depose a monarch, even if it is clear by every criterion that he is a tyrant. A people accustomed to royal authority and held in check only by it, will despise any lesser authority and hold it in contempt. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 18.07) | |
A reaction: He is obviously thinking of Charles I and Cromwell. I suspect that the respect for Cromwell in the 1650s was only as a great soldier. If the people miss royal authority, the correct response is probably 'get over it!' |
19931 | Every state is more frightened of its own citizens than of external enemies [Spinoza] |
Full Idea: People have never succeeded in devising a form of government that was not in greater danger from its own citizens than from foreign foes, and which was not more fearful of the former than of the latter. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.04) | |
A reaction: The sort of lovely clear-headed and accurate observation for which we love Spinoza. Only very powerful despots can afford to ignore the threat from the people. Stalin was paranoid, but eventually murdered almost everyone who seemed a threat. |
19920 | Democracy is a legitimate gathering of people who do whatever they can do [Spinoza] |
Full Idea: Democracy is properly defined as a united gathering of people which collectively has the sovereign right to do all that it has the power to do. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.08) | |
A reaction: Representative democracy doesn't fit this definition. What 'unites' the people, and where do they get their sovereign right? If my neighbouring village votes to invade mine, I spurn their pathetic 'sovereign right'. |
19938 | Allowing religious ministers any control of the state is bad for both parties [Spinoza] |
Full Idea: How pernicious it is both for religion and the state to allow ministers of things sacred to acquire the right to make decrees or handle the business of government. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 18.06 (1)) | |
A reaction: Interesting that he holds it to be bad for the religion as well as the state. In Britain we have bishops in the House of Lords. |
19933 | If religion is law, then piety is justice, impiety is crime, and non-believers must leave [Spinoza] |
Full Idea: [In the first Hebrew state] religious dogmas were not doctrines but rather laws and decrees, piety being regarded as justice and impiety as crime. Anyone who defected from this religion ceased to be a citizen. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.08) | |
A reaction: Presumably speeding offences count as impiety, and failing to pray is a crime. A critical question will be how far religious doubts must extend before one actually has to leave. Mere doctrinal differences, or full atheism? |
19923 | Slavery is not just obedience, but acting only in the interests of the master [Spinoza] |
Full Idea: It is not acting on command in itself that makes someone a slave, but rather the reason for so acting. ...A slave is someone obliged to obey commands from a master which look only to the advantage of the master. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.10) | |
A reaction: So if I forcibly enslaved you, and then only commanded things which were for your own good, that would not be slavery? If the master feeds the slave, is that not part of the slavery? Most jobs might count as slavery by this account? |
19939 | Government is oppressive if opinions can be crimes, because people can't give them up [Spinoza] |
Full Idea: Government is bound to become extremely oppressive where dissident opinions which are within the domain of each individual, a right which no one can give up, are treated as a crime. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 18.06 (2)) | |
A reaction: One might compare illicit desires, such as those of a paedophile, where it is a crime to act on them, but presumably they cannot be given up, so there is no point in legislating against the mere desires. |
19944 | Without liberty of thought there is no trust in the state, and corruption follows [Spinoza] |
Full Idea: If liberty of thought is suppressed ...this would undemine the trust which is the first essential of a state; detestable flattery and deceit would flourish, giving rise to intrigues and every sort of honest behaviour. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 20.11) | |
A reaction: Spinoza specifically defends philosophy, as the epitome of freedom of thought. |
19942 | Treason may be committed as much by words as by deeds [Spinoza] |
Full Idea: We cannot altogether deny that treason may be committed as much by words as by deeds. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 20.05) | |
A reaction: For example, betraying a major state secret. This is an important idea, for anyone who simplistically demands utter freedom of speech. There is also subversive speech, which is very hard to assess. Incitements can be crimes in Britain. |
19924 | The freest state is a rational one, where people can submit themselves to reason [Spinoza] |
Full Idea: The freest state is that whose laws are founded on sound reason; for there each man can be free whenever he wishes, that is, he can live under the guidance of reason with his whole mind. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.10) | |
A reaction: I wonder if is not so much that the state is rational as that it is right. Freedom is submission to the truth. Rationality is only good because it arrives at truth. But is there a 'truth' about how a state should be run? Enlightenment optimism. |
7827 | Spinoza wanted democracy based on individual rights, and is thus the first modern political philosopher [Stewart,M on Spinoza] |
Full Idea: Spinoza's advocacy of democracy on the basis of individual rights was extraordinarily bold for its time, and it qualifies him as the first truly modern political philosopher. | |
From: comment on Baruch de Spinoza (Tractatus Theologico-Politicus [1670]) by Matthew Stewart - The Courtier and the Heretic Ch. 6 | |
A reaction: Sounds right. Hobbes may have been the 'first modern man', but his politics was fairly medieval. John Lilburne and co. may have campaigned for rights and democracy, but they weren't really philosophers. |
19926 | The sovereignty has absolute power over citizens [Spinoza] |
Full Idea: No offence can be committed against subjects by sovereigns, since they are of right permitted to do all things., and therefore offences occur only between private persons obliged by law not to harm one another. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.14) | |
A reaction: This slightly alarming remark is the consequence of Spinoza's denial of natural rights. Nowadays we have international law to appeal to. Locke thinks revolution could be justified, but this implies the Spinoza does not? |
19928 | No one, in giving up their power and right, ceases to be a human being [Spinoza] |
Full Idea: No one will ever be able to transfer his power and (consequently) his right to another person in such a way that he ceases to be a human being. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.01) | |
A reaction: Spinoza disdains natural rights, but this is a modest (and pretty uncontroversial) concession. |
19918 | Forming a society meant following reason, and giving up dangerous appetites and mutual harm [Spinoza] |
Full Idea: People had to make a firm decision to decide everything by the sole dictates of reason (which no one dares contradict openly). They had to curb their appetites if it would hurt someone else, and not do to others what they did not want done to themselves. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.05) | |
A reaction: The last bit invokes the Golden Rule. Being in society does indeed meaning curbing appetites, such as envy and lust. |
19919 | People only give up their rights, and keep promises, if they hope for some greater good [Spinoza] |
Full Idea: No one will give up his right to all things, and absolutely no one will keep his promises, except from fear of a greater ill or hope of a greater good. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.06) | |
A reaction: I think Locke and Rousseau would agree with this. It is hard to imagine doing anything other than in hope of a greater good. But what to do when your hopes are disappointed? |
19921 | Once you have given up your rights, there is no going back [Spinoza] |
Full Idea: If people had wanted to keep any right for themselves, they should have made this provision at the same time as they could have safely defended it. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.08) | |
A reaction: Spinoza is wonderful for grasping nettles. The other fans of social contracts seem blithely cheerful about how it is going to work out. But forming a society is like marriage - a risky commitment which could go horribly wrong. |
19925 | In democracy we don't abandon our rights, but transfer them to the majority of us [Spinoza] |
Full Idea: In a democracy no one transfers their natural right to another in such a way that they are not thereafter consulted, but rather to the majority of the whole society of which they are part. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.11) | |
A reaction: At this time democracy means Athenian direct democracy. In representative democracy you are only consulted once every few years, and in between the government can ignore the people (as Rousseau pointed out). |
19929 | Everyone who gives up their rights must fear the recipients of them [Spinoza] |
Full Idea: People have never given up their right and transferred their power to another in such a way that they did not fear the very persons who received their right and power, and put the government at greater risk from its own citizens than from its enemies. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.01) | |
A reaction: I take this idea to be Rousseau's key motivation for the idea of the general will, because you are there supposed to be alienating your natural rights to yourself (sort of). In a democracy you alienate them partly to yourself. |
19932 | The early Hebrews, following Moses, gave up their rights to God alone [Spinoza] |
Full Idea: The Hebrews being in this natural state, they resolved, on the advice of Moses in whom they all had the greatest trust, to transfer their right to no mortal man but rather to God alone. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.07) | |
A reaction: [He cites Exodus 24:7] He calls this the first Hebrew state, which seems to have depended heavily on Moses. Priests and prophets become crucial in this situation, and they may be in conflict about God's commands. |
19916 | The order of nature does not prohibit anything, and allows whatever appetite produces [Spinoza] |
Full Idea: The order of nature, under which all human beings are born and for the most part live, prohibits nothing but what no one desires or no one can do; it does not prohibit strife or hatred or anger or anything at all that appetite foments. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.04) | |
A reaction: This is as vigorous a rejection of natural law as I have met with. It is hard to see on what grounds anyone could disagree, other than hopeful sentiment. |
19927 | State and religious law can clash, so the state must make decisions about religion [Spinoza] |
Full Idea: No one would be obliged by law if he considered it against his faith, and everyone could claim licence to do anything. Since the law of the state would then be wholly violated, it follows that the right of deciding about religion belongs to the sovereign. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 16.21) | |
A reaction: This is an era when British puritans emigrate to America, because the state is not sufficiently tolerant. The needs of sovereignty and of religion can be very far apart. You can see those with great religious devotion not liking this idea. |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
From: Plato (Parmenides [c.364 BCE], 135a) |
225 | The unlimited has no shape and is endless [Plato] |
Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
From: Plato (Parmenides [c.364 BCE], 137e) |
233 | Some things do not partake of the One [Plato] |
Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
From: Plato (Parmenides [c.364 BCE], 159d) | |
A reaction: Compare Idea 231 |
2062 | The only movement possible for the One is in space or in alteration [Plato] |
Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
From: Plato (Parmenides [c.364 BCE], 138b) |
231 | Everything partakes of the One in some way [Plato] |
Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
From: Plato (Parmenides [c.364 BCE], 157c) | |
A reaction: Compare Idea 233. |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
From: Plato (Parmenides [c.364 BCE], 160d) |
19934 | Hebrews were very hostile to other states, who had not given up their rights to God [Spinoza] |
Full Idea: Having transferred their right to God, the Hebrews believed their kingdom was the kingdom of God, that they alone were the children of God, and that other nations were enemies of God, whom for that reason they regarded with extreme hostility. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670], 17.23) | |
A reaction: [He cites Psalm 139:21-2] So, according to Spinoza, they did not become the chosen people because they thought God had chosen then, but because they were the only state trying to align itself with God. |
4300 | The Bible has nothing in common with reasoning and philosophy [Spinoza] |
Full Idea: The Bible leaves reason absolutely free and has nothing in common with philosophy. | |
From: Baruch de Spinoza (Tractatus Theologico-Politicus [1670]) | |
A reaction: Hm. The Bible may not contain reasoning, but it contains the fruits of reasoning, and it is obviously possible for reasoning to contradict its message. |