86 ideas
| 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) |
| 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. |
| 16295 | Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach] |
| Full Idea: Tarski's Theorem states that under fairly generally applicable conditions, the assumption that there is a definition of truth within a given theory for the language of that same theory leads to a contradiction. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 1 | |
| A reaction: That might leave room for a definition outside the given theory. I take the main motivation for the axiomatic approach to be a desire to get a theory of truth within the given theory, where Tarski's Theorem says traditional approaches are just wrong. |
| 15342 | Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten] |
| Full Idea: Tarski's Theorem on the undefinability of truth says in a language sufficiently rich to talk about itself (which Gödel proved possible, via coding) the liar paradox can be carried out. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 02.2 | |
| A reaction: The point is that truth is formally indefinable if it leads inescapably to contradiction, which the liar paradox does. This theorem is the motivation for all modern attempts to give a rigorous account of truth. |
| 19069 | 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski] |
| Full Idea: The possibility of a consistent use of 'true sentence' which is in harmony with the laws of logic and the spirit of everyday language seems to be very questionable, so the same doubt attaches to the possibility of constructing a correct definition. | |
| From: Alfred Tarski (The Concept of Truth for Formalized Languages [1933], §1) | |
| A reaction: This is often cited as Tarski having conclusively proved that 'true' cannot be defined from within a language, but his language here is much more circumspect. Modern critics say the claim depends entirely on classical logic. |
| 16296 | Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach] |
| Full Idea: Tarski's Theorem applies to any sufficient precise version of the correspondence theory of truth, and all the other traditional theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 1 | |
| A reaction: This is the key reason why modern thinkers have largely dropped talk of the correspondence theory. See Idea 16295. |
| 10672 | Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack] |
| Full Idea: Tarskian semantics says that a sentence is true iff it is satisfied by every sequence, where a sequence is a set-theoretic individual, a set of ordered pairs each with a natural number as its first element and an object from the domain for its second. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Keith Hossack - Plurals and Complexes 3 |
| 15339 | Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten] |
| Full Idea: Tarski emancipated truth theory from traditional philosophy, by no longer posing Pilate's question (what is truth? or what is the essence of truth?) but instead 'how is truth used?', 'how does truth function?' and 'how can its functioning be described?'. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 02.2 | |
| A reaction: Horsten, later in the book, does not give up on the essence of truth, and modern theorists are trying to get back to that question by following Tarski's formal route. Modern analytic philosophy at its best, it seems to me. |
| 16302 | Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach] |
| Full Idea: Tarski did not settle for a definition of truth, taking its adequacy for granted. Rather he proposed an adequacy criterion for evaluating the adequacy of definitions of truth. The criterion is his famous Convention T. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 | |
| A reaction: Convention T famously says the sentence is true if and only if a description of the sentence is equivalent to affirming the sentence. 'Snow is white' iff snow is white. |
| 19135 | Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski] |
| Full Idea: Tarski does not tell us how to apply his concept of truth to a new case, whether the new case is a new language or a word newly added to a language. This is because enumerating cases gives no clue for the next or general case. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: His account has been compared to a telephone directory. We aim to understand the essence of anything, so that we can fully know it, and explain and predict how it will behave. Either truth is primitive, or I demand to know its essence. |
| 19138 | Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski] |
| Full Idea: Tarski defined the class of true sentences by giving the extension of the truth predicate, but he did not give the meaning. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: This is analogous to giving an account of the predicate 'red' as the set of red objects. Since I regard that as a hopeless definition of 'red', I am inclined to think the same of Tarski's account of truth. It works in the logic, but so what? |
| 4699 | Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady] |
| Full Idea: Tarski's account doesn't hold for natural languages. The general notion of truth is replaced by "true-in-L", where L is a formal language. Hence truth is relativized to each artificial language. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Paul O'Grady - Relativism Ch.2 | |
| A reaction: This is a pretty good indication that Tarski's theory is NOT a correspondence theory, even if its structure may sometimes give that impression. |
| 19324 | Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski] |
| Full Idea: Tarski has to define truths so as not to make explicit the relation between a true sentence and an obtaining state of affairs. ...He has to list each sentence separately, and simply assign it a state of affairs. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.8 | |
| A reaction: He has to avoid semantic concepts like 'reference', because he wants a physicalist theory, according to Kirkham. Thus the hot interest in theories of reference in the 1970s/80s. And also attempts to give a physicalist account of meaning. |
| 15410 | Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski] |
| Full Idea: In Tarski's theory of truth, although the notion of truth is applicable only to closed formulas, to define it we must define a more general notion of satisfaction applicable to open formulas. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by John P. Burgess - Philosophical Logic 1.8 | |
| A reaction: This is a helpful pointer to what is going on in the Tarski definition. It culminates in the 'satisfaction of all sequences', which presumable delivers the required closed formula. |
| 18811 | Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt] |
| Full Idea: Tarski invoked the notion of a sentential function, where components are replaced by appropriate variables. A function is then satisfied by assigning objects to variables. An assignment satisfies if the function is true of the things assigned. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [very compressed] This use of sentential functions, rather than sentences, looks like the key to Tarski's definition of truth. |
| 15365 | We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten] |
| Full Idea: The truth predicate, says Tarski, should be defined in terms of the more primitive satisfaction relation: the relation of being 'true of'. The fundamental notion is a formula (containing the free variables) being true of a sequence of objects as values. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 06.3 |
| 19314 | For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham] |
| Full Idea: Tarski, a physicalist, reduced semantics to physical and/or logicomathematical concepts. He defined all semantic concepts, save satisfaction, in terms of truth. Then truth is defined in terms of satisfaction, and satisfaction is given non-semantically. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.1 | |
| A reaction: The term 'logicomathematical' is intended to cover set theory. Kirkham says you can remove these restrictions from Tarski's theory, and the result is a version of the correspondence theory. |
| 19316 | Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham] |
| Full Idea: Tarski's great insight is find another property, since open sentences are not truth. It must be had by open and genuine sentences. Clauses having it must generate it for the whole sentence. Truth can be defined for sentences by using it. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.4 | |
| A reaction: The proposed property is 'satisfaction', which can (unlike truth) be a feature open sentences (such as 'x is green', which is satisfied by x='grass'), |
| 19175 | Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson] |
| Full Idea: Tarski turned his axiomatic characterisation of satisfaction into an explicit definition of the satisfaction-predicate using some fancy set theoretical apparatus, and this in turn leads to the explicit definition of the truth predicate. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 7 |
| 16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
| Full Idea: Tarski's proof of the definability of truth allowed him to establish truth as a respectable notion by his standards. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 |
| 19134 | Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski] |
| Full Idea: Tarski defined various predicates of the form 's is true in L', each applicable to a single language, but he failed to define a predicate of the form 's is true in L' for variable 'L'. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: You might say that no one defines 'tree' to be just 'in English', but we might define 'multiplies' to be in Peano Arithmetic. This indicates the limited and formal nature of what Tarski was trying to achieve. |
| 16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski] |
| Full Idea: Every really adequate theory of truth should also prove the law of non-contradiction. Therefore Tarski's notion of adequacy in Convention T fails to capture the intuitive notion of adequacy he is after. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 | |
| A reaction: Tarski points out this weakness, in a passage quoted by Halbach. This obviously raises the question of what truth theories should prove, and this is explored by Halbach. If they start to prove arithmetic, we get nervous. Non-contradiction and x-middle? |
| 2571 | Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack] |
| Full Idea: Tarski says "we may remain naïve realists or idealists, empiricists or metaphysicians… The semantic conception is completely neutral toward all these issues." | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Susan Haack - Philosophy of Logics 7.5 |
| 10821 | Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H] |
| Full Idea: Tarski work was to persuade physicalist that eliminating semantics was on the wrong track, and that we should explicate notions in the theory of reference nonsemantically rather than simply get rid of them. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Hartry Field - Tarski's Theory of Truth §3 |
| 10822 | A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski] |
| Full Idea: We need to add theories of primitive reference to Tarski's account if we are to establish the notion of truth as a physicalistically acceptable notion. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Hartry Field - Tarski's Theory of Truth §4 | |
| A reaction: This is the main point of Field's paper, and sounds very plausible to me. There is something major missing from Tarski, and at some point there needs to be a 'primitive' notion of thought and language making contact with the world, as it can't be proved. |
| 10969 | Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read] |
| Full Idea: Besides a theory of truth of his own, Tarski developed a theory of theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Stephen Read - Thinking About Logic Ch.1 | |
| A reaction: The famous snow biconditional is the latter, and the recursive account based on satisfaction is the former. |
| 17746 | Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki] |
| Full Idea: Tarski's analysis of the concept of 'truth' ...is given a precise treatment as a particular relation between syntax (language) and semantics (the world). | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Michal Walicki - Introduction to Mathematical Logic History E.1 | |
| A reaction: My problem is that the concept of truth seems to apply to animal minds, which are capable of making right or wrong judgements, and of realising their errors. Tarski didn't make universal claims for his account. |
| 10904 | Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski] |
| Full Idea: The Tarskian account of truth neglects the atomic sentences. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Mulligan/Simons/Smith - Truth-makers §1 | |
| A reaction: Yes! The whole Tarskian edifice is built on a foundation which it is taboo even to mention. If truth is just the assignment of 'T' and 'F', that isn't even the beginnings of a theory of 'truth'. |
| 15322 | Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten] |
| Full Idea: Tarski's work is the earliest axiomatic theory of truth that meets minimal adequacy conditions. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 01.1 | |
| A reaction: This shows a way in which Tarski gave a new direction to the study of truth. Subsequent theories have been 'stronger'. |
| 16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach] |
| Full Idea: Tarski preferred a definition of truth, but from that an axiomatisation can be extracted. His induction clauses can be turned into axioms. Hence he opened the way to axiomatic theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 |
| 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
| Full Idea: Tarski showed that the only binary relations invariant under arbitrary permutations are the universal relation, the empty relation, identity and non-identity, thus giving us a reason to include '=' among the logical terms. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 6 | |
| A reaction: Tarski was looking for a criterion to distinguish logical from non-logical terms, since his account of logical validity depended on it. This idea lies behind whether a logic is or is not specified to be 'with identity' (i.e. using '='). |
| 10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
| Full Idea: To say that the name x denotes a given object a is the same as to stipulate that the object a ... satisfies a sentential function of a particular type. | |
| From: Alfred Tarski (The Concept of Truth for Formalized Languages [1933], p.194) |
| 18756 | Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee] |
| Full Idea: Tarski discovered how to give a compositional semantics for predicate calculus, defining truth in terms of satisfaction, and showing how satisfaction for a complicated formula depends on satisfaction of the simple subformulas. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 4 | |
| A reaction: The problem was that the subformulas may contain free variables, and thus not be sentences with truth values. 'Satisfaction' can handle this, where 'truth' cannot (I think). |
| 19313 | Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham] |
| Full Idea: Tarski invented a formal semantics for quantified predicate logic, the logic of reasoning about mathematics. The heart of this great accomplishment is his theory of truth. It has been called semantic 'theory' of truth, but Tarski preferred 'conception'. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.1 |
| 16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
| Full Idea: Tarski's distinction between object and metalanguage forms the basis of model theory. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 11 |
| 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 |
| 8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
| Full Idea: In Tarski's account of truth, self-reference (as found in the Liar Paradox) is prevented because the truth predicate for any given object language is never a part of that object language, and so a sentence can never predicate truth of itself. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Jennifer Fisher - On the Philosophy of Logic 03.I | |
| A reaction: Thus we solve the Liar Paradox by ruling that 'you are not allowed to say that'. Hm. The slightly odd result is that in any conversation about whether p is true, we end up using (logically speaking) two different languages simultaneously. Hm. |
| 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. |
| 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
| Full Idea: Tarski's theory of truth has been most influential in eventually creating a shift from the entirely syntactic way of doing things in metamathematics (promoted by Hilbert in the 1920s, in his theory of proofs), towards a set-theoretical, semantic approach. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Feferman / Feferman - Alfred Tarski: life and logic Int III |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 17000 | We might fix identities for small particulars, but it is utopian to hope for such things [Kripke] |
| Full Idea: Maybe strict identity only applies to the particulars (the molecules) in a case of vague identity. …It seems, however, utopian to suppose that we will ever reach a level of ultimate, basic particulars for which identity relations are never vague. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 18) | |
| A reaction: I agree with this. Ladyman and Ross laugh at the unscientific picture found in dreams of 'simples'. |
| 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? |
| 11868 | A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke] |
| Full Idea: Could the artificer not, when he made the table, have taken other pieces? Surely he could. [n37: I venture to think that Kripke's argument in note 56 for the necessity of constitution depends on treating constitution as if it were identity]. | |
| From: comment on Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 56) by David Wiggins - Sameness and Substance Renewed 4.11 | |
| A reaction: Suppose the craftsman completed the table, then changed a piece of wood in it for some reason. Has he now made a second table and destroyed the first one? Wiggins seems to be right. |
| 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. |
| 17044 | A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke] |
| Full Idea: Some philosophers have thought that a relation, being essentially two-termed, cannot hold between a thing and itself. This position is plainly absurd ('he is his own worst enemy'). Identity is nothing but the smallest reflexive relation. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 50) | |
| A reaction: I have no idea what 'smallest' means here. I can't be 'to the left of myself', so not all of my relations can be reflexive. I just don't understand what it means to say something is 'identical with itself'. You've got the thing - what have you added? |
| 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. |
| 16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke] |
| Full Idea: When the identity relation is vague, it may seem intransitive; a claim of apparent identity may yield an apparent non-identity. Some sort of 'counterpart' notion may have some utility here. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 18) | |
| A reaction: He firmly rejects the full Lewis apparatus of counterparts. The idea would be that a river at different times had counterpart relations, not strict identity. I like the word 'same' for this situation. Most worldly 'identity' is intransitive. |
| 17058 | What many people consider merely physically necessary I consider completely necessary [Kripke] |
| Full Idea: My third lecture suggests that a good deal of what contemporary philosophy regards as mere physical necessity is actually necessary tout court. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], Add (g)) | |
| A reaction: He avoids the term 'metaphysically necessary', which most people would not use for this point. |
| 4970 | What is often held to be mere physical necessity is actually metaphysical necessity [Kripke] |
| Full Idea: My third lecture suggests that a good deal of what contemporary philosophy regards as mere physical necessity is actually necessary 'tout court'. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], Add (g)) | |
| A reaction: This huge claim rides in on the back of Kripke's very useful clarifications. It is the 'new essentialism', and seems to me untenable in this form. There is no answer to Hume's request for evidence of necessity. Why can't essences (and laws) change? |
| 17059 | Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke] |
| Full Idea: If the unicorn myth is supposed to be a particular species, with insufficient internal structure to determine it uniquely, then there is no actual or possible species of which we can say that it would have been the species of unicorns. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], Add (a)) | |
| A reaction: Dummett and Rumfitt discuss this proposal elsewhere. |
| 4950 | Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke] |
| Full Idea: The apparatus of possible worlds has (I hope) been very useful as far as the set-theoretic model-theory of quantified modal logic is concerned, but has encouraged philosophical pseudo-problems and misleading pictures. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 15) | |
| A reaction: This is presumably a swipe at David Lewis, who claims possible worlds are real. The fact that the originator of possible worlds sees them as unproblematic doesn't mean they are. Fine if they are a game, but if they assert truth, they need a metaphysics. |
| 17003 | Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke] |
| Full Idea: It is useful to have an operator which transforms each description into a term which rigidly designates the object actually satisfying the description. David Kaplan has proposed such an operator and calls it 'Dthat'. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 22) |
| 9221 | The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider] |
| Full Idea: The most famous objection to counterparts is Kripke's objection that Hubert Humphrey wouldn't care if he thought that his counterpart might have won the 1972 election. He wishes that he had won it. | |
| From: report of Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 12) by Theodore Sider - Reductive Theories of Modality 3.10 | |
| A reaction: Like Sider, I find this unconvincing. If there is a world in which I don't exist, but my very close counterpart does (say exactly me, but with a finger missing), I am likely to care more about such a person than about complete strangers. |
| 17052 | The a priori analytic truths involving fixing of reference are contingent [Kripke] |
| Full Idea: If statements whose a priori truth is known via the fixing of a reference are counted as analytic, then some analytic truths are contingent. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 63) |
| 4969 | I regard the mind-body problem as wide open, and extremely confusing [Kripke] |
| Full Idea: I regard the mind-body problem as wide open, and extremely confusing. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 77) | |
| A reaction: Kripke opposes reductive physicalism, but is NOT committed to dualism. He seems to be drawn to Davidson or Nagel (see his note 73). I think his discussion of contingent mind-brain identity is confused. |
| 4956 | A description may fix a reference even when it is not true of its object [Kripke] |
| Full Idea: In some cases an object may be identified, and the reference of a name fixed, using a description which may turn out to be false of its object. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 34) | |
| A reaction: This is clearly possible. Someone could be identified as 'the criminal' when they were actually innocent. Nevertheless, how do you remember which person was baptised 'Aristotle' if you don't hang on to a description, even a false one? |
| 17032 | Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke] |
| Full Idea: If a Gödelian fraud were exposed, Gödel would no longer be called 'the author of the incompleteness theorem', but he would still be called 'Gödel'. The description, therefore, does not abbreviate the name. | |
| From: Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 37) | |
| A reaction: Clearly we can't make the description a necessary fact about Gödel, but that doesn't invalidate the idea that successful reference needs some description. E.g. Gödel is a person. |
| 20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
| Full Idea: Taste is the faculty for judging an object or a kind of representation through a satisfaction or a dissatisfaction, ...where the object of such a satisfaction is called beautiful. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Elizabeth Schellekens - Immanuel Kant (aesthetics) 1 | |
| A reaction: We usually avoid the word 'faculty' nowadays, because it implies a specific mechanism, but 'capacity' will do. Kant is said to focus specifically on beauty, whereas modern aestheticians have a broader view of the type of subject matter. |
| 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) |