98 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. |
9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
Full Idea: Two propositions are 'contradictory' if they are never both true and never both false either, which means that ¬(A↔B) is a tautology. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
Full Idea: We write 'not-P' as ¬P. This is called the 'negation' of P. The 'double negation' of P (not not-P) would be written as ¬¬P. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.2) | |
A reaction: Lemmons use of -P is no longer in use for 'not'. A tilde sign (squiggle) is also used for 'not', but some interpreters give that a subtly different meaning (involving vagueness). The sign ¬ is sometimes called 'hook' or 'corner'. |
9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
Full Idea: We write 'if P then Q' as P→Q. This is called a 'conditional', with P as its 'antecedent', and Q as its 'consequent'. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.2) | |
A reaction: P→Q can also be written as ¬P∨Q. |
9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
Full Idea: If P and Q are any two propositions, the proposition that either P or Q is called the 'disjunction' of P and Q, and is written P∨Q. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.3) | |
A reaction: This is inclusive-or (meaning 'P, or Q, or both'), and not exlusive-or (Boolean XOR), which means 'P, or Q, but not both'. The ∨ sign is sometimes called 'vel' (Latin). |
9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
Full Idea: If we say that A and B are 'interderivable' from one another (that is, A |- B and B |- A), then we may write A -||- B. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9508 | The sign |- may be read as 'therefore' [Lemmon] |
Full Idea: I introduce the sign |- to mean 'we may validly conclude'. To call it the 'assertion sign' is misleading. It may conveniently be read as 'therefore'. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.2) | |
A reaction: [Actually no gap between the vertical and horizontal strokes of the sign] As well as meaning 'assertion', it may also mean 'it is a theorem that' (with no proof shown). |
9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
Full Idea: If P and Q are any two propositions, the proposition that both P and Q is called the 'conjunction' of P and Q, and is written P∧Q. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.3) | |
A reaction: [I use the more fashionable inverted-v '∧', rather than Lemmon's '&', which no longer seems to be used] P∧Q can also be defined as ¬(¬P∨¬Q) |
9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
Full Idea: We write 'P if and only if Q' as P↔Q. It is called the 'biconditional', often abbreviate in writing as 'iff'. It also says that P is both sufficient and necessary for Q, and may be written out in full as (P→Q)∧(Q→P). | |
From: E.J. Lemmon (Beginning Logic [1965], 1.4) | |
A reaction: If this symbol is found in a sequence, the first move in a proof is to expand it to the full version. |
9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
Full Idea: If A and B are expressible in propositional calculus notation, they are 'subcontrary' if they are never both false, which may be tested by the truth-table for A∨B, which is a tautology if they are subcontrary. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
Full Idea: One proposition A 'implies' a proposition B if whenever A is true B is true (but not necessarily conversely), which is only the case if A→B is tautologous. Hence B 'is implied' by A. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
Full Idea: A 'well-formed formula' of the propositional calculus is a sequence of symbols which follows the rules for variables, ¬, →, ∧, ∨, and ↔. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.1) |
9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
Full Idea: A 'theorem' of logic is the conclusion of a provable sequent in which the number of assumptions is zero. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
A reaction: This is what Quine and others call a 'logical truth'. |
9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
Full Idea: If a well-formed formula of propositional calculus takes the value T for all possible assignments of truth-values to its variables, it is said to be a 'tautology'. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
Full Idea: If a well-formed formula of propositional calculus takes at least one T and at least one F for all the assignments of truth-values to its variables, it is said to be 'contingent'. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
Full Idea: The 'scope' of a connective in a certain formula is the formulae linked by the connective, together with the connective itself and the (theoretically) encircling brackets | |
From: E.J. Lemmon (Beginning Logic [1965], 2.1) |
9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
Full Idea: If a well-formed formula of propositional calculus takes the value F for all possible assignments of truth-values to its variables, it is said to be 'inconsistent'. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
Full Idea: A 'substitution-instance' is a wff which results by replacing one or more variables throughout with the same wffs (the same wff replacing each variable). | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
Full Idea: If A and B are expressible in propositional calculus notation, they are 'contrary' if they are never both true, which may be tested by the truth-table for ¬(A∧B), which is a tautology if they are contrary. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
Full Idea: Two propositions are 'equivalent' if whenever A is true B is true, and whenever B is true A is true, in which case A↔B is a tautology. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
Full Idea: Conditional Proof (CP): Given a proof of B from A as assumption, we may derive A→B as conclusion, on the remaining assumptions (if any). | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9393 | A: we may assume any proposition at any stage [Lemmon] |
Full Idea: Assumptions (A): any proposition may be introduced at any stage of a proof. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
Full Idea: And-Elimination (∧E): Given A∧B, we may derive either A or B separately. The conclusions will depend on the assumptions of the premiss. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
Full Idea: Or-Elimination (∨E): Given A∨B, we may derive C if it is proved from A as assumption and from B as assumption. This will also depend on prior assumptions. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
Full Idea: And-Introduction (&I): Given A and B, we may derive A∧B as conclusion. This depends on their previous assumptions. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
Full Idea: Reduction ad Absurdum (RAA): Given a proof of B∧¬B from A as assumption, we may derive ¬A as conclusion, depending on the remaining assumptions (if any). | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
Full Idea: Modus Tollendo Tollens (MTT): Given ¬B and A→B, we derive ¬A as a conclusion. ¬A depends on any assumptions that have been made | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
Full Idea: Double Negation (DN): Given A, we may derive ¬¬A as a conclusion, and vice versa. The conclusion depends on the assumptions of the premiss. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
Full Idea: Modus Ponendo Ponens (MPP): Given A and A→B, we may derive B as a conclusion. B will rest on any assumptions that have been made. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
Full Idea: Or-Introduction (∨I): Given either A or B separately, we may derive A∨B as conclusion. This depends on the assumption of the premisses. | |
From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
Full Idea: 'Modus ponendo tollens' (MPT) says that if the negation of a conjunction holds and also one of its conjuncts, then the negation of the other conjunct holds. Thus P, ¬(P ∧ Q) |- ¬Q may be introduced as a theorem. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
A reaction: Unlike Modus Ponens and Modus Tollens, this is a derived rule. |
9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
Full Idea: 'Modus tollendo ponens' (MTP) says that if a disjunction holds and also the negation of one of its disjuncts, then the other disjunct holds. Thus ¬P, P ∨ Q |- Q may be introduced as a theorem. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
A reaction: Unlike Modus Ponens and Modus Tollens, this is a derived rule. |
9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
Full Idea: The proof that P→Q -||- ¬(P ∧ ¬Q) is useful for enabling us to change conditionals into negated conjunctions | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
Full Idea: The proof that P→Q -||- ¬P ∨ Q is useful for enabling us to change conditionals into disjunctions. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
Full Idea: The forms of De Morgan's Laws [P∨Q -||- ¬(¬P ∧ ¬Q); ¬(P∨Q) -||- ¬P ∧ ¬Q; ¬(P∧Q) -||- ¬P ∨ ¬Q); P∧Q -||- ¬(¬P∨¬Q)] transform negated conjunctions and disjunctions into non-negated disjunctions and conjunctions respectively. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
Full Idea: The Distributive Laws say that P ∧ (Q∨R) -||- (P∧Q) ∨ (P∧R), and that P ∨ (Q∨R) -||- (P∨Q) ∧ (P∨R) | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
Full Idea: The proof that P∧Q -||- ¬(P → ¬Q) is useful for enabling us to change conjunctions into negated conditionals. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
9537 | Truth-tables are good for showing invalidity [Lemmon] |
Full Idea: The truth-table approach enables us to show the invalidity of argument-patterns, as well as their validity. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.4) |
9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
Full Idea: A truth-table test is entirely mechanical, ..and in propositional logic we can even generate proofs mechanically for tautological sequences, ..but this mechanical approach breaks down with predicate calculus, and proof-discovery is an imaginative process. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.5) |
9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
Full Idea: If any application of the nine derivation rules of propositional logic is made on tautologous sequents, we have demonstrated that the result is always a tautologous sequent. Thus the system is consistent. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.4) | |
A reaction: The term 'sound' tends to be used now, rather than 'consistent'. See Lemmon for the proofs of each of the nine rules. |
9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
Full Idea: A logical system is complete is all expressions of a specified kind are derivable in it. If we specify tautologous sequent-expressions, then propositional logic is complete, because we can show that all tautologous sequents are derivable. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.5) | |
A reaction: [See Lemmon 2.5 for details of the proofs] |
13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
Full Idea: Just as '(∀x)(...)' is to mean 'take any x: then....', so we write '(∃x)(...)' to mean 'there is an x such that....' | |
From: E.J. Lemmon (Beginning Logic [1965], 3.1) | |
A reaction: [Actually Lemmon gives the universal quantifier symbol as '(x)', but the inverted A ('∀') seems to have replaced it these days] |
13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
Full Idea: A predicate letter followed by one name expresses a property ('Gm'), and a predicate-letter followed by two names expresses a relation ('Pmn'). We could write 'Pmno' for a complex relation like betweenness. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.1) |
13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
Full Idea: I define a 'symbol' (of the predicate calculus) as either a bracket or a logical connective or a term or an individual variable or a predicate-letter or reverse-E (∃). | |
From: E.J. Lemmon (Beginning Logic [1965], 4.1) |
13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
Full Idea: Quantifier-notation might be thus: first, render into sentences about 'properties', and use 'predicate-letters' for them; second, introduce 'variables'; third, introduce propositional logic 'connectives' and 'quantifiers'. Plus letters for 'proper names'. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.1) |
13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
Full Idea: Our rule of universal quantifier elimination (UE) lets us infer that any particular object has F from the premiss that all things have F. It is a natural extension of &E (and-elimination), as universal propositions generally affirm a complex conjunction. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.2) |
13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
Full Idea: In predicate calculus we take over the propositional connectives and propositional variables - but we need additional rules for handling quantifiers: four rules, an introduction and elimination rule for the universal and existential quantifiers. | |
From: E.J. Lemmon (Beginning Logic [1965]) | |
A reaction: This is Lemmon's natural deduction approach (invented by Gentzen), which is largely built on introduction and elimination rules. |
13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
Full Idea: The elimination rule for the universal quantifier concerns the use of a universal proposition as a premiss to establish some conclusion, whilst the introduction rule concerns what is required by way of a premiss for a universal proposition as conclusion. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.2) | |
A reaction: So if you start with the universal, you need to eliminate it, and if you start without it you need to introduce it. |
13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
Full Idea: If there are just three objects and each has F, then by an extension of &I we are sure everything has F. This is of no avail, however, if our universe is infinitely large or if not all objects have names. We need a new device, Universal Introduction, UI. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.2) |
13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
Full Idea: Univ Elim UE - if everything is F, then something is F; Univ Intro UI - if an arbitrary thing is F, everything is F; Exist Intro EI - if an arbitrary thing is F, something is F; Exist Elim EE - if a proof needed an object, there is one. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.3) | |
A reaction: [My summary of Lemmon's four main rules for predicate calculus] This is the natural deduction approach, of trying to present the logic entirely in terms of introduction and elimination rules. See Bostock on that. |
13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
Full Idea: If all objects in a given universe had names which we knew and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex conjunction. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.2) |
13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
Full Idea: It is a common mistake to render 'some Frenchmen are generous' by (∃x)(Fx→Gx) rather than the correct (∃x)(Fx&Gx). 'All Frenchmen are generous' is properly rendered by a conditional, and true if there are no Frenchmen. | |
From: E.J. Lemmon (Beginning Logic [1965], 3.1) | |
A reaction: The existential quantifier implies the existence of an x, but the universal quantifier does not. |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
Full Idea: The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q. That is, since Napoleon was French, then if the moon is blue then Napoleon was French; and since Napoleon was not Chinese, then if Napoleon was Chinese, the moon is blue. | |
From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
A reaction: This is why the symbol → does not really mean the 'if...then' of ordinary English. Russell named it 'material implication' to show that it was a distinctively logical operator. |
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 |
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. |
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. |
22180 | Multiple realisability is said to make reduction impossible [Okasha] |
Full Idea: Philosophers have often invoked multiple realisability to explain why psychology cannot be reduced to physics or chemistry, but in principle the explanation works for any higher-level science. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 3) | |
A reaction: He gives the example of a 'cell' in biology, which can be implemented in all sorts of ways. Presumably that can be reduced to many sorts of physics, but not just to one sort. The high level contains patterns that vanish at the low level. |
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. |
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) |
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) |
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) |
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) |
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. |
22172 | Not all sciences are experimental; astronomy relies on careful observation [Okasha] |
Full Idea: Not all sciences are experimental - astronomers obviously cannot do experiments on the heavens, but have to content themselves with careful observation instead. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 1) | |
A reaction: Biology too. Psychology tries hard to be experimental, but I doubt whether the main theories emerge from experiments. |
22177 | Randomised Control Trials have a treatment and a control group, chosen at random [Okasha] |
Full Idea: In the Randomised Controlled Trial for a new drug, patients are divided at random into a treatment group who receive the drug, and a control group who do not. Randomisation is important to eliminate confounding factors. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
A reaction: [compressed] Devised in the 1930s, and a major breakthrough in methodology for that kind of trial. Psychologists use the method all the time. Some theorists say it is the only reliable method. |
22174 | The discoverers of Neptune didn't change their theory because of an anomaly [Okasha] |
Full Idea: Adams and Leverrier began with Newton's theory of gravity, which made an incorrect prediction about the orbit of Uranus. They explained away the conflicting observations by postulating a new planet, Neptune. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 1) | |
A reaction: The falsificationists can say that the anomalous observation did not falsify the theory, because they didn't know quite what they were observing. It was not in fact an anomaly for Newtonian theory at all. |
22175 | Science mostly aims at confirming theories, rather than falsifying them [Okasha] |
Full Idea: The goal of science is not solely to refute theories, but also to determine which theories are true (or probably true). When a scientist collects data …they are trying to show that their own theory is true. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
A reaction: This is the aim of 'accommodation' to a wide set of data, rather than prediction or refutation. |
22182 | Theories with unobservables are underdetermined by the evidence [Okasha] |
Full Idea: According to anti-realists, scientific theories which posit unobservable entities are underdetermined by the empirical data - there will always be a number of competing theories which can account for the data equally well. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 4) | |
A reaction: The fancy version is Putnam's model theoretic argument, explored by Tim Button. The reply, apparently, is that there are other criteria for theory choice, apart from the data. And we don't have to actually observe everything in a theory. |
22185 | Two things can't be incompatible if they are incommensurable [Okasha] |
Full Idea: If two things are incommensurable they cannot be incompatible. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 5) | |
A reaction: Kuhn had claimed that two rival theories are incompatible, which forces the paradigm shift. He can't stop the slide off into total relativism. The point is there cannot be a conflict if there cannot even be a comparison. |
22176 | Induction is inferences from examined to unexamined instances of a given kind [Okasha] |
Full Idea: Some philosophers use 'inductive' to just mean not deductive, …but we reserve it for inferences from examined to unexamined instances of a given kind. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
A reaction: The instances must at least be comparable. Must you know the kind before you start? Surely you can examine a sequence of things, trying to decide whether or not they are of one kind? Is checking the uniformity of a kind induction? |
22178 | If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha] |
Full Idea: If the only objective constraints concern how we should change our credences, but what our initial credences should be is entirely subjective, then individuals with very bizarre opinions about the world will count as perfectly rational. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
A reaction: The important rationality has to be the assessement of a diverse batch of evidence, for which there can never be any rules or mathematics. |
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. |
22173 | Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha] |
Full Idea: Galileo's most enduring contribution lay in mechanics, where he refuted the Aristotelian theory that heavier bodies fall faster than lighter. | |
From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
A reaction: This must the first idea in the theory of mechanics, allowing mathematical treatment and accurate comparisons. |
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) |