168 ideas
| 14912 | There is no test for metaphysics, except devising alternative theories [Ladyman/Ross] |
| Full Idea: The metaphysician has no test for the truth of her beliefs except that other metaphysicians can't think of obviously superior alternative beliefs. (They can always think of possibly superior ones, in profusion). | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.7) | |
| A reaction: [they cite Van Fraassen for this view] At least this seems to concede that some metaphysical views can be rejected by the observation of beliefs that are superior. Almost everyone has rejected Lewis on possible worlds for this reason. |
| 14904 | Metaphysics builds consilience networks across science [Ladyman/Ross] |
| Full Idea: Metaphysics is the enterprise of critically elucidating consilience networks across the sciences. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: I don't disagree with this. The issue, I think, is how abstract you are prepared to go. At high levels of abstraction, it is very hard to keep in touch with the empirical research. There are truths, though, at that high level. It is clearest in logic. |
| 14907 | Progress in metaphysics must be tied to progress in science [Ladyman/Ross] |
| Full Idea: To the extent that metaphysics is closely motivated by science, we should expect to make progress in metaphysics iff we can expect to make progress in science. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: To defer to and respect science does not necessitate that metaphysics cannot do independent work. I take there to be truths at a high-level of abstraction that are independent of the physical sciences, just as there are truths of chess or economics. |
| 14908 | Metaphysics must involve at least two scientific hypotheses, one fundamental, and add to explanation [Ladyman/Ross] |
| Full Idea: Principle of Naturalist Closure: A serious metaphysical claim must involve at least two scientific hypotheses, at least one from fundamental physics, and explain more than what the two hypotheses explain separately. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: [compressed, from their longer qualified version] The idea that metaphysics should add to explanation is close to my heart. I am musing over whether essences add to explanation, which would be total anathema to Ladyman and Ross. |
| 14910 | Some science is so general that it is metaphysical [Ladyman/Ross] |
| Full Idea: Some scientific propositions are sufficiently general as themselves to be metaphysical. Our notion of metaphysics is thus recursive, and requires no attempt to identify a boundary between metaphysical and scientific propositions. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.5 n45) | |
| A reaction: Note that this still leaves room for some metaphysics which is not science, though see Idea 14904 for their views on that. |
| 14940 | Cutting-edge physics has little to offer metaphysics [Ladyman/Ross] |
| Full Idea: There is little positive by way of implications for metaphysics that we can adduce from cutting-edge physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: My personal suspicion is that this will always be the case, even though there may be huge advances in physics, and I offer that as a reason why metaphysicians do not (pace Ladyman and Ross) need to study physics. They grasp 'negative' lessons. |
| 14945 | The aim of metaphysics is to unite the special sciences with physics [Ladyman/Ross] |
| Full Idea: The demand to unify the special sciences with physics is, according to us, the motivation for having any metaphysics at all. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.1) | |
| A reaction: The crunch question is whether metaphysicians are allowed to develop their own concepts for this task, or whether they can only make links between the concepts employed by the scientists. I vote for the former. |
| 14898 | Modern metaphysics pursues aesthetic criteria like story-writing, and abandons scientific truth [Ladyman/Ross] |
| Full Idea: The criteria of adequacy for metaphysics have come apart from anything to do with truth. Rather they are internal and peculiar to philosophy, they are semi-aesthetic, and they have more in common with the virtues of story-writing than with science. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.1) | |
| A reaction: Part of a sustained polemic against contemporary analytic metaphysics. I love metaphysics, but they may be right. Writers like Sider, Fine, Lowe, Lewis, Stalnaker, Kripke, Armstrong, Dummett seem to tell independent stories, that really are works of art. |
| 14899 | Why think that conceptual analysis reveals reality, rather than just how people think? [Ladyman/Ross] |
| Full Idea: Why should we think that the products of conceptual analysis reveal anything about the deep structure of reality, rather than telling us about how some class of people think about and categorize reality? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.2) | |
| A reaction: One line, associated with Jackson, is that analysis tells you not about reality, but about what to make of your experiences of reality when you have them. It would be a foolish scientist who paid no attention to his or her conceptual scheme. |
| 14936 | A metaphysics based on quantum gravity could result in almost anything [Ladyman/Ross] |
| Full Idea: We cannot say what the metaphysical implications of quantum gravity are, but they range from eleven dimensions to two, from continuous fundamental structure to a discrete one, and from universal symmetries to no symmetries. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: I offer this observation as a good reason for doubting whether the project of building our metaphysics directly onto our fundamental physics has much prospect of success. Quantum gravity is the unified theory they are all hoping for. |
| 14897 | We should abandon intuitions, especially that the world is made of little things, and made of something [Ladyman/Ross] |
| Full Idea: Abandoning intuitions is usually regarded as a cost rather than a benefit. By contrast, as naturalists we are not concerned with preserving intuitions at all (especially that the world is composed of little things, and that it must be made of something). | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.1) |
| 14905 | The supremacy of science rests on its iterated error filters [Ladyman/Ross] |
| Full Idea: The epistemic supremacy of science rests on repeated iteration of institutional error filters. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: You could add repeated iteration of institutional error filters to journals about astrology, but it wouldn't thereby acquire epistemic supremacy. It is the tangible nature of the evidence which bestows the authority. |
| 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. |
| 13439 | Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock] |
| Full Idea: Venn Diagrams are a traditional method to test validity of syllogisms. There are three interlocking circles, one for each predicate, thus dividing the universe into eight possible basic elementary quantifications. Is the conclusion in a compartment? | |
| From: David Bostock (Intermediate Logic [1997], 3.8) |
| 13421 | 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock] |
| Full Idea: 'Disjunctive Normal Form' (DNF) is rearranging the occurrences of ∧ and ∨ so that no conjunction sign has any disjunction in its scope. This is achieved by applying two of the distribution laws. | |
| From: David Bostock (Intermediate Logic [1997], 2.6) |
| 13422 | 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock] |
| Full Idea: 'Conjunctive Normal Form' (CNF) is rearranging the occurrences of ∧ and ∨ so that no disjunction sign has any conjunction in its scope. This is achieved by applying two of the distribution laws. | |
| From: David Bostock (Intermediate Logic [1997], 2.6) |
| 13355 | 'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock] |
| Full Idea: The Principle of Disjunction says that Γ,φ∨ψ |= iff Γ,φ |= and Γ,ψ |=. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.G) | |
| A reaction: That is, a disjunction leads to a contradiction if they each separately lead to contradictions. |
| 13350 | 'Assumptions' says that a formula entails itself (φ|=φ) [Bostock] |
| Full Idea: The Principle of Assumptions says that any formula entails itself, i.e. φ |= φ. The principle depends just upon the fact that no interpretation assigns both T and F to the same formula. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.A) | |
| A reaction: Thus one can introduce φ |= φ into any proof, and then use it to build more complex sequents needed to attain a particular target formula. Bostock's principle is more general than anything in Lemmon. |
| 13351 | 'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock] |
| Full Idea: The Principle of Thinning says that if a set of premisses entails a conclusion, then adding further premisses will still entail the conclusion. It is 'thinning' because it makes a weaker claim. If γ|=φ then γ,ψ|= φ. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.B) | |
| A reaction: It is also called 'premise-packing'. It is the characteristic of a 'monotonic' logic - where once something is proved, it stays proved, whatever else is introduced. |
| 13356 | The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock] |
| Full Idea: The Conditional Principle says that Γ |= φ→ψ iff Γ,φ |= ψ. With the addition of negation, this implies φ,φ→ψ |= ψ, which is 'modus ponens'. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.H) | |
| A reaction: [Second half is in Ex. 2.5.4] |
| 13352 | 'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock] |
| Full Idea: The Principle of Cutting is the general point that entailment is transitive, extending this to cover entailments with more than one premiss. Thus if γ |= φ and φ,Δ |= ψ then γ,Δ |= ψ. Here φ has been 'cut out'. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.C) | |
| A reaction: It might be called the Principle of Shortcutting, since you can get straight to the last conclusion, eliminating the intermediate step. |
| 13353 | 'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock] |
| Full Idea: The Principle of Negation says that Γ,¬φ |= iff Γ |= φ. We also say that φ,¬φ |=, and hence by 'thinning on the right' that φ,¬φ |= ψ, which is 'ex falso quodlibet'. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.E) | |
| A reaction: That is, roughly, if the formula gives consistency, the negation gives contradiction. 'Ex falso' says that anything will follow from a contradiction. |
| 13354 | 'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock] |
| Full Idea: The Principle of Conjunction says that Γ |= φ∧ψ iff Γ |= φ and Γ |= ψ. This implies φ,ψ |= φ∧ψ, which is ∧-introduction. It is also implies ∧-elimination. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.F) | |
| A reaction: [Second half is Ex. 2.5.3] That is, if they are entailed separately, they are entailed as a unit. It is a moot point whether these principles are theorems of propositional logic, or derivation rules. |
| 13610 | A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock] |
| Full Idea: For ¬,→ Schemas: (A1) |-φ→(ψ→φ), (A2) |-(φ→(ψ→ξ)) → ((φ→ψ)→(φ→ξ)), (A3) |-(¬φ→¬ψ) → (ψ→φ), Rule:DET:|-φ,|-φ→ψ then |-ψ | |
| From: David Bostock (Intermediate Logic [1997], 5.2) | |
| A reaction: A1 says everything implies a truth, A2 is conditional proof, and A3 is contraposition. DET is modus ponens. This is Bostock's compact near-minimal axiom system for proposition logic. He adds two axioms and another rule for predicate logic. |
| 13846 | A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock] |
| Full Idea: A 'free' logic is one in which names are permitted to be empty. A 'universally free' logic is one in which the domain of an interpretation may also be empty. | |
| From: David Bostock (Intermediate Logic [1997], 8.6) |
| 13346 | Truth is the basic notion in classical logic [Bostock] |
| Full Idea: The most fundamental notion in classical logic is that of truth. | |
| From: David Bostock (Intermediate Logic [1997], 1.1) | |
| A reaction: The opening sentence of his book. Hence the first half of the book is about semantics, and only the second half deals with proof. Compare Idea 10282. The thought seems to be that you could leave out truth, but that makes logic pointless. |
| 13545 | Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock] |
| Full Idea: In very general terms, we cannot express the distinction between what is finite and what is infinite without moving essentially beyond the resources available in elementary logic. | |
| From: David Bostock (Intermediate Logic [1997], 4.8) | |
| A reaction: This observation concludes a discussion of Compactness in logic. |
| 13822 | Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock] |
| Full Idea: Discourse about fictional characters leads to a breakdown of elementary logic. We accept P or ¬P if the relevant story says so, but P∨¬P will not be true if the relevant story says nothing either way, and P∧¬P is true if the story is inconsistent. | |
| From: David Bostock (Intermediate Logic [1997], 8.5) | |
| A reaction: I really like this. Does one need to invent a completely new logic for fictional characters? Or must their logic be intuitionist, or paraconsistent, or both? |
| 13623 | The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock] |
| Full Idea: The syntactic turnstile |- φ means 'There is a proof of φ' (in the system currently being considered). Another way of saying the same thing is 'φ is a theorem'. | |
| From: David Bostock (Intermediate Logic [1997], 5.1) |
| 13347 | Validity is a conclusion following for premises, even if there is no proof [Bostock] |
| Full Idea: The classical definition of validity counts an argument as valid if and only if the conclusion does in fact follow from the premises, whether or not the argument contains any demonstration of this fact. | |
| From: David Bostock (Intermediate Logic [1997], 1.2) | |
| A reaction: Hence validity is given by |= rather than by |-. A common example is 'it is red so it is coloured', which seems true but beyond proof. In the absence of formal proof, you wonder whether validity is merely a psychological notion. |
| 13348 | It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock] |
| Full Idea: In practice we avoid quotation marks and explicitly set-theoretic notation that explaining |= as 'entails' appears to demand. Hence it seems more natural to explain |= as simply representing the word 'therefore'. | |
| From: David Bostock (Intermediate Logic [1997], 1.3) | |
| A reaction: Not sure I quite understand that, but I have trained myself to say 'therefore' for the generic use of |=. In other consequences it seems better to read it as 'semantic consequence', to distinguish it from |-. |
| 13349 | Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock] |
| Full Idea: If we write Γ |= φ, with one formula to the right, then the turnstile abbreviates 'entails'. For a sequent of the form Γ |= it can be read as 'is inconsistent'. For |= φ we read it as 'valid'. | |
| From: David Bostock (Intermediate Logic [1997], 1.3) |
| 13614 | MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock] |
| Full Idea: The Rule of Detachment is a version of Modus Ponens, and says 'If |=φ and |=φ→ψ then |=ψ'. This has no assumptions. Modus Ponens is the more general rule that 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ'. | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: Modus Ponens is actually designed for use in proof based on assumptions (which isn't always the case). In Detachment the formulae are just valid, without dependence on assumptions to support them. |
| 13617 | MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock] |
| Full Idea: Modus Ponens is equivalent to the converse of the Deduction Theorem, namely 'If Γ |- φ→ψ then Γ,φ|-ψ'. | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: See 13615 for details of the Deduction Theorem. See 13614 for Modus Ponens. |
| 14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
| Full Idea: It is claimed that mathematical logic can be understood in terms of information-processing. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.5) | |
| A reaction: [They cite Chaitin 1987] I don't understand how this would work, but it is still worth quoting. This would presumably make logic rest on processes rather than on entities. I quite like that. |
| 13799 | The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock] |
| Full Idea: We shall use 'a=b' as short for 'a is the same thing as b'. The sign '=' thus expresses a particular two-place predicate. Officially we will use 'I' as the identity predicate, so that 'Iab' is as formula, but we normally 'abbreviate' this to 'a=b'. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13800 | |= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock] |
| Full Idea: We usually take these two principles together as the basic principles of identity: |= α=α and α=β |= φ(α/ξ) ↔ φ(β/ξ). The second (with scant regard for history) is known as Leibniz's Law. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13803 | If we are to express that there at least two things, we need identity [Bostock] |
| Full Idea: To say that there is at least one thing x such that Fx we need only use an existential quantifier, but to say that there are at least two things we need identity as well. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) | |
| A reaction: The only clear account I've found of why logic may need to be 'with identity'. Without it, you can only reason about one thing or all things. Presumably plural quantification no longer requires '='? |
| 13357 | Truth-functors are usually held to be defined by their truth-tables [Bostock] |
| Full Idea: The usual view of the meaning of truth-functors is that each is defined by its own truth-table, independently of any other truth-functor. | |
| From: David Bostock (Intermediate Logic [1997], 2.7) |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| Full Idea: We can talk of a 'zero-place' function, which is a new-fangled name for a familiar item; it just has a single value, and so it has the same role as a name. | |
| From: David Bostock (Intermediate Logic [1997], 8.2) |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| Full Idea: Usually we allow that a function is defined for arguments of a suitable kind (a 'partial' function), but we can say that each function has one value for any object whatever, from the whole domain that our quantifiers range over (a 'total' function). | |
| From: David Bostock (Intermediate Logic [1997], 8.2) | |
| A reaction: He points out (p.338) that 'the father of..' is a functional expression, but it wouldn't normally take stones as input, so seems to be a partial function. But then it doesn't even take all male humans either. It only takes fathers! |
| 13360 | In logic, a name is just any expression which refers to a particular single object [Bostock] |
| Full Idea: The important thing about a name, for logical purposes, is that it is used to make a singular reference to a particular object; ..we say that any expression too may be counted as a name, for our purposes, it it too performs the same job. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: He cites definite descriptions as the most notoriously difficult case, in deciding whether or not they function as names. I takes it as pretty obvious that sometimes they do and sometimes they don't (in ordinary usage). |
| 13361 | An expression is only a name if it succeeds in referring to a real object [Bostock] |
| Full Idea: An expression is not counted as a name unless it succeeds in referring to an object, i.e. unless there really is an object to which it refers. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: His 'i.e.' makes the existence condition sound sufficient, but in ordinary language you don't succeed in referring to 'that man over there' just because he exists. In modal contexts we presumably refer to hypothetical objects (pace Lewis). |
| 13814 | Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock] |
| Full Idea: Although a definite description looks like a complex name, and in many ways behaves like a name, still it cannot be a name if names must always refer to objects. Russell gave the first proposal for handling such expressions. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: I take the simple solution to be a pragmatic one, as roughly shown by Donnellan, that sometimes they are used exactly like names, and sometimes as something else. The same phrase can have both roles. Confusing for logicians. Tough. |
| 13816 | Because of scope problems, definite descriptions are best treated as quantifiers [Bostock] |
| Full Idea: Because of the scope problem, it now seems better to 'parse' definition descriptions not as names but as quantifiers. 'The' is to be treated in the same category as acknowledged quantifiers like 'all' and 'some'. We write Ix - 'for the x such that..'. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: This seems intuitively rather good, since quantification in normal speech is much more sophisticated than the crude quantification of classical logic. But the fact is that they often function as names (but see Idea 13817). |
| 13817 | Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock] |
| Full Idea: In practice, definite descriptions are for the most part treated as names, since this is by far the most convenient notation (even though they have scope). ..When a description is uniquely satisfied then it does behave like a name. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: Apparent names themselves have problems when they wander away from uniquely picking out one thing, as in 'John Doe'. |
| 13848 | We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock] |
| Full Idea: If it is really true that definite descriptions have scopes whereas names do not, then Russell must be right to claim that definite descriptions are not names. If, however, this is not true, then it does no harm to treat descriptions as complex names. | |
| From: David Bostock (Intermediate Logic [1997], 8.8) |
| 13813 | Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock] |
| Full Idea: It is natural to suppose one only uses a definite description when one believes it describes only one thing, but exceptions are 'there is no such thing as the greatest prime number', or saying something false where the reference doesn't occur. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) |
| 13815 | Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock] |
| Full Idea: In orthodox logic names are not regarded as having scope (for example, in where a negation is placed), whereas on Russell's theory definite descriptions certainly do. Russell had his own way of dealing with this. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) |
| 13438 | 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock] |
| Full Idea: A formula is said to be in 'prenex normal form' (PNF) iff all its quantifiers occur in a block at the beginning, so that no quantifier is in the scope of any truth-functor. | |
| From: David Bostock (Intermediate Logic [1997], 3.7) | |
| A reaction: Bostock provides six equivalences which can be applied to manouevre any formula into prenex normal form. He proves that every formula can be arranged in PNF. |
| 13818 | If we allow empty domains, we must allow empty names [Bostock] |
| Full Idea: We can show that if empty domains are permitted, then empty names must be permitted too. | |
| From: David Bostock (Intermediate Logic [1997], 8.4) |
| 13801 | An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock] |
| Full Idea: An 'informal proof' is not in any particular proof system. One may use any rule of proof that is 'sufficiently obvious', and there is quite a lot of ordinary English in the proof, explaining what is going on at each step. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13619 | Quantification adds two axiom-schemas and a new rule [Bostock] |
| Full Idea: New axiom-schemas for quantifiers: (A4) |-∀ξφ → φ(α/ξ), (A5) |-∀ξ(ψ→φ) → (ψ→∀ξφ), plus the rule GEN: If |-φ the |-∀ξφ(ξ/α). | |
| From: David Bostock (Intermediate Logic [1997], 5.6) | |
| A reaction: This follows on from Idea 13610, where he laid out his three axioms and one rule for propositional (truth-functional) logic. This Idea plus 13610 make Bostock's proposed axiomatisation of first-order logic. |
| 13622 | Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock] |
| Full Idea: Notably axiomatisations of first-order logic are by Frege (1879), Russell and Whitehead (1910), Church (1956), Lukasiewicz and Tarski (1930), Lukasiewicz (1936), Nicod (1917), Kleene (1952) and Quine (1951). Also Bostock (1997). | |
| From: David Bostock (Intermediate Logic [1997], 5.8) | |
| A reaction: My summary, from Bostock's appendix 5.8, which gives details of all of these nine systems. This nicely illustrates the status and nature of axiom systems, which have lost the absolute status they seemed to have in Euclid. |
| 13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
| Full Idea: If a group of formulae prove a conclusion, we can 'conditionalize' this into a chain of separate inferences, which leads to the Deduction Theorem (or Conditional Proof), that 'If Γ,φ|-ψ then Γ|-φ→ψ'. | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: This is the rule CP (Conditional Proof) which can be found in the rules for propositional logic I transcribed from Lemmon's book. |
| 13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
| Full Idea: Use of the Deduction Theorem greatly simplifies the search for proof (or more strictly, the task of showing that there is a proof). | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: See 13615 for details of the Deduction Theorem. Bostock is referring to axiomatic proof, where it can be quite hard to decide which axioms are relevant. The Deduction Theorem enables the making of assumptions. |
| 13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
| Full Idea: By repeated transformations using the Deduction Theorem, any proof from assumptions can be transformed into a fully conditionalized proof, which is then an axiomatic proof. | |
| From: David Bostock (Intermediate Logic [1997], 5.6) | |
| A reaction: Since proof using assumptions is perhaps the most standard proof system (e.g. used in Lemmon, for many years the standard book at Oxford University), the Deduction Theorem is crucial for giving it solid foundations. |
| 13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
| Full Idea: Like the Deduction Theorem, one form of Reductio ad Absurdum (If Γ,φ|-[absurdity] then Γ|-¬φ) 'discharges' an assumption. Assume φ and obtain a contradiction, then we know ¬&phi, without assuming φ. | |
| From: David Bostock (Intermediate Logic [1997], 5.7) | |
| A reaction: Thus proofs from assumption either arrive at conditional truths, or at truths that are true irrespective of what was initially assumed. |
| 13753 | Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock] |
| Full Idea: Natural deduction takes the notion of proof from assumptions as a basic notion, ...so it will use rules for use in proofs from assumptions, and axioms (as traditionally understood) will have no role to play. | |
| From: David Bostock (Intermediate Logic [1997], 6.1) | |
| A reaction: The main rules are those for introduction and elimination of truth functors. |
| 13755 | Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock] |
| Full Idea: Many books take RAA (reductio) and DNE (double neg) as the natural deduction introduction- and elimination-rules for negation, but RAA is not a natural introduction rule. I prefer TND (tertium) and EFQ (ex falso) for ¬-introduction and -elimination. | |
| From: David Bostock (Intermediate Logic [1997], 6.2) |
| 13758 | In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock] |
| Full Idea: When looking for a proof of a sequent, the best we can do in natural deduction is to work simultaneously in both directions, forward from the premisses, and back from the conclusion, and hope they will meet in the middle. | |
| From: David Bostock (Intermediate Logic [1997], 6.5) |
| 13754 | Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock] |
| Full Idea: Natural deduction adopts for → as rules the Deduction Theorem and Modus Ponens, here called →I and →E. If ψ follows φ in the proof, we can write φ→ψ (→I). φ and φ→ψ permit ψ (→E). | |
| From: David Bostock (Intermediate Logic [1997], 6.2) | |
| A reaction: Natural deduction has this neat and appealing way of formally introducing or eliminating each connective, so that you know where you are, and you know what each one means. |
| 13611 | Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock] |
| Full Idea: A tableau proof is a proof by reduction ad absurdum. One begins with an assumption, and one develops the consequences of that assumption, seeking to derive an impossible consequence. | |
| From: David Bostock (Intermediate Logic [1997], 4.1) |
| 13613 | A completed open branch gives an interpretation which verifies those formulae [Bostock] |
| Full Idea: An open branch in a completed tableau will always yield an interpretation that verifies every formula on the branch. | |
| From: David Bostock (Intermediate Logic [1997], 4.7) | |
| A reaction: In other words the open branch shows a model which seems to work (on the available information). Similarly a closed branch gives a model which won't work - a counterexample. |
| 13612 | Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock] |
| Full Idea: Rules for semantic tableaus are of two kinds - non-branching rules and branching rules. The first allow the addition of further lines, and the second requires splitting the branch. A branch which assigns contradictory values to a formula is 'closed'. | |
| From: David Bostock (Intermediate Logic [1997], 4.1) | |
| A reaction: [compressed] Thus 'and' stays on one branch, asserting both formulae, but 'or' splits, checking first one and then the other. A proof succeeds when all the branches are closed, showing that the initial assumption leads only to contradictions. |
| 13761 | In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock] |
| Full Idea: In a tableau system no sequent is established until the final step of the proof, when the last branch closes, and until then we are simply exploring a hypothesis. | |
| From: David Bostock (Intermediate Logic [1997], 7.3) | |
| A reaction: This compares sharply with a sequence calculus, where every single step is a conclusive proof of something. So use tableaux for exploring proofs, and then sequence calculi for writing them up? |
| 13757 | Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock] |
| Full Idea: With semantic tableaux there are recipes for proof-construction that we can operate, whereas with natural deduction there are not. | |
| From: David Bostock (Intermediate Logic [1997], 6.5) |
| 13756 | A tree proof becomes too broad if its only rule is Modus Ponens [Bostock] |
| Full Idea: When the only rule of inference is Modus Ponens, the branches of a tree proof soon spread too wide for comfort. | |
| From: David Bostock (Intermediate Logic [1997], 6.4) |
| 13762 | Tableau rules are all elimination rules, gradually shortening formulae [Bostock] |
| Full Idea: In their original setting, all the tableau rules are elimination rules, allowing us to replace a longer formula by its shorter components. | |
| From: David Bostock (Intermediate Logic [1997], 7.3) |
| 13759 | Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock] |
| Full Idea: A sequent calculus keeps an explicit record of just what sequent is established at each point in a proof. Every line is itself the sequent proved at that point. It is not a linear sequence or array of formulae, but a matching array of whole sequents. | |
| From: David Bostock (Intermediate Logic [1997], 7.1) |
| 13760 | A sequent calculus is good for comparing proof systems [Bostock] |
| Full Idea: A sequent calculus is a useful tool for comparing two systems that at first look utterly different (such as natural deduction and semantic tableaux). | |
| From: David Bostock (Intermediate Logic [1997], 7.2) |
| 13364 | Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG] |
| Full Idea: There are two approaches to an 'interpretation' of a logic: the first method assigns objects to names, and then defines connectives and quantifiers, focusing on truth; the second assigns objects to variables, then variables to names, using satisfaction. | |
| From: report of David Bostock (Intermediate Logic [1997], 3.4) by PG - Db (lexicon) | |
| A reaction: [a summary of nine elusive pages in Bostock] He says he prefers the first method, but the second method is more popular because it handles open formulas, by treating free variables as if they were names. |
| 13821 | Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock] |
| Full Idea: Extensionality is built into the semantics of ordinary logic. When a name-letter is interpreted as denoting something, we just provide the object denoted. All that we provide for a one-place predicate-letter is the set of objects that it is true of.. | |
| From: David Bostock (Intermediate Logic [1997]) | |
| A reaction: Could we keep the syntax of ordinary logic, and provide a wildly different semantics, much closer to real life? We could give up these dreadful 'objects' that Frege lumbered us with. Logic for processes, etc. |
| 13362 | If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock] |
| Full Idea: If two names refer to the same object, then in any proposition which contains either of them the other may be substituted in its place, and the truth-value of the proposition of the proposition will be unaltered. This is the Principle of Extensionality. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: He acknowledges that ordinary language is full of counterexamples, such as 'he doesn't know the Morning Star and the Evening Star are the same body' (when he presumably knows that the Morning Star is the Morning Star). This is logic. Like maths. |
| 13541 | For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock] |
| Full Idea: Any system of proof S is said to be 'negation-consistent' iff there is no formula such that |-(S)φ and |-(S)¬φ. | |
| From: David Bostock (Intermediate Logic [1997], 4.5) | |
| A reaction: Compare Idea 13542. This version seems to be a 'strong' version, as it demands a higher standard than 'absolute consistency'. Both halves of the condition would have to be established. |
| 13542 | A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock] |
| Full Idea: Any system of proof S is said to be 'absolutely consistent' iff it is not the case that for every formula we have |-(S)φ. | |
| From: David Bostock (Intermediate Logic [1997], 4.5) | |
| A reaction: Bostock notes that a sound system will be both 'negation-consistent' (Idea 13541) and absolutely consistent. 'Tonk' systems can be shown to be unsound because the two come apart. |
| 13540 | A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock] |
| Full Idea: 'Γ |=' means 'Γ is a set of closed formulae, and there is no (standard) interpretation in which all of the formulae in Γ are true'. We abbreviate this last to 'Γ is inconsistent'. | |
| From: David Bostock (Intermediate Logic [1997], 4.5) | |
| A reaction: This is a semantic approach to inconsistency, in terms of truth, as opposed to saying that we cannot prove both p and ¬p. I take this to be closer to the true concept, since you need never have heard of 'proof' to understand 'inconsistent'. |
| 13544 | Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock] |
| Full Idea: Being 'compact' means that if we have an inconsistency or an entailment which holds just because of the truth-functors and quantifiers involved, then it is always due to a finite number of the propositions in question. | |
| From: David Bostock (Intermediate Logic [1997], 4.8) | |
| A reaction: Bostock says this is surprising, given the examples 'a is not a parent of a parent of b...' etc, where an infinity seems to establish 'a is not an ancestor of b'. The point, though, is that this truth doesn't just depend on truth-functors and quantifiers. |
| 13618 | Compactness means an infinity of sequents on the left will add nothing new [Bostock] |
| Full Idea: The logic of truth-functions is compact, which means that sequents with infinitely many formulae on the left introduce nothing new. Hence we can confine our attention to finite sequents. | |
| From: David Bostock (Intermediate Logic [1997], 5.5) | |
| A reaction: This makes it clear why compactness is a limitation in logic. If you want the logic to be unlimited in scope, it isn't; it only proves things from finite numbers of sequents. This makes it easier to prove completeness for the system. |
| 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 |
| 13358 | Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock] |
| Full Idea: The principle of mathematical (or ordinary) induction says suppose the first number, 0, has a property; suppose that if any number has that property, then so does the next; then it follows that all numbers have the property. | |
| From: David Bostock (Intermediate Logic [1997], 2.8) | |
| A reaction: Ordinary induction is also known as 'weak' induction. Compare Idea 13359 for 'strong' or complete induction. The number sequence must have a first element, so this doesn't work for the integers. |
| 13359 | Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock] |
| Full Idea: The principle of complete induction says suppose that for every number, if all the numbers less than it have a property, then so does it; it then follows that every number has the property. | |
| From: David Bostock (Intermediate Logic [1997], 2.8) | |
| A reaction: Complete induction is also known as 'strong' induction. Compare Idea 13358 for 'weak' or mathematical induction. The number sequence need have no first element. |
| 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) |
| 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. |
| 14942 | Only admit into ontology what is explanatory and predictive [Ladyman/Ross] |
| Full Idea: We reject any grounds other than explanatory and predictive utility for admitting something into our ontology. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.3) | |
| A reaction: Now you are talking. This is something like my thesis (which I take to be Aristotelian) - that without the drive for explanation we wouldn't even think of metaphysics, and so metaphysics should be understood in that light. |
| 14948 | To be is to be a real pattern [Ladyman/Ross] |
| Full Idea: To be is to be a real pattern. ....Real patterns carry information about other real patterns. ...It's patterns all the way down. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.4) | |
| A reaction: I've plucked these bleeding from context, but they are obviously intended as slogans. Is there pattern 'inside' an electron? Are electrons all exterior? |
| 14947 | Any process can be described as transfer of measurable information [Ladyman/Ross] |
| Full Idea: Reference to transfer of some (in principle) quantitatively measurable information is a highly general way of describing any process. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.3) | |
| A reaction: That does not, of course, mean that that is what a process is. A waterfall is an archetypal process, but it is a bit more than a bunch of information. Actually its complexity may place its information beyond measurement. |
| 14941 | We say there is no fundamental level to ontology, and reality is just patterns [Ladyman/Ross] |
| Full Idea: The tentative metaphysical hypothesis of this book, which is open to empirical falsification, is that there is no fundamental level, that the real patterns criterion of reality is the last word in ontology. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.3) | |
| A reaction: I wouldn't hold your breath waiting for the empirical falsification to arrive (or vanish). Their commitment to real patterns (or structures) leaves me a bit baffled. |
| 10493 | If concrete is spatio-temporal and causal, and abstract isn't, the distinction doesn't suit physics [Ladyman/Ross] |
| Full Idea: It is said that concrete objects have causal powers while abstract ones do not, or that concrete objects exist in space and time while abstract ones do not, but these categories seem crude and inappropriate for modern physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.6) | |
| A reaction: I don't find this convincing. He gives example of peculiar causation, but I don't believe modern physics proposes any entities which are totally acausal and non-spatiotemporal. Maybe the distinction needs a defence. |
| 14934 | Concrete and abstract are too crude for modern physics [Ladyman/Ross] |
| Full Idea: The categories of concrete and abstract seem crude and inappropriate for modern physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.6) | |
| A reaction: They don't persuade me of this idea. At some point physicists need to decide the ontological status of the basic stuffs they are investigating. I'll give them a thousand years, and then I want an answer. Do they only deal in 'ideal' entities? |
| 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) |
| 14909 | Physicalism is 'part-whole' (all parts are physical), or 'supervenience/levels' (dependence on physical) [Ladyman/Ross] |
| Full Idea: There is part-whole physicalism, that everything is exhausted by basic constituents that are themselves physical, or supervenience or levels physicalism, that the putatively non-physical is dependent on the physical. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.3) | |
| A reaction: The cite Hüttemann and Papineau 2005. I am not convinced by this distinction. Ladyman and Ross oppose the first one. I'm thinking the second one either collapses into the first one, or it isn't physicalism. Higher levels are abstractions. |
| 14926 | Relations without relata must be treated as universals, with their own formal properties [Ladyman/Ross] |
| Full Idea: The best sense that can be made of a relation without relata is the idea of a universal. Thus the relation 'larger than' has formal properties that are independent of the contingencies of their instantiation. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: Russell was keen on the idea that relations are universals, and presumably for this reason. I struggle to grasp uninstantiated but nevertheless real 'greater than' relations. They are abstractions from things, not separate universals. |
| 14929 | A belief in relations must be a belief in things that are related [Ladyman/Ross] |
| Full Idea: Many philosophers say that one cannot intelligibly subscribe to the reality of relations unless one is also committed to the fact of some things that are related. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5) | |
| A reaction: Ladyman and Ross try to argue against this view, but the idea makes a strong impression on me. Your ontology seems to be rather strange if you have a set of structural relations that await things to slot into the structure. |
| 14925 | The normal assumption is that relations depend on properties of the relata [Ladyman/Ross] |
| Full Idea: The idea that there could be relations which do not supervene on the properties of their relata runs counter to a deeply entrenched way of thinking. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: Ladyman and Ross are trying to defend the idea of 'structure' which is independent of the objects that occupy the nodes of the structure. Tricky. |
| 14931 | That there are existent structures not made of entities is no stranger than the theory of universals [Ladyman/Ross] |
| Full Idea: Is the main metaphysical idea we propose (of existent structures that are not composed out of more basic entities) any more obscure or bizarre than the instantiation relation in the theory of universals? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5) | |
| A reaction: No, it is not more bizarre than that, but that isn't much of a reason to believe their theory. See Idea 8699, and many ideas about structure in mathematics. Ladyman and Ross still smack of platonism, even if they are rooted in particle physics. |
| 13802 | Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock] |
| Full Idea: A relation is 'one-many' if for anything on the right there is at most one on the left (∀xyz(Rxz∧Ryz→x=y), and is 'many-one' if for anything on the left there is at most one on the right (∀xyz(Rzx∧Rzy→x=y). | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13543 | A relation is not reflexive, just because it is transitive and symmetrical [Bostock] |
| Full Idea: It is easy to fall into the error of supposing that a relation which is both transitive and symmetrical must also be reflexive. | |
| From: David Bostock (Intermediate Logic [1997], 4.7) | |
| A reaction: Compare Idea 14430! Transivity will take you there, and symmetricality will get you back, but that doesn't entitle you to take the shortcut? |
| 14932 | Causal essentialism says properties are nothing but causal relations [Ladyman/Ross] |
| Full Idea: Causal essentialism is the doctrine that the causal relations that properties bear to other properties exhaust their natures. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5 n50) | |
| A reaction: [They cite Shoemaker, Mumford and Bird for this] Personally I don't see this view as offering relations as fundamental. The whole point is to explain everything. The only plausible primitive notion is of a power - which then generates the relations. |
| 14920 | If science captures the modal structure of things, that explains why its predictions work [Ladyman/Ross] |
| Full Idea: If theorists are able sometimes to capture the objective modal structure of the world then it is no surprise that successful novel prediction sometimes works. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.4) | |
| A reaction: This is a rather important idea, particularly for my approach. I say we should demand more explanations, and explanations of successful prediction are far from obvious in a regularity account of nature. |
| 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) |
| 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) |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 14952 | Things are constructs for tracking patterns (and not linguistic, because animals do it) [Ladyman/Ross] |
| Full Idea: Individual things are constructs built for second-best tracking of real patterns. They are not necessarily linguistic constructions, since some non-human animals almost certainly cognitively construct them. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: Delighted to see animals making an appearance. Fans of language-based metaphysics please note. If they are fictional constructs, why do they do such a good job of tracking? What generates the 'superficial' appearance that there are objects? |
| 14950 | Maybe individuation can be explained by thermodynamic depth [Ladyman/Ross] |
| Full Idea: Scientists have developed principles for understanding individuation in terms of the production of thermodynamic depth. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: [They cite J.Collier for this view] Interesting, even though I don't really understand 'thermodynamic depth'. Ladyman and Ross reject it, but there is a whiff of a theory of individuation from within physics. |
| 14927 | Physics seems to imply that we must give up self-subsistent individuals [Ladyman/Ross] |
| Full Idea: There is growing convergence among philosophers of physics that physics motivates abandonment of a metaphysics that posits fundamental self-subsistent individuals. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: They cite fermions as an example, which only seem to be given an identity by the relations into which they enter. It is a bit cheeky to simultaneously offer this idea, and despise van Inwagen and Merricks for the same object nihilism. |
| 14944 | There is no single view of individuals, because different sciences operate on different scales [Ladyman/Ross] |
| Full Idea: There is no single account of what individuals there are because, we argue, the special sciences may disagree about the bounds and status of individuals since they describe the world at different scales. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.8) | |
| A reaction: This seems to deny that nature has actual joints, and so seems to me to be a form of anti-realism (which they would deny). Why shouldn't there be a single view which unites all of these special sciences? |
| 14946 | There are no cats in quantum theory, and no mountains in astrophysics [Ladyman/Ross] |
| Full Idea: At the quantum scale there are no cats; at scales appropriate for astrophysics there are no mountains. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.2) | |
| A reaction: I don't find this convincing. Since cats are made of quantised entities, they do exist in that world, but are of little interest when trying to understand it. Similarly, astrophysicists hardly deny the existence of mountains! |
| 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. |
| 14928 | Things are abstractions from structures [Ladyman/Ross] |
| Full Idea: Individual things are locally focused abstractions from modal structure. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.4) | |
| A reaction: I am a fan of the role of abstraction in our understanding of the world, despite my limited progress in trying to explicate the idea. I can't decide whether or not there are any things. A bit basic, that! |
| 14892 | The idea of composition, that parts of the world are 'made of' something, is no longer helpful [Ladyman/Ross] |
| Full Idea: It is no longer helpful to conceive of either the world, or particular systems of the world that we study in partial isolation, as 'made of' anything at all. …Our target here is the metaphysical idea of composition. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.1) | |
| A reaction: This is argued by them from the point of view of fundamental physics as the provider of our basic metaphysics about the world. Personally I really really want to know what electrons are made of, but I know no one is going to tell me. They may even laugh. |
| 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. |
| 14949 | A sum of things is not a whole if the whole does not support some new generalisation [Ladyman/Ross] |
| Full Idea: A nostril, a city and a trumpet solo is not a real pattern, because identification of it supports no generalisations not supported by identification of the three conjuncts considered separately. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.4) | |
| A reaction: This is a nice try at offering a criterion for unity, but I doubt whether it will work, because an ingenious person could come up with wild generalisations. These three combined make possible a charming new line of poetry. |
| 14951 | We treat the core of a pattern as an essence, in order to keep track of it [Ladyman/Ross] |
| Full Idea: We focus on diagnostic features of real patterns that we can treat as 'core', which reliably predict that our attention is still tracking the same real pattern. These are Locke's 'essence of particulars', or Putnam's 'hidden structures'. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: They seemed to be ashamed of themselves for proposing this, and call it a 'second-best' epistemological device. They seem to imply that they are useful fictions, but why shouldn't the hidden structures be real? They might both identify and explain. |
| 14958 | A continuous object might be a type, with instances at each time [Ladyman/Ross] |
| Full Idea: Why should not 'Napoleon' be a type, of which 'Napoleon in 1805' and 'Napoleon in 1813' are instances? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.6) | |
| A reaction: That is very nice. That might be a view that suits presentism, where the timed instances never co-exist, and so have the sort of abstract existence that we associate with types. |
| 13847 | If non-existent things are self-identical, they are just one thing - so call it the 'null object' [Bostock] |
| Full Idea: If even non-existent things are still counted as self-identical, then all non-existent things must be counted as identical with one another, so there is at most one non-existent thing. We might arbitrarily choose zero, or invent 'the null object'. | |
| From: David Bostock (Intermediate Logic [1997], 8.6) |
| 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. |
| 13820 | The idea that anything which can be proved is necessary has a problem with empty names [Bostock] |
| Full Idea: The common Rule of Necessitation says that what can be proved is necessary, but this is incorrect if we do not permit empty names. The most straightforward answer is to modify elementary logic so that only necessary truths can be proved. | |
| From: David Bostock (Intermediate Logic [1997], 8.4) |
| 14903 | Quantum mechanics seems to imply single-case probabilities [Ladyman/Ross] |
| Full Idea: Quantum mechanics seems to imply single-case probabilities. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) | |
| A reaction: I know they keep telling us about such things, but I remain cautious. I think all the physicists have done is delved a bit deeper into something they don't understand. |
| 14923 | In quantum statistics, two separate classical states of affairs are treated as one [Ladyman/Ross] |
| Full Idea: In quantum statistics, what would be regarded as two possible states of affairs classically is treated as one possible state of affairs. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.1) |
| 14955 | Rats find some obvious associations easier to learn than less obvious ones [Ladyman/Ross] |
| Full Idea: Contrary to early behaviourist dogma, associations are not all equally learnable. Rats learn to associate eating with nausea, and a flash with a shock, much more easily than either complementary pairing. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.2) | |
| A reaction: That looks like an argue for some sort of innate knowledge, but experiments to disentangle eating from nausea must be rather hard to set up. |
| 14918 | The doctrine of empiricism does not itself seem to be empirically justified [Ladyman/Ross] |
| Full Idea: If to be an empiricist is to believe that 'experience is the sole source of information about the world', the problem is that this does not itself seem to be justifiable by experience. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.3.1) | |
| A reaction: [The quotation is from Van Fraassen 1985 p.253] This is the classic 'turning the tables' move in argument, invented by the Greeks. It is hard to offer anything other than intuition in the first move of any metaphysical theory. |
| 14891 | There is no reason to think our intuitions are good for science or metaphysics [Ladyman/Ross] |
| Full Idea: There is no reason to imagine that our habitual intuitions and inferential responses are well designed for science or for metaphysics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.1) |
| 14915 | The theory of evolution was accepted because it explained, not because of its predictions [Ladyman/Ross] |
| Full Idea: Darwin's theory of evolution was accepted by the scientific community because of its systematizing and explanatory power, and in spite of its lack of novel predictive success. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.3) | |
| A reaction: I am keen on the centrality of explanation to all of our thinking, metaphysical as well as physical, so I like this one. In general I like accounts of science that pay more attention to biology, and less to physics. |
| 14916 | What matters is whether a theory can predict - not whether it actually does so [Ladyman/Ross] |
| Full Idea: We suggest a modal account of novel prediction. That a theory could predict some unknown phenomenon is what matters, not whether it actually did so predict. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.3) | |
| A reaction: They also emphasise predicting new types of thing, rather than particular items. Some theories are powerful on explanation, but not so concerned with prediction. See Idea 14915. |
| 14922 | The Ramsey sentence describes theoretical entities; it skips reference, but doesn't eliminate it [Ladyman/Ross] |
| Full Idea: It is a mistake to think that the Ramsey sentence allows us to eliminate theoretical entities, for it still states that they exist. It is just that they are referred to not directly, by means of theoretical terms, but by description. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.4.1) |
| 14921 | The Ramsey-sentence approach preserves observations, but eliminates unobservables [Ladyman/Ross] |
| Full Idea: If one replaces the assertions of a first-order theory with its Ramsey sentence (giving a quantified predicate variable for a theoretical term), the observational consequences are carried over, but direct reference to unobservables is eliminated. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.4.1) | |
| A reaction: Thus this rewriting of theories is popular with empiricists, and this draws attention to the way you can change the ontological commitments simply by paraphrase. ...However, see Idea 14922. |
| 14953 | Induction is reasoning from the observed to the unobserved [Ladyman/Ross] |
| Full Idea: Induction is any form of reasoning that proceeds from claims about observed phenomena to claims about unobserved phenomena. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: Most accounts of induction seem to imply that they lead to generalisations, rather than just some single unobserved thing. This definition is in line with David Lewis's. |
| 14914 | Inductive defences of induction may be rule-circular, but not viciously premise-circular [Ladyman/Ross] |
| Full Idea: The inductive defence of induction may be circular but not viciously so, because it is rule circular (defending the rule being used) but not premise circular (where the conclusion is in one of the premises). | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.2) | |
| A reaction: [They cite Braithwaite 1953 and Carnap 1952 for this] This strikes me as clutching at straws, when the whole procedure of induction is inescapably precarious. It is simply all we have available. |
| 14913 | We explain by deriving the properties of a phenomenon by embedding it in a large abstract theory [Ladyman/Ross] |
| Full Idea: Theoretical explanation is the derivation of the properties of a relatively concrete and observable phenomenon by means of an embedding into some larger, relatively abstract and unobservable theoretical structure. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 2.1.1) | |
| A reaction: [they are citing Michael Friedman 1981 p.1] This sounds like covering law explanation, but the theoretical structure will be a set of intersecting laws, rather than a single law. How do you explain the theoretical structure? |
| 14930 | Maybe the only way we can think about a domain is by dividing it up into objects [Ladyman/Ross] |
| Full Idea: Speculating cautiously about psychology, it is possible that dividing a domain up into objects is the only way we can think about it. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.5) | |
| A reaction: Typical physicists - they speculate about psychology instead of studying it. Have they no respect for science? Neverthless my speculative psychology agrees with theirs. This fact may well be the key to all of metaphysics. |
| 14939 | Two versions of quantum theory say that the world is deterministic [Ladyman/Ross] |
| Full Idea: In the Bohm version of quantum theory, and the Everett approach, the world comes out deterministic after all. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: This is just in case anyone wants to trumpet the idea that quantum theory has established indeterminism. It is particularly daft to think that quantum indeterminacy makes free will possible (or even actual). |
| 14911 | Science is opposed to downward causation [Ladyman/Ross] |
| Full Idea: When someone pronounces for downward causation they are in opposition to science. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.6 n54) | |
| A reaction: Downward causation is the key issue in any debate about whether minds exhibit excitingly 'emergent' properties that somehow put them outside the realm of normal physics. I take that to be nonsense, and I side with science here. |
| 13363 | A (modern) predicate is the result of leaving a gap for the name in a sentence [Bostock] |
| Full Idea: A simple way of approaching the modern notion of a predicate is this: given any sentence which contains a name, the result of dropping that name and leaving a gap in its place is a predicate. Very different from predicates in Aristotle and Kant. | |
| From: David Bostock (Intermediate Logic [1997], 3.2) | |
| A reaction: This concept derives from Frege. To get to grips with contemporary philosophy you have to relearn all sorts of basic words like 'predicate' and 'object'. |
| 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. |
| 14956 | Explanation by kinds and by clusters of properties just express the stability of reality [Ladyman/Ross] |
| Full Idea: Philosophers sometimes invoke natural kinds as if they explain the possibility of explanation. This is characteristically neo-scholastic. That anything can be explained, and that properties cluster together, express one fact: reality is relatively stable. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.6) | |
| A reaction: Odd idea. I would have thought that if there are indeed kinds and clusters, this would explain a great deal more than mere stability. Or, more accurately, they would invite a more substantial explanation than mere stability would seem to need. |
| 14957 | There is nothing more to a natural kind than a real pattern in nature [Ladyman/Ross] |
| Full Idea: Everything that a naturalist could legitimately want from the concept of a natural kind can be had simply by reference to real patterns. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 5.6) | |
| A reaction: I think I agree with this, and with the general idea that natural kinds are overrated. There are varying degrees of stability in nature, and where there is a lot of stability our inductive reasoning can get to work. And that's it. |
| 14954 | Causation is found in the special sciences, but may have no role in fundamental physics [Ladyman/Ross] |
| Full Idea: The idea of causation, as it is used in science, finds its exemplars in the special sciences, and it is presently open empirical question whether that notion will have any ultimate role to play in fundamental physics. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 4.5) | |
| A reaction: Note that they seem to always have a notion of 'ultimate' physics hovering over their account. I wonder. There is nothing in this idea to make me think that I should eliminate the idea of causation from my metaphysics. |
| 14902 | Science may have uninstantiated laws, inferred from approaching some unrealised limit [Ladyman/Ross] |
| Full Idea: It is possible that uninstantiated laws can be established in science, and consequently bear explanatory weight, ..if we need reasons for thinking that the closer conditions get to some limit, the more they approximate to some ideal. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) | |
| A reaction: [The cite Hüttemann 2004] I am dubious about laws, but I take this to be a point in favour of inference to the best explanation, and against accounts of laws as supervenient of how things actually are. |
| 14937 | That the universe must be 'made of' something is just obsolete physics [Ladyman/Ross] |
| Full Idea: It is a metaphysical residue of obsolete physics to suppose that the universe is 'made of' anything. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2) | |
| A reaction: They quote Smolin as saying that it is 'processes' which are fundamental. And yet surely there must be something there to undergo a process? Surely we don't have eternal platonic processes? |
| 14900 | In physics, matter is an emergent phenomenon, not part of fundamental ontology [Ladyman/Ross] |
| Full Idea: Physics has taught us that matter in the sense of extended stuff is an emergent phenomenon that has no counterpart in fundamental ontology. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) | |
| A reaction: They contrast this point with futile debates among philosopher between atomists (partless particles) and gunkists (parts all the way down). |
| 14901 | Spacetime may well be emergent, rather than basic [Ladyman/Ross] |
| Full Idea: Contemporary physics takes very seriously the idea that spacetime itself is emergent from some more fundamental structure. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 1.2.3) |
| 14924 | If spacetime is substantial, what is the substance? [Ladyman/Ross] |
| Full Idea: It is fair to ask: if spacetime is a substance, what is the substance in question? | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.2) | |
| A reaction: Personally I love the question 'If it exists, what is it made of?', though physicists seem to think that this reveals a gormless misunderstanding. To my question Keith Hossack retorted 'What are the atoms made of?' |
| 14938 | A fixed foliation theory of quantum gravity could make presentism possible [Ladyman/Ross] |
| Full Idea: It has been pointed out that presentism is an open question in so far as a fixed foliation theory of quantum gravity has not been ruled out. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.2 n75) | |
| A reaction: [They cite B.Monton for this point] I don't understand this idea, but I'll have it anyway. Google 'fixed foliation' for me, as I'm too busy. |
| 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) |