101 ideas
| 7846 | Nietzsche thinks philosophy makes us more profound, but not better [Nietzsche, by Ansell Pearson] |
| Full Idea: Nietzsche does not think philosopher exists to make us better human beings - but it can make us more profound ones. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Keith Ansell Pearson - How to Read Nietzsche Intro | |
| A reaction: What is the point of being more 'profound' if that isn't 'better'? Are we sure that Kant is more 'profound' than a Yanomamo Indian? Personally I think philosophy tends to produce moral improvement, but I have seen a few striking counterexamples. |
| 20107 | How many mediocre thinkers are occupied with influential problems! [Nietzsche] |
| Full Idea: It is a terrible thought to contemplate that an immense number of mediocre thinkers are occupied with really influential matters. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 03 | |
| A reaction: [in a journal of 1867] What would he say now, with the plethora of academics and students aspiring to the highest levels of human thought? If I face up to the fact that I am 'mediocre', should I stop? And become mediocre at something else? |
| 20352 | Nietzsche has a metaphysics, as well as perspectives - the ontology is the perspectives [Nietzsche, by Richardson] |
| Full Idea: Nietzsche's thought includes both a metaphysics and a perspectivism, once these are more complexly grasped. But I argue that the metaphysics is basic: it's an ontology of perspectives. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by John Richardson - Nietzsche's System Intro | |
| A reaction: Very good. If it was just gormless relativism, which is what many people hope for in Nietzsche, why is it many perspectives? If they are just relative, having lots of them is no help. The point is they sum, and increase verisimilitude. |
| 20379 | Reason is just another organic drive, developing late, and fighting for equality [Nietzsche] |
| Full Idea: Reason is a support organ that slowly develops itself, ...and emancipates itself slowly to equal rights with the organic drives - so that reason (belief and knowledge) fights with the drives, as itself a new drive, very late come to preponderance. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 9/11[243]), quoted by John Richardson - Nietzsche's System 4.3.2 n55 | |
| A reaction: A very powerful and fascinating idea. There is a silly post-modern tendency to think that Nietzsche denegrates and trivialises reason because of remarks like this, but he takes ranking the drives to be the supreme activity. I rank reason high. |
| 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. |
| 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). |
| 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) |
| 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) |
| 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? |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 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. |
| 20123 | First see nature as non-human, then fit ourselves into this view of nature [Nietzsche] |
| Full Idea: My task is the dehumanisation of nature, and then the naturalisation of humanity once it has attained the pure concept of 'nature'. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 9.525), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 10 | |
| A reaction: Safranski sees this as summarising Nietzsche's project, and it could be a mission statement for naturalism. This idea pinpoints why I take Nietzsche to be important - as a pioneer of the naturalistic view of people. |
| 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? |
| 20105 | Storms are wonderful expressions of free powers! [Nietzsche] |
| Full Idea: How different the lightning, the storm, the hail, free powers, without ethics! How happy, how powerful they are, pure will, untarnished by intellect! | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 2.122), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 02 | |
| A reaction: Nietzsche was a perfect embodiment of the Romantic Movement! I take this to be a deep observation, since I think raw powers are the most fundamental aspect of nature. Schopenhauer is behind this idea. |
| 20376 | We begin with concepts of kinds, from individuals; but that is not the essence of individuals [Nietzsche] |
| Full Idea: The overlooking of individuals gives us the concept and with this our knowledge begins: in categorising, in the setting up of kinds. But the essence of things does not correspond to this. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], p.51) | |
| A reaction: [dated c1873] Aha! So Nietzsche agrees with me in my defence of individual essences, against kind essences (which seem to me to obviously derive from the nature of individuals). Deep in my heart I knew I would find this quotation one day. |
| 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) |
| 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) |
| 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'. |
| 22501 | Nietzsche classified actions by the nature of the agent, not the nature of the act [Nietzsche, by Foot] |
| Full Idea: Nietzsche thought profoundly mistaken a taxonomy that classified actions as the doing of this or that, insisting that the true nature of an action depended rather on the nature of the individual who did it. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 7) by Philippa Foot - Natural Goodness 7 | |
| A reaction: This is more in the spirit of Aristotle than in the modern legalistic style. It seems to totally ignore consequences, which would puzzle victims or beneficiaries of the action. |
| 22500 | Nietzsche failed to see that moral actions can be voluntary without free will [Foot on Nietzsche] |
| Full Idea: To threaten morality Nietzsche needed to show not only that free will was an illusion, but also that no other distinction between voluntary and involuntary action (Aristotle's, for instance) would do instead. He seems to be wrong about this. | |
| From: comment on Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 7) by Philippa Foot - Natural Goodness | |
| A reaction: Just the idea I have been seeking! There is no free will, so in what way are we responsible? Simple: we are responsible for any act which can be shown to be voluntary. It can't just be any action we fully caused, because of accidents. |
| 20128 | Each person has a fixed constitution, which makes them a particular type of person [Nietzsche, by Leiter] |
| Full Idea: Nietzsche's view (which we may call the 'Doctrine of Types') is that each person has a fixed psycho-physical constitution, which defines him as a particular type of person. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Brian Leiter - Nietzsche On Morality 1 'What kind' | |
| A reaction: An interestesting variant, standing between the Aristotelian picture of one shared human nature, and the existentialist picture of our endlessly malleable nature. So what type am I, and what type are you? How many types are there? |
| 22503 | Nietzsche could only revalue human values for a different species [Nietzsche, by Foot] |
| Full Idea: It is only for a different species that Nietzsche's most radical revaluation of values could be valid. It is not valid for us as we are, or are ever likely to be. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Philippa Foot - Natural Goodness 7 | |
| A reaction: This is the Aristotelian view, that our values and virtues arise out of our human nature, with which I largely agree, though we should resist its rather conservative tendencies. |
| 8041 | The superman is a monstrous oddity, not a serious idea [MacIntyre on Nietzsche] |
| Full Idea: The Übermensch belongs in the pages of a philosophical bestiary rather than in serious discussion. | |
| From: comment on Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Alasdair MacIntyre - After Virtue: a Study in Moral Theory Ch.2 | |
| A reaction: It may just be an empirical and historical fact that the value-systems of a culture arise from the characters of a few strong-willed and charismatic individuals, rather than from collective need - let along collective philosophising. |
| 20135 | Nietzsche's higher type of man is much more important than the idealised 'superman' [Nietzsche, by Leiter] |
| Full Idea: The 'superman' has received far more attention from commentators than it warrants: the higher type of human being (a Goethe or a Nietzsche) is much more important than the hyperbolic, and often obscure, Zarathustrian rhetoric about the über-mensch. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Brian Leiter - Nietzsche On Morality 4 'Higher' n2 | |
| A reaction: Leiter says the über-mensch idea almost entirely drops out of Nietzsche's mature work. |
| 20353 | The 'will to power' is basically applied to drives and forces, not to people [Nietzsche, by Richardson] |
| Full Idea: 'Will to power' is most basically applied not to people but to 'drives' or 'forces', simpler units which Nietzsche sometimes calls 'points' and 'power quanta'. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 1) by John Richardson - Nietzsche's System 1 | |
| A reaction: This strikes as a correct account of Nietzsche, and a hugely important interpretative point. He wasn't saying that all human beings would conquer the world if they could. The point is there are many conflicting and combining wills to power. |
| 20113 | Friendly chats undermine my philosophy; wanting to be right at the expense of love is folly [Nietzsche] |
| Full Idea: My entire philosophy wavers after just an hour of friendly conversation with complete strangers. It strikes me as so foolish to insist on being right at the expense of love. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 6.37), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 09 | |
| A reaction: [Letter to Gast, 1880] Strangers who met Nietzsche on walks reported how kind and friendly he was. Most people want to be right most of the time, but a few people have this vice in rather excessive form. Especially philosophers! |
| 22475 | Moral generalisation is wrong, because we should evaluate individual acts [Nietzsche, by Foot] |
| Full Idea: Nietzsche believed that moral generalisation was impossible because the proper subject of evaluation was, instead, a person's individual act. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Philippa Foot - Nietzsche's Immoralism p.155 | |
| A reaction: This suggests a different type of particularism, focusing on the particular decision, rather than on the details of the situation. Presumable no two moral decisions are ever sufficiently the same to be compared. But a lie is a lie. |
| 22476 | Nietzsche thought our psychology means there can't be universal human virtues [Nietzsche, by Foot] |
| Full Idea: Nietzsche believed, in effect, that as the facts of human psychology really were, there could be no such thing as human virtues, dispositions good in any man. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Philippa Foot - Nietzsche's Immoralism p.157 | |
| A reaction: Presumably each individual can only have virtues appropriate to their individual nature, which is something like channelling their personal psychological drives. Can't we each have our individual version of courage or honesty? |
| 20104 | Nietzsche tried to lead a thought-provoking life [Safranski on Nietzsche] |
| Full Idea: All of us ponder our existences, but Nietzsche strove to lead the kind of life that would yield food for thought. | |
| From: comment on Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 01) by Rüdiger Safranski - Nietzsche: a philosophical biography 01 | |
| A reaction: Could Nietzsche possibly be a role model for us in this respect? If I were starting afresh, guided by this thought, I'm not sure how I would go about it. It is Nietzsche's astonishing independence of thought that hits you. |
| 7847 | Initially nihilism was cosmic, but later Nietzsche saw it as a cultural matter [Nietzsche, by Ansell Pearson] |
| Full Idea: Nietzsche's first presentation of nihilism is an existential affair arising from cosmic problems, but he later stressed nihilism as a historical and cultural problem of values, where mankind's highest values reach a point of devaluation. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Keith Ansell Pearson - How to Read Nietzsche Ch.1 | |
| A reaction: The second version seems to imply a quasi-Marxist determinism about social progress. Then you would have to ask, what is the point of fighting against it? I wonder if Nietzsche's values are anti-nihilist, but his metaethics makes nihilism unavoidable? |
| 9782 | Nietzsche urges that nihilism be active, and will nothing itself [Nietzsche, by Zizek] |
| Full Idea: Nietzsche opposes active to passive nihilism - it is better to actively will nothing itself than not to will anything. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Slavoj Zizek - Conversations, with Glyn Daly §3 | |
| A reaction: To 'actively will nothing' sounds to me indistinguishable from suicide, which I don't believe was ever on Nietzsche's agenda. It is hard, though, to disentangle Nietzsche's attitude to nihilism. |
| 20102 | Flight from boredom leads to art [Nietzsche] |
| Full Idea: Flight from boredom is the mother of all art. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 8.432), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography Intro | |
| A reaction: I might even say that all human achievement comes from boredom. |
| 20106 | Nietzsche was fascinated by a will that can turn against itself [Nietzsche, by Safranski] |
| Full Idea: Nietzsche was fascinated by the idea of a will that turns against itself, against its usual impulses. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by Rüdiger Safranski - Nietzsche: a philosophical biography 03 | |
| A reaction: This strikes me as very existentialist - a case of existence before essence. |
| 20124 | Reliving life countless times - this gives the value back to life which religion took away [Nietzsche] |
| Full Idea: "Is this something I want to do countless times?" ....Let us etch the image of eternity onto our own lives! This thought embodies more than all religions, which taught us to disdain life as something ephemeral and to look toward an unspecified other life. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 9.496,503), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 10 | |
| A reaction: You can't get away from eternal recurrence being an imaginative trick, to focus value onto our choices. For a while Nietzsche tried to persuade himself that the recurrence actually occurred, but we all know it doesn't. |
| 20367 | Individual development is more important than the state, but a community is necessary [Nietzsche] |
| Full Idea: All states and communities are something lower than the individual, but necessary kinds for his higher development. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 10/7[98]), quoted by John Richardson - Nietzsche's System 2.4 n104 | |
| A reaction: This indicates why Nietzsche should not really be taken as a political thinker, though I would say there is a sort of communitarianism implied in this, just as for Aristotle virtue is supreme, which needs social expression. |
| 20371 | Nietzsche thinks we should join a society, in order to criticise, heal and renew it [Nietzsche, by Richardson] |
| Full Idea: Nietzsche thinks the best way of both joining and opposing a society is to find where it's sick, to be its merciless critic and exposer, and to help heal and renew it. | |
| From: report of Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885]) by John Richardson - Nietzsche's System 3.3 | |
| A reaction: This sounds like the great Victorian sages, such as Ruskin and Arnold. Christopher Hitchens was a nice recent example. Maybe these have been the finest British citizens? |
| 20108 | Every culture loses its identity and power if it lacks a major myth [Nietzsche] |
| Full Idea: Without myth every culture loses its natural healthy creating power: only a horizon encircled with myths can mark off a cultural movement as a discrete unit. | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 1.145) | |
| A reaction: In the early part of his career this was a big idea for Nietzsche, especially associated with Wagner's Ring, but he moved away from the idea later. |
| 20887 | A rape disregards the status of being a person - but so does all assault [Foa] |
| Full Idea: In a rape a person is used without proper regard for her personhood - but this is true of every kind of assault. | |
| From: Pamela Foa (What's Wrong with Rape? [1977], 1) | |
| A reaction: This is a good step towards her attempt to pin down what is specifically wrong with rape, which strikes me as an extremely important question, and not merely in order to justify punishments. |
| 20888 | Rape of children is dreadful, but no one thinks children should have a right of consent [Foa] |
| Full Idea: Rape of children is at least as heinous as rape of adults, though few believe that children have or ought to have the same large domain of consent adults (male and female) ought to have. | |
| From: Pamela Foa (What's Wrong with Rape? [1977], 1) | |
| A reaction: A powerful point. She is not quite spelling out the crux, which is that no one thinks children should have a right to consent to sexual intercourse, which means that consent is irrelevant in such a case of rape. So it can't be the key to adult rape? |
| 20889 | If men should lust and women shouldn't, that makes rape the prevalent sexual model [Foa] |
| Full Idea: We are taught that sexual desires are desires women ought not to have and men must have. This is the model which makes necessary an eternal battle of the sexes. It explains why rape is the prevalent model of sexuality. | |
| From: Pamela Foa (What's Wrong with Rape? [1977], 3) | |
| A reaction: A striking thought. See 'The Origins of Sex' by F.Dabhoiwala, which claims that women used to be seen as the sexual predators, and the balance shifted in the 18thC. Are women obliged to exhibit lust, in order to defuse rapacious desires? |