107 ideas
| 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). |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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? |
| 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) |
| 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) |
| 14528 | Maybe modal thought is unavoidable, as a priori recognition of necessary truth-preservation in reasoning [Hale/Hoffmann,A] |
| Full Idea: There are 'transcendental' arguments saying that modal thought is unavoidable - recognition, a priori, of the necessarily truth-preserving character of some forms of inference is a precondition for rational thought in general, and scientific theorizing. | |
| From: Bob Hale/ Aviv Hoffmann (Introduction to 'Modality' [2010], 1) | |
| A reaction: So the debate about the status of logical truths and valid inference, are partly debates about whether out thought has to involve modality, or whether it could just be about the actual world. I take possibilities and necssities to be features of nature. |
| 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) |
| 20043 | Evolutionary explanations look to the past or the group, not to the individual [Stout,R] |
| Full Idea: In evolutionary explanations you may explain a population trait in terms of what it is for the sake of an individual, or explain it in terms of what it was for the sake of in earlier generations, but never in terms of what the trait is for the sake of. | |
| From: Rowland Stout (Action [2005], 2 'Functions') | |
| A reaction: So my ears are for the sake of my ability to hear, but that does not explain why I have ears. Should we say there is 'impersonal teleology' here, but no 'personal teleology'? Interesting. |
| 20058 | Not all explanation is causal. We don't explain a painting's beauty, or the irrationality of root-2, that way [Stout,R] |
| Full Idea: Not all explanation is causal. Explaining the beauty of a painting is not explaining why something happened. or why a move in chess is illegal, or why the square root of two is not a rational number. | |
| From: Rowland Stout (Action [2005], 5 'Argument') | |
| A reaction: It is surely plausible that the illegality of the chess move is caused (or 'determined', as I prefer to say) by the laws created for chess. The painting example seems right, though; what determined its configuration (think Pollock!) does not explain it. |
| 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'. |
| 20035 | Philosophy of action studies the nature of agency, and of deliberate actions [Stout,R] |
| Full Idea: The philosophy of action is concerned with the nature of agency: what it is to be a full-blown agent, and what it is to realise one's agency in acting deliberately on things. | |
| From: Rowland Stout (Action [2005], 1 'Being') | |
| A reaction: 'Full-blown' invites the question of whether there could be a higher level of agency, beyond the capacity of human beings. Perhaps AI should design a theoretical machine that taps into those higher levels, if we can conceive of them. Meta-coherence! |
| 20084 | Agency is causal processes that are sensitive to justification [Stout,R] |
| Full Idea: My conclusion is that wherever you can identify causal processes that are sensitive to the recommendations of systems of justification, there you have found agency. | |
| From: Rowland Stout (Action [2005], 9b 'Conclusion') | |
| A reaction: [the last paragraph of his book] Justification seems an awfully grand notion for a bee pollinating a flower, and I don't see human action as profoundly different. A reason might be a bad justification, but it might not even aspire to be a justification. |
| 20061 | Mental states and actions need to be separate, if one is to cause the other [Stout,R] |
| Full Idea: If psychological states and action results cannot be identified independently of one another, then it does not make sense to describe one as causing the other. | |
| From: Rowland Stout (Action [2005], 5 'Conclusion') | |
| A reaction: This summarises a widely cited unease about the causal theory of action. Any account in action theory will need to separate out some components and explain their interrelation. Otherwise actions are primitives, and we can walk away. |
| 20079 | Are actions bodily movements, or a sequence of intention-movement-result? [Stout,R] |
| Full Idea: Are actions identical with bodily movements? Or are they identical with sequences of things starting inside the agent's mind with their intentions, going through their body movements and finishing with the external results being achieved? | |
| From: Rowland Stout (Action [2005], 9 'What is action') | |
| A reaction: If bodily movements are crucial, this presumably eliminates speech acts. Speech or writing may involve some movement, but the movement is almost irrelevant to the nature of the action. Telepathy would do equally well. |
| 20080 | If one action leads to another, does it cause it, or is it part of it? [Stout,R] |
| Full Idea: When we do one action 'by' doing another, either the first action causes the process of the second, or the first action is part of the process of the second | |
| From: Rowland Stout (Action [2005], 9 'What is by') | |
| A reaction: Stout says the second view is preferable, because pressing a switch does not cause my action of turning on the light (though it does cause the light to come on). |
| 20059 | I do actions, but not events, so actions are not events [Stout,R] |
| Full Idea: I do not do an event; I do an action; so actions are not events. | |
| From: Rowland Stout (Action [2005], 5 'Are actions') | |
| A reaction: Sounds conclusive, but it places a lot of weight on the concepts of 'I' and 'do', which leaves room for some discussion. This point is opposed to the causal theory of action, because causation concerns events. |
| 20081 | Bicycle riding is not just bodily movement - you also have to be on the bicycle [Stout,R] |
| Full Idea: You do not ride a bicycle just by moving your body in a certain way. You have to be on the bicycle to move in the right sort of way | |
| From: Rowland Stout (Action [2005], 9 'Are body') | |
| A reaction: My favourite philosophical ideas are simple and conclusive. He also observes that walking involves the ground being walked on. In complex actions 'feedback' with the environment is involved. |
| 20044 | The rationalistic approach says actions are intentional when subject to justification [Stout,R] |
| Full Idea: The rationalistic approach to agency says that what characterises intentional action is that it is subject to justification. | |
| From: Rowland Stout (Action [2005], 2 'Conclusion') | |
| A reaction: [Anscombe is the chief articulator of this view] This seems to incorporate action into an entirely intellectual and even moral framework. |
| 20039 | The causal theory says that actions are intentional when intention (or belief-desire) causes the act [Stout,R] |
| Full Idea: The causal theory of action asserts that what characterises intentional action is the agent's intentions, or perhaps their beliefs and desires, causing their behaviour in the appropriate way. | |
| From: Rowland Stout (Action [2005], 1 'Outline') | |
| A reaction: The agent's intentions are either sui generis (see Bratman), or reducible to beliefs and desires (as in Hume). The classic problem for the causal theory is said to be 'deviant causal chains'. |
| 20047 | Deciding what to do usually involves consulting the world, not our own minds [Stout,R] |
| Full Idea: In the vast majority of actions you need to look outwards to work out what you should do. An exam invigilator should consult the clock to design when to end the exam, not her state of mind. | |
| From: Rowland Stout (Action [2005], 3 'The belief-') | |
| A reaction: Stout defends externalist intentions. I remain unconvinced. It is no good looking at a clock if you don't form a belief about what it says, and the belief is obviously closer than the clock to the action. Intellectual virtue requires checking the facts. |
| 20065 | Should we study intentions in their own right, or only as part of intentional action? [Stout,R] |
| Full Idea: Should we try to understand what it is to have an intention in terms of what it is to act intentionally, or should we try to understand what it is to have an intention independently of what it is to act intentionally? | |
| From: Rowland Stout (Action [2005], 7 'Acting') | |
| A reaction: Since you can have an intention to act, and yet fail to act, it seems possible to isolate intentions, but not to say a lot about them. Intention may be different prior to actions, and during actions. Early Davidson offered the derived view. |
| 20067 | You can have incompatible desires, but your intentions really ought to be consistent [Stout,R] |
| Full Idea: Intentions are unlike desires. You can simultaneously desire two things that you know are incompatible. But when you form intentions you are embarking on a course of action, and there is a much stronger requirement of consistency. | |
| From: Rowland Stout (Action [2005], 7 'Relationship') | |
| A reaction: I'm not sure why anyone would identify intentions with desires. I would quite like to visit Japan, but have no current intention of doing so. I assume that the belief-plus-desire theory doesn't deny that an uninteresting intention is also needed. |
| 20078 | The normativity of intentions would be obvious if they were internal promises [Stout,R] |
| Full Idea: One way to incorporate this [normative] feature of intentions would be to treat them like internal promises. | |
| From: Rowland Stout (Action [2005], 8 'Intention') | |
| A reaction: Interesting. The concept of a promise is obviously closely linked to an intention. If you tell your companion exactly where you intend your golf ball to land, you can thereby be held accountable, in a manner resembling a promise (but not a promise). |
| 20036 | Intentional agency is seen in internal precursors of action, and in external reasons for the act [Stout,R] |
| Full Idea: It is plausible that we find something characteristic of intentional agency when we look inward to the mental precursors of actions, and also when we look outward, to the sensitivity of action to what the environment gives us reasons to do. | |
| From: Rowland Stout (Action [2005], 1 'How') | |
| A reaction: This is Stout staking a claim for his partly externalist view of agency. I warm less and less to the various forms of externalism. How often does the environment 'give us reasons' to do things? How can we act, without internalising those reasons? |
| 20066 | Speech needs sustained intentions, but not prior intentions [Stout,R] |
| Full Idea: The intentional action of including the word 'big' in a sentence does not require a prior intention to say it. What is required is that you say it with the intention of saying it. | |
| From: Rowland Stout (Action [2005], 7 'Relationship') | |
| A reaction: This seems right, but makes it a lot harder to say what an intention is, and to separate it out for inspection. You can't speak a good English sentence while withdrawing the intention involved. |
| 20073 | Bratman has to treat shared intentions as interrelated individual intentions [Stout,R] |
| Full Idea: Bratman has to construe what we think of as shared intentions as not literally involving shared intentions, but as involving interrelating of individual intentions. | |
| From: Rowland Stout (Action [2005], 7 'Conclusion') | |
| A reaction: Stout rejects this, for an account based on adaptability of behaviour. To me, naturalism and sparse ontology favour Bratman (1984) . I like my idea that shared intentions are conditional individual intentions. If the group refuses, I drop the intention. |
| 20069 | A request to pass the salt shares an intention that the request be passed on [Stout,R] |
| Full Idea: When one person says to another 'please pass the salt', and the other engages with this utterance and understands it, they share the intention that this request is passed from the first person to the second. | |
| From: Rowland Stout (Action [2005], 7 'Shared') | |
| A reaction: Simple and intriguing. We form an intention, and then ask someone else to take over our intention. When the second person takes over the intention, I give up the intention to acquire the salt, because it is on its way. It's political. |
| 20070 | An individual cannot express the intention that a group do something like moving a piano [Stout,R] |
| Full Idea: It is unnatural to describe an individual as intending that the group do something together. ...What could possibly express my intention that we move the piano upstairs? | |
| From: Rowland Stout (Action [2005], 7 'Shared') | |
| A reaction: Two possible answers: it makes sense if I have great authority within the group. 'I'm going to move the piano - you take that end'. Or, such expressions are implicitly conditional - 'I intend to move the piano (if you will also intend it)'. |
| 20071 | An intention is a goal to which behaviour is adapted, for an individual or for a group [Stout,R] |
| Full Idea: An individual intention is a goal to which an individual's behaviour adapts. A shared intention is a goal to which a group of people's behaviour collectively adapts. | |
| From: Rowland Stout (Action [2005], 7 'Shared') | |
| A reaction: This is part of Stout's externalist approach to actions. One would have thought that an intention was a state of mind, not a goal in the world. The individual's goal can be psychological, but a group's goal has to be an abstraction. |
| 20038 | If the action of walking is just an act of will, then movement of the legs seems irrelevant [Stout,R] |
| Full Idea: If volitionism identifies the action with an act of will, this has the unpalatable consequence (for a Cartesian dualist) that walking does not happen in the material world. It would be the same act of walking if you had no legs, or no body at all. | |
| From: Rowland Stout (Action [2005], 1 'Volitionism') | |
| A reaction: Is this attacking a caricature version of volitionism? Descartes would hardly subscribe to the view that no legs are needed for walking. If my legs spasmodically move without an act of will, we typically deny that this is an action. |
| 20050 | Most philosophers see causation as by an event or state in the agent, rather than the whole agent [Stout,R] |
| Full Idea: Most philosophers are uneasy with understanding the causal aspect of actions in terms of an 'agent' making something happen. They prefer to think of some event in the agent, or state of the agent, making something happen. | |
| From: Rowland Stout (Action [2005], 4 'The causal') | |
| A reaction: There is a bit of a regress if you ask what caused the event or state of affairs. It is tempting to stop the buck at the whole agent, or else carry the reduction on down to neurons, physics and the outside world. |
| 20052 | If you don't mention an agent, you aren't talking about action [Stout,R] |
| Full Idea: Once you lose the agent from an account of action it stops being an account of action at all. | |
| From: Rowland Stout (Action [2005], 4 'Agent') | |
| A reaction: [he refers to Richard Taylor 1966] This could be correct without implying that agents offer a unique mode of causation. The concept of 'agent' is reducible. |
| 20077 | If you can judge one act as best, then do another, this supports an inward-looking view of agency [Stout,R] |
| Full Idea: Weakness of will is a threat to the outward-looking approach to agency. It seems you can hold one thing to be the thing to do, and at the same time do something else. Many regard this as a decisive reason to follow a more inward-looking approach. | |
| From: Rowland Stout (Action [2005], 8 'Weakness') | |
| A reaction: It hadn't struck me before that weakness of will is a tool for developing an accurate account of what is involved in normal agency. Some facts that guide action are internal to the agent, such as greed for sugary cakes. |
| 20049 | Maybe your emotions arise from you motivations, rather than being their cause [Stout,R] |
| Full Idea: Instead of assuming that your motivation depends on your emotional state, we might say that your emotional state depends on how you are motivated to act. | |
| From: Rowland Stout (Action [2005], 3 'Emotions') | |
| A reaction: [He says this move is made by Kant, Thomas Nagel and McDowell] Stout favours the view that it is external facts which mainly give rise to actions, and presumably these facts are intrinsically motivating, prior to any emotions. I don't disagree. |
| 20046 | For an ascetic a powerful desire for something is a reason not to implement it [Stout,R] |
| Full Idea: If wanting something most were the same as having the most powerful feelings about it, then as an ascetic (rejecting what you most powerfully desire), your wanting most to eat a bun would be your reason for not eating the bun. | |
| From: Rowland Stout (Action [2005], 3 'The belief-') | |
| A reaction: This sounds like reason overruling desire, but the asceticism can always be characterised as a meta-desire. |
| 20060 | Beliefs, desires and intentions are not events, so can't figure in causal relations [Stout,R] |
| Full Idea: Beliefs, desires and intentions are states of mind rather than events, but events are the only things that figure in causal relations. | |
| From: Rowland Stout (Action [2005], 5 'Do beliefs') | |
| A reaction: This is exactly why we have the concept of 'the will' - because it is a mental state to which we attribute active causal powers. We then have to explain how this 'will' is related to the other mental states (which presume motivate or drive it?). |
| 20055 | A standard view says that the explanation of an action is showing its rational justification [Stout,R] |
| Full Idea: The idea running through the work of Aristotle, Kant, Anscombe and Davidson is that explanation of action involves justifying that action or making it rationally intelligible. | |
| From: Rowland Stout (Action [2005], 5 'Psychological') | |
| A reaction: Stout goes on to say that instead you could give the 'rationalisation' of the action, which is psychological facts which explain the action, without justifying it. The earlier view may seem a little optimistic and intellectualist. |
| 20056 | In order to be causal, an agent's reasons must be internalised as psychological states [Stout,R] |
| Full Idea: It is widely accepted that to get involved in the causal process of acting an agent's reasons must be internalised as psychological states. | |
| From: Rowland Stout (Action [2005], 5 'Psychological') | |
| A reaction: This doesn't say whether the 'psychological states' have to be fully conscious. That seems unlikely, given the speed with which we perform some sequences of actions, such as when driving a car, or playing a musical instrument. |
| 20053 | An action is only yours if you produce it, rather than some state or event within you [Stout,R] |
| Full Idea: For action to be properly yours it must be you who is the causal originator of the action, rather than some state or event within you. | |
| From: Rowland Stout (Action [2005], 4 'Agent') | |
| A reaction: [He invokes Chisholm 1966] The idea here is that we require not only 'agent causation', but that the concept of agent must include free will. It seems right we ought to know whether or not an action is 'mine'. Nothing too fancy is needed for this! |
| 20048 | There may be a justification relative to a person's view, and yet no absolute justification [Stout,R] |
| Full Idea: In a relativistic notion of justification, in a particular system, there is a reason for a vandal to smash public property, even though, using an absolute conception of justification, there is no reason for him to do so. | |
| From: Rowland Stout (Action [2005], 3 'The difference') | |
| A reaction: I suppose Kantians would say that the aim of morality is to make your personal (relative) justification coincide with what seems to be the absolute justification. |
| 20068 | Describing a death as a side-effect rather than a goal may just be good public relations [Stout,R] |
| Full Idea: The real signficance of the doctrine of double effect can be public relations. You can put a better spin on an action by describing a death as an unfortunate collateral consequence, rather than as a goal of the action | |
| From: Rowland Stout (Action [2005], 7 'Doctrine') | |
| A reaction: The problem is that it the principle is usually invoked in situations where it is not clear where some bad effect is intended, and it is very easy to lie in such situations. In football, we can never quite decide whether a dangerous tackle was intended. |
| 20083 | Aristotelian causation involves potentiality inputs into processes (rather than a pair of events) [Stout,R] |
| Full Idea: In the Aristotelian approach to causation (unlike the Humean approach, involving separate events), A might cause B by being an input into some process (realisation of potentiality) that results in B. | |
| From: Rowland Stout (Action [2005], 9 'Trying') | |
| A reaction: Stout relies quite heavily on this view for his account of human action. I like processes, so am sympathetic to this view. If there are two separate events, it is not surprising that Hume could find nothing to bridge the gap between them. |