110 ideas
| 22223 | Being-in-the-world is projection to possibilities, thrownness among them, and fallenness within them [Heidegger, by Caputo] |
| Full Idea: Being-in-the-world is a phenomenon of 'care' with a tripartite structure: a) projection towards its possibilities, b) thrownness among those possibilities, so Dasein is not free, and c) fallenness among worldly possibilities, to neglect of its own. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.227 | |
| A reaction: Sounds a bit Californian to me. Just living among the world's possibilities is evidently a bad thing, because you could be concentrating on yourself and your own development instead? |
| 22158 | Pheomenology seeks things themselves, without empty theories, problems and concepts [Heidegger] |
| Full Idea: 'Phenomenology' can be formulated as 'To the things themselves!' It is opposed to all free-floating constructions and accidental findings, and to conceptions which only seem to have been demonstrated. It is opposed to traditiona' pseudo-problems. | |
| From: Martin Heidegger (Being and Time [1927], Intro II.07) | |
| A reaction: It sounds as if we are invited to look at the world the way a dog might look at it. I am not at all clear what it to be gained from this approach. |
| 15574 | 'Logos' really means 'making something manifest' [Heidegger, by Polt] |
| Full Idea: Heidegger concludes that 'logos' essentially means 'making something manifest'. | |
| From: report of Martin Heidegger (Being and Time [1927], 56/33) by Richard Polt - Heidegger: an introduction 3.§7 | |
| A reaction: It would at least seem to involve revealing the truth of something, though truth doesn't seem to be central to Heidegger's thought. 'Logos' is often translated as 'an account', as well as a 'reason', so Heidegger may be right. |
| 15569 | Heidegger says truth is historical, and never absolute [Heidegger, by Polt] |
| Full Idea: Heidegger is a relentless enemy of ahistorical, absolutist concepts of truth. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Richard Polt - Heidegger: an introduction 1 | |
| A reaction: I presume that if truth is not absolute then it must be relative, but Polt is a little coy about saying so. For me, anyone who says truth is relative doesn't understand the concept, and is talking about something else. |
| 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. |
| 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] |
| 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. |
| 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. |
| 9560 | S5 provides the correct logic for necessity in the broadly logical sense [Fine,K] |
| Full Idea: S5 provides the correct logic for necessity in the broadly logical sense. | |
| From: Kit Fine (Model Theory for Modal Logic I [1978], 151), quoted by Charles Chihara - A Structural Account of Mathematics | |
| A reaction: I have no view on this, but I am prejudiced in favour of the idea that there is a correct logic for such things, whichever one it may be. Presumably the fact that S5 has no restrictions on accessibility makes it more comprehensive and 'metaphysical'. |
| 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) |
| 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) |
| 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 |-. |
| 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. |
| 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. |
| 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) |
| 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! |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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? |
| 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. |
| 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'. |
| 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. |
| 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. |
| 21897 | Reducing being to the study of beings too readily accepts the modern scientific view [Heidegger, by May] |
| Full Idea: Continental philosophers, following Heidegger, see in the attempt to reduce the question of being to that of beings a symptom of an age that is too ready to accept the terms in which science conceives the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Todd May - Gilles Deleuze 1.04 | |
| A reaction: Interesting. I take the idea that this is a failing of the modern age to be ridiculous, since I take it to be the key metaphysical move made by Aristotle. Neverthless, Aristotle is closely in tune with modern science. For 'beings', read 'objects'. |
| 15573 | For us, Being is constituted by awareness of other sorts of Being [Heidegger] |
| Full Idea: We are Dasein - the entity who possesses - as constitutive for its understanding of existence - an understanding of the Being of all entities of a character other than its own. | |
| From: Martin Heidegger (Being and Time [1927], 34/13), quoted by Richard Polt - Heidegger: an introduction 3.§4 | |
| A reaction: This seems to connect to the emerging 'externalist' view of mind that comes with the external view of content coming from Purnam's Twin Earth idea. |
| 9273 | Heidegger turns to 'Being' to affirm the uniqueness of humans in the world [Heidegger, by Gray] |
| Full Idea: Heidegger turns to 'Being' for the same reason that Christians turn to God - to affirm the unique place of humans in the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John Gray - Straw Dogs 2.4 | |
| A reaction: This is the first remark I have encountered that makes sense of Heidegger's Being to me! It places Heidegger as a modernist philosopher, trying to grapple with the decline of religion. I'll stick with Bertrand Russell on that. |
| 22157 | Dasein is a mode of Being distinguished by concern for its own Being [Heidegger] |
| Full Idea: Dasein is an entity which does not just occur among other entities. Rather it is ontically distinguished by the fact that, in its very Being, that Being is an issue for it. | |
| From: Martin Heidegger (Being and Time [1927], Intro I.04) | |
| A reaction: How do you distinguish the Being of normal humans from the Being of someone in a deep coma, who has no existential issues? Has that Dasein ceased to be? Why does angst create a new mode of Being, but flying doesn't? |
| 8137 | Dasein is ahead of itself in the world, and alongside encountered entities [Heidegger] |
| Full Idea: The formal existential totality of Dasein's ontological structural whole is: the Being of Dasein means ahead-of-itself-Being-already-in-(the-world) as Being-alongside (entities encountered within-the-world). | |
| From: Martin Heidegger (Being and Time [1927], I.6 41) | |
| A reaction: If you find that thought really illuminating, you are probably on the wrong website. However, the thought that we exist 'ahead of ourselves' might be a fruitful line for existentialists to explore. |
| 21951 | In company with others one's Dasein dissolves, and even the others themselves dissolve [Heidegger] |
| Full Idea: This being-with-one-another dissolves one's own Dasein completely into the kind of being of 'the others', in such a way, indeed, that the others, as distinguishable and explicit, vanish more and more. | |
| From: Martin Heidegger (Being and Time [1927], p.164), quoted by Mark Wrathall - Heidegger: how to read 5 | |
| A reaction: He seems to be describing the psychology of someone who joins a small crowd which gradually increases in size. I take this relation to others to be the basic existential dilemma, of retaining individual authenticity within a community. |
| 20745 | 'Dasein' expresses not 'what' the entity is, but its being [Heidegger] |
| Full Idea: When we designate this entity with the term 'Dasein' we are expressing not its 'what' (as if it were a table, house, or tree) but its being. | |
| From: Martin Heidegger (Being and Time [1927], p.297), quoted by Kevin Aho - Existentialism: an introduction 2 'Phenomenology' | |
| A reaction: Presumably analytic discussions of persons try to be too objective. Heidegger is trying to capture the thought at the heart of Kierkegaard's existentialism. Objectivity and subjectivity are never in conflict. Is there really a different mode of existence? |
| 8134 | The word 'dasein' is used to mean 'the manner of Being which man possesses', and also the human creature [Heidegger, by Cooper,DE] |
| Full Idea: Heidegger borrows a common German word 'dasein', meaning 'being' or 'existence', to refer both to 'the manner of Being which... man... possesses', and to the creature which possesses it. | |
| From: report of Martin Heidegger (Being and Time [1927], p.32) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: This just strikes me as an elementary ontological mistake. Because something has startling properties it doesn't follow that we have a different type of Being. Magnets don't have a different type of being from ordinary iron. |
| 8135 | 'Dasein' is Being which is laid claim to, and which matters to its owner [Heidegger, by Cooper,DE] |
| Full Idea: We each of us not only have Dasein (our kind of Being), but we can lay claim to it. Also the Dasein of a thing 'is an issue for it' - we care about the kinds of creatures we can make ourselves into. | |
| From: report of Martin Heidegger (Being and Time [1927], p.67) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: Heidegger says other more puzzling things about Dasein. The second half of the idea is what makes Heidegger an existentialist, and an inspiration for Sartre. |
| 21948 | Dasein is being which can understand itself, and possess itself in a way allowing authenticity [Heidegger] |
| Full Idea: Dasein is an entity which, in its very being, comports itself understandingly towards that being. ...Mineness belongs to an existent Dasein, and belongs to it as the condition which makes authenticity and inauthenticity possible. | |
| From: Martin Heidegger (Being and Time [1927], p.78), quoted by Mark Wrathall - Heidegger: how to read 1 | |
| A reaction: He might eventually persuade me that Dasein is so different from mere material being that it deserves a category of its own. But a reductive account of mind is also a reductive account of being. |
| 7680 | Ontology is possible only as phenomenology [Heidegger] |
| Full Idea: Ontology is possible only as phenomenology. | |
| From: Martin Heidegger (Being and Time [1927], p.31), quoted by Dale Jacquette - Ontology Ch.1 | |
| A reaction: Jacquette argues against this claim. The idea seems to be the ultimate extension of Kant, and it is not a big move to say that the only real phenomenology we can discuss is our semantics. Wrong, wrong, wrong. |
| 22161 | Readiness-to-hand defines things in themselves ontologically [Heidegger] |
| Full Idea: Readiness-to-hand is the way in which entities as they are 'in themselves' are defined ontologico-categorially. | |
| From: Martin Heidegger (Being and Time [1927], I.3.15) | |
| A reaction: I assume this is a direct reference to the problem idealists had with the thing-in-itself. It seems that the reality of a thing consists of the strengthened relationship it has with Dasein, which sounds fairly idealist to me. |
| 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) |
| 15576 | Heidegger seeks a non-traditional concept of essence as 'essential unfolding' [Heidegger, by Polt] |
| Full Idea: Heidegger tries to develop a non-traditional concept of essence as 'essential unfolding' ('wesen' as a verb). | |
| From: report of Martin Heidegger (Being and Time [1927], I.4.27) by Richard Polt - Heidegger: an introduction 3.§25-7 |
| 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) |
| 15578 | Propositions don't provide understanding, because the understanding must come first [Heidegger, by Polt] |
| Full Idea: Propositions are not a good clue to the essence of understanding, because we must already understand things before we formulate propositions about them. | |
| From: report of Martin Heidegger (Being and Time [1927], I.5.31) by Richard Polt - Heidegger: an introduction 3.§31-3 | |
| A reaction: I like this, because I think the most important aspects of our thought and understanding are entirely non-verbal - even in cases where they seem to be highly specific and verbal. We don't understand ourselves at all! |
| 22159 | If we posit 'I' as the starting point, we miss the mind's phenomenal content [Heidegger] |
| Full Idea: One of our first tasks will be to prove that if we posit an 'I' or subject as that which is proximally given, we shall completely miss the phenomenal content of Dasein. | |
| From: Martin Heidegger (Being and Time [1927], I.1.10) | |
| A reaction: Descartes had thrown doubt on the informativeness of the phenomena, so presumably your phenomenologist is not interested in whether they reveal any truth. So why are unreliable phenomena of any interest? |
| 22160 | Our relationship to a hammer strengthens when we use [Heidegger] |
| Full Idea: The less we stare at the hammer-Thing, and the more we seize hold of it and use it, the more primordial does our relationship to it become. ...The kind of Being which equipment possesses... we call 'readiness-to-hand' [Zuhandenheit]. | |
| From: Martin Heidegger (Being and Time [1927], I.3.15) | |
| A reaction: This example would be well at home in the writings of the pragmatists. It is also an important example for existentialists. In analytic philosophy we might say the experience combines perception with direct exerience of causation. |
| 15580 | There are no raw sense-data - our experiences are of the sound or colour of something [Heidegger] |
| Full Idea: We always take a noise as the sound of something; we always take a hue as the color of something. We simply do not experience raw, uninterpreted sense-data - these are the inventions of philosophers. | |
| From: Martin Heidegger (Being and Time [1927], 207/163-4), quoted by Richard Polt - Heidegger: an introduction 3.§31-3 | |
| A reaction: This is something like the modern view of sense-data as promoted by John McDowell, rather than the experiential atoms of Russell and Moore. Experience is holistic, but that doesn't mean we can't analyse it into components. |
| 20749 | Perceived objects always appear in a context [Heidegger] |
| Full Idea: The perceptual 'something' is always in the middle of something else, it always forms part of a 'field'. | |
| From: Martin Heidegger (Being and Time [1927], p.4), quoted by Kevin Aho - Existentialism: an introduction 3 'Perceptual' | |
| A reaction: Sounds like our knowledge of electrons. Nice point. Standard analytic discussions of perceiving a glass always treat it in isolation, when it is on an expensive table near a brandy bottle. Or near a hammer. |
| 22163 | The scandal of philosophy is expecting to prove reality when the prover's Being is vague [Heidegger] |
| Full Idea: The 'scandal of philosophy' is not that this proof [of external things] has yet to be given, but that such proofs are expected and attempted again and again. ...The kind of Being of the entity which does the proving has not been made definite enough. | |
| From: Martin Heidegger (Being and Time [1927], I.6.43a) | |
| A reaction: The 'scandal' was a remark of Kant's. Presumably Heidegger's exploration of Dasein aims to establish the Being of the prover sufficiently to solve this problem (via phenomenology). |
| 21949 | Having thoughts and feelings need engagement in the world [Heidegger, by Wrathall] |
| Full Idea: Heidegger argues that having thoughts and feelings is only possible for entity that is actually engaged in the world. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Mark Wrathall - Heidegger: how to read 1 | |
| A reaction: This seems to be an a priori exclusion of the possibility of a brain in a vat. I guess the ancestor of this idea is Schopenhauer. |
| 22222 | Dasein finds itself already amongst others [Heidegger, by Caputo] |
| Full Idea: The world is a world shared with others, so that far from being a solipsistic ego ...Dasein finds itself already amongst others. | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.226 | |
| A reaction: Phenomenologists don't seem bothered about the problem of knowing other minds. If you take something for granted, it ceases to be a problem to be solved! |
| 8136 | If we work and play with other people, they are bound to be 'Dasein', intelligent agents [Heidegger, by Cooper,DE] |
| Full Idea: How do I know that other people have minds? The question is a bad one. Precisely because I encounter them at work, play and the like, it is guaranteed that they, too, are Dasein, intelligent agents. | |
| From: report of Martin Heidegger (Being and Time [1927], p.153-) by David E. Cooper - Heidegger Ch.3 | |
| A reaction: I've seen film of someone playing peek-a-boo with a bonobo ape, so presumably they have Dasein. It might be easier for the AI community to aim at building a robot with Dasein, than one which was simply conscious. |
| 22164 | When Dasein grasps something it exists externally alongside the thing [Heidegger] |
| Full Idea: When Dasein directs itself towards something and grasps it, it does not somehow first get out of an inner sphere in which it has been proximally encapsulated, but its primary kind of Being is such that it is always 'outside' alongside entities. | |
| From: Martin Heidegger (Being and Time [1927], I.2.13) | |
| A reaction: This is the first plausible fruit of phenomenology I have been able to discover. Analysing the passive mind is not very promising, but seeing what happens when we become more proactive is revealing. |
| 22162 | There is an everyday self, and an authentic self, when it is grasped in its own way [Heidegger] |
| Full Idea: The self of everyday Dasein is the they-self [das Man-selbst], which we distinguish from the authentic self - that is, from the Self which has been taken hold of in its own way. | |
| From: Martin Heidegger (Being and Time [1927], I.4.27) | |
| A reaction: To a novice this sounds like a requirement for increased self-consciousness during daily activity. 'Be a good animal, true to your animal self' said one of Lawrence's characters. |
| 20114 | Everyone is other, and no one is himself [Heidegger] |
| Full Idea: Everyone is other, and no one is himself. | |
| From: Martin Heidegger (Being and Time [1927], p.165), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 09 | |
| A reaction: Safranski describes this as the idea of 'structural self-evasion'. He detects the same idea in Nietzsche's 'Daybreak'. |
| 15577 | Moods are more fundamentally revealing than theories - as when fear reveals a threat [Heidegger, by Polt] |
| Full Idea: For Heidegger moods are disclosive; they show us things in a more fundamental way than theoretical propositions ever can. For example, fear reveals something as a threat. | |
| From: report of Martin Heidegger (Being and Time [1927], I.5.30) by Richard Polt - Heidegger: an introduction 3.§30 | |
| A reaction: Most modern students of emotion seem to agree. Even though they may not have specific content, it is always possible to consider the underlying cause of the mood. |
| 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'. |
| 20748 | We do not add value to naked things; its involvement is disclosed in understanding it [Heidegger] |
| Full Idea: We do not throw a 'signification' over some naked thing which is present-at-hand, we do not stick a value on it; but when something is encountered as such, the thing in question has an involvement which is disclosed in our understanding of the world. | |
| From: Martin Heidegger (Being and Time [1927], p.190-1), quoted by George Dickie - The Myth of the Aesthetic Attitude 3 'Undoing' | |
| A reaction: Analytic philosophy and science have tried to dismantle experience, and Heidegger wants to put it back together. I would say there is a big difference between encountering a thing (which is a bit facty), and understanding it (which is more valuey). |
| 22166 | Dasein has the potential to be itself, but must be shown this in the midst of ordinariness [Heidegger] |
| Full Idea: Because Dasein is lost in the 'they', it must first find itself. It must be 'shown' to itself in its possible authenticity. In terms of its possibility, Dasein is already a potentiality-for-Being-its-self, but it needs to have this potentiality attested. | |
| From: Martin Heidegger (Being and Time [1927], II.2.54) | |
| A reaction: I wish there was some criterion for knowing when you are being yourself and when you are not. |
| 22165 | Anxiety reveals the possibility and individuality of Dasein [Heidegger] |
| Full Idea: Anxiety discloses Dasein as Being-possible, and indeed as the only kind of thing which it can be of its own accord as something individualised in individualisation. | |
| From: Martin Heidegger (Being and Time [1927], I.6.40) | |
| A reaction: Is sounds like insecurity, as a sort of trauma that shocks one into self-realisation. The idea means very little to me personally. |
| 21952 | Anxiety about death frees me to live my own life [Heidegger, by Wrathall] |
| Full Idea: For Heidegger, as a consequence of my anxiety in the face of death, I am set free to live my life as my own rather than doing things merely because others expect me to do them. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Mark Wrathall - Heidegger: how to read 7 | |
| A reaction: Contrary to Epicurus, Heidegger thinks anxiety about death is a good thing. The point is, I suppose, that we all die alone, and people who are very socially contrained need to face up to death in order to grasp their autonomy. |
| 22224 | Anxiety is the uncanniness felt when constantly fleeing from asserting one's own freedom [Heidegger, by Caputo] |
| Full Idea: Anxiety [angst] is the disturbing sense of uncanniness by which Dasein is overtaken (thrownness) when it discovers there is nothing other than its own freedom to sustain its projects (projection), and from which Dasein constantly takes flight (falling). | |
| From: report of Martin Heidegger (Being and Time [1927]) by John D. Caputo - Heidegger p.227 | |
| A reaction: This seems to be Kierkegaard's idea, unamended. In my experience anxiety only comes when I am forced into making decisions by worldly situations. An 'existential crisis' is a sort of blankness appearing where a future life was supposed to be. |
| 15572 | Being what it is (essentia) must be conceived in terms of Being (existence) [Heidegger] |
| Full Idea: Dasein's Being-what-it-is (essentia) must….be conceived in terms of its Being (existentia). | |
| From: Martin Heidegger (Being and Time [1927], 67/42), quoted by Richard Polt - Heidegger: an introduction 3.§2 | |
| A reaction: This seems to be the origin of Sartre's famous slogan 'existence before essence'. It seems to be a rebellion against Husserl's quest for essences. |
| 20453 | Heidegger says we must either choose an inauthentic hero, or choose yourself as hero [Heidegger, by Critchley] |
| Full Idea: Heidegger says you must choose your hero; either you choose 'das Man', the inauthentic life, or you choose yourself - the point being that you have to choose yourself as your hero in order to be authentic. | |
| From: report of Martin Heidegger (Being and Time [1927]) by Simon Critchley - Impossible Objects: interviews 5 | |
| A reaction: If Nietzsche's 'Ecce Homo' is the model for choosing yourself as hero, I am not too sure about this idea. Needing a hero seems awfully German and romantic. Ein Heldenleben. Be your own anit-hero (like a standup comedian)? |