158 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| Full Idea: Aristotle takes wisdom to come in two forms, the practical and the theoretical, the former of which is good judgement about how to act, and the latter of which is deep knowledge or understanding. | |
| From: report of Aristotle (works [c.330 BCE]) by Dennis Whitcomb - Wisdom Intro | |
| A reaction: The interesting question is then whether the two are connected. One might be thoroughly 'sensible' about action, without counting as 'wise', which seems to require a broader view of what is being done. Whitcomb endorses Aristotle on this idea. |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value. | |
| From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26 |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos | |
| From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95 |
| 21267 | Supposing many principles is superfluous if a few will do it [Aquinas] |
| Full Idea: It is superfluous to suppose that what can be accounted for by a few principles has been produced by many. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Ob2) | |
| A reaction: Notice that this is 'superfluous' rather than 'wrong'. But ten people can lift a piano which could have been lifted by eight. Note that this is 150 years before Ockham. |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us. | |
| From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51 | |
| A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'. |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined. | |
| From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157 | |
| A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus? |
| 23176 | Truth is universal, but knowledge of it is not [Aquinas] |
| Full Idea: The truth is the same for all, but is not equally known to all. | |
| From: Thomas Aquinas (Summa Theologicae [1265], I-II Q94 4) | |
| A reaction: Amazing how many modern thinkers fail to grasp this simple distinction. However, the truth is not quite the same for all if diverse persons are expressing a single truth with different concepts and languages. The word 'facts' is helpful here. |
| 20621 | Types of lying: Speak lies, intend lies, intend deception, aim at deceptive goal? [Aquinas, by Tuckness/Wolf] |
| Full Idea: Lying can involve (1) speaking false words, (2) the intention to speak false words, (3) the intention of bringing about deception, and (4) the ultimate goal of one's deception. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265], Q110) by Tuckness,A/Wolf,C - This is Political Philosophy 10 'Lying' | |
| A reaction: It's a start, but much more is needed to clarify lying. Irony is an obvious problem with (1). |
| 21248 | If the existence of truth is denied, the 'Truth does not exist' must be true! [Aquinas] |
| Full Idea: Whoever denies the existence of truth grants that truth does not exist: and if truth does not exist, then the proposition 'Truth does not exist' is true: and if there is anything true, there must be truth. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Art 1, Obj 3) | |
| A reaction: A classic example of turning the tables, also applicable to anyone who firmly denies knowledge, or that words are meaningful, or says that meaning needs verification. However, one measily truth is not much consolation. |
| 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) |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12 | |
| A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit. |
| 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? |
| 23173 | If a syllogism admits one absurdity, others must follow [Aquinas] |
| Full Idea: In syllogistic arguments, granted one absurdity, others must follow too. | |
| From: Thomas Aquinas (Summa Theologicae [1265], I-II Q19 6) | |
| A reaction: This asserts the necessity of logical consequence, which he derives from Aristotle. |
| 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 '='? |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
| From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
| 13357 | Truth-functors are usually held to be defined by their truth-tables [Bostock] |
| Full Idea: The usual view of the meaning of truth-functors is that each is defined by its own truth-table, independently of any other truth-functor. | |
| From: David Bostock (Intermediate Logic [1997], 2.7) |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| Full Idea: We can talk of a 'zero-place' function, which is a new-fangled name for a familiar item; it just has a single value, and so it has the same role as a name. | |
| From: David Bostock (Intermediate Logic [1997], 8.2) |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| Full Idea: Usually we allow that a function is defined for arguments of a suitable kind (a 'partial' function), but we can say that each function has one value for any object whatever, from the whole domain that our quantifiers range over (a 'total' function). | |
| From: David Bostock (Intermediate Logic [1997], 8.2) | |
| A reaction: He points out (p.338) that 'the father of..' is a functional expression, but it wouldn't normally take stones as input, so seems to be a partial function. But then it doesn't even take all male humans either. It only takes fathers! |
| 13360 | In logic, a name is just any expression which refers to a particular single object [Bostock] |
| Full Idea: The important thing about a name, for logical purposes, is that it is used to make a singular reference to a particular object; ..we say that any expression too may be counted as a name, for our purposes, it it too performs the same job. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: He cites definite descriptions as the most notoriously difficult case, in deciding whether or not they function as names. I takes it as pretty obvious that sometimes they do and sometimes they don't (in ordinary usage). |
| 13361 | An expression is only a name if it succeeds in referring to a real object [Bostock] |
| Full Idea: An expression is not counted as a name unless it succeeds in referring to an object, i.e. unless there really is an object to which it refers. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: His 'i.e.' makes the existence condition sound sufficient, but in ordinary language you don't succeed in referring to 'that man over there' just because he exists. In modal contexts we presumably refer to hypothetical objects (pace Lewis). |
| 13814 | Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock] |
| Full Idea: Although a definite description looks like a complex name, and in many ways behaves like a name, still it cannot be a name if names must always refer to objects. Russell gave the first proposal for handling such expressions. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: I take the simple solution to be a pragmatic one, as roughly shown by Donnellan, that sometimes they are used exactly like names, and sometimes as something else. The same phrase can have both roles. Confusing for logicians. Tough. |
| 13816 | Because of scope problems, definite descriptions are best treated as quantifiers [Bostock] |
| Full Idea: Because of the scope problem, it now seems better to 'parse' definition descriptions not as names but as quantifiers. 'The' is to be treated in the same category as acknowledged quantifiers like 'all' and 'some'. We write Ix - 'for the x such that..'. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: This seems intuitively rather good, since quantification in normal speech is much more sophisticated than the crude quantification of classical logic. But the fact is that they often function as names (but see Idea 13817). |
| 13817 | Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock] |
| Full Idea: In practice, definite descriptions are for the most part treated as names, since this is by far the most convenient notation (even though they have scope). ..When a description is uniquely satisfied then it does behave like a name. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: Apparent names themselves have problems when they wander away from uniquely picking out one thing, as in 'John Doe'. |
| 13848 | We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock] |
| Full Idea: If it is really true that definite descriptions have scopes whereas names do not, then Russell must be right to claim that definite descriptions are not names. If, however, this is not true, then it does no harm to treat descriptions as complex names. | |
| From: David Bostock (Intermediate Logic [1997], 8.8) |
| 13813 | Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock] |
| Full Idea: It is natural to suppose one only uses a definite description when one believes it describes only one thing, but exceptions are 'there is no such thing as the greatest prime number', or saying something false where the reference doesn't occur. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) |
| 13815 | Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock] |
| Full Idea: In orthodox logic names are not regarded as having scope (for example, in where a negation is placed), whereas on Russell's theory definite descriptions certainly do. Russell had his own way of dealing with this. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) |
| 13438 | 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock] |
| Full Idea: A formula is said to be in 'prenex normal form' (PNF) iff all its quantifiers occur in a block at the beginning, so that no quantifier is in the scope of any truth-functor. | |
| From: David Bostock (Intermediate Logic [1997], 3.7) | |
| A reaction: Bostock provides six equivalences which can be applied to manouevre any formula into prenex normal form. He proves that every formula can be arranged in PNF. |
| 13818 | If we allow empty domains, we must allow empty names [Bostock] |
| Full Idea: We can show that if empty domains are permitted, then empty names must be permitted too. | |
| From: David Bostock (Intermediate Logic [1997], 8.4) |
| 13801 | An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock] |
| Full Idea: An 'informal proof' is not in any particular proof system. One may use any rule of proof that is 'sufficiently obvious', and there is quite a lot of ordinary English in the proof, explaining what is going on at each step. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13619 | Quantification adds two axiom-schemas and a new rule [Bostock] |
| Full Idea: New axiom-schemas for quantifiers: (A4) |-∀ξφ → φ(α/ξ), (A5) |-∀ξ(ψ→φ) → (ψ→∀ξφ), plus the rule GEN: If |-φ the |-∀ξφ(ξ/α). | |
| From: David Bostock (Intermediate Logic [1997], 5.6) | |
| A reaction: This follows on from Idea 13610, where he laid out his three axioms and one rule for propositional (truth-functional) logic. This Idea plus 13610 make Bostock's proposed axiomatisation of first-order logic. |
| 13622 | Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock] |
| Full Idea: Notably axiomatisations of first-order logic are by Frege (1879), Russell and Whitehead (1910), Church (1956), Lukasiewicz and Tarski (1930), Lukasiewicz (1936), Nicod (1917), Kleene (1952) and Quine (1951). Also Bostock (1997). | |
| From: David Bostock (Intermediate Logic [1997], 5.8) | |
| A reaction: My summary, from Bostock's appendix 5.8, which gives details of all of these nine systems. This nicely illustrates the status and nature of axiom systems, which have lost the absolute status they seemed to have in Euclid. |
| 13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
| Full Idea: If a group of formulae prove a conclusion, we can 'conditionalize' this into a chain of separate inferences, which leads to the Deduction Theorem (or Conditional Proof), that 'If Γ,φ|-ψ then Γ|-φ→ψ'. | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: This is the rule CP (Conditional Proof) which can be found in the rules for propositional logic I transcribed from Lemmon's book. |
| 13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
| Full Idea: Use of the Deduction Theorem greatly simplifies the search for proof (or more strictly, the task of showing that there is a proof). | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: See 13615 for details of the Deduction Theorem. Bostock is referring to axiomatic proof, where it can be quite hard to decide which axioms are relevant. The Deduction Theorem enables the making of assumptions. |
| 13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
| Full Idea: By repeated transformations using the Deduction Theorem, any proof from assumptions can be transformed into a fully conditionalized proof, which is then an axiomatic proof. | |
| From: David Bostock (Intermediate Logic [1997], 5.6) | |
| A reaction: Since proof using assumptions is perhaps the most standard proof system (e.g. used in Lemmon, for many years the standard book at Oxford University), the Deduction Theorem is crucial for giving it solid foundations. |
| 13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
| Full Idea: Like the Deduction Theorem, one form of Reductio ad Absurdum (If Γ,φ|-[absurdity] then Γ|-¬φ) 'discharges' an assumption. Assume φ and obtain a contradiction, then we know ¬&phi, without assuming φ. | |
| From: David Bostock (Intermediate Logic [1997], 5.7) | |
| A reaction: Thus proofs from assumption either arrive at conditional truths, or at truths that are true irrespective of what was initially assumed. |
| 13753 | Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock] |
| Full Idea: Natural deduction takes the notion of proof from assumptions as a basic notion, ...so it will use rules for use in proofs from assumptions, and axioms (as traditionally understood) will have no role to play. | |
| From: David Bostock (Intermediate Logic [1997], 6.1) | |
| A reaction: The main rules are those for introduction and elimination of truth functors. |
| 13755 | Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock] |
| Full Idea: Many books take RAA (reductio) and DNE (double neg) as the natural deduction introduction- and elimination-rules for negation, but RAA is not a natural introduction rule. I prefer TND (tertium) and EFQ (ex falso) for ¬-introduction and -elimination. | |
| From: David Bostock (Intermediate Logic [1997], 6.2) |
| 13758 | In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock] |
| Full Idea: When looking for a proof of a sequent, the best we can do in natural deduction is to work simultaneously in both directions, forward from the premisses, and back from the conclusion, and hope they will meet in the middle. | |
| From: David Bostock (Intermediate Logic [1997], 6.5) |
| 13754 | Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock] |
| Full Idea: Natural deduction adopts for → as rules the Deduction Theorem and Modus Ponens, here called →I and →E. If ψ follows φ in the proof, we can write φ→ψ (→I). φ and φ→ψ permit ψ (→E). | |
| From: David Bostock (Intermediate Logic [1997], 6.2) | |
| A reaction: Natural deduction has this neat and appealing way of formally introducing or eliminating each connective, so that you know where you are, and you know what each one means. |
| 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) |
| 13611 | Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock] |
| Full Idea: A tableau proof is a proof by reduction ad absurdum. One begins with an assumption, and one develops the consequences of that assumption, seeking to derive an impossible consequence. | |
| From: David Bostock (Intermediate Logic [1997], 4.1) |
| 13613 | A completed open branch gives an interpretation which verifies those formulae [Bostock] |
| Full Idea: An open branch in a completed tableau will always yield an interpretation that verifies every formula on the branch. | |
| From: David Bostock (Intermediate Logic [1997], 4.7) | |
| A reaction: In other words the open branch shows a model which seems to work (on the available information). Similarly a closed branch gives a model which won't work - a counterexample. |
| 13612 | Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock] |
| Full Idea: Rules for semantic tableaus are of two kinds - non-branching rules and branching rules. The first allow the addition of further lines, and the second requires splitting the branch. A branch which assigns contradictory values to a formula is 'closed'. | |
| From: David Bostock (Intermediate Logic [1997], 4.1) | |
| A reaction: [compressed] Thus 'and' stays on one branch, asserting both formulae, but 'or' splits, checking first one and then the other. A proof succeeds when all the branches are closed, showing that the initial assumption leads only to contradictions. |
| 13761 | In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock] |
| Full Idea: In a tableau system no sequent is established until the final step of the proof, when the last branch closes, and until then we are simply exploring a hypothesis. | |
| From: David Bostock (Intermediate Logic [1997], 7.3) | |
| A reaction: This compares sharply with a sequence calculus, where every single step is a conclusive proof of something. So use tableaux for exploring proofs, and then sequence calculi for writing them up? |
| 13756 | A tree proof becomes too broad if its only rule is Modus Ponens [Bostock] |
| Full Idea: When the only rule of inference is Modus Ponens, the branches of a tree proof soon spread too wide for comfort. | |
| From: David Bostock (Intermediate Logic [1997], 6.4) |
| 13762 | Tableau rules are all elimination rules, gradually shortening formulae [Bostock] |
| Full Idea: In their original setting, all the tableau rules are elimination rules, allowing us to replace a longer formula by its shorter components. | |
| From: David Bostock (Intermediate Logic [1997], 7.3) |
| 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. |
| 15812 | Being implies distinctness, which implies division, unity, and multitude [Aquinas] |
| Full Idea: What first comes to mind is being; secondly, that this being is not that being, and thus we apprehend division as a consequence; thirdly, comes the notion of one; fourthly the notion of multitude. | |
| From: Thomas Aquinas (Summa Theologicae [1265], I Q11 ar2 ad4), quoted by Roderick Chisholm - Person and Object 1.5 | |
| A reaction: This is one of the best things I have read on 'being'. It is the Aristotelian recognition that we can only study being by studying identity, and that this leads on to wider metaphysics. Other approaches to being are dead ends. |
| 21268 | Non-human things are explicable naturally, and voluntary things by the will, so God is not needed [Aquinas] |
| Full Idea: All natural things can be reduced to one principle, which is nature; and all voluntary things can be reduced to one principle, which is human reason, or will. Therefore God does not exist. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Ob2) | |
| A reaction: Not, of course, the opinion of Aquinas. So the possibility of naturalism (assuming the human will can be further reduced to nature) was a clear option in the thirteenth century. In reply Aquinas cites his Fifth Way. |
| 13802 | Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock] |
| Full Idea: A relation is 'one-many' if for anything on the right there is at most one on the left (∀xyz(Rxz∧Ryz→x=y), and is 'many-one' if for anything on the left there is at most one on the right (∀xyz(Rzx∧Rzy→x=y). | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13543 | A relation is not reflexive, just because it is transitive and symmetrical [Bostock] |
| Full Idea: It is easy to fall into the error of supposing that a relation which is both transitive and symmetrical must also be reflexive. | |
| From: David Bostock (Intermediate Logic [1997], 4.7) | |
| A reaction: Compare Idea 14430! Transivity will take you there, and symmetricality will get you back, but that doesn't entitle you to take the shortcut? |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| Full Idea: Aristotle's discussion of the unmoved mover and of the soul confirms the suspicion that form, when it is not thought of as the object represented in a definition, plays the role of the ultimate mereological atom within his system. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 6.6 | |
| A reaction: Aristotle is concerned with which things are 'divisible', and he cites these two examples as indivisible, but they may be too unusual to offer an actual theory of how Aristotle builds up wholes from atoms. He denies atoms in matter. |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| Full Idea: Thus in Aristotle we may think of an object's formal components as a sort of recipe for how to build wholes of that particular kind. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.5 | |
| A reaction: In the elusive business of pinning down what Aristotle means by the crucial idea of 'form', this analogy strikes me as being quite illuminating. It would fit DNA in living things, and the design of an artifact. |
| 16765 | Humans only have a single substantial form, which contains the others and acts for them [Aquinas] |
| Full Idea: A human being has no substantial form other than the intellective soul alone, and it contains the sensitive and nutritive souls, and all lower forms, and it alone brings about whatever it is that less perfect forms bring about in other things. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia Q76 4c), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.1 | |
| A reaction: He says brutes and plants also have a single soul. Pasnau says this is Aquinas's most distinctive doctrine, because other thinkers postulate a whole hierarchy of substantial forms. |
| 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) |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| Full Idea: Aristotle thinks that in general we have knowledge or understanding when we grasp causes, and he distinguishes three fundamental types of knowledge - theoretical, practical and productive. | |
| From: report of Aristotle (works [c.330 BCE]) by Alan D. Code - Aristotle | |
| A reaction: Productive knowledge we tend to label as 'knowing how'. The centrality of causes for knowledge would get Aristotle nowadays labelled as a 'naturalist'. It is hard to disagree with his three types, though they may overlap. |
| 23175 | The conclusions of speculative reason about necessities are certain [Aquinas] |
| Full Idea: Since the speculative reason is concerned chiefly with necessary things, which cannot be otherwise than they are, its proper conclusions, like the universal principles, contain the truth without fail. | |
| From: Thomas Aquinas (Summa Theologicae [1265], I-II Q94 4) | |
| A reaction: This seems over-confident, and to confuse the facts with our knowledge of the facts. Simple arithmetic may seem certain, but long and intricate proofs are always a little uncertain. |
| 21337 | A knowing being possesses a further reality, the 'presence' of the thing known [Aquinas] |
| Full Idea: Knowing beings are differentiated from non-knowing beings by this: non-knowing beings have only their own reality, but knowing beings are capable of possessing also the reality of something else, ...a presence of the thing known produced by this thing. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,q.Q14,art 1) | |
| A reaction: [Quoted by Ryan Meade in a talk at Pigotts] A famous and much discussed remark. Aquinas was a direct realist about perception, so this presence seems to be the thing itself, rather than a 'representation'. |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| Full Idea: The notion of a priori truth is conspicuously absent in Aristotle. | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
| A reaction: Cf. Idea 11240. |
| 21249 | Some things are self-evident to us; others are only self-evident in themselves [Aquinas] |
| Full Idea: A thing can be self-evident in either of two ways: on the one hand, self-evident in itself, though not to us; on the other hand, self-evident in itself, and to us. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Art 1, Obj 3) | |
| A reaction: A clear distinction, which is hard to deny, though there are lots of borderline cases. Self-evident to genius, and self-evident to future genius. Self-evident to almost everyone. Goldbach's Conjecture may be self-evident but unknowable. |
| 21250 | A proposition is self-evident if the predicate is included in the essence of the subject [Aquinas] |
| Full Idea: A proposition is self-evident because the predicate is included in the essence of the subject. E.g. Man is an animal, because animal is included in the essence of man. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Art 1, Obj 3) | |
| A reaction: Aquinas focuses on the essence of the subject, where Kant embraces the whole concept of the subject. Is it self-evident that we are genetically related to apes? Yes, to a geneticiist. Is that part of human essence? No. So Kant wins. |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| Full Idea: Aristotle is a rationalist …but reason for him is a disposition which we only acquire over time. Its acquisition is made possible primarily by perception and experience. | |
| From: report of Aristotle (works [c.330 BCE]) by Michael Frede - Aristotle's Rationalism p.173 | |
| A reaction: I would describe this process as the gradual acquisition of the skill of objectivity, which needs the right knowledge and concepts to evaluate new experiences. |
| 20224 | Sensation prepares the way for intellectual knowledge, which needs the virtues of reason [Aquinas] |
| Full Idea: Knowledge of truth is not consummated in the sensitive powers of apprehension, for these prepare the way to intellectual knowledge. And therefore in these powers there are none of the virtues by which we know truth; these are in the intellect or reason. | |
| From: Thomas Aquinas (Summa Theologicae [1265], I-II Q56 a5 obj3), quoted by Linda Trinkaus Zagzebski - Virtues of the Mind III 2.2 | |
| A reaction: A gem of a quotation for Zagzebski's thesis, that knowledge is defined in terms of the intellectual virtues. The only virtues of perception are in focusing and paying attention to features. Good eyesight is a biological 'virtue', I suppose. |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| Full Idea: Since Aristotle generally prefers a metaphysical theory that accords with common intuitions, he frequently relies on facts about language to guide his metaphysical claims. | |
| From: report of Aristotle (works [c.330 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.5 | |
| A reaction: I approve of his procedure. I take intuition to be largely rational justifications too complex for us to enunciate fully, and language embodies folk intuitions in its concepts (especially if the concepts occur in many languages). |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| Full Idea: Plato's unity of science principle states that all - legitimate - sciences are ultimately about the Forms. Aristotle's principle states that all sciences must be, ultimately, about substances, or aspects of substances. | |
| From: report of Aristotle (works [c.330 BCE], 1) by Julius Moravcsik - Aristotle on Adequate Explanations 1 |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| Full Idea: For Aristotle things which explain (the explanantia) are facts, which should not be associated with the modern view that says explanations are dependent on how we conceive and describe the world (where causes are independent of us). | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 2.1 | |
| A reaction: There must be some room in modern thought for the Aristotelian view, if some sort of robust scientific realism is being maintained against the highly linguistic view of philosophy found in the twentieth century. |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| Full Idea: The standard Aristotelian doctrine of species and genus in the theory of anything whatever involves specifying what the thing is in terms of something more general. | |
| From: report of Aristotle (works [c.330 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.10 |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| Full Idea: The view that essential properties are those in virtue of which other significant properties of the subjects under investigation can be explained is encountered repeatedly in Aristotle's work. | |
| From: report of Aristotle (works [c.330 BCE]) by Joan Kung - Aristotle on Essence and Explanation IV | |
| A reaction: What does 'significant' mean here? I take it that the significant properties are the ones which explain the role, function and powers of the object. |
| 22107 | Sensations are transmitted to 'internal senses' in the brain, chiefly to 'phantasia' and 'imagination' [Aquinas, by Kretzmann/Stump] |
| Full Idea: Sensory species received in external senses are transmitted to 'internal senses', organs located in the brain. The most important of these for cognition are 'phantasia' and 'imagination' (part of phantasia), which produce and preserve 'phantasms'. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265]) by Kretzmann/Stump - Aquinas, Thomas 11 | |
| A reaction: This seems to make Aquinas a representative realist. I add this to my portfolio of philosophical faculties - those required by philosophy, rather than by psychology or neuroscience. |
| 9098 | Mental activity combines what we sense with imagination of what is not present [Aquinas] |
| Full Idea: Mental activity combines two activities which in the senses are distinct: exterior perception in which we are simply affected by what we sense, and interior imagination in which we create images of things that are not, and never have been present. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.2) | |
| A reaction: Geach cites this thought to show that he is anti-abstractionist, since mind creates images, and these can arise from things which have not been experienced. Any defence of abstractionism must allow an active power to imagination. |
| 9092 | Abstracting A from B generates truth, as long as the connection is not denied [Aquinas] |
| Full Idea: Abstacting A from B can mean denying A's connection with B, or simply thinking A without thinking B. Abstracting what in reality is connected generates falsehood if done the first way, but not if done the second. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.1) | |
| A reaction: Despite Geach's denials, this seems to make Aquinas a classic abstractionist. He goes on to distinguish two sorts of abstraction, but he certainly thinks of abstraction from sense experience as a revelation about the nature of reality. |
| 9093 | We understand the general nature of things by ignoring individual peculiarities [Aquinas] |
| Full Idea: If we think what defines a stone, man or horse, without thinking of any individual peculiarities it may have, this is precisely what we do when we abstract the general nature of what we understand from any particular way in which we imagine it. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.1) | |
| A reaction: This may not be simple abstraction from sense experience, since there would obviously be a threatened circularity in the process. Do you need to know the essential definition first, in order to discard the individual peculiarities? |
| 9097 | The mind abstracts generalities from images, but also uses images for understanding [Aquinas] |
| Full Idea: Our mind both abstracts the species from images when it attends to the general nature of things, and understand the species in the images when it has recourse to the images in order to understand the things whose species it has abstracted. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.1) | |
| A reaction: Geach claims that the second half of this idea means that Aquinas is not an abstractionist, but he seems to be explictly abstractionist about the way in which we create higher level concepts from lower ones. |
| 9095 | Very general ideas (being, oneness, potentiality) can be abstracted from thought matter in general [Aquinas] |
| Full Idea: There are even things we can abstract from thought matter in general, things like being and oneness and potentiality and realization. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.1) | |
| A reaction: The Aristotelian 'potentiality' means possibility, which means that modality is understood by abstraction. Aquinas seems to have four levels: particular perceived, general perceived, particular thought, and general thought. This is the highest level. |
| 9099 | Particular instances come first, and (pace Plato) generalisations are abstracted from them [Aquinas] |
| Full Idea: The generality attaching to a nature - its relatedness to many particular instances - results from abstraction, so in this sense a generalized nature presupposes its instances, and does not, as Plato thought, precede them. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.2) | |
| A reaction: This seems to be a quite explicit endorsement of abstractionism by Aquinas, despite all Geach's assertions to the contrary. |
| 10508 | Species are abstracted from appearances by ignoring individual conditions [Aquinas] |
| Full Idea: The agent intellect abstracts intelligible species from phantasms insofar as through the power of the agent intellect we can take into our consideration the natures of the species without the individual conditions. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Q85 Ad4) | |
| A reaction: There might be a threatened circularity here, in trying to decide which features to ignore and which to retain. If we saw a hundred horses with a white nose blaze, we still wouldn't be sure that this was essential to a horse. Innate notions of species?? |
| 22111 | Aquinas attributes freedom to decisions and judgements, and not to the will alone [Aquinas, by Kretzmann/Stump] |
| Full Idea: Aquinas conceives of freedom as free decision or judgement, which cannot be attributed to the will alone. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265]) by Kretzmann/Stump - Aquinas, Thomas 12 | |
| A reaction: This idea might improve the free will debate considerably, because it is not clear what sort of thing a 'will' is, and it is not clear how an entity can be 'free' in isolation, by its intrinsic nature. Isn't all freedom contextual? |
| 22105 | The human intellectual soul is an incorporeal, subsistent principle [Aquinas] |
| Full Idea: It is necessary to say that that which is the principle of intellective activity, what we call the soul of a human being, is an incorporeal, subsistent principle. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia.Q75 2c), quoted by Kretzmann/Stump - Aquinas, Thomas 10 | |
| A reaction: Note 'subsistent' rather than 'existent' (capable of independence?). This identifies the immortal soul with the conscious mind. 'Principle' is an odd word, presumably with roots in Aristotle. It seems to be an Aristotelian 'form' [morphe]. |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| Full Idea: Aristotle, and also the Stoics, denied rationality to animals. …The Platonists, the Pythagoreans, and some more independent Aristotelians, did grant reason and intellect to animals. | |
| From: report of Aristotle (works [c.330 BCE]) by Richard Sorabji - Rationality 'Denial' | |
| A reaction: This is not the same as affirming or denying their consciousness. The debate depends on how rationality is conceived. |
| 22108 | First grasp what it is, then its essential features; judgement is their compounding and division [Aquinas] |
| Full Idea: The intellect first apprehends the quiddity of a thing. ...Then it acquires the properties, accidents and dispositions associated with the thing's essence. It must proceed from one compounding or dividing of aspects to another, which is reasoning. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia.Q85 5c), quoted by Kretzmann/Stump - Aquinas, Thomas 11 | |
| A reaction: [compressed] Tracking the process of acquiring knowledge of a thing (rather than necessary and sufficient conditions for full knowledge) is closer to Quine's naturalised epistemology than to the standard analytic approach to the concept of knowledge. |
| 10503 | We abstract forms from appearances, and acquire knowledge of immaterial things [Aquinas] |
| Full Idea: To cognize that which is in individual matter, not as it is in such matter, is to abstract the form from the individual matter that the phantasms represents. Thus we come to a degree of cognition of immaterial things. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Q85 1 Reply) | |
| A reaction: This offers abstraction as a kind of inference to best explanation which takes us beyond immediate empirical experience to what is behind it. Aquinas thinks the concepts and explanation are spiritual, but they may be generalities and essences. |
| 10509 | Understanding consists entirely of grasping abstracted species [Aquinas] |
| Full Idea: Of the thing understood all that is within the actually understanding intellect is the abstracted intelligible species. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Q85 Art2) | |
| A reaction: Abstraction is never supposed to be a luxury bolt-on, but is always seen (in this tradition, and presumably in the modern one), as essential to the intellect, and its way of coming to understand the world. Aristotelian definition is behind this idea. |
| 10506 | Mathematics can be abstracted from sensible matter, and from individual intelligible matter [Aquinas] |
| Full Idea: Intellect can abstract mathematical species from sensible matter, both individual and common. Yet it cannot abstract such species from common intelligible matter, but only from individual intelligible matter. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Q85 Ad2) | |
| A reaction: The idea is that common intelligible matter lacks underlying substance, which is where quantity is to be found. |
| 9094 | Mathematical objects abstract both from perceived matter, and from particular substance [Aquinas] |
| Full Idea: Objects of mathematics abstract from perceived matter both in particular and in general, though from thought matter (substance as underlying quality) only in particular and not in general. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.1) | |
| A reaction: This appears to be a thoroughly abstractionist view of the way in which humans create mathematics. Aquinas explicitly denies the Platonic view that the numbers already have abstract existence, awaiting our discovery. |
| 10505 | We can just think of an apple's colour, because the apple is not part of the colour's nature [Aquinas] |
| Full Idea: The apple is not part of the nature of the colour, and so nothing prevents one from understanding the colour while understanding nothing of the apple. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Q85 1 Ad 1) | |
| A reaction: This helps to clarify why the procedure of 'ignoring' features is possible. It suggests that some features might be too entangled with the substance (too essential?) to be thus ignored. I can't think of an example, though. Why not?! |
| 10504 | Abstracting either treats something as separate, or thinks of it separately [Aquinas] |
| Full Idea: Abstracting takes place in two ways: by composition and division, understanding something to be not in another or to be separated from it; and by a simple and unconditioned consideration, understanding one thing while not considering the other at all. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Q85 1 Ad 1) | |
| A reaction: The second way is by 'ignoring', which he says cannot contain error. The first seems to be considering some mode of a thing to be actually separate from the thing, which could clearly be erroneous. Ignoring makes to commitment to a unity. |
| 10507 | Numbers and shapes are abstracted by ignoring their sensible qualities [Aquinas] |
| Full Idea: Quantities such as numbers and dimensions, and also shapes (which are the limits of quantities) can be considered without their sensible qualities, which is for them to be abstracted from sensible matter. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Q85 Ad2) | |
| A reaction: His account relies on underlying substance, which is where quantity is to be found (presumably because a substance is the epitome of a unit). |
| 9096 | The mind must produce by its own power an image of the individual species [Aquinas] |
| Full Idea: The agent mind must itself turn to images, and produce by its own power in the receptive mind a representation as to species of whatever the images represent as individual. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ch.5 Q85.1) | |
| A reaction: Unlike much of this section, this sentence supports Geach's claim that Aquinas agrees with him - that the mind creates its concepts, rather than 'abstracting' them from experience. |
| 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'. |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| Full Idea: The notion of analytic truth is conspicuously absent in Aristotle. | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
| A reaction: Cf. Idea 11239. |
| 23180 | The will is the rational appetite [Aquinas] |
| Full Idea: The will is the rational appetite. | |
| From: Thomas Aquinas (Summa Theologicae [1265], II-II Q58 4) | |
| A reaction: Defining the will in terms of reason sounds more like an Enlightenment optimist than a medieval theologian. I suspect that for him it is tautological the reason is involved, if only the reason can make decisions. Hobbes prefers to ruling appetite. |
| 22112 | For humans good is accordance with reason, and bad is contrary to reason [Aquinas] |
| Full Idea: A human being's good is existing in accordance with reason, while what is bad for a human being is whatever is contrary to reason. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia IIae.Q18.5c), quoted by Kretzmann/Stump - Aquinas, Thomas 13 | |
| A reaction: For anyone who thought Kant invented the idea that morality derives from reason. This idea of Aquinas is a fairly precise echo of the stoic view (which influenced Kant). Is there a circularity? Is it irrational because bad, or bad because irrational? |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| Full Idea: To the best of my knowledge (and somewhat to my surprise), Aristotle never actually says that man is a rational animal; however, he all but says it. | |
| From: report of Aristotle (works [c.330 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: When I read this I thought that this database would prove Fogelin wrong, but it actually supports him, as I can't find it in Aristotle either. Descartes refers to it in Med.Two. In Idea 5133 Aristotle does say that man is a 'social being'. But 22586! |
| 22494 | We must know the end, know that it is the end, and know how to attain it [Aquinas] |
| Full Idea: Perfect knowledge of the end consists in not only apprehending the thing which is the end but also knowing it under the aspect of the end and the relation of the means to that end. | |
| From: Thomas Aquinas (Summa Theologicae [1265], II-I.Q132), quoted by Philippa Foot - Natural Goodness 4 | |
| A reaction: We don't talk much now about 'perfect' knowledge of something, but I suppose this is the necessary and sufficient conditions. If you complete the checklist, your knowledge should be perfect (if the list is right). |
| 23181 | All acts of virtue relate to justice, which is directed towards the common good [Aquinas] |
| Full Idea: The good of any virtue …is referable to the common good, to which justice directs, so that all acts of virtue can pertain to justice insofar as it directs man to the common good. | |
| From: Thomas Aquinas (Summa Theologicae [1265], II-II Q58 5) | |
| A reaction: Michael Sandel has recently lamented to fading of the concept of 'the common good' from our moral and political life. In which case this thought of Aquinas takes on great importance. I certainly like it. It seems to apply to courage, for example. |
| 8009 | Aquinas wanted, not to escape desire, but to transform it for moral ends [Aquinas, by MacIntyre] |
| Full Idea: The Aristotelianism of Thomas Aquinas (unlike St Augustine's Platonism) is not concerned with escaping from the snares of the world and of desire, but with transforming desire for moral ends. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265]) by Alasdair MacIntyre - A Short History of Ethics Ch.9 | |
| A reaction: This is very close to Aristotle himself, for whom education of the feelings (into good habits, and then true virtues) was central. Education of feelings should be central to all education (though young psychopaths may show resistance). |
| 23182 | Legal justice is supreme, because it directs the other virtues to the common good [Aquinas] |
| Full Idea: There must be one supreme virtue essentially distinct from every other virtue, which directs all the virtues to the common good, and this virtue is legal justice. | |
| From: Thomas Aquinas (Summa Theologicae [1265], II-II Q58 6) | |
| A reaction: This concept of legal justice is underpinned, for Aquinas, by the concept of natural law, which has divine backing. Positive law could hardly fulfil such a major role, given that it could be corrupt. |
| 22399 | Temperance prevents our passions from acting against reason [Aquinas] |
| Full Idea: The passions may incite us to something against reason, and so we need a curb, which we name 'temperance'. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia 2ae Q61 a.3), quoted by Philippa Foot - Virtues and Vices II | |
| A reaction: I am increasingly unclear what 'reason' means in contexts like these. It seems to mean no more than the awareness of greater goods than the indulgence of passion. Without that awareness, high intelligence couldn't produce temperance. |
| 23177 | Justice directs our relations with others, because it denotes a kind of equality [Aquinas] |
| Full Idea: It is proper to justice, as compared with the other virtues, to direct man in his relations with others, because it denotes a kind of equality, as its very name implies; indeed we are wont to say that things are 'adjusted' when they are made equal. | |
| From: Thomas Aquinas (Summa Theologicae [1265], II-II Q57 1) | |
| A reaction: Even if you say justice is giving people what they deserve, rather than mere equality, they must still be equal in receiving like for like. Legal justice implies equality before the law (except for monarchs?). |
| 23179 | People differ in their social degrees, and a particular type of right applies to each [Aquinas] |
| Full Idea: There are many differences of degrees among men, for instance, some are soldiers, some are priests, some are princes. Therefore some special kind of right should be alloted to them. | |
| From: Thomas Aquinas (Summa Theologicae [1265], II-II Q57 4) | |
| A reaction: An objection (3), but Aquinas endorses it in his reply. In 58.10 he says striking a prince is worse that striking a commoner. The shift to the idea that everyone is supposed to be equal before the law has been slow, and we are not quite there yet. |
| 23174 | Natural law is a rational creature's participation in eternal law [Aquinas] |
| Full Idea: It is evident that the natural law is nothing else than the rational creature's participation of the eternal law. | |
| From: Thomas Aquinas (Summa Theologicae [1265], I-II Q91 2) | |
| A reaction: It is not enough merely that God decrees eternal laws. It is also necessary for us to use reason in order to participate. I'm not sure what reasoning process is involved. |
| 22113 | Right and wrong actions pertain to natural law, as perceived by practical reason [Aquinas] |
| Full Idea: All things to be done or to be avoided pertain to the precepts of natural law, which practical reasoning apprehends naturally as being human goods. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia IIae.Q94.2c), quoted by Kretzmann/Stump - Aquinas, Thomas 13 | |
| A reaction: No mention of God, but you feel the divine presence in the background. He also cites 'eternal law'. No coincidence that the atheist Hobbes rejected natural law. Personally I would offer an atheistic defence of natural law, based on human nature. |
| 22114 | Tyrannical laws are irrational, and so not really laws [Aquinas] |
| Full Idea: A tyrannical law, since it is not in accord with reason, is not unconditionally a law, but is rather a perversion of law. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia IIae.Q92.1, ad 4), quoted by Kretzmann/Stump - Aquinas, Thomas 13 | |
| A reaction: Only a belief in natural law can give a basis for such a claim. Positivists will say a tyrannical law is unconditionally a law like any other, but a bad one. |
| 7291 | For Aquinas a war must be in a just cause, have proper authority, and aim at good [Aquinas, by Grayling] |
| Full Idea: Aquinas argued that on three conditions war can be justified: first, that there is a just cause; second, that it is begun on proper authority; and third, that it is waged with right intention, for 'the advancement of good, or the avoidance of evil'. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265], II) by A.C. Grayling - Among the Dead Cities Ch.6 | |
| A reaction: But see also Idea 7292. Nowadays we are rightly suspicious of all three conditions. Evil people seem to think their cause is just; authority has often been seized by violence, or is being abused; and people seem confused about what is good or evil. |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| Full Idea: It is the mark of an educated mind to be able to entertain an idea without accepting it. | |
| From: Aristotle (works [c.330 BCE]) | |
| A reaction: The epigraph on a David Chalmers website. A wonderful remark, and it should be on the wall of every beginners' philosophy class. However, while it is in the spirit of Aristotle, it appears to be a misattribution with no ancient provenance. |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| Full Idea: Aristotle was asked how much educated men were superior to those uneducated; "As much," he said, "as the living are to the dead." | |
| From: report of Aristotle (works [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 05.1.11 |
| 5508 | Aquinas says a fertilized egg is not human, and has no immortal soul [Aquinas, by Martin/Barresi] |
| Full Idea: In Aquinas's view the fertilized egg is not, either at the moment of conception or for quite a while afterwards, endowed with an immortal soul. In fact, technically speaking, it is not even human. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265]) by R Martin / J Barresi - Introduction to 'Personal Identity' p.20 | |
| A reaction: It is pointed at that therefore Aquinas does not give good support for modern Catholic views on abortion. There is certainly no reason why a human zygote should be ensouled from the start, as God may do this whenever He wishes. |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent. | |
| From: report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3 | |
| A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle. |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter. | |
| From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2 | |
| A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now. |
| 16687 | Bodies are three-dimensional substances [Aquinas] |
| Full Idea: Bodies are those substances in which one finds three dimensions. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia Q18.2c), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 16.2 | |
| A reaction: Pasnau points out that this extensional view of physical bodies was a commonplace long before Descartes. Presumably there are also non-dimensional substances (such as angels?). |
| 23178 | Divine law commands some things because they are good, while others are good because commanded [Aquinas] |
| Full Idea: The divine law commands certain things because they are good and forbids others because they are evil, while others are good because they are prescribed, and others evil because they are forbidden. | |
| From: Thomas Aquinas (Summa Theologicae [1265], II-II Q57 2) | |
| A reaction: This is a fifty-fifty response to the Euthyphro dilemma, but it seems to leave the theological puzzle of the source of the goodness which is prescribed because it is in fact good. |
| 21251 | We can't know God's essence, so his existence can't be self-evident for us [Aquinas] |
| Full Idea: Because we do not know the essence of God, the proposition 'God exists' is not self-evident to us, but needs to be demonstrated by things that are more known to us. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Art 1, Obj 3) | |
| A reaction: Depends on his definition of self-evidence (Idea 21250), which needs knowledge of the essence of the subject. Anselm required 'understanding' of the concept. One might understand the existence criteria without knowing the whole essence. Anselm wins. |
| 5614 | If you assume that there must be a necessary being, you can't say which being has this quality [Kant on Aquinas] |
| Full Idea: To those who assume the existence of a necessary being, and would only know which among all things had to be regarded as such a thing, one could not answer: This thing here is the necessary being | |
| From: comment on Thomas Aquinas (Summa Theologicae [1265]) by Immanuel Kant - Critique of Pure Reason A612/B640 | |
| A reaction: See Aquinas in Idea 1431. Kant makes a nice point. You might turn out to be the necessary being? How could you tell? You only know that there must be one lurking somewhere. I could be a slug. Aquinas makes a huge leap to God. |
| 21269 | Way 1: the infinite chain of potential-to-actual movement has to have a first mover [Aquinas] |
| Full Idea: A thing can only be reduced from potentiality to actuality by something actual. A thing can never be in actuality and potentiality in the same respect. So what is moved must be moved by another. But this cannot go on to infinity, with no first mover. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Reply) | |
| A reaction: [compressed] This relies on the Aristotelian ideas of potentiality and actuality. We might talk about things moving, but lacking the 'power' to move. This is almost identical to Plato in 'The Laws' (which I guess Aquinas knew nothing of). |
| 21270 | Way 2: no effect without a cause, and this cannot go back to infinity, so there is First Cause [Aquinas] |
| Full Idea: If there is no first cause among efficient causes, there is no ultimate or intermediate cause. That in efficient causes it is possible to go on to infinity is plainly false. So it is necessary to admit a first efficient cause, which everyone calls God. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Reply) | |
| A reaction: [compressed] It doesn't seem to follow at all that the First Cause is God. There could be a single thing like the Phoenix, with unique self-causing properties. Or a quantum fluctuation. |
| 21271 | Way 3: contingent beings eventually vanish, so continuity needs a necessary being [Aquinas] |
| Full Idea: That which can not-be at some time is not. So if everything can not-be, then once there was nothing in existence. If so, it would have been impossible for anything to have begun to exist. So there must be some being having of itself its own necessity. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Reply) | |
| A reaction: [compressed] Why can't things take it in turns to not-be, so that something is always on duty? Maybe it is a feature of things that they bring other things into existence (e.g. virtual particles)? |
| 21272 | Way 4: the source of all qualities is their maximum, so something (God) causes all perfections [Aquinas] |
| Full Idea: More and less are predicated of different things according as they resemble in their different ways something which is the maximum. The maximum of a genus is the cause of all in that genus. So there must be something causing the perfections of all beings. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Reply) | |
| A reaction: [compressed] The argument makes a startling jump from each quality (like heat or nobility) having a maximum, to their being a single entity (a 'being' at that) which is the sole source of all human perfections. |
| 21273 | Way 5: mindless things act towards an obvious end, so there is an intelligent director [Aquinas] |
| Full Idea: Things which lack knowledge, such as natural bodies, act for an end, which is usually in the same way, to obtain the best result. Hence they achieve their end designedly. Hence some intelligent being exists by whom all natural things are directed. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Reply) | |
| A reaction: [compressed] This is Greek teleology with a vengeance. Plants probably illustrate best what he has in mind. There is obvious teleology in human affairs, and there is a sort of teleology in living things, but we take the end to be reinforced by success. |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |
| Full Idea: Aristotle said that the conception of gods arose among mankind from two originating causes, namely from events which concern the soul and from celestial phenomena. | |
| From: report of Aristotle (works [c.330 BCE], Frag 10) by Sextus Empiricus - Against the Physicists (two books) I.20 | |
| A reaction: The cosmos suggests order, and possible creation. What do events of the soul suggest? It doesn't seem to be its non-physical nature, because Aristotle is more of a functionalist. Puzzling. (It says later that gods are like the soul). |
| 20211 | Life aims at the Beatific Vision - of perfect happiness, and revealed truth [Aquinas, by Zagzebski] |
| Full Idea: Aquinas describes the ultimate end of human life as the Beatific Vision, a state that is simultaneously the enjoyment of perfect happiness and a perfect revelation of truth. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265]) by Linda Trinkaus Zagzebski - Virtues of the Mind II 4.2 | |
| A reaction: I like that a lot, even though my idea of the revelation of truth is very distant from that of Aquinas. Ignorant happiness is not much of an aspiration. |
| 22106 | Aquinas saw angels as separated forms, rather than as made of 'spiritual matter' [Aquinas, by Kretzmann/Stump] |
| Full Idea: Unlike some of his contemporaries, Aquinas does not think that there is a 'spiritual matter' that angels or disembodied souls have as one of their components, but rather that they are separated forms that configure no matter at all. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265]) by Kretzmann/Stump - Aquinas, Thomas 10 | |
| A reaction: 'Separated forms' sounds like the modern concept of abstract entities, meaning that souls and angels exist in the way that platonists believe numbers exist. How else might Aquinas have understood them? |
| 23306 | Humans have a non-physical faculty of reason, so they can be immortal [Aquinas, by Sorabji] |
| Full Idea: Aquinas infers from Aristotle that intellectual understanding is the only operation of the soul that is performed without a physical organ, so that only human souls, and not animal ones, can be immortal. | |
| From: report of Thomas Aquinas (Summa Theologicae [1265], I, q75, a3, resp) by Richard Sorabji - Rationality 'Reason' | |
| A reaction: This shows why so many thinkers are desperate to hang on to dualism, of some sort. Interesting that he only claims partial dualism. |
| 4412 | Those in bliss have their happiness increased by seeing the damned punished [Aquinas] |
| Full Idea: In order that the bliss of the saints may be more delightful for them, and they may render more copious thanks to God for it, it is given to them to see perfectly the punishment of the damned. | |
| From: Thomas Aquinas (Summa Theologicae [1265], III Supp Q94,1), quoted by Friedrich Nietzsche - On the Genealogy of Morals I.§15 | |
| A reaction: This has probably been repudiated by the Church of England. Justice should be seen to be done. Presumably you mustn't gloat, or you join them. |
| 21266 | God does not exist, because He is infinite and good, and so no evil should be discoverable [Aquinas] |
| Full Idea: If one of two contraries be infinite, the other would be altogether destroyed. But the name God means that He is infinite goodness. If therefore God existed there would be no evil discoverable; but there is evil in the world. Therefore God does not exist. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Ob1) | |
| A reaction: This is not, of course, the opinion of Aquinas. I love the way he states the opposition's arguments so lucidly. The modern problem usually talks of God's omnipotence, rather than infinity. His formulation allows that there might be undiscoverable evil. |
| 21274 | It is part of God's supreme goodness that He brings good even out of evil [Aquinas] |
| Full Idea: As Augustine says, God would not allow any evil to exist in his works, unless he were to bring good even out of evil. It is part of the infinite goodness of God, that He allows evil to exist and out of it produces good. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Ob1rep) | |
| A reaction: Are God's powers so limited that He could not have achieved an equal amount of good without having to indulge in some evil first? |