117 ideas
| 7911 | Theory vanishes when one has obtained wisdom [Rahulabhadra] |
| Full Idea: As the drops of dew in contact/ With the sun's rays disappear,/ So all theorizings vanish,/ Once one has obtained wisdom. | |
| From: Rahulabhadra (Hymn to Perfect Wisdom [c.150], v 10) | |
| A reaction: I suspect that the western view is that wisdom is good theory. This sounds like the sort of thing Wittgenstein would have said. Remarks like this encourage people to skip study, with the illusion that they can go straight to wisdom. |
| 11283 | There is pure deductive reasoning, and explanatory demonstration reasoning [Aristotle, by Politis] |
| Full Idea: Aristotle distinguishes between deductive reasoning (sullogismos) and demonstration (apodeixis). All demonstration is deductive reasoning, but not all deductive reasoning is demonstration. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE], Bk I.2) by Vassilis Politis - Aristotle and the Metaphysics 5.3 | |
| A reaction: This sounds not far off the distinction between single-turnstile (formal proof) and double-turnstile (semantic consequence). Politis says, though, that the key point is the demonstration is explanatory. |
| 1672 | Maybe everything could be demonstrated, if demonstration can be reciprocal or circular [Aristotle] |
| Full Idea: Some optimists think understanding arises only through demonstration, but say there could be demonstration of everything, for it is possible to demonstrate in a circle or reciprocally. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b16) | |
| A reaction: I'm an optimist in this sense, though what is being described would probably best be called 'large-scale coherence'. Two reciprocal arguments look bad, but a hundred look good. |
| 1684 | Two falsehoods can be contrary to one another [Aristotle] |
| Full Idea: There are falsehoods which are contrary to one another and cannot be the case together e.g. that a man is a horse or a cow. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88a29) |
| 12145 | Definitions are of what something is, and that is universal [Aristotle] |
| Full Idea: Definitions are thought to be of what something is, and what something is is in every case universal and positive. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b05) | |
| A reaction: This is exhibit A for those who think that Aristotelian essences concern the genus, rather than the particular. I suspect that this idea is best expressed as 'all we can say by way of definition of a particular thing involves the use of universals'. |
| 12075 | An Aristotelian definition is causal [Aristotle, by Witt] |
| Full Idea: An Aristotelian definition is causal. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE], Bk II.2) by Charlotte Witt - Substance and Essence in Aristotle 1.5 | |
| A reaction: [She refers us to Posterior Analytics II.2] This is important if we are tempted to follow a modern line of saying that we want Aristotelian essences, and that these are definitions. We ain't thinking of dictionaries. |
| 12384 | Definition by division needs predicates, which are well ordered and thorough [Aristotle] |
| Full Idea: To establish a definition through division, you must aim for three things: you must take what is predicated in what the thing is; you must order these items as first or second; and you must ensure that these are all there are. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 97a23) | |
| A reaction: This gives an indication of the thoroughness that Aristotle expects from a definition. They aren't like dictionary definitions of words. He expects definitions to often be very lengthy (see Idea 12292). |
| 9066 | You can define objects by progressively identifying what is the same and what is different [Aristotle] |
| Full Idea: Find what is in common among items similar and undifferentiated, then do the same for items of the same kind as the first group but a different form, and so on, till you come to a single account: this will be the definition of the object. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 97b07-14) | |
| A reaction: [His example is distinguishing 'magnanimity' from 'indifference to fortune' among people] Presumably this process works for the formation of new concepts (e.g. in biology), as well as for the definition of familiars in terms of other familiars. |
| 12382 | What it is and why it is are the same; screening defines and explains an eclipse [Aristotle] |
| Full Idea: What it is and why it is are the same. What is an eclipse? Privation of light from the moon by screening of the earth. Why is there an eclipse? ...What is a harmony? A numerical ratio between high and low. Why do the high and low harmonize? The ratio. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90a15) | |
| A reaction: This is right at the heart of Aristotelian essentialism, and (I take it) modern scientific essentialism. If you fully know what cigarette tars are, and what human cell structure is, you understand immediately why cigarettes cause cancer. |
| 1668 | An axiom is a principle which must be understood if one is to learn anything [Aristotle] |
| Full Idea: An axiom is a principle which must be grasped if anyone is going to learn anything whatever. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a17) |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| Full Idea: Each line of a truth table is, in effect, a model. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6) | |
| A reaction: I find this comment illuminating. It is being connected with the more complex models of modal logic. Each line of a truth table is a picture of how the world might be. |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| Full Idea: For modal logic we add to the syntax of classical logic two new unary operators □ (necessarily) and ◊ (possibly). | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.3) |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| Full Idea: We let 'R' be the accessibility relation: xRy is read 'y is accessible from x'. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.5) |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| Full Idea: The symbol ||- is used for the 'forcing' relation, as in 'Γ ||- P', which means that P is true in world Γ. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6) |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| Full Idea: A 'prefix' is a finite sequence of positive integers. A 'prefixed formula' is an expression of the form σ X, where σ is a prefix and X is a formula. A prefix names a possible world, and σ.n names a world accessible from that one. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| Full Idea: In 'constant domain' semantics, the domain of each possible world is the same as every other; in 'varying domain' semantics, the domains need not coincide, or even overlap. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.5) |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| Full Idea: Modern modal logic takes into consideration the way the modal relates the possible worlds, called the 'accessibility' relation. .. We let R be the accessibility relation, and xRy reads as 'y is accessible from x. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.5) | |
| A reaction: There are various types of accessibility, and these define the various modal logics. |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
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Full Idea:
A 'model' is a frame plus a specification of which propositional letters are true at which worlds. It is written as |
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| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6) |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
|
Full Idea:
A 'frame' consists of a non-empty set G, whose members are generally called possible worlds, and a binary relation R, on G, generally called the accessibility relation. We say the frame is the pair |
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| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6) |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| Full Idea: A relation R is 'reflexive' if every world is accessible from itself; 'transitive' if the first world is related to the third world (ΓRΔ and ΔRΩ → ΓRΩ); and 'symmetric' if the accessibility relation is mutual. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.7) | |
| A reaction: The different systems of modal logic largely depend on how these accessibility relations are specified. There is also the 'serial' relation, which just says that any world has another world accessible to it. |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| Full Idea: If a proposition is possibly true in a world, then it is also true in some world which is accessible from that world. That is: Γ ||- ◊X ↔ for some Δ ∈ G, ΓRΔ then Δ ||- X. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6) |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| Full Idea: If a proposition is necessarily true in a world, then it is also true in all worlds which are accessible from that world. That is: Γ ||- □X ↔ for every Δ ∈ G, if ΓRΔ then Δ ||- X. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6) |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| Full Idea: General tableau rules for conjunctions: a) if σ X ∧ Y then σ X and σ Y b) if σ ¬(X ∧ Y) then σ ¬X or σ ¬Y | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| Full Idea: General tableau rules for biconditionals: a) if σ (X ↔ Y) then σ (X → Y) and σ (Y → X) b) if σ ¬(X ↔ Y) then σ ¬(X → Y) or σ ¬(Y → X) | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| Full Idea: General tableau rules for implications: a) if σ ¬(X → Y) then σ X and σ ¬Y b) if σ X → Y then σ ¬X or σ Y | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| Full Idea: General tableau rules for universal modality: a) if σ ¬◊ X then σ.m ¬X b) if σ □ X then σ.m X , where m refers to a world that can be seen (rather than introducing a new world). | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) | |
| A reaction: Note that the universal rule of □, usually read as 'necessary', only refers to worlds which can already be seen, whereas possibility (◊) asserts some thing about a new as yet unseen world. |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| Full Idea: General tableau rule for negation: if σ ¬¬X then σ X | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| Full Idea: General tableau rules for disjunctions: a) if σ ¬(X ∨ Y) then σ ¬X and σ ¬Y b) if σ X ∨ Y then σ X or σ Y | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| Full Idea: General tableau rules for existential modality: a) if σ ◊ X then σ.n X b) if σ ¬□ X then σ.n ¬X , where n introduces some new world (rather than referring to a world that can be seen). | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2) | |
| A reaction: Note that the existential rule of ◊, usually read as 'possibly', asserts something about a new as yet unseen world, whereas □ only refers to worlds which can already be seen, |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| Full Idea: System T reflexive rules (also for B, S4, S5): a) if σ □X then σ X b) if σ ¬◊X then σ ¬X | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3) |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| Full Idea: System D serial rules (also for T, B, S4, S5): a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3) |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| Full Idea: System B symmetric rules (also for S5): a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [where n is a world which already occurs] | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3) |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| Full Idea: System 4 transitive rules (also for K4, S4, S5): a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [where n is a world which already occurs] | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3) |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| Full Idea: System 4r reversed-transitive rules (also for S5): a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [where n is a world which already occurs] | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3) |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| Full Idea: Simplified S5 rules: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X. 'n' picks any world; in a) and b) 'k' asserts a new world; in c) and d) 'k' refers to a known world | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3) |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| Full Idea: The system K has no frame conditions imposed on its accessibility relation. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) | |
| A reaction: The system is named K in honour of Saul Kripke. |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| Full Idea: System D is usually thought of as Deontic Logic, concerning obligations and permissions. □P → P is not valid in D, since just because an action is obligatory, it does not follow that it is performed. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.12.2 Ex) |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| Full Idea: The system D has the 'serial' condition imposed on its accessibility relation - that is, every world must have some world which is accessible to it. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| Full Idea: The system T has the 'reflexive' condition imposed on its accessibility relation - that is, every world must be accessible to itself. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| Full Idea: The system K4 has the 'transitive' condition imposed on its accessibility relation - that is, if a relation holds between worlds 1 and 2 and worlds 2 and 3, it must hold between worlds 1 and 3. The relation carries over. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| Full Idea: The system B has the 'reflexive' and 'symmetric' conditions imposed on its accessibility relation - that is, every world must be accessible to itself, and any relation between worlds must be mutual. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| Full Idea: The system S4 has the 'reflexive' and 'transitive' conditions imposed on its accessibility relation - that is, every world is accessible to itself, and accessibility carries over a series of worlds. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| Full Idea: The system S5 has the 'reflexive', 'symmetric' and 'transitive' conditions imposed on its accessibility relation - that is, every world is self-accessible, and accessibility is mutual, and it carries over a series of worlds. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.8) | |
| A reaction: S5 has total accessibility, and hence is the most powerful system (though it might be too powerful). |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| Full Idea: P→◊P is usually considered to be valid, but its converse, ◊P→P is not, so (by Frege's own criterion) P and possibly-P differ in conceptual content, and there is no reason why logic should not be widened to accommodate this. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.2) | |
| A reaction: Frege had denied that modality affected the content of a proposition (1879:p.4). The observation here is the foundation for the need for a modal logic. |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| Full Idea: In epistemic logic the knower is treated as logically omniscient. This is puzzling because one then cannot know something and yet fail to know that one knows it (the Principle of Positive Introspection). | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.11) | |
| A reaction: This is nowadays known as the K-K Problem - to know, must you know that you know. Broadly, we find that externalists say you don't need to know that you know (so animals know things), but internalists say you do need to know that you know. |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| Full Idea: In epistemic logic we read Υ as 'KaP: a knows that P', and ◊ as 'PaP: it is possible, for all a knows, that P' (a is an individual). For belief we read them as 'BaP: a believes that P' and 'CaP: compatible with everything a believes that P'. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.11) | |
| A reaction: [scripted capitals and subscripts are involved] Hintikka 1962 is the source of this. Fitting and Mendelsohn prefer □ to read 'a is entitled to know P', rather than 'a knows that P'. |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| Full Idea: We introduce four future and past tense operators: FP: it will sometime be the case that P. PP: it was sometime the case that P. GP: it will always be the case that P. HP: it has always been the case that P. (P itself is untensed). | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.10) | |
| A reaction: Temporal logic begins with A.N. Prior, and starts with □ as 'always', and ◊ as 'sometimes', but then adds these past and future divisions. Two different logics emerge, taking □ and ◊ as either past or as future. |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| Full Idea: The Converse Barcan says nothing passes out of existence in alternative situations. The Barcan says that nothing comes into existence. The two together say the same things exist no matter what the situation. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.9) | |
| A reaction: I take the big problem to be that these reflect what it is you want to say, and that does not keep stable across a conversation, so ordinary rational discussion sometimes asserts these formulas, and 30 seconds later denies them. |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| Full Idea: The Barcan formula corresponds to anti-monotonicity, and the Converse Barcan formula corresponds to monotonicity. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 6.3) |
| 12376 | Demonstrations by reductio assume excluded middle [Aristotle] |
| Full Idea: Demonstrations by reduction to the impossible assume that everything is asserted or denied. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 77a23) | |
| A reaction: This sounds like the lynchpin of classical logic. |
| 12373 | Something holds universally when it is proved of an arbitrary and primitive case [Aristotle] |
| Full Idea: Something holds universally when it is proved of an arbitrary and primitive case. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 73b33) | |
| A reaction: A key idea in mathematical logic, but it always puzzles me. If you snatch a random person in London, and they are extremely tall, does that prove that people of London are extremely tall? How do we know the arbitrary is representative? |
| 12363 | Everything is either asserted or denied truly [Aristotle] |
| Full Idea: Of the fact that everything is either asserted or denied truly, we must believe that it is the case. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71a14) | |
| A reaction: Presumably this means that every assertion which could possibly be asserted must come out as either true or false. This will have to include any assertions with vague objects or predicates, and any universal assertions, and negative assertions. |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| Full Idea: 'Predicate abstraction' is a key idea. It is a syntactic mechanism for abstracting a predicate from a formula, providing a scoping mechanism for constants and function symbols similar to that provided for variables by quantifiers. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], Pref) |
| 13004 | Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz] |
| Full Idea: Aristotle's way with axioms, rather than Euclid's, is as assumptions which we are willing to agree on while awaiting an opportunity to prove them | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE], 76b23-) by Gottfried Leibniz - New Essays on Human Understanding 4.07 | |
| A reaction: Euclid's are understood as basic self-evident truths which will be accepted by everyone, though the famous parallel line postulate undermined that. The modern view of axioms is a set of minimum theorems that imply the others. I like Aristotle. |
| 12377 | Mathematics is concerned with forms, not with superficial properties [Aristotle] |
| Full Idea: Mathematics is concerned with forms [eide]: its objects are not said of any underlying subject - for even if geometrical objects are said of some underlying subject, still it is not as being said of an underlying subject that they are studied. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 79a08) | |
| A reaction: Since forms turn out to be essences, in 'Metaphysics', this indicates an essentialist view of mathematics. |
| 12372 | The essence of a triangle comes from the line, mentioned in any account of triangles [Aristotle] |
| Full Idea: Something holds of an item in itself if it holds of it in what it is - e.g., line of triangles and point of lines (their essence comes from these items, which inhere in the account which says what they are). | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 73a35) | |
| A reaction: A helpful illustration of how a definition gives us the essence of something. You could not define triangles without mentioning straight lines. The lines are necessary features, but they are essential for any explanation, and for proper understanding. |
| 12369 | A unit is what is quantitatively indivisible [Aristotle] |
| Full Idea: Arithmeticians posit that a unit is what is quantitatively indivisible. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a22) | |
| A reaction: Presumably indeterminate stuff like water is non-quantitatively divisible (e.g. Moses divides the Red Sea), as are general abstracta (curved shapes from rectilinear ones). Does 'quantitative' presupposes units, making the idea circular? |
| 18910 | To seek truth, study the real connections between subjects and attributes [Aristotle] |
| Full Idea: If, however, one is aiming at truth, one must be guided by the real connexions of subjects and attributes. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 81b22), quoted by George Engelbretsen - Trees, Terms and Truth 3 | |
| A reaction: I take this to be a warning that predicates that indicate mere 'Cambridge properties' (such as relations, locations, coincidences etc) have nothing to do with ontology. See Shoemaker on properties. |
| 1675 | Separate Forms aren't needed for logic, but universals (one holding of many) are essential [Aristotle] |
| Full Idea: There need be no forms (one item apart from the many) for demonstrations. But there must be universals, where one thing holds of the many. Without universals there are no middle terms, and so no demonstrations. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 77a05) |
| 1677 | We can forget the Forms, as they are irrelevant, and not needed in giving demonstrations [Aristotle] |
| Full Idea: We can say goodbye to the forms. They are nonny-noes; and if there are any they are irrelevant - for demonstrations are not concerned with them. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 83a34) |
| 1687 | Why are being terrestrial and a biped combined in the definition of man, but being literate and musical aren't? [Aristotle] |
| Full Idea: Why will a man be a two-footed terrestrial animal and not an animal and terrestrial? Assumptions do not make it necessary that what is predicated form a unity - rather, it is as if the same man were musical and literate. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 92a30) |
| 1681 | Units are positionless substances, and points are substances with position [Aristotle] |
| Full Idea: A unit is a positionless substance, and a point a substance having position. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 87a36) |
| 12146 | Definitions recognise essences, so are not themselves essences [Aristotle] |
| Full Idea: If a definition is the recognition of some essence, it is clear that such items are not essences. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b17) | |
| A reaction: So definitions are not themselves essences (as some modern thinkers claim). The idea seems obvious to me, but it is a warning against a simplistic view of Aristotelian essences, and a reminder that such things are real, not verbal. |
| 17039 | The predicates of a thing's nature are necessary to it [Aristotle] |
| Full Idea: Whatever is predicated in what something is is necessary. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 96b03) | |
| A reaction: This does NOT say that the essence is just the necessities. He goes on to say to say separately that certain properties of a triplet are part of the essence, as well as being necessary. This shows the nature of a thing is also necessary. |
| 11994 | Aristotelian essences are properties mentioned at the starting point of a science [Aristotle, by Kung] |
| Full Idea: As Aristotle uses the term 'essence', only those properties which are mentioned in or relatively close to the starting points of the science will be essential. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Joan Kung - Aristotle on Essence and Explanation II | |
| A reaction: I take this to be the correct way to understand Aristotelian essence - as something understood by its role in scientific explanations. We may, of course, work back to the starting point of a science, by disentangling the mess in the middle. |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| Full Idea: Equality has caused much grief for modal logic. Many of the problems, which have struck at the heart of the coherence of modal logic, stem from the apparent violations of the Indiscernibility of Identicals. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 7.1) | |
| A reaction: Thus when I say 'I might have been three inches taller', presumably I am referring to someone who is 'identical' to me, but who lacks one of my properties. A simple solution is to say that the person is 'essentially' identical. |
| 12381 | What is necessary cannot be otherwise [Aristotle] |
| Full Idea: What is necessary cannot be otherwise. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88b32) | |
| A reaction: If the next interesting question is the source of necessity, then the question seems to be 'what prevents it from being otherwise?'. |
| 1690 | A stone travels upwards by a forced necessity, and downwards by natural necessity [Aristotle] |
| Full Idea: There are two types of necessity, one according to nature and impulse, the other by force and contrary to impulse. A stone travels upwards and downwards from different necessities. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 94b38) |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| Full Idea: If □ is to be sensitive to the quality of the truth of a proposition in its scope, then it must be sensitive as to whether an object is picked out by an essential property or by a contingent one. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.3) | |
| A reaction: This incredibly simple idea strikes me as being powerful and important. ...However, creating illustrative examples leaves me in a state of confusion. You try it. They cite '9' and 'number of planets'. But is it just nominal essence? '9' must be 9. |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| Full Idea: The property of 'possibly being a Republican' is as much a property of Bill Clinton as is 'being a democrat'. So we don't peel off his properties from world to world. Hence the bundle theory fits our treatment of objects better than bare particulars. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 7.3) | |
| A reaction: This bundle theory is better described in recent parlance as the 'modal profile'. I am reluctant to talk of a modal truth about something as one of its 'properties'. An objects, then, is a bundle of truths? |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| Full Idea: The main technical problem with counterpart theory is that the being-a-counterpart relation is, in general, neither symmetric nor transitive, so no natural logic of equality is forthcoming. | |
| From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 4.5) | |
| A reaction: That is, nothing is equal to a counterpart, either directly or indirectly. |
| 12072 | For Aristotle knowledge is explanatory, involving understanding, and principles or causes [Aristotle, by Witt] |
| Full Idea: For Aristotle, knowledge is explanatory, for to know something is to understand it, and to understand something is to grasp its principles or causes. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Charlotte Witt - Substance and Essence in Aristotle 1.2 | |
| A reaction: Thus the kind of 'knowledge' displayed in quiz shows would not count as knowledge at all, if it was mere recall of facts. To know is to be able to explain, which is to be able to teach. See Idea 11241. |
| 12073 | 'Episteme' means grasping causes, universal judgments, explanation, and teaching [Aristotle, by Witt] |
| Full Idea: For Aristotle, a person who has 'episteme' grasps the cause of a given phenomenon, can make a universal judgment about it, can explain it, and can teach others about it. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Charlotte Witt - Substance and Essence in Aristotle 1.2 | |
| A reaction: This I take to be the context in which we should understand what Aristotle means by an 'essence' - it is the source of all of the above, so it both makes a thing what it is, and explains why it shares features with other such things. |
| 12378 | The reason why is the key to knowledge [Aristotle] |
| Full Idea: Study of the reason why has the most importance for knowledge. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 79a24) | |
| A reaction: I take the study of reasons for belief to be much more central to epistemology than finding ways to answer radical sceptics about the basic possibility of knowledge. |
| 12364 | We understand a thing when we know its explanation and its necessity [Aristotle] |
| Full Idea: We understand something simpliciter when we think we know of the explanation because of which the object holds that it is its explanation, and also that it is not possible for it to be otherwise. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b10) | |
| A reaction: The second half sounds odd, since we ought to understand that something could have been otherwise, and knowing whether or not it could have been otherwise is part of the understanding. It sounds like Spinozan determinism. |
| 12370 | Some understanding, of immediate items, is indemonstrable [Aristotle] |
| Full Idea: Not all understanding is demonstrative: rather, in the case of immediate items understanding is indemonstrable. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b19) | |
| A reaction: These are the foundations of Aristotle's epistemology, and I take it that they can be both empiricist and rationalist - sense experiences, and a priori intuitions. |
| 12366 | We only understand something when we know its explanation [Aristotle] |
| Full Idea: We only understand something when we know its explanation. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b30) | |
| A reaction: If we believe that the whole aim of philosophy is 'understanding' (Idea 543) - and if it isn't then I am not sure what the aim is, and alternative aims seem a lot less interesting - then we should care very much about explanations, as well as reasons. |
| 1685 | No one has mere belief about something if they think it HAS to be true [Aristotle] |
| Full Idea: No one holds something as an opinion when he thinks that it is impossible for it to be otherwise - for then he thinks he understands it. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 89a07) |
| 1673 | Knowledge proceeds from principles, so it is hard to know if we know [Aristotle] |
| Full Idea: It is difficult to know whether you know something or not. For it is difficult to know whether or not our knowledge of something proceeds from its principles - and this is what it is to know something. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 76a25) |
| 12379 | You cannot understand anything through perception [Aristotle] |
| Full Idea: You cannot understand anything through perception. Demonstrations are universal, and universals cannot be perceived. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 87b28) |
| 16725 | Some knowledge is lost if you lose a sense, and there is no way the knowledge can be replaced [Aristotle] |
| Full Idea: The loss of any one of the senses entails the loss of a corresponding portion of knowledge, and since we learn either by induction or by demonstration, this knowledge cannot be acquired. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 81a37) | |
| A reaction: This suggests Jackson's 'knowledge argument', that raw experience contains some genuine knowledge, for which there is no mechanistic substitute. Not that I accept…. |
| 23309 | Aristotle's concepts of understanding and explanation mean he is not a pure empiricist [Aristotle, by Frede,M] |
| Full Idea: It is a certain notion of understanding and, correspondingly, explanation which makes Aristotle think that knowledge, properly speaking, could not be a matter of mere experience. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Michael Frede - Aristotle's Rationalism p.160 | |
| A reaction: Frede says this means that Aristotle is a rationalist, though few empiricists think understanding is 'merely' a matter of experience. My own epistemology is Explanatory Empiricism, which I see as more empiricist than rationalist. |
| 1693 | Animals may have some knowledge if they retain perception, but understanding requires reasons to be given [Aristotle] |
| Full Idea: In some animals the perception is retained, and in some not. Without retention knowledge is impossible. Some animals go further and form an account based on the perception. This leads to memory and experience, and so to either skill or understanding. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 99b35-) |
| 9067 | Many memories of the same item form a single experience [Aristotle] |
| Full Idea: When it occurs often in connection with the same item, ..memories which are many in number form a single experience. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100a05) | |
| A reaction: This is Aristotle at his most empirical. He is not describing an operation of the understanding, but a process of association. The process he alludes to is at the heart of the abstractionist view of concept-formation. |
| 1671 | Sceptics say justification is an infinite regress, or it stops at the unknowable [Aristotle] |
| Full Idea: Sceptics say that there is either an infinite regress of ideas based on one another, or things come to a stop at primitives which are unknowable (because they can't be demonstrated). | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b09) | |
| A reaction: This is one strand of what eventually becomes the classic Agrippa's Trilemma (Idea 8850). For Aristotle's view on this one, see Idea 562. |
| 1670 | When you understand basics, you can't be persuaded to change your mind [Aristotle] |
| Full Idea: Anyone who understands anything simpliciter (as basic) must be incapable of being persuaded to change his mind. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72b04) | |
| A reaction: A typical Aristotle test which seems rather odd to us. Surely I can change my mind, and decide that something is not basic after all? But, says Aristotle, then you didn't really think it was basic. |
| 1691 | Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes [Aristotle] |
| Full Idea: Divide a whole into its primitives, then try to get definitions of these. Thus you establish the kind, and then study the attributes through the primitive common items. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 96b16) |
| 12383 | There must be definitions before demonstration is possible [Aristotle] |
| Full Idea: There is no demonstration of anything of which there is no definition. Definitions are of what something is, i.e. of its essence, but all demonstrations clearly suppose and assume what a thing is. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b30) | |
| A reaction: Note that while essentialism rests on definitions, the job is not yet complete once the definitions are done. With good definitions, it should be easy to show how the pieces of the jigsaw fit together. |
| 1674 | All demonstration is concerned with existence, axioms and properties [Aristotle] |
| Full Idea: All demonstrative science [apodeiktike episteme] is concerned with three things: what it posits to exist (the kind), the axioms (primitives basic to demonstration), and the attributes. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 76b12) |
| 24068 | Demonstration is more than entailment, as the explanatory order must match the causal order [Aristotle, by Koslicki] |
| Full Idea: Aristotle's demonstration encompasses more than deductive entailment, in that the explanatory order of priority represented in a successful demonstration must mirror precisely the causal order of priority in the phenomena in question. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Kathrin Koslicki - Form, Matter and Substance 4.5 | |
| A reaction: Interesting. I presume this is correct, but is not an aspect I had registered. In Metaphysics his essentialist explanations are causal, so it all hangs together. |
| 17310 | Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Aristotle, by Koslicki] |
| Full Idea: In Aristotle's system, the relevant notion of asymmetric consequence that is operative in his model of scientific explanation is that of demonstration. ...It is a theoretical/linguistic reflection of an asymmetric real-world relation of causal priority. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Kathrin Koslicki - Varieties of Ontological Dependence 7.3 n7 | |
| A reaction: The asymmetry is required for explanation, and for grounding. |
| 21359 | Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi on Aristotle] |
| Full Idea: There is a conflict between the syllogistic theory of demonstration of the Posterior Analytics, with its austere programme of certainties, and how Aristotle actually does science. | |
| From: comment on Aristotle (Posterior Analytics [c.327 BCE]) by Armand Marie LeRoi - The Lagoon: how Aristotle invented science 104 | |
| A reaction: Leroi observes that there are no demonstrations anywhere in the biological writings. Biology probably lends itself least to such an approach. |
| 1667 | Premises must be true, primitive and immediate, and prior to and explanatory of conclusions [Aristotle] |
| Full Idea: Demonstrative understanding must proceed from items which are true and primitive and immediate and more familiar and prior to and explanatory of the conclusions. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b22) |
| 12365 | We can know by demonstration, which is a scientific deduction leading to understanding [Aristotle] |
| Full Idea: We know things through demonstration, by which I mean a scientific deduction, and by 'scientific' I mean a deduction by possessing which we understand something. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 71b17) | |
| A reaction: This is a distinctively Aristotelian account of what science aims at, and which seems to have dropped out of modern accounts of science, which are still under the influence of logical positivism. Time to revive it. |
| 10918 | Demonstrative understanding rests on necessary features of the thing in itself [Aristotle] |
| Full Idea: If demonstrative understanding proceeds from necessary principles, and whatever holds of an object in itself is necessary, then it is clear that demonstrative deductions will proceed from certain items of this sort. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 74b05-) | |
| A reaction: This is the characterization of the essence of something in terms of what counts as a good explanation of that thing. Although explanation is a bit subjective, I like this approach, because you will dig down to the source of the powers of the thing. |
| 12374 | Demonstrations must be necessary, and that depends on the middle term [Aristotle] |
| Full Idea: If you understand something demonstratively, it must hold from necessity, so it is plain that your demonstration must proceed through a middle term which is necessary. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 75a13) | |
| A reaction: How can a middle 'term' be necessary, if it is not a proposition? Presumably Socrates is necessarily a man, and men are necessarily mortal, so it is the predication which is necessary. |
| 12148 | Demonstrations are syllogisms which give explanations [Aristotle] |
| Full Idea: Demonstrations are probative deductions [sullogismos] which give the explanation [aitias] and the reason why. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 85b24) | |
| A reaction: This notion seems to have slipped out of modern philosophy of science, because (while scientists have just pressed on) philosophers of science have raised so many sceptical questions that they have, I would say, lost the plot. |
| 1679 | Universal demonstrations are about thought; particular demonstrations lead to perceptions [Aristotle] |
| Full Idea: Universal demonstrations are objects of thought, particular demonstrations terminate in perception. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 86a30) |
| 1680 | Demonstration is better with fewer presuppositions, and it is quicker if these are familiar [Aristotle] |
| Full Idea: A demonstration is superior if it depends on fewer suppositions or propositions - for if these are familiar, knowledge will come more quickly, and this is preferable. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 86a35) |
| 12147 | The principles of demonstrations are definitions [Aristotle] |
| Full Idea: The principles of demonstrations are definitions. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 90b25) | |
| A reaction: This I take to be a key idea linking Aristotle's desire to understand the world, by using demonstrations to reach good explanations. Definitions turn out to rest on essences, so our understanding of the world rests on essences. |
| 12371 | A demonstration is a deduction which proceeds from necessities [Aristotle] |
| Full Idea: A demonstration is a deduction which proceeds from necessities. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 73a24) | |
| A reaction: Elsewhere he tells us that demonstration that brings understanding (Idea 12365), so this is an interesting gloss. He says that the middle term of the syllogism gives the understanding, but necessities reside in the whole propositions of the premisses. |
| 1683 | We learn universals from many particulars [Aristotle] |
| Full Idea: It is from many particulars that the universal becomes plain. Universals are valuable because they make the explanation plain. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88a05) |
| 12367 | What is most universal is furthest away, and the particulars are nearest [Aristotle] |
| Full Idea: What is most universal is furthest away, and the particulars are nearest. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a05) | |
| A reaction: This is the puzzle that bother Aristotle about explanation, that we can only grasp the universals, when we want to explain the particulars. |
| 12385 | Are particulars explained more by universals, or by other particulars? [Aristotle] |
| Full Idea: Which of the middle terms is explanatory for the particulars - the one which is primitive in the direction of the universal, or the one which is primitive in the direction of the particular? | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 99b09) | |
| A reaction: I'm not clear about this, but it shows Aristotle wrestling with the issue of whether explanations are of particulars or universals, and whether they employ particulars as well as employing universals. The particular must be defined! |
| 12380 | Universals are valuable because they make the explanations plain [Aristotle] |
| Full Idea: Universals are valuable because they make the explanations plain. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 88a06) | |
| A reaction: Everything in Aristotle comes back to human capacity to understand. There seems to be an ideal explanation consisting entirely of particulars, but humans are not equipped to grasp it. We think in a broad brush way. |
| 1689 | Explanation is of the status of a thing, inferences to it, initiation of change, and purpose [Aristotle] |
| Full Idea: There are four sorts of explanation: what it is to be something, that if certain items hold it is necessary for this to hold, what initiated the change, and the purpose. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 94a21) | |
| A reaction: This might be summed up as: 'we want to know the essence, the necessary conditions, the cause, and the purpose'. Can anyone improve on that as the aims of explanation? The second explanation (necessary preconditions) isn't in 'Physics' - Idea 8332. |
| 1686 | What we seek and understand are facts, reasons, existence, and identity [Aristotle] |
| Full Idea: The things we seek are equal in number to those we understand: the fact, the reason why, if something is, and what something is. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 89b24) |
| 12357 | Explanation and generality are inseparable [Aristotle, by Wedin] |
| Full Idea: For Aristotle, explanation and generality are fellow-travellers. | |
| From: report of Aristotle (Posterior Analytics [c.327 BCE]) by Michael V. Wedin - Aristotle's Theory of Substance X.11 | |
| A reaction: This isn't 'lawlike' explanation, but it is interestingly close to it. It seems to be based on the fact that predicates are universals, so we can only state truths in general terms. |
| 1669 | The foundation or source is stronger than the thing it causes [Aristotle] |
| Full Idea: Something always holds better because of that because of which it holds - e.g. that because of which we love something is better loved. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a30) |
| 1678 | Universals give better explanations, because they are self-explanatory and primitive [Aristotle] |
| Full Idea: Universals are more explanatory (for something which holds in itself is itself explanatory of itself; and universals are primitive; hence universals are explanatory) - so universal demonstrations are better. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 85b25) |
| 9068 | Perception creates primitive immediate principles by building a series of firm concepts [Aristotle] |
| Full Idea: Primitive immediate principles ...come about from perception - as in a battle, when a rout has occurred, first one man makes a stand, then another, and then another, until a position of strength is reached. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100a12) | |
| A reaction: Philosophers don't create imagery like that any more. This empiricist account of how concepts and universals are created is part of a campaign against Plato's theory of forms. [Idea 9069 continues his idea] |
| 9069 | A perception lodging in the soul creates a primitive universal, which becomes generalised [Aristotle] |
| Full Idea: When one undifferentiated item in perception makes a stand, there is a primitive universal in the soul; for although you perceive particulars, perception is of universals - e.g. of man, not of Callias the man. One animal makes a stand, until animal does. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100a15-) | |
| A reaction: This is the quintessential account of abstractionism, with the claim that primitive universals arise directly in perception, but only in repeated perception. How the soul does it is a mystery to Aristotle, just as associations are a mystery to Hume. |
| 9070 | We learn primitives and universals by induction from perceptions [Aristotle] |
| Full Idea: We must get to know the primitives by induction; for this is the way in which perception instils universals. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 100b04) | |
| A reaction: This statement is so strongly empirical it could have come from John Stuart Mill. The modern post-Fregean view of universals is essentially platonist - that they have a life and logic of their own, and their method of acquisition is irrelevant. |
| 12368 | Negation takes something away from something [Aristotle] |
| Full Idea: The part of a contradictory pair which says something of something is an affirmation; the part which takes something from something is a negation. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 72a14) | |
| A reaction: So affirmation is predication about an object ['Fa'], and negation is denial of predication. We have a scope problem: there is nothing which is F [¬∃x(Fx)], or there is a thing which is not-F [∃x(¬Fx)]. Aristotle seems to mean the latter. |
| 1692 | If you shouldn't argue in metaphors, then you shouldn't try to define them either [Aristotle] |
| Full Idea: If you should not argue in metaphors, it is plain too that you should neither define by metaphors nor define what is said in metaphors; for then you will necessarily argue in metaphors. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 97b37) | |
| A reaction: Impeccable logic, but seeing a similarity can be a wonderful shortcut to seeing a great truth. |
| 12375 | Whatever holds of a kind intrinsically holds of it necessarily [Aristotle] |
| Full Idea: In each kind, whatever holds of something in itself and as such holds of it from necessity. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 75a30) | |
| A reaction: This seems to confirm the view that essential properties are necessary, but it does not, of course, follow that all necessary properties are essential properties (e.g. trivial necessities are not essential). |
| 1688 | Properties must be proved, but not essence; but existents are not a kind, so existence isn't part of essence [Aristotle] |
| Full Idea: Everything which a thing is must be proved through a demonstration - except its essence. But existence is not the essence of anything; for the things that exist do not constitute a kind. | |
| From: Aristotle (Posterior Analytics [c.327 BCE], 92b14) |