103 ideas
| 24047 | An account is either a definition or a demonstration [Aristotle] |
| Full Idea: Every account is either a definition or a demonstration. | |
| From: Aristotle (De Anima [c.329 BCE], 407a24) | |
| A reaction: That is, it is either a summary of the thing's essential nature, or it is a proof of some natural fact, starting from first principles. |
| 24052 | From one thing alone we can infer its contrary [Aristotle] |
| Full Idea: One member of a pair of contraries is sufficient to discern both itself and its opposite. | |
| From: Aristotle (De Anima [c.329 BCE], 411a02) | |
| A reaction: This obviously requires prior knowledge of what the opposite is. He says you can infer the crooked from the straight. You can hardly use light in isolation to infer dark [see DA 418b17]. What's the opposite of a pig? |
| 9540 | A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell] |
| Full Idea: A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: In the interpreted version of the logic, 1 and 0 would become T (true) and F (false). The procedure seems to be called nowadays a 'valuation'. |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| Full Idea: Formulas provable from no premises at all are often called 'theorems'. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.6) |
| 9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
| Full Idea: The Law of Transposition says that (P→Q) → (¬Q→¬P). | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: That is, if the consequent (Q) of a conditional is false, then the antecedent (P) must have been false. |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| Full Idea: The method of truth tables assumes truth functionality. Truth tables are just pictures of truth functions. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3) |
| 9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
| Full Idea: An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then ¬α is not valid. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| Full Idea: Deontic accessibility seems not to be reflexive (that it ought to be true doesn't make it true). One could argue that it is serial (that there is always a world where something is acceptable). | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3.1) |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| Full Idea: In D we add to K a new axiom saying that 'what's necessary is possible' (□φ→◊φ), ..and it can then be proved that tautologies are possible and contradictions are not necessary. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.4.2) |
| 13711 | System B introduces iterated modalities [Sider] |
| Full Idea: With system B we begin to be able to say something about iterated modalities. ..S4 then takes a different stand on the iterated modalities, and neither is an extension of the other. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.4.4) |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| Full Idea: S5 is the strongest system, since it has the most valid formulas. That's because it has the fewest models; it's easy to be S5-valid since there are so few potentially falsifying models. K is the weakest system, for opposite reasons. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3.2) | |
| A reaction: Interestingly, the orthodox view is that S5 is the correct logic for metaphysics, but it sounds a bit lax. Compare Idea 13707. |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| Full Idea: Epistemic accessibility should be required to be reflexive (allowing Kφ→φ). S4 allows the 'KK principle', or 'positive introspection' (Kφ→KKφ), and S5 allows 'negative introspection' (¬Kφ→K¬Kφ). | |
| From: Theodore Sider (Logic for Philosophy [2010], 7.2) |
| 13714 | We can treat modal worlds as different times [Sider] |
| Full Idea: We can think of the worlds of modal logic as being times, rather than 'possible' worlds. | |
| From: Theodore Sider (Logic for Philosophy [2010], 7.3.3) |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| Full Idea: The Converse Barcan Formula reads □∀αφ→∀α□φ (or an equivalent using ◊). | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.5.2) | |
| A reaction: I would read that as 'if all the αs happen to be φ, then αs have to be φ'. Put like that, I would have thought that it was obviously false. Sider points out that some new object could turn up which isn't φ. |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| Full Idea: The Barcan Formula ∀x□Fx→□∀xFx is often regarded as a defect of Simple Quantified Modal Logic, though this most clearly seen in its equivalent form ◊∃xFx→∃x◊Fx. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.5.2) | |
| A reaction: [See Idea 13719 for an explanation why it might be a defect] I translate the first one as 'if xs must be F, then they are always F', and the second one as 'for x to be possibly F, there must exist an x which is possibly F'. Modality needs existence. |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| Full Idea: The proof of the Barcan Formula require System B. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.7) |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| Full Idea: Not everyone who employs intuitionistic logic is an intuitionist about mathematics. | |
| From: Theodore Sider (Logic for Philosophy [2010], 7.4.1) | |
| A reaction: This seems worthy of note, since it may be tempting to reject the logic because of the implausibility of the philosophy of mathematics. I must take intuitionist logic more seriously. |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| Full Idea: On the question of the nature of genuine logical consequence, ...the most popular answer is the semantic, or model-theoretic one. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: Reading the literature, one might be tempted to think that this is the only account that anyone takes seriously. Substitutional semantics seems an interesting alternative. |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| Full Idea: Another answer to the question about the nature of logical consequence is a proof-theoretic one, according to which it is more a matter of provability than of truth-preservation. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: I don't like this, and prefer the model-theoretic or substitutional accounts. Whether you can prove that something is a logical consequence seems to me entirely separate from whether you can see that it is so. Gödel seems to agree. |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| Full Idea: The 'modal' account of logical consequence is that it is not possible for the premises to be true and the consequent false (under some suitable notion of possibility). | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: Sider gives a nice summary of five views of logical consequence, to which Shapiro adds substitutional semantics. |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| Full Idea: There is a 'primitivist' account, according to which logical consequence is a primitive notion. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.5) | |
| A reaction: While sympathetic to substitutional views (Idea 13674), the suggestion here pushes me towards thinking that truth must be at the root of it. The trouble, though, is that a falsehood can be a good logical consequence of other falsehoods. |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| Full Idea: A 'theorem' is defined as the last line of a proof in which each line is either an axiom or follows from earlier lines by a rule. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.7) | |
| A reaction: In other words, theorems are the axioms and their implications. |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| Full Idea: When a variable is not combined with a quantifier (and so is 'free'), the result is, intuitively, semantically incomplete, and incapable of truth or falsity. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.2) |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| Full Idea: Calling a function a 'total' function 'over D' means that the function must have a well-defined output (which is a member of D) whenever it is given as inputs any n members of D. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.2) |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| Full Idea: We might prefer λx(Fx∧Gx)(a) as the symbolization of 'John is cold and hungry', since it treats 'is cold and hungry' as a single predicate. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.5) |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| Full Idea: Since they are the foundations on which a proof rests, the axioms in a good axiomatic system ought to represent indisputable logical truths. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.6) |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| Full Idea: Axiomatic systems do not allow reasoning with assumptions, and therefore do not allow conditional proof or reductio ad absurdum. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.6) | |
| A reaction: Since these are two of the most basic techniques of proof which I have learned (in Lemmon), I shall avoid axiomatic proof systems at all costs, despites their foundational and Ockhamist appeal. |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| Full Idea: The style of proof called 'induction on formula construction' (or 'on the number of connectives', or 'on the length of the formula') rest on the fact that all formulas are built up from atomic formulas according to strict rules. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.7) | |
| A reaction: Hence the proof deconstructs the formula, and takes it back to a set of atomic formulas have already been established. |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| Full Idea: A proof by induction starts with a 'base case', usually that an atomic formula has some property. It then assumes an 'inductive hypothesis', that the property is true up to a certain case. The 'inductive step' then says it will be true for the next case. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.7) | |
| A reaction: [compressed] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| Full Idea: The method of natural deduction is popular in introductory textbooks since it allows reasoning with assumptions. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.5) | |
| A reaction: Reasoning with assumptions is generally easier, rather than being narrowly confined to a few tricky axioms, You gradually show that an inference holds whatever the assumption was, and so end up with the same result. |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| Full Idea: We can construct proofs not out of well-formed formulae ('wffs'), but out of sequents, which are some premises followed by their logical consequence. We explicitly keep track of the assumptions upon which the conclusion depends. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.5.1) | |
| A reaction: He says the method of sequents was invented by Gerhard Gentzen (the great nazi logician) in 1935. The typical starting sequents are the introduction and elimination rules. E.J. Lemmon's book, used in this database, is an example. |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| Full Idea: A valuation function in predicate logic will assign truth values to formulas relative to variable assignments. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.2) | |
| A reaction: Sider observes that this is a 'double' relativisation (due to Tarski), since propositional logic truth was already relative to an interpretation. Now we are relative to variable assignments as well. |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| Full Idea: The semantical notion of a logical truth is that of a valid formula, which is true in all interpretations. In propositional logic they are 'tautologies'. | |
| From: Theodore Sider (Logic for Philosophy [2010], 2.3) | |
| A reaction: This implies that there is a proof-theoretic account of logical truth as well. Intuitively a logical truth is a sequent which holds no matter which subject matter it refers to, so the semantic view sounds OK. |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| Full Idea: It isn't clear which formulas of modal propositional logic are logical truths, ...especially for sentences that contain iterations of modal operators. Is □P→□□P a logical truth? It's hard to say. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3) | |
| A reaction: The result, of course, is that there are numerous 'systems' for modal logic, so that you can choose the one that gives you the logical truths you want. His example is valid in S4 and S5, but not in the others. |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| Full Idea: In model theory one normally defines some notion of truth in a model, and then uses it to define validity as truth in all models, and semantic consequence as the preservation of truth in models. | |
| From: Theodore Sider (Logic for Philosophy [2010], 10.1) |
| 9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
| Full Idea: To say that an axiom system is 'weakly complete' is to say that every valid wff of the system is derivable as a thesis. ..The system is 'strongly complete' if it cannot have any more theses than it has without falling into inconsistency. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [They go on to say that Propositional Logic is strongly complete, but Modal Logic is not] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| Full Idea: You can establish facts of the form Γ|-φ while avoiding the agonies of axiomatic proofs by reasoning directly about models to conclusions about semantic consequence, and then citing completeness. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.5) | |
| A reaction: You cite completeness by saying that anything which you have shown to be a semantic consequence must therefore be provable (in some way). |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| Full Idea: Compactness is intuitively surprising, ..because one might have thought there could be some contradiction latent within some infinite set, preventing it from being satisfiable, only discovered when you consider the whole set. But this can't happen. | |
| From: Theodore Sider (Logic for Philosophy [2010], 4.5) |
| 1729 | We perceive number by the denial of continuity [Aristotle] |
| Full Idea: Number we perceive by the denial of continuity. | |
| From: Aristotle (De Anima [c.329 BCE], 425a19) | |
| A reaction: This is a key thought. A being (call it 'Parmenides') which sees all Being as One would make no distinctions of identity, and so could not count anything. Why would they want numbers? |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| Full Idea: A single second-order sentence has second-order semantic consequences which are all and only the truths of arithmetic, but this is cold comfort because of incompleteness; no axiomatic system draws out the consequences of this axiom. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.4.3) |
| 24057 | What is prior is always potentially present in what is next in order [Aristotle] |
| Full Idea: What is prior is always potentially present in what is next in order … - for example, the triangle in the quadrilateral, or the nutritive part of animate things in the perceptual part. | |
| From: Aristotle (De Anima [c.329 BCE], 414a28) | |
| A reaction: 'Prior' seems to be a value for Aristotle, which is never present in modern discussions of ontological relations and structure. Priority tracks back to first principles. |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| Full Idea: For a 'precisification' we take a trivalent interpretation and preserve the T and F values, and then assign all the third values in some way to either T or F. | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) | |
| A reaction: [my informal summary of Sider's formal definition] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| Full Idea: Supervaluation preserves classical logic (even though supervaluations are three-valued), except when we add the Δ operator (meaning 'definitely' or 'determinately'). | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| Full Idea: In a 'supervaluation' we take a trivalent interpretation, and assign to each wff T (or F) if it is T (or F) in every precisification, leaving the third truth-value in any other cases. The wffs are then 'supertrue' or 'superfalse' in the interpretation. | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) | |
| A reaction: [my non-symbolic summary] Sider says the Ts and Fs in the precisifications are assigned 'in any way you like', so supervaluation is a purely formal idea, not a technique for eliminating vagueness. |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| Full Idea: We can introduce 'sharpenings', to make vague terms precise without disturbing their semantics. Then truth (or falsity) becomes true(false)-in-all-sharpenings. You are only 'rich' if you are rich-on-all-sharpenings of the word. | |
| From: Theodore Sider (Logic for Philosophy [2010], 3.4.5) | |
| A reaction: Not very helpful. Lots of people might be considered rich in many contexts, but very few people would be considered rich in all contexts. You are still left with some vague middle ground. |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| Full Idea: A relation is just a feature of multiple objects taken together. | |
| From: Theodore Sider (Logic for Philosophy [2010], 1.8) | |
| A reaction: Appealingly simple, especially for a logician, who can then just list the relevant objects as members of a set, and the job is done. But if everyone to the left of me is also taller than me, this won't quite do. |
| 16752 | Sight is the essence of the eye, fitting its definition; the eye itself is just the matter [Aristotle] |
| Full Idea: If the eye were an animal, sight would have been its soul, for sight is the substance or essence of the eye which corresponds to the formula, the eye being merely the matter of seeing; when seeing is removed it is no longer an eye,except in name. | |
| From: Aristotle (De Anima [c.329 BCE], 412b18) | |
| A reaction: This is a drastic view of form as merely function, which occasionally appears in Aristotle. To say a blind eye is not an eye is a tricky move in metaphysics. So what is it? In some sense it is still an eye. |
| 24058 | The substance is the cause of a thing's being [Aristotle] |
| Full Idea: The cause of its being for everything is its substance. | |
| From: Aristotle (De Anima [c.329 BCE], 415b12) | |
| A reaction: It sounds as if 'substance' here means essence. We no longer see the cause of something's being as intrinsic to the thing. Only previous causes produce things. The 'form' must be the intrinsic cause of being. |
| 24055 | Matter is potential, form is actual [Aristotle] |
| Full Idea: Matter is potentiality, whereas form is actuality. | |
| From: Aristotle (De Anima [c.329 BCE], 412a09) | |
| A reaction: Plato said mud has no Form. What did Aristotle think of that? I only ask because to me mud looks like unformed actuality. |
| 24040 | Scientists explain anger by the matter, dialecticians by the form and the account [Aristotle] |
| Full Idea: For a dialectician anger is a desire for retaliation or something like that, where for a natural scientist it is a boiling of the blood and hoot stuff around the heart. The scientist gives the matter, where the dialectician give the form and the account. | |
| From: Aristotle (De Anima [c.329 BCE], 403a30) | |
| A reaction: A nice illumination of hylomorphism. Notice that the dialectician also give the account [logos]. |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| Full Idea: The identity of indiscernibles (∀x∀y(∀X(Xx↔Xy)→x=y) is necessarily true, provided that we construe 'property' very broadly, so that 'being a member of such-and-such set' counts as a property. | |
| From: Theodore Sider (Logic for Philosophy [2010], 5.4.3) | |
| A reaction: Sider's example is that if the two objects are the same they must both have the property of being a member of the same singleton set, which they couldn't have if they were different. |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| Full Idea: 'Strong necessity' requires the truth of 'necessarily φ' is all possible worlds. 'Weak necessity' merely requires that 'necessarily φ' be true in all worlds in which objects referred to within φ exist. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.6.3) | |
| A reaction: This seems to be a highly desirably distinction, given the problem of Idea 13719. It is weakly necessary that humans can't fly unaided, assuming we are referring the current feeble wingless species. That hardly seems to be strongly necessary. |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| Full Idea: Some argue that metaphysical accessibility is intransitive. The individuals involved mustn't be too different from the actual world. A world in which I am a frog isn't metaphysically possible. Perhaps the logic is modal system B or T. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.3.1) | |
| A reaction: This sounds rather plausible and attractive to me. We don't want to say that I am necessarily the way I actually am, though, so we need criteria. Essence! |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| Full Idea: On any sense of necessity, surely logical truths must be necessary. | |
| From: Theodore Sider (Logic for Philosophy [2010], 6.4) |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| Full Idea: To show the semantic difference between counterfactuals and indicative conditionals, 'If Booth hadn't shot Lincoln someone else would have' is false, but 'If Booth didn't shoot Lincoln then someone else did' is true. | |
| From: Theodore Sider (Logic for Philosophy [2010], 8) | |
| A reaction: He notes that indicative conditionals also differ in semantics from material and strict conditionals. The first example allows a world where Lincoln was not shot, but the second assumes our own world, where he was. Contextual domains? |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| Full Idea: There is no problem of transworld identification with de dicto modal sentence, for their evaluation does not require taking an individual from one possible world and reidentifying it in another. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.2) | |
| A reaction: If 'de dicto' is about the sentence and 'de re' is about the object (Idea 5732), how do you evaluate the sentence without at least some notion of the object to which it refers. Nec the Prime Minister chairs the cabinet. Could a poached egg do the job? |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| Full Idea: A problem with the Barcan Formula is it might be possible for there to exist a ghost, even though there in fact exists nothing that could be a ghost. There could have existed some 'extra' thing which could be a ghost. | |
| From: Theodore Sider (Logic for Philosophy [2010], 9.5.2) | |
| A reaction: Thus when we make modal claims, do they only refer to what actually exists, or is specified in our initial domain? Can a claim enlarge the domain? Are domains 'variable'? Simple claims about what might have existed seem to be a problem. |
| 5051 | The intellect has potential to think, like a tablet on which nothing has yet been written [Aristotle] |
| Full Idea: The intellect is in a way potentially the object of thought, but nothing in actuality before it thinks, and the potentiality is like that of the tablet on which there is nothing actually written. | |
| From: Aristotle (De Anima [c.329 BCE], 429b31) | |
| A reaction: This passage is referred to by Leibniz, and is the origin of the concept of the 'tabula rasa'. Aristotle need not be denying innate ideas, but merely describing the phenomenology of the moment before a train of thought begins. |
| 16723 | Perception of sensible objects is virtually never wrong [Aristotle] |
| Full Idea: Perception of the special objects of sense is never in error or admits the least possible amount of falsehood. | |
| From: Aristotle (De Anima [c.329 BCE], 428b19) | |
| A reaction: This is, surprisingly, the view which was raised and largely rejected in 'Theaetetus'. It became a doctrine of Epicureanism, and seems to make Aristotle a thoroughgoing empiricist, though that is not so clear elsewhere. I think Aristotle is right. |
| 1724 | Perception necessitates pleasure and pain, which necessitates appetite [Aristotle] |
| Full Idea: Where there is perception there is also pleasure and pain, and where there are these, of necessity also appetite. | |
| From: Aristotle (De Anima [c.329 BCE], 413b23) |
| 1730 | Why do we have many senses, and not just one? [Aristotle] |
| Full Idea: A possible line of inquiry would be into the question for what purpose we have many senses and not just one. | |
| From: Aristotle (De Anima [c.329 BCE], 425b04) |
| 17711 | Our minds take on the form of what is being perceived [Aristotle, by Mares] |
| Full Idea: Aristotle famously holds that in perception our minds take on the form of what is being perceived. | |
| From: report of Aristotle (De Anima [c.329 BCE]) by Edwin D. Mares - A Priori 08.2 | |
| A reaction: [References in Aristotle needed here...] |
| 1725 | Why can't we sense the senses? And why do senses need stimuli? [Aristotle] |
| Full Idea: Why is there not also a sense of the senses themselves? And why don't the senses produce sensation without external bodies, since they contain elements? | |
| From: Aristotle (De Anima [c.329 BCE], 417a03) |
| 1732 | Sense organs aren't the end of sensation, or they would know what does the sensing [Aristotle] |
| Full Idea: Flesh is not the ultimate sense-organ. To suppose that it is requires the supposition that on contact with the object the sense-organ itself discerns what is doing the discerning. | |
| From: Aristotle (De Anima [c.329 BCE], 426b16) |
| 1728 | Many objects of sensation are common to all the senses [Aristotle] |
| Full Idea: Common sense-objects are movement, rest, number, shape and size, which are not special to any one sense, but common to all. | |
| From: Aristotle (De Anima [c.329 BCE], 418a18) |
| 1727 | Some objects of sensation are unique to one sense, where deception is impossible [Aristotle] |
| Full Idea: Now I call that sense-object 'special' that does not admit of being perceived by another sense and about which it is impossible to be deceived. | |
| From: Aristotle (De Anima [c.329 BCE], 418a15) |
| 1734 | In moral thought images are essential, to be pursued or avoided [Aristotle] |
| Full Idea: In the thinking soul, images play the part of percepts, and the assertion or negation of good or bad is invariably accompanied by avoidance or pursuit, which is the reason for the soul's never thinking without an image. | |
| From: Aristotle (De Anima [c.329 BCE], 431a15) |
| 1726 | We may think when we wish, but not perceive, because universals are within the mind [Aristotle] |
| Full Idea: Perception is of particular things, but knowledge is of universals, which are in a way in the soul itself. Thus a man may think whenever he wishes, but not perceive. | |
| From: Aristotle (De Anima [c.329 BCE], 417b22) |
| 16647 | Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties [Aristotle] |
| Full Idea: In demonstration a definition of the essence is required as starting point, so that definitions which do not enable us to discover the derived properties, or which fail to facilitate even a conjecture about them, must obviously be dialectical and futile. | |
| From: Aristotle (De Anima [c.329 BCE], 402b25) | |
| A reaction: Interesting to see 'dialectical' used as a term of abuse! Illuminating. For scientific essentialism, then, demonstration is filling out the whole story once the essence has been inferred. It is circular, because essence is inferred from accidents. |
| 24048 | Demonstrations move from starting-points to deduced conclusions [Aristotle] |
| Full Idea: Demonstrations are both from a starting-point and have a sort of end, namely the deduction or the conclusion. | |
| From: Aristotle (De Anima [c.329 BCE], 407a25) | |
| A reaction: A starting point has to be a first principle [arché]. It has been observed that Aristotle explains demonstration very carefully, but rarely does it in his writings. |
| 16646 | To understand a triangle summing to two right angles, we need to know the essence of a line [Aristotle] |
| Full Idea: In mathematics it is useful for the understanding of the property of the equality of the interior angles of a triangle to two right angles to know the essential nature of the straight and the curved or of the line and the plane. | |
| From: Aristotle (De Anima [c.329 BCE], 402b18) | |
| A reaction: Although Aristotle was cautious about this, he clearly endorses here the idea that essences play an explanatory role in geometry. The caution is in the word 'useful', rather than 'vital'. How else can we arrive at this result, though? |
| 1714 | Mind involves movement, perception, incorporeality [Aristotle] |
| Full Idea: The soul seems to be universally defined by three features, so to speak, the production of movement, perception and incorporeality. | |
| From: Aristotle (De Anima [c.329 BCE], 405b12) | |
| A reaction: 'Incorporeality' begs the question, but its appearance is a phenomenon that needs explaining. 'Movement' is an interesting Greek view. Nowadays we would presumably added intentional states, and the contents and meaning of thoughts. No 'reason'? |
| 5507 | Aristotle led to the view that there are several souls, all somewhat physical [Aristotle, by Martin/Barresi] |
| Full Idea: On the later views inspired by Aristotle's 'De Anima' there was no longer just one soul, but several, and each of them had a great deal in common with the body. | |
| From: report of Aristotle (De Anima [c.329 BCE]) by R Martin / J Barresi - Introduction to 'Personal Identity' p.17 | |
| A reaction: Is this based on the faculties of sophia, episteme, nous, techne and phronesis, or is it based on the vegetative, appetitive and rational parts? The latter, I presume. Not so interesting, not so modular. |
| 24051 | Soul is seen as what moves, or what is least physical, or a combination of elements [Aristotle] |
| Full Idea: Three ways have been handed down in which people define the soul: what is most capable of moving things, since it moves itself; or a body which is the most fine-grained and least corporeal; or that it is composed of the elements. | |
| From: Aristotle (De Anima [c.329 BCE], 409b19) | |
| A reaction: A nice example of Aristotle beginning an investigation by idenfying the main explanations which have been 'handed down' from previous generations. These three aren't really in competition, and might all be true. |
| 12086 | Psuché is the form and actuality of a body which potentially has life [Aristotle] |
| Full Idea: Soul is substance as the form of a natural body which potentially has life, and since this substance is actuality, soul will be the actuality of such a body. | |
| From: Aristotle (De Anima [c.329 BCE], 412a20) | |
| A reaction: To understand what Aristotle means by 'form' you must, I'm afraid, read the 'Metaphysics'. Form isn't shape, but rather the essence which bestows the individual identity on the thing. 'Psuche is the essence of man' might be a better slogan. |
| 16754 | The soul is the cause or source of movement, the essence of body, and its end [Aristotle] |
| Full Idea: The soul is the cause [aitia] of its body alike in three senses which we explicitly recognise. It is (a) the source or origin of movement, it is (b) the end, and it is (c) the essence of the whole living body. | |
| From: Aristotle (De Anima [c.329 BCE], 415b09) | |
| A reaction: 'Aitia' also means explanation, so these are three ways to explain a human being, by what it does, why what it is for, and by what it intrinsically is. Activity, purpose and nature. |
| 24046 | Understanding is impossible, if it involves the understanding having parts [Aristotle] |
| Full Idea: How could a spatial understanding understand anything? Wiil it do so with parts, seen as magnitudes or as points? If it is points, the understanding will never get through them all. If magnitudes, it will understand things an unlimited number of times. | |
| From: Aristotle (De Anima [c.329 BCE], 407a09) | |
| A reaction: This seems to be a strong commitment to the idea that the mind is not physical because it is necessarily non-spatial. |
| 1717 | If the soul is composed of many physical parts, it can't be a true unity [Aristotle] |
| Full Idea: If the soul is composed of parts of the body, or the harmony of the elements composing the body, there will be many souls, and everywhere in the body. | |
| From: Aristotle (De Anima [c.329 BCE], 408a15) | |
| A reaction: We will ignore "everywhere in the body", but the rest seems to me exactly right. The idea of the unity of the soul is an understandable and convenient assumption, but it leads to all sorts of confusion. A crowd remains unified if half its members leave. |
| 24053 | If a soul have parts, what unites them? [Aristotle] |
| Full Idea: What is it that holds the soul together, if it by nature has parts? For surely it cannot be the body. For it seems on the contrary that it is rather the soul that holds the body together? | |
| From: Aristotle (De Anima [c.329 BCE], 411b05) | |
| A reaction: This is the hylomorphic view of a human, that the soul is the form that give unity to the matter. To do the job, presumably the form or soul need an intrinsic unity of its own, and hence cannot have parts. Apart from the need for unifying glue. |
| 1721 | What unifies the soul would have to be a super-soul, which seems absurd [Aristotle] |
| Full Idea: If soul has parts, what holds them together? Not body, because that is united by soul. If a thing unifies the soul, then THAT is the soul (unless it too has parts, which would lead to an infinite regress). Best to say the soul is a unity. | |
| From: Aristotle (De Anima [c.329 BCE], 411b10) | |
| A reaction: You don't need a 'thing' to unify something (like a crowd). I say the body holds the soul together, not physically, but because the body's value permeates thought. The body is the focused interest of the soul, like parents kept together by their child. |
| 1735 | In a way the soul is everything which exists, through its perceptions and thoughts [Aristotle] |
| Full Idea: The soul is in a way all the things that exist, for all the things that exist are objects either of perception or of thought. | |
| From: Aristotle (De Anima [c.329 BCE], 431b20) | |
| A reaction: Sounds very like Berkeley's empirical version of idealism. It also seems to imply modern externalist (anti-individualist) understandings of the mind (which strike me as false). |
| 24061 | If we divide the mind up according to its capacities, there are a lot of them [Aristotle] |
| Full Idea: For those who divide the soul into parts, and divide and separate them in accord with their capacities, the parts turn out to be very many. | |
| From: Aristotle (De Anima [c.329 BCE], 433a32) | |
| A reaction: I accept the warning. The capacities which interest me are those which seem to generate our basic ontology, but if the capacities become fine-grained, they are legion. |
| 24062 | Self-moving animals must have desires, and that entails having imagination [Aristotle] |
| Full Idea: If an animal has a desiring part, it is capable of moving itself. A desiring part, however, cannot exist without an imagination, and all imagination is either rationally calculative or perceptual. Hence in the latter the other animals also have a share. | |
| From: Aristotle (De Anima [c.329 BCE], 433b27) | |
| A reaction: Maybe if you asked people whether other animals are imaginative they would say no, but this argument is strong support for the positive view. |
| 1710 | Emotion involves the body, thinking uses the mind, imagination hovers between them [Aristotle] |
| Full Idea: Most affections (like anger) seem to involve the body, but thinking seems distinctive of the soul. But if this requires imagination, it too involves the body. Only pure mental activity would prove the separation of the two. | |
| From: Aristotle (De Anima [c.329 BCE], 403a08-) | |
| A reaction: What an observant man! Modern neuroscience is bringing out the fact that emotion is central to all mental life. We can't recognise faces without it. I say imagination is essential to pure reason, and that seems emotional too. Reason is physical. |
| 24039 | All the emotions seem to involve the body, simultaneously with the feeling [Aristotle] |
| Full Idea: The affections of the soul - spiritedness, fear, pity, confidence, joy, loving, hating - would all seem to involve the body, since at the same time as these the body is affected in a certain way. | |
| From: Aristotle (De Anima [c.329 BCE], 403a16) | |
| A reaction: Aristotle was not a physicalist, but this resembles the pilot-in-the-ship passage in Descartes, accepting the very close links. |
| 24056 | The soul (or parts of it) is not separable from the body [Aristotle] |
| Full Idea: That the soul is not separable from the body - or that certain parts of it are not, if it naturally has parts - is quite clear. | |
| From: Aristotle (De Anima [c.329 BCE], 413a04) | |
| A reaction: This doesn't make him a physicalist. I've seen him described in modern terms as a functionalist, but that makes the mind abstract and the body concrete. Perhaps he is an 'Integrationist' (as Descartes might be in his 'pilot' passage). |
| 24050 | If soul is separate from body, why does it die when the body dies? [Aristotle] |
| Full Idea: If the soul is something distinct from the mixture, why then are the being for flesh and for the other parts of the animal destroyed at the same time? | |
| From: Aristotle (De Anima [c.329 BCE], 408a25) | |
| A reaction: An obvious response to this reasonable question is to say that we see the body die, but not the soul, so the soul doesn't die. The problem is then to find some evidence for the soul's continued existence. |
| 24049 | Thinkers place the soul within the body, but never explain how they are attached [Aristotle] |
| Full Idea: There is another absurdity which follows, …since they attach the soul to a body, and place it in the body, without further determining the cause due to which this attachment comes about. …Yet this seems necessary, because this association produces action. | |
| From: Aristotle (De Anima [c.329 BCE], 407b14) | |
| A reaction: A clear statement of the interaction objection to full substance dualism. Critics say that dualists have to invoke a 'miracle' at this point. |
| 1514 | Early thinkers concentrate on the soul but ignore the body, as if it didn't matter what body received the soul [Aristotle] |
| Full Idea: Early thinkers try only to describe the soul, but they fail to go into any kind of detail about the body which is to receive the soul, as if it were possible (as it is in the Pythagorean tales) for just any old soul to be clothed in just any old body. | |
| From: Aristotle (De Anima [c.329 BCE], 407b20) | |
| A reaction: Precisely. Anyone who seriously believes that a human mind can be reincarnated in a flea needs their mind examined. Actually they need their brain examined, but that probably wouldn't impress them. I can, of course, imagine moving into a flea. |
| 2683 | Aristotle has a problem fitting his separate reason into the soul, which is said to be the form of the body [Ackrill on Aristotle] |
| Full Idea: In 'De Anima' Aristotle cannot fit his account of separable reason - which is not the form of a body - into his general theory that the soul is the form of the body. | |
| From: comment on Aristotle (De Anima [c.329 BCE]) by J.L. Ackrill - Aristotle on Eudaimonia p.33 | |
| A reaction: A penetrating observation. Possibly the biggest challenge for a modern physicalist is to give a reductive account of 'pure' reason, in terms of brain events or brain functions. |
| 1718 | Does the mind think or pity, or does the whole man do these things? [Aristotle] |
| Full Idea: Perhaps it would be better not to say that the soul pities or learns or thinks, but that the man does in virtue of the soul. | |
| From: Aristotle (De Anima [c.329 BCE], 408b12) | |
| A reaction: This can be seen as incipient behaviourism in Aristotle's view. It echoes the functionalist view that what matters is not what the mind is, or is made of, but what it does. |
| 13275 | The soul and the body are inseparable, like the imprint in some wax [Aristotle] |
| Full Idea: We should not enquire whether the soul and the body are one thing, any more than whether the wax and its imprint are, or in general whether the matter of each thing is one with that of which it is the matter. | |
| From: Aristotle (De Anima [c.329 BCE], 412b06) | |
| A reaction: This is his hylomorphist view of objects, so that the soul is the 'form' which bestows identity (and power) on the matter of which it is made. This remark is thoroughly physicalist. |
| 1733 | Thinking is not perceiving, but takes the form of imagination and speculation [Aristotle] |
| Full Idea: Thinking, then, is something other than perceiving, and its two kinds are held to be imagination and supposition. | |
| From: Aristotle (De Anima [c.329 BCE], 427b28) |
| 23307 | Aristotle makes belief a part of reason, but sees desires as separate [Aristotle, by Sorabji] |
| Full Idea: Aristotle insists [against Plato] that desires, even rational desires, are a capacity distinct from reason, as is perception. Belief is included within reason. And he sometimes distinguishes steps of reasoning from insight. | |
| From: report of Aristotle (De Anima [c.329 BCE], 428-432) by Richard Sorabji - Rationality 'Shifting' | |
| A reaction: So the standard picture of desire as permanently in conflict with reason comes from Aristotle. Maybe Plato is right on that one (though he doesn't say much about it). Since objectivity needs knowledge, reason does need belief. |
| 24060 | Self-controlled follow understanding, when it is opposed to desires [Aristotle] |
| Full Idea: Self-controlled people, even when they desire and have an appetite for things, do not do these things for which they have the desire, but instead follow the understanding. | |
| From: Aristotle (De Anima [c.329 BCE], 433a06) | |
| A reaction: If modern discussions would stop talking of 'weakness of will', and talk instead of 'control' and its lack, the whole issue would become clearer. Akrasia is then seen, for example, as an action of the whole person, not of some defective part. |
| 4376 | Pleasure and pain are perceptions of things as good or bad [Aristotle] |
| Full Idea: To experience pleasure or pain is to be active with the perceptive mean in relation to good or bad as such. | |
| From: Aristotle (De Anima [c.329 BCE], 431a10) | |
| A reaction: A bizarre view which is interesting, but strikes me as wrong. We are drawn towards pleasure, but judgement can pull us away again, and 'good' is in the judgement, not in the feeling. |
| 1740 | Nature does nothing in vain [Aristotle] |
| Full Idea: Nature does nothing in vain. | |
| From: Aristotle (De Anima [c.329 BCE], 434a31) |
| 1739 | If all movement is either pushing or pulling, there must be a still point in between where it all starts [Aristotle] |
| Full Idea: Every movement being either a push or a pull, there must be a still point as with the circle, and this will be the point of departure for the movement. | |
| From: Aristotle (De Anima [c.329 BCE], 433b26) |
| 24045 | Movement is spatial, alteration, withering or growth [Aristotle] |
| Full Idea: There a four sorts of movement - spatial movement, alteration, withering and growth. | |
| From: Aristotle (De Anima [c.329 BCE], 406a12) | |
| A reaction: Large parts of Aristotle's writings attempt to explain these four. |
| 1738 | Practical reason is based on desire, so desire must be the ultimate producer of movement [Aristotle] |
| Full Idea: There seem to be two producers of movement, either desire or practical intellect, but practical reason begins in desire. | |
| From: Aristotle (De Anima [c.329 BCE], 433a16) |
| 24044 | Movement can be intrinsic (like a ship) or relative (like its sailors) [Aristotle] |
| Full Idea: It is not necessary for what moves things to be itself moving. For a thing can be moving in two ways - with reference to something else, or intrinsically. A ship is moving intrinsically, but sailors move because they are in something that is moving. | |
| From: Aristotle (De Anima [c.329 BCE], 406a03) | |
| A reaction: I love the way that Aristotle is desperate to explain the puzzle of movement, yet we just take it for granted. Very illuminating about puzzles. Newton's First Law of Motion. |
| 24064 | If something is pushed, it pushes back [Aristotle] |
| Full Idea: What has pushed something else makes the latter push as well. | |
| From: Aristotle (De Anima [c.329 BCE], 435b30) | |
| A reaction: Aristotle seems to have spotted that this is intrinsic to massive bodies, and is not just friction etc. Newton adds a vector to Aristotle's insight. |
| 24063 | What is born has growth, a prime, and a withering away [Aristotle] |
| Full Idea: What has been born must have growth, a prime of life, and a time of withering away. | |
| From: Aristotle (De Anima [c.329 BCE], 434a23) | |
| A reaction: Modern biologists don't seem much interested in the 'prime of life', but for Aristotle it is crucial, as the fulfilment of a thing's essential nature. Nietzsche would probably agree with Aristotle on this. We dread seeing one period of life as 'superior'. |