103 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 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? |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 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? |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 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. |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 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]. |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 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. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 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...] |
| 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) |
| 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) |
| 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) |
| 19722 | We could know the evidence for our belief without knowing why it is such evidence [Mittag] |
| Full Idea: While one might understand the proposition entailed by one's evidence, one might have no idea how or why one's evidence entails it. This seems to imply one is not justified in believing the proposition on the basis of one's evidence. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Evidential') | |
| A reaction: An example might be seen if a layman tours a physics lab. This looks like a serious problem for evidentialism. Once you see why the evidence entails the proposition, you are getting closer to understanding than to knowledge. Explanation. |
| 19723 | Evidentialism can't explain that we accept knowledge claims if the evidence is forgotten [Mittag] |
| Full Idea: If one came to believe p with good evidence, but has since forgotten that evidence, we might think one can continue to believe justifiably, but evidentialism appears unable to account for this. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Forgotten') | |
| A reaction: We would still think that the evidence was important, and we would need to trust the knower's claim that the forgotten evidence was good. So it doesn't seem to destroy the evidentialist thesis. |
| 19720 | Evidentialism concerns the evidence for the proposition, not for someone to believe it [Mittag] |
| Full Idea: Evidentialism is not a theory about when one's believing is justified; it is a theory about what makes one justified in believing a proposition. It is a thesis regarding 'propositional justification', not 'doxastic justification'. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Preliminary') | |
| A reaction: Thus it is entirely about whether the evidence supports the proposition, and has no interest in who believes it or why. Knowledge is when you believe a true proposition which has good support. This could be internalist or externalist? |
| 19721 | Coherence theories struggle with the role of experience [Mittag] |
| Full Idea: Traditional coherence theories seem unable to account for the role experience plays in justification. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Evidence') | |
| A reaction: I'm inclined to say that experience only becomes a justification when it has taken propositional (though not necessarily lingistic) form. That is, when you see it 'as' something. Uninterpreted shape and colour can justify virtually nothing. |
| 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. |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 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) |
| 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. |
| 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) |
| 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'. |