60 ideas
19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
Full Idea: Aristotle takes wisdom to come in two forms, the practical and the theoretical, the former of which is good judgement about how to act, and the latter of which is deep knowledge or understanding. | |
From: report of Aristotle (works [c.330 BCE]) by Dennis Whitcomb - Wisdom Intro | |
A reaction: The interesting question is then whether the two are connected. One might be thoroughly 'sensible' about action, without counting as 'wise', which seems to require a broader view of what is being done. Whitcomb endorses Aristotle on this idea. |
1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value. | |
From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26 |
1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos | |
From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95 |
17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
Full Idea: As Kreisel has remarked, what is important is not the existence of mathematical objects, but the objectivity of mathematical statements. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: [see Maddy 2011:115 for the history of this idea] It seems rather unclear where Frege stands on objectivity. Maddy embraces it, following up this idea, and Tyler Burge's fat book on objectivity. |
8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us. | |
From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51 | |
A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'. |
4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined. | |
From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157 | |
A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus? |
10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
Full Idea: A classic reduction is the class of ordered pairs <x,y> being reduced to the class of sets of the form {{x},{x,y}}. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
Full Idea: In 1938 Gödel proved that the Axiom of Choice is consistent with the other axioms of set theory. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
A reaction: Hence people now standardly accept ZFC, rather than just ZF. |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
Full Idea: Zermelo's Axiom of Choice asserts that for any set of non-empty sets that (pairwise) have no elements in common, then there is a set that 'simultaneously chooses' exactly one element from each set. Note that this is an existential claim. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
A reaction: The Axiom is now widely accepted, after much debate in the early years. Even critics of the Axiom turn out to be relying on it. |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
Full Idea: The Axiom of Choice seems clearly true from the Platonistic point of view, independently of how sets may be defined, but is rejected by those who think such existential claims must show how to pick out or define the object claimed to exist. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
A reaction: The typical critics are likely to be intuitionists or formalists, who seek for both rigour and a plausible epistemology in our theory. |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
Full Idea: The Trichotomy Principle (any number is less, equal to, or greater than, another number) turned out to be equivalent to the Axiom of Choice. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
A reaction: [He credits Sierpinski (1918) with this discovery] |
10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
Full Idea: We may suppose that with each set is associated an object as its cardinal number, but we have no systematic way, without appeal to the Axiom of Choice, of selecting a representative set of each cardinality. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
Full Idea: The Axiom of Choice is a pure existence statement, without defining conditions. It was necessary to provide a foundation for Cantor's theory of transfinite cardinals and ordinal numbers, but its nonconstructive character engendered heated controversy. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12 | |
A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit. |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
Full Idea: A structure is said to be a 'model' of an axiom system if each of its axioms is true in the structure (e.g. Euclidean or non-Euclidean geometry). 'Model theory' concerns which structures are models of a given language and axiom system. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
A reaction: This strikes me as the most interesting aspect of mathematical logic, since it concerns the ways in which syntactic proof-systems actually connect with reality. Tarski is the central theoretician here, and his theory of truth is the key. |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
Full Idea: In the late 1950s Tarski and Vaught defined and established basic properties of the relation of elementary equivalence between two structures, which holds when they make true exactly the same first-order sentences. This is fundamental to model theory. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
A reaction: This is isomorphism, which clarifies what a model is by giving identity conditions between two models. Note that it is 'first-order', and presumably founded on classical logic. |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
Full Idea: The Löwenheim-Skolem Theorem, the earliest in model theory, states that if a countable set of sentences in a first-order language has a model, then it has a countable model. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
A reaction: There are 'upward' (sentences-to-model) and 'downward' (model-to-sentences) versions of the theory. |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
Full Idea: Before Tarski's work in the 1930s, the main results in model theory were the Löwenheim-Skolem Theorem, and Gödel's establishment in 1929 of the completeness of the axioms and rules for the classical first-order predicate (or quantificational) calculus. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
Full Idea: Completeness is when, if a sentences holds in every model of a theory, then it is logically derivable from that theory. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
Full Idea: 'Recursion theory' is the subject of what can and cannot be solved by computing machines | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Ch.9) | |
A reaction: This because 'recursion' will grind out a result step-by-step, as long as the steps will 'halt' eventually. |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
Full Idea: In 1936 Church showed that Principia Mathematica is undecidable if it is ω-consistent, and a year later Rosser showed that Peano Arithmetic is undecidable, and any consistent extension of it. | |
From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int IV) |
10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
Full Idea: In the intuitionist view, the notion of an intuitive proof cannot be expected to coincide with that of a proof in a formal system, and Gödel's incompleteness theorem is thus unsurprising from an intuitionist point of view. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
Full Idea: From the intuitionist point of view natural numbers are mental constructions, so their totality is only potential, but it is neverthless a fully determinate totality. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: This could only be if the means of constructing the numbers was fully determinate, so how does that situation come about? |
10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
Full Idea: Dummett distinguishes, roughly, between those concrete objects which can be possible objects of ostension, and abstract objects which can only be referred to by functional expressions whose argument is some other object. | |
From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
A reaction: At least someone has proposed a theory! Hale gives a nice critical discussion of the proposal. It is a moot point whether in the second case, when you pick out the 'other object', you are thereby able to refer to some new abstract object. |
10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
Full Idea: The dichotomy between concrete and abstract objects comes to seem far too crude: to which of the two categories should we assign the Mistral, for instance? | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: He has previously given colours and points as difficult borderline cases. We can generalise this particular problem case as the question of whether a potentiality or possibility is abstract or concrete. |
10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
Full Idea: There is no reason for wanting a sharp distinction between concrete and abstract objects. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: This rather depends on your ontology. If you are happy for reality to be full of weird non-physical entities, then the blurring won't bother you. If the boundary is blurred but still real, it is a very interesting one. |
10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
Full Idea: If abstractions were defined by whether they could affect human sense-organs, light-waves would be concrete but radio waves abstract. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: This is a pretty good baseline example. No account should draw an abstract/concrete line through the electromagnetic spectrum. |
10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
Full Idea: The dictum that a name has meaning only in the context of a sentence repudiates the conception of a special philosophical sense of 'existence', which claims that numbers do not exist while affirming existential statements about them. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: He refers to Frege's Context Principle. Personally I would say you could make plenty of 'affirmations' about arithmetic without them having to be 'existential'. I can say there 'is' a number between 6 and 8, without huge existential claims. |
10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
Full Idea: What objects we recognise the world as containing depends upon the structure of our language. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: The background to this claim is the Fregean idea that there are no objects for us if there are no concepts. Dummett is adding that there are no concepts if there is no language. I say animals have concepts and recognise objects. |
10532 | We can understand universals by studying predication [Dummett] |
Full Idea: It is by the study of the character of predication that we shall come to understand the essential nature of universals. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: I haven't founded a clearer manifesto for linguistic philosophy than that! Personally I find it highly dubious, given the shifting nature of linguistic forms, and the enormous variation between remote languages. |
10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
Full Idea: The original sense of 'nominalism' is the denial of universals, that is the denial of reference to either predicates or to abstract nouns. The modern sense (of Nelson Goodman) is the denial of the existence of abstract objects. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: This is why you find loads of modern philosophers vigorous attacking nominalism, only to gradually realise that they don't actually believe in universals, as traditionally understood. It's hard to keep up, when words shift their meaning. |
10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
Full Idea: We cannot simply distinguish concrete objects as objects of ostension, if it literally involves a pointing gesture, as this would exclude a colourless gas, a sound or a smell. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: He shifts to verbal ostension as a result, since we can talk of 'this smell'. On p.491 he suggests that affecting our senses is a sufficient condition to be concrete, but not a necessary one. |
10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
Full Idea: To say that an abstract object cannot be the cause of change seems plausible enough, but the thesis that it cannot be the subject of change is problematic. The shape of an object can change, or the number of sheep on a hill. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: This seems a pretty crucial difficulty for the standard notion of abstracta as non-causal. I would say that it is an acid which could eat away the whole edifice if you thought about it for long enough. He shifts shape-change to the physical object. |
10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
Full Idea: For intuitionists, it ceases to be true that abstract objects are not observable and cannot be involved in causal interaction, since such intuitive apprehension of them may be regarded as just such an interaction. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: I would say that since abstract objects can be involved in causal interactions, in the mind, and since the mind is entirely physical (oh yes), this makes abstract objects entirely physical, which may come as a shock to some people. |
10543 | Abstract objects must have names that fall within the range of some functional expression [Dummett] |
Full Idea: For an object to be abstract, we require only that an understanding of any name of that object involves a recognition that the object is in the range of some functional expression. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: I'm not sure I understand this, but a function must involve a relation between some objects, such that a unique object is consequently picked out. |
10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
Full Idea: Dummett's best argument for excluding abstract nouns relies upon the entirely Fregean requirement that with any genuine singular term there must be associated a criterion of identity. | |
From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Bob Hale - Abstract Objects Ch.2.II | |
A reaction: This sounds a rather rigid test. Must the criteria be logically precise, or must you just have some vague idea of what you are talking about? |
10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
Full Idea: An abstract object can be referred to only by means of a verbal phrase, ...and no confrontation with an abstract object is possible. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: So does this mean that animals are incapable of entertaining abstract concepts? Some research suggests otherwise. Does a dog understand what a 'walk' is, without use of the word? Dummett disgracefully neglects animals in his theories. |
10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
Full Idea: The notion of 'object', as it is now commonly used in philosophical contexts, is a modern notion, one first introduced by Frege. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: If we say 'objects exist', I think it is crucial that if we are going to introduce 'object' as a term of art, then 'exist' had better stick to normal usage. If that drifts into a term of art as well (incorporating 'subsist', or some such) we have no hope! |
13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
Full Idea: Aristotle's discussion of the unmoved mover and of the soul confirms the suspicion that form, when it is not thought of as the object represented in a definition, plays the role of the ultimate mereological atom within his system. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 6.6 | |
A reaction: Aristotle is concerned with which things are 'divisible', and he cites these two examples as indivisible, but they may be too unusual to offer an actual theory of how Aristotle builds up wholes from atoms. He denies atoms in matter. |
13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
Full Idea: Thus in Aristotle we may think of an object's formal components as a sort of recipe for how to build wholes of that particular kind. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.5 | |
A reaction: In the elusive business of pinning down what Aristotle means by the crucial idea of 'form', this analogy strikes me as being quite illuminating. It would fit DNA in living things, and the design of an artifact. |
5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
Full Idea: Aristotle thinks that in general we have knowledge or understanding when we grasp causes, and he distinguishes three fundamental types of knowledge - theoretical, practical and productive. | |
From: report of Aristotle (works [c.330 BCE]) by Alan D. Code - Aristotle | |
A reaction: Productive knowledge we tend to label as 'knowing how'. The centrality of causes for knowledge would get Aristotle nowadays labelled as a 'naturalist'. It is hard to disagree with his three types, though they may overlap. |
11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
Full Idea: The notion of a priori truth is conspicuously absent in Aristotle. | |
From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
A reaction: Cf. Idea 11240. |
23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
Full Idea: Aristotle is a rationalist …but reason for him is a disposition which we only acquire over time. Its acquisition is made possible primarily by perception and experience. | |
From: report of Aristotle (works [c.330 BCE]) by Michael Frede - Aristotle's Rationalism p.173 | |
A reaction: I would describe this process as the gradual acquisition of the skill of objectivity, which needs the right knowledge and concepts to evaluate new experiences. |
16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
Full Idea: Since Aristotle generally prefers a metaphysical theory that accords with common intuitions, he frequently relies on facts about language to guide his metaphysical claims. | |
From: report of Aristotle (works [c.330 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.5 | |
A reaction: I approve of his procedure. I take intuition to be largely rational justifications too complex for us to enunciate fully, and language embodies folk intuitions in its concepts (especially if the concepts occur in many languages). |
16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
Full Idea: Plato's unity of science principle states that all - legitimate - sciences are ultimately about the Forms. Aristotle's principle states that all sciences must be, ultimately, about substances, or aspects of substances. | |
From: report of Aristotle (works [c.330 BCE], 1) by Julius Moravcsik - Aristotle on Adequate Explanations 1 |
11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
Full Idea: For Aristotle things which explain (the explanantia) are facts, which should not be associated with the modern view that says explanations are dependent on how we conceive and describe the world (where causes are independent of us). | |
From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 2.1 | |
A reaction: There must be some room in modern thought for the Aristotelian view, if some sort of robust scientific realism is being maintained against the highly linguistic view of philosophy found in the twentieth century. |
3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
Full Idea: The standard Aristotelian doctrine of species and genus in the theory of anything whatever involves specifying what the thing is in terms of something more general. | |
From: report of Aristotle (works [c.330 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.10 |
12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
Full Idea: The view that essential properties are those in virtue of which other significant properties of the subjects under investigation can be explained is encountered repeatedly in Aristotle's work. | |
From: report of Aristotle (works [c.330 BCE]) by Joan Kung - Aristotle on Essence and Explanation IV | |
A reaction: What does 'significant' mean here? I take it that the significant properties are the ones which explain the role, function and powers of the object. |
23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
Full Idea: Aristotle, and also the Stoics, denied rationality to animals. …The Platonists, the Pythagoreans, and some more independent Aristotelians, did grant reason and intellect to animals. | |
From: report of Aristotle (works [c.330 BCE]) by Richard Sorabji - Rationality 'Denial' | |
A reaction: This is not the same as affirming or denying their consciousness. The debate depends on how rationality is conceived. |
19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
Full Idea: Real functions map objects onto objects, but concepts map objects onto truth value, ...so Dummett says that concepts are not functions, but that they have a 'functional character'. | |
From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Donald Davidson - Truth and Predication 6 |
10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
Full Idea: Since we cannot pick an abstract object out from its surrounding, all that we need to master is the use of statements of identity between objects of a certain kind. | |
From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
A reaction: This is the necessary Fregean preliminary to using a principle of abstraction to identify two objects which are abstract (when the two objects are in an equivalence relation). Presumably circular squares and square circles are identical? |
10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
Full Idea: Dummett claims that a realistic conception of reference can be sustained for concrete objects (possible objects of ostension), but breaks down for (putative) names of (pure) abstract objects. | |
From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
A reaction: An extremely hard claim to evaluate, because a case must first be made for abstract objects which are fundamentally different in kind. Realistic reference must certainly deal with these hard cases. Field rejects Dummett's abstract points. |
11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
Full Idea: The notion of analytic truth is conspicuously absent in Aristotle. | |
From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
A reaction: Cf. Idea 11239. |
6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
Full Idea: To the best of my knowledge (and somewhat to my surprise), Aristotle never actually says that man is a rational animal; however, he all but says it. | |
From: report of Aristotle (works [c.330 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
A reaction: When I read this I thought that this database would prove Fogelin wrong, but it actually supports him, as I can't find it in Aristotle either. Descartes refers to it in Med.Two. In Idea 5133 Aristotle does say that man is a 'social being'. But 22586! |
11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
Full Idea: It is the mark of an educated mind to be able to entertain an idea without accepting it. | |
From: Aristotle (works [c.330 BCE]) | |
A reaction: The epigraph on a David Chalmers website. A wonderful remark, and it should be on the wall of every beginners' philosophy class. However, while it is in the spirit of Aristotle, it appears to be a misattribution with no ancient provenance. |
3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
Full Idea: Aristotle was asked how much educated men were superior to those uneducated; "As much," he said, "as the living are to the dead." | |
From: report of Aristotle (works [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 05.1.11 |
8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent. | |
From: report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3 | |
A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle. |
12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter. | |
From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2 | |
A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now. |
22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |
Full Idea: Aristotle said that the conception of gods arose among mankind from two originating causes, namely from events which concern the soul and from celestial phenomena. | |
From: report of Aristotle (works [c.330 BCE], Frag 10) by Sextus Empiricus - Against the Physicists (two books) I.20 | |
A reaction: The cosmos suggests order, and possible creation. What do events of the soul suggest? It doesn't seem to be its non-physical nature, because Aristotle is more of a functionalist. Puzzling. (It says later that gods are like the soul). |