116 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. |
| 5196 | Philosophy is a department of logic [Ayer] |
| Full Idea: Philosophy is a department of logic. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: Personally I would invert that. Philosophy is concerned with human rationality, of which precise logic appears to be a rather limited subdivision. I see philosophy as the 'master' subject, not the 'servant' subject (as Locke had implied). |
| 5189 | Philosophers should abandon speculation, as philosophy is wholly critical [Ayer] |
| Full Idea: We can overthrow speculative philosophy, and see that the function of philosophy is wholly critical. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: This seems to imply that we CAN speculate, which appeared to be rendered impossible by the verification principle. Personally I think speculation is central to philosophy, but Ayer should always stand as a warning against bogus truth-claims. |
| 7919 | Humeans rejected the a priori synthetic, and so rejected even Kantian metaphysics [Ayer, by Macdonald,C] |
| Full Idea: Thinkers from Hume to the logical positivists took exception to Kant's view that some synthetic propositions could be known a priori, and so rejected the possibility of metaphysics as Kant conceived of it. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936]) by Cynthia Macdonald - Varieties of Things Ch.1 | |
| A reaction: See Idea 7918 for Kant's epistemological view of metaphysics. This strikes me as a big misunderstanding by empiricists, even though they are quite right to insist on evidence and proof. Metaphysics is essential, but its excess is the worst nonsense. |
| 5195 | Critics say analysis can only show the parts, and not their distinctive configuration [Ayer] |
| Full Idea: Critics say an analyst is obliged by his atomistic metaphysics to regard an object consisting of parts a, b, c and d in a distinctive configuration as being simply a+b+c+d, and thus giving an entirely false account of its nature. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: Ayer refers the critics to gestatl psychology. Personally I prefer to talk about the ontology rather than the psychology. If we include (as Russell suggests) relations as part of the analysis, there seems to be no problem. |
| 5179 | Philosophy deals with the questions that scientists do not wish to handle [Ayer] |
| Full Idea: If there are any questions which science leaves it to philosophy to answer, a straightforward process of elimination must lead to their discovery. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This is characteristic of the feeble-mindedness that British philosophy slipped into in the age of Wittgenstein, and for a while thereafter. Personally I regard scientists as servants, who are sent off on exploratory errands, and must report back. |
| 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 |
| 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? |
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| Full Idea: In a sense, satisfaction is the notion of 'truth in a model', and (as Hodes 1984 elegantly puts it) 'truth in a model' is a model of 'truth'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: So we can say that Tarski doesn't offer a definition of truth itself, but replaces it with a 'model' of truth. |
| 4749 | We cannot analyse the concept of 'truth', because it is simply a mark that a sentence is asserted [Ayer] |
| Full Idea: When one says that "Queen Anne is dead" is true or false, these terms 'true' and 'false' connote nothing, but function in the sentence simply as marks of assertion and denial, so there is no sense in asking us to analyse the concept of 'truth'. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.5) | |
| A reaction: "I am ill" may be true when you say it, and false when I say it. The word 'true' has a useful function in 'x is true if y'. "If that is true, Freddie, I will hit you". |
| 13643 | Aristotelian logic is complete [Shapiro] |
| Full Idea: Aristotelian logic is complete. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5) | |
| A reaction: [He cites Corcoran 1972] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| Full Idea: If, for every b∈d, a∈b entails that a∈d, the d is said to be 'transitive'. In other words, d is transitive if it contains every member of each of its members. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.2) | |
| A reaction: The alternative would be that the members of the set are subsets, but the members of those subsets are not themselves members of the higher-level set. |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| Full Idea: The axiom of choice is essential for proving the downward Löwenheim-Skolem Theorem. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| Full Idea: Is there a notion of set in the jurisdiction of logic, or does it belong to mathematics proper? | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: It immediately strikes me that they might be neither. I don't see that relations between well-defined groups of things must involve number, and I don't see that mapping the relations must intrinsically involve logical consequence or inference. |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| Full Idea: In set theory it is central to the iterative conception that the membership relation is well-founded, ...which means there are no infinite descending chains from any relation. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.4) |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| Full Idea: The argument behind Russell's paradox shows that in set theory there are logical sets (i.e. classes) that are not iterative sets. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: In his preface, Shapiro expresses doubts about the idea of a 'logical set'. Hence the theorists like the iterative hierarchy because it is well-founded and under control, not because it is comprehensive in scope. See all of pp.19-20. |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| Full Idea: Iterative sets do not exhibit a Boolean structure, because the complement of an iterative set is not itself an iterative set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| Full Idea: A 'well-ordering' of a set X is an irreflexive, transitive, and binary relation on X in which every non-empty subset of X has a least element. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.3) | |
| A reaction: So there is a beginning, an ongoing sequence, and no retracing of steps. |
| 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. |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| Full Idea: There is no question of finding the 'correct' or 'true' logic underlying a part of natural language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: One needs the context of Shapiro's defence of second-order logic to see his reasons for this. Call me romantic, but I retain faith that there is one true logic. The Kennedy Assassination problem - can't see the truth because drowning in evidence. |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| Full Idea: A logic can be seen as the ideal of what may be called 'relative justification', the process of coming to know some propositions on the basis of others. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.3.1) | |
| A reaction: This seems to be the modern idea of logic, as opposed to identification of a set of 'logical truths' from which eternal necessities (such as mathematics) can be derived. 'Know' implies that they are true - which conclusions may not be. |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| Full Idea: Bernays (1918) formulated and proved the completeness of propositional logic, the first precise solution as part of the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.1) |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| Full Idea: In 1910 Weyl observed that set theory seemed to presuppose natural numbers, and he regarded numbers as more fundamental than sets, as did Fraenkel. Dedekind had developed set theory independently, and used it to formulate numbers. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.2) |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| Full Idea: Skolem and Gödel were the main proponents of first-order languages. The higher-order language 'opposition' was championed by Zermelo, Hilbert, and Bernays. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2) |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| Full Idea: Almost all the systems developed in the first part of the twentieth century are higher-order; first-order logic was an afterthought. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| Full Idea: The 'triumph' of first-order logic may be related to the remnants of failed foundationalist programmes early this century - logicism and the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: Being complete must also be one of its attractions, and Quine seems to like it because of its minimal ontological commitment. |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| Full Idea: Tharp (1975) suggested that compactness, semantic effectiveness, and the Löwenheim-Skolem properties are consequences of features one would want a logic to have. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: I like this proposal, though Shapiro is strongly against. We keep extending our logic so that we can prove new things, but why should we assume that we can prove everything? That's just what Gödel suggests that we should give up on. |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| Full Idea: The notion of finitude is explicitly 'built in' to the systems of first-order languages in one way or another. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1) | |
| A reaction: Personally I am inclined to think that they are none the worse for that. No one had even thought of all these lovely infinities before 1870, and now we are supposed to change our logic (our actual logic!) to accommodate them. Cf quantum logic. |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| Full Idea: Shapiro preferred second-order logic to set theory because second-order logic refers only to the relations and operations in a domain, and not to the other things that set-theory brings with it - other domains, higher-order relations, and so forth. | |
| From: report of Stewart Shapiro (Foundations without Foundationalism [1991]) by Shaughan Lavine - Understanding the Infinite VII.4 |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| Full Idea: Three systems of semantics for second-order languages: 'standard semantics' (variables cover all relations and functions), 'Henkin semantics' (relations and functions are a subclass) and 'first-order semantics' (many-sorted domains for variable-types). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: [my summary] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
|
Full Idea:
In 'Henkin' semantics, in a given model |
|
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| Full Idea: In the standard semantics of second-order logic, by fixing a domain one thereby fixes the range of both the first-order variables and the second-order variables. There is no further 'interpreting' to be done. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) | |
| A reaction: This contrasts with 'Henkin' semantics (Idea 13650), or first-order semantics, which involve more than one domain of quantification. |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| Full Idea: The counterparts of Completeness, Compactness and the Löwenheim-Skolem theorems all fail for second-order languages with standard semantics, but hold for Henkin or first-order semantics. Hence such logics are much like first-order logic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: Shapiro votes for the standard semantics, because he wants the greater expressive power, especially for the characterization of infinite structures. |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| Full Idea: It follows from Gödel's incompleteness theorem that the semantic consequence relation of second-order logic is not effective. For example, the set of logical truths of any second-order logic is not recursively enumerable. It is not even arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I don't fully understand this, but it sounds rather major, and a good reason to avoid second-order logic (despite Shapiro's proselytising). See Peter Smith on 'effectively enumerable'. |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| Full Idea: Second-order logic is inherently incomplete, so its semantic consequence relation is not effective. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| Full Idea: It is sometimes difficult to find a formula that is a suitable counterpart of a particular sentence of natural language, and there is no acclaimed criterion for what counts as a good, or even acceptable, 'translation'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) |
| 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. |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| Full Idea: The main role of substitutional semantics is to reduce ontology. As an alternative to model-theoretic semantics for formal languages, the idea is to replace the 'satisfaction' relation of formulas (by objects) with the 'truth' of sentences (using terms). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: I find this very appealing, and Ruth Barcan Marcus is the person to look at. My intuition is that logic should have no ontology at all, as it is just about how inference works, not about how things are. Shapiro offers a compromise. |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| Full Idea: The 'satisfaction' relation may be thought of as a function from models, assignments, and formulas to the truth values {true,false}. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: This at least makes clear that satisfaction is not the same as truth. Now you have to understand how Tarski can define truth in terms of satisfaction. |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| Full Idea: Typically, model-theoretic semantics is formulated in set theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5.1) |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| Full Idea: An axiomatization is 'categorical' if all its models are isomorphic to one another; ..hence it has 'essentially only one' interpretation [Veblen 1904]. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| Full Idea: Categoricity cannot be attained in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.3) |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| Full Idea: A language has the Downward Löwenheim-Skolem property if each satisfiable countable set of sentences has a model whose domain is at most countable. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't employ an infinite model to represent a fact about a countable set. |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| Full Idea: A language has the Upward Löwenheim-Skolem property if for each set of sentences whose model has an infinite domain, then it has a model at least as big as each infinite cardinal. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't have a countable model to represent a fact about infinite sets. |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorems mean that no first-order theory with an infinite model is categorical. If Γ has an infinite model, then it has a model of every infinite cardinality. So first-order languages cannot characterize infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: So much of the debate about different logics hinges on characterizing 'infinite structures' - whatever they are! Shapiro is a leading structuralist in mathematics, so he wants second-order logic to help with his project. |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| Full Idea: The Upward Löwenheim-Skolem theorem fails (trivially) with substitutional semantics. If there are only countably many terms of the language, then there are no uncountable substitution models. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: Better and better. See Idea 13674. Why postulate more objects than you can possibly name? I'm even suspicious of all real numbers, because you can't properly define them in finite terms. Shapiro objects that the uncountable can't be characterized. |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| Full Idea: A logic is 'weakly sound' if every theorem is a logical truth, and 'strongly sound', or simply 'sound', if every deduction from Γ is a semantic consequence of Γ. Soundness indicates that the deductive system is faithful to the semantics. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: Similarly, 'weakly complete' is when every logical truth is a theorem. |
| 13628 | We can live well without completeness in logic [Shapiro] |
| Full Idea: We can live without completeness in logic, and live well. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: This is the kind of heady suggestion that American philosophers love to make. Sounds OK to me, though. Our ability to draw good inferences should be expected to outrun our ability to actually prove them. Completeness is for wimps. |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| Full Idea: It is sometimes said that non-compactness is a defect of second-order logic, but it is a consequence of a crucial strength - its ability to give categorical characterisations of infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: The dispute between fans of first- and second-order may hinge on their attitude to the infinite. I note that Skolem, who was not keen on the infinite, stuck to first-order. Should we launch a new Skolemite Crusade? |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| Full Idea: Compactness is a corollary of soundness and completeness. If Γ is not satisfiable, then, by completeness, Γ is not consistent. But the deductions contain only finite premises. So a finite subset shows the inconsistency. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: [this is abbreviated, but a proof of compactness] Since all worthwhile logics are sound, this effectively means that completeness entails compactness. |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| Full Idea: A logical language is 'semantically effective' if the collection of logically true sentences is a recursively enumerable set of strings. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| Full Idea: 'Definitions' of integers as pairs of naturals, rationals as pairs of integers, reals as Cauchy sequences of rationals, and complex numbers as pairs of reals are reductive foundations of various fields. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.1) | |
| A reaction: On p.30 (bottom) Shapiro objects that in the process of reduction the numbers acquire properties they didn't have before. |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| Full Idea: The main problem of characterizing the natural numbers is to state, somehow, that 0,1,2,.... are all the numbers that there are. We have seen that this can be accomplished with a higher-order language, but not in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| Full Idea: By convention, the natural numbers are the finite ordinals, the integers are certain equivalence classes of pairs of finite ordinals, etc. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.3) |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| Full Idea: The 'continuum' is the cardinality of the powerset of a denumerably infinite set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.2) |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| Full Idea: Few theorists consider first-order arithmetic to be an adequate representation of even basic number theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5 n28) | |
| A reaction: This will be because of Idea 13656. Even 'basic' number theory will include all sorts of vast infinities, and that seems to be where the trouble is. |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| Full Idea: There are sets of natural numbers definable in set-theory but not in arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.3.3) |
| 5202 | Maths and logic are true universally because they are analytic or tautological [Ayer] |
| Full Idea: The principles of logic and mathematics are true universally simply because we never allow them to be anything else; …in other words, they are analytic propositions, or tautologies. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is obviously a very appealing idea, but it doesn's explain WHY we have invented these particular tautologies (which seem surprisingly useful). The 'science of patterns' can be empirical and a priori and useful (but not tautological). |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| Full Idea: It is claimed that aiming at a universal language for all contexts, and the thesis that logic does not involve a process of abstraction, separates the logicists from algebraists and mathematicians, and also from modern model theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I am intuitively drawn to the idea that logic is essentially the result of a series of abstractions, so this gives me a further reason not to be a logicist. Shapiro cites Goldfarb 1979 and van Heijenoort 1967. Logicists reduce abstraction to logic. |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| Full Idea: I extend Quinean holism to logic itself; there is no sharp border between mathematics and logic, especially the logic of mathematics. One cannot expect to do logic without incorporating some mathematics and accepting at least some of its ontology. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I have strong sales resistance to this proposal. Mathematics may have hijacked logic and warped it for its own evil purposes, but if logic is just the study of inferences then it must be more general than to apply specifically to mathematics. |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| Full Idea: Some authors (Poincaré and Russell, for example) were disposed to reject properties that are not definable, or are definable only impredicatively. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I take Quine to be the culmination of this line of thought, with his general rejection of 'attributes' in logic and in metaphysics. |
| 6523 | Positivists regard ontology as either meaningless or stipulated [Ayer, by Robinson,H] |
| Full Idea: Positivists tend to be prejudiced against ontology, regarding very general questions about what sort of things exist either as meaningless, or as questions to be settled by stipulation. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936]) by Howard Robinson - Perception IX.4 | |
| A reaction: So much the worse for positivists, because they are missing all the fun. I consider one of the central activities of philosophy to be speculating about explanations. Ontology is at the heart of what explanation aims at. |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| Full Idea: Properties are often taken to be intensional; equiangular and equilateral are thought to be different properties of triangles, even though any triangle is equilateral if and only if it is equiangular. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: Many logicians seem to want to treat properties as sets of objects (red being just the set of red things), but this looks like a desperate desire to say everything in first-order logic, where only objects are available to quantify over. |
| 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. |
| 5183 | Only tautologies can be certain; other propositions can only be probable [Ayer] |
| Full Idea: No proposition, other than a tautology, can possibly be anything more than a probable hypothesis. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: A nice clear empiricist rejection of all attempts to assert necessary truths about nature. This also seems to be a rejection of empiricist foundationalism. A problem case seems to be introspective observations, which seem irrefutable and obvious. |
| 6525 | Logical positivists could never give the sense-data equivalent of 'there is a table next door' [Robinson,H on Ayer] |
| Full Idea: Logical positivist phenomenalism has few supporters these days; ..no one ever seemed clear what the sense-datum equivalent of 'there is a table in the next room' could be. | |
| From: comment on A.J. Ayer (Language,Truth and Logic [1936]) by Howard Robinson - Perception IX.4 | |
| A reaction: But do the critics know what they mean by 'there is a table in the next room'? Does it just mean 'I am hoping there is'? You can't refer to the table in the next room without sticking your ontological neck out - and that is 'best explanation'. |
| 5170 | Material things are constructions from actual and possible occurrences of sense-contents [Ayer] |
| Full Idea: The existence of a material thing is defined in terms of the actual and possible occurrence of the sense-contents which constitute it as a logical construction. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: Obviously we need 'possible' experiences so that unperceived trees can still exist, but it is a can of worms. Is speculation about a possible world an account of possible experiences? Realists want to know WHY we think certain experiences are possible. |
| 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. |
| 5198 | We could verify 'a thing can't be in two places at once' by destroying one of the things [Ierubino on Ayer] |
| Full Idea: It is possible to challenge the proposition 'a material thing cannot be in two places at once' empirically; if you destroy one object, the other should also instantly be destroyed if they are a single thing. | |
| From: comment on A.J. Ayer (Language,Truth and Logic [1936], Ch.2) by Virgil Ierubino - works | |
| A reaction: This leaves us having to decide whether the proposition is metaphysically necessary, or is empirical, or is tautological. This idea inclines me towards the view that it is empirical. Imagine two 'separate' objects which responded identically to stimuli. |
| 2619 | Whether geometry can be applied to reality is an empirical question outside of geometry [Ayer] |
| Full Idea: Whether a geometry can be applied to the actual physical world or not, is an empirical question which falls outside the scope of the geometry itself. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is a key objection to rationalism by empiricists. You may say that geometry applies to your car, but your car may have been pulverised while you were talking. Why, though, did Einstein find non-Euclidean geometry so useful? |
| 5197 | By changing definitions we could make 'a thing can't be in two places at once' a contradiction [Ayer] |
| Full Idea: The proposition that 'a material thing cannot be in two places at once' is not empirical at all, but linguistic; ..we could so alter our definitions that the proposition came to express a self-contradiction instead of a necessary truth. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: This seems a striking anticipation of Quine's famous challenge to the analytic/synthetic distinction. |
| 5204 | To say that a proposition is true a priori is to say that it is a tautology [Ayer] |
| Full Idea: To say that a proposition is true a priori is to say that it is a tautology. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is Ayer's splendidly clearcut anti-rationalism. However, one might concede that one cannot know a priori about remote possible worlds (though I'm not so sure), but still claim a priori extrapolations from our current experiences. |
| 6524 | Positivists prefer sense-data to objects, because the vocabulary covers both illusions and perceptions [Ayer, by Robinson,H] |
| Full Idea: Positivists prefer the sense-datum vocabulary because it is more inclusive than physical object vocabulary; it can report after-images, hallucinations, illusions and bodily sensations, as well as veridical perceptions. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936]) by Howard Robinson - Perception IX.4 | |
| A reaction: The assumption of this is that illusions and perceptions are frequently indistinguishable, but that is just nonsense. Illusions usually appeal to one sense only, when you are ill, and in an unclear way. Sensible people know objects when they see them. |
| 5193 | Causal and representative theories of perception are wrong as they refer to unobservables [Ayer] |
| Full Idea: The fact that all causal and representative theories of perception treat material things as if they were unobservable entities entitles us to rule them out a priori. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: It seems to me that we can accept a causal/representative account of perception if we think of it in terms of 'best explanation' rather than observables. Explanation requires speculation, which logical positivists can't cope with. |
| 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. |
| 5200 | The main claim of rationalism is that thought is an independent source of knowledge [Ayer] |
| Full Idea: The fundamental tenet of rationalism is that thought is an independent source of knowledge. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: Presumably one should add that thought gives synthetic knowledge. Thought is also an experience, so empiricists will always acknowledge that we could have some knowledge (of thought) by thought alone. |
| 4729 | Empiricism lacked a decent account of the a priori, until Ayer said it was entirely analytic [O'Grady on Ayer] |
| Full Idea: Ayer's gives an account of the a priori (as analytic) that readily meshes with empiricism, and empiricism had long been lacking an adequate account of the a priori | |
| From: comment on A.J. Ayer (Language,Truth and Logic [1936]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: Ayer's logical positivist view was based on Hume's 'relations of ideas', as opposed to 'matters of fact'. Personally I see no reason why some facts about reality shouldn't be self-evident to thought, just as others are self-evident to the senses. |
| 5180 | All propositions (especially 'metaphysics') must begin with the senses [Ayer] |
| Full Idea: One way to attack a metaphysician would be to enquire from what premises his propositions were deduced. Must he not begin, as other men do, with the evidence of his senses? | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This simple idea is the core of empiricism. This is a heavily criticised doctrine, but you must start somewhere. Hume and Russell agreed. Don't forget, though, that Descartes's first move is to reject the senses as untrustworthy. |
| 5169 | My empiricism logically distinguishes analytic and synthetic propositions, and metaphysical verbiage [Ayer] |
| Full Idea: The empiricist doctrine to which we are committed is a logical doctrine concerning the distinction between analytic propositions, synthetic propositions, and metaphysical verbiage. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This is the tough logical positivist version of empiricism. The whole project stumbles on the relationship between a synthetic proposition and its verifying experiences. How close? What of wild speculations? The analytic part is interesting, though. |
| 5185 | It is further sense-experience which informs us of the mistakes that arise out of sense-experience [Ayer] |
| Full Idea: It is further sense-experience which informs us of the mistakes that arise out of sense-experience. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This is a wonderfull plain-spoken challenge to anyone who thinks they can demonstrate facts a priori about reality. 'I see this object in two places at once'? 'This object appears to be both red and green'? |
| 5199 | Empiricism, it is said, cannot account for our knowledge of necessary truths [Ayer] |
| Full Idea: The objection which is commonly brought against empiricism is that it is impossible on empiricist principles to account for our knowledge of necessary truths. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This criticism goes back at least to Leibniz. Ayer's distinctive contribution to empiricism (with help) is to emphasise that we can only know necessities if they are tautologies. Hume always challenged our knowledge of natural necessities. |
| 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 |
| 5190 | The induction problem is to prove generalisations about the future based on the past [Ayer] |
| Full Idea: The problem of induction is (roughly) finding a way to prove that certain empirical generalisations which are derived from past experience will hold good also in the future. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: This doesn't seem to be the only problem. It seems self-evident (since Hume) that you cannot use deductive reasoning to prove that the future will be like the past. In fact, we should obviously be cautious, as things could easily change. |
| 5191 | We can't use the uniformity of nature to prove induction, as that would be circular [Ayer] |
| Full Idea: It is often said that we can justify induction by invoking the uniformity of nature, but that principle merely states (in a misleading fashion) the assumption that past experience is a reliable guide to the future. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2) | |
| A reaction: That is correct, but it seems to me that if you take the uniformity of nature as a provisional unproven axiom, then induction is an account of how rational creatures cope with the situation. If nature ceases to be uniform, our reason cannot cope. |
| 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. |
| 5177 | Other minds are 'metaphysical' objects, because I can never observe their experiences [Ayer] |
| Full Idea: On the view that we are discussing, I must regard other people as metaphysical objects; for it is assumed that their experiences are completely inaccessible to my observation. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: 'Metaphysical' is here a dirty word. This is the strictly empirical view of other minds, which pushes Ayer towards behaviourism on this subject. He should have asked about the 'best explanation' of the behaviour of others'. |
| 5178 | A conscious object is by definition one that behaves in a certain way, so behaviour proves consciousness [Ayer] |
| Full Idea: If I know that an object behaves in every way as a conscious being must, by definition, behave, then I know that it is really conscious. This is an analytical proposition. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This treats the Turing test as proof of consciousness, and is open to all the usual objections to behaviourism. To say behaviour IS consciousness is ridiculous. It just counts as evidence. Presumably Ayer would later have become a functionalist. |
| 5172 | If the self is meaningful, it must be constructed from sense-experiences [Ayer] |
| Full Idea: The self, if it is not to be treated as a metaphysical entity, must be held to be a logical construction out of sense-experiences. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: It is striking how people differ in their reports when they try to see the self by introspection. The self could be beyond sense-experience, and yet still be the best explanation of what we actually DO experience. It is a 'transcendental sensation'? |
| 5173 | Two experiences belong to one self if their contents belong with one body [Ayer] |
| Full Idea: For any two sense-experiences to belong to the sense-history of the same self it is necessary and sufficient that they should contain organic sense-contents which are elements of the same body. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This makes more sense if you are a realist about organic bodies, but less sense if (like Ayer) you define the body in terms of sense-experiences. It is a stab at what is now called 'animalism', but needs an account of brain transplant thought-experiments. |
| 5176 | Empiricists can define personal identity as bodily identity, which consists of sense-contents [Ayer] |
| Full Idea: We have solved Hume's problem by defining personal identity in terms of bodily identity, and bodily identity is to be defined in terms of the resemblance and continuity of sense-contents. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: This is a phenomenalist account of personal identity, so it has no independent account of the body apart from the contents of the mind. Personally I think we must distinguish 'central' mental events from 'peripheral' ones. |
| 5171 | The supposed 'gulf' between mind and matter is based on the senseless concept of 'substances' [Ayer] |
| Full Idea: The problems of bridging the 'gulf' between mind and matter, in knowledge or in action, are all fictitious problems arising out of the senseless metaphysical conception of mind and matter as 'substances'. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.7) | |
| A reaction: He is presumably implying that there is only one 'substance', the stuff of physics, thus voting for Spinoza's dual aspect theory. There could still be a 'gulf', between incommensurable properties, or untranslatable levels of description. |
| 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. |
| 5181 | A sentence is factually significant to someone if they know how to verify its proposition [Ayer] |
| Full Idea: A sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: 'I can't verify it, but I know a bloke who can'? 'If only I could think of a way to verify x'? 'This is unverifiable, but it is the only remaining possibility'? 'X is unverifiable, but it would nice if it was true'? Etc. |
| 5184 | Factual propositions imply (in conjunction with a few other premises) possible experiences [Ayer] |
| Full Idea: The mark of a genuinely factual proposition is that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those premises alone. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: I.Berlin showed that any statement S could pass this test, because if you assert 'S' and 'If S then O', these two statements entail O, which could be some random observation. Verificationism kept meeting problems of this kind. |
| 5186 | Tautologies and empirical hypotheses form the entire class of significant propositions [Ayer] |
| Full Idea: Tautologies and empirical hypotheses form the entire class of significant propositions. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This appears to be false. Possibly the problem is that Ayer takes the whole proposition to be the unit of meaning, but actually meaninfulness only requires that we build up a claim about a possible world from semantic units. Blue bees live on square suns. |
| 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. |
| 5205 | Moral intuition is worthless if there is no criterion to decide between intuitions [Ayer] |
| Full Idea: Unless it is possible to provide some criterion by which one may decide between conflicting intuitions, a mere appeal to intuition is worthless as a test of a proposition's validity. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: It is a bit much to expect a 'proof' of its 'validity'! If moral judgements are reflected in consequences, then reliable intuitions (i.e. wisdom) could be demonstrated by getting it right (for happiness, or flourishing). |
| 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! |
| 23725 | Ayer defends the emotivist version of expressivism [Ayer, by Smith,M] |
| Full Idea: Ayer defends emotivism, which is his own favoured form of expressivism. | |
| From: report of A.J. Ayer (Language,Truth and Logic [1936], Ch.6) by Michael Smith - The Moral Problem 2.1 | |
| A reaction: A helpful distinction of terminology. Expressivism is the broad theory, and emotivism is a sub-type, saying that it is emotions which are expressed. The alternative (such as Prescriptivism) is to express pro- and con- attitudes. |
| 5206 | To say an act is wrong makes no further statement about it, but merely expresses disapproval [Ayer] |
| Full Idea: In adding 'You acted wrongly in…' to 'you stole my money' I am not making any further statement about it; I am simply evincing my moral disapproval of it. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: A basic claim of emotivism. Perhaps an understandable response to (e.g.) Kantian claims that we have duties, but to no one in particular. Most people mean by moral criticism that there will be long-term bad consequences, or virtue is lacking. |
| 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. |
| 5208 | A person with non-empirical attributes is unintelligible. [Ayer] |
| Full Idea: The notion of a person whose essential attributes are non-empirical is not an intelligible notion at all. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: Non-empirical and non-causal are not quite the same thing. A being which never had any effects is a bizarre, and probably pointless, fantasy. A being which affected our world (through ideas, say) but is unobservable is a perfectly good theory. |
| 5187 | When we ascribe an attribute to a thing, we covertly assert that it exists [Ayer] |
| Full Idea: When we ascribe an attribute to a thing, we covertly assert that it exists. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.1) | |
| A reaction: This is an unsurprising endorsement from logical positivism that Kant's claim that the ontological argument is probably tautological is correct. We could of course say "Imagine a non-existent being with dirty toenails". |
| 5207 | If theism is non-sensical, then so is atheism. [Ayer] |
| Full Idea: If the assertion that there is a god is non-sensical, then the atheist's assertion that there is no god is equally non-sensical. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: Ayer urgently needs the concept of 'best explanation'. If we observe only footprints, we infer creatures; if there are no footprints, lack of creatures looks like a good theory. The design argument is perfectly meaningful. |
| 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). |
| 5209 | The 'truths' expressed by theists are not literally significant [Ayer] |
| Full Idea: There cannot be any transcendent truths of religion, for the sentences which the theist uses to express such 'truths' are not literally significant. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.6) | |
| A reaction: Ayer claims that only tautologies or empirically verifiable statements have literal significance. I say speculations, wild theories and fantasies are perfectly meaningful. Nevertheless, the words of many hymns and prayers look like empty rhetoric. |