108 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. |
| 20121 | Grammar only reveals popular metaphysics [Nietzsche] |
| Full Idea: The snares of grammar are the metaphysics of the people. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: If you have this elitist view of metaphysics, then linguistic analysis is just a branch of anthropology. |
| 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? |
| 24082 | Is the will to truth the desire to avoid deception? [Nietzsche] |
| Full Idea: This unconditional will to truth: what is it? Is it the will not to let oneself be deceived? Is it the will not to deceive? | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §344) | |
| A reaction: He is hunting for the evolutionary origin of the love of truth, in the needs of a community. In that sense, I would have thought it was just the pressure to get the facts right, because error is dangerous. Nice thought, though. |
| 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. |
| 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) |
| 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. |
| 20360 | We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche] |
| Full Idea: We Germans are Hegelians insofar as we instinctively attribute a deeper sense and richer value to becoming and development than to what 'is'. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §357) | |
| A reaction: I always doubt Nietzsche's claims about 'we Germans' or 'we philosophers'. They say that, intellectually, everyone is either French or German, and my immediate response was to embrace being German. So becoming is where it's 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. |
| 24077 | Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche] |
| Full Idea: Necessity is supposed to be the cause of something coming to be: in truth it is often only an effect of what has come to be. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §205) | |
| A reaction: This sounds like an account of the traditional idea of destiny - which sees inevitability in some major event, which was previously unpredictable. |
| 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. |
| 20126 | The strength of knowledge is not its truth, but its entrenchment in our culture [Nietzsche] |
| Full Idea: The strength of knowledge does not depend on its degree of truth but on its age, on the degree to which it has been incoporated, in its character as a condition of life. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §110) | |
| A reaction: This seems to be the rather modern idea (in Foucault, perhaps) of knowledge as a central component of culture, rather than as an eternal revelation of facts. Note that he is talking about its 'strength', not its veracity or degree of support. |
| 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. |
| 20119 | We became increasingly conscious of our sense impressions in order to communicate them [Nietzsche] |
| Full Idea: The emergence of our sense impressions into our consciousness, the ability to fix them and, as it were, exhibit them externally, increased proportionally with the need to communicate them to others by means of signs. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: He says in the same section that such ideas (plus his thoughts on consciousness) are the essence of his 'Perspectivism'. In effect, knowledge is not an individual activity, but a team game |
| 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). |
| 20122 | We have no organ for knowledge or truth; we only 'know' what is useful to the human herd [Nietzsche] |
| Full Idea: We simply lack any organ for knowledge, for 'truth'; we 'know' [das Erkennen] (or believe or imagine) just as much as may be useful in the interests of the human herd, the species; and this 'utility' is ultimately also a mere belief. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: [Section §354 is fascinating!] An odd idea, that we can only have truth is we have an 'organ' for it. It seems plausible that the whole brain is a truth machine. This seems like pure pragmatism, with all its faults. Falsehoods can be useful. |
| 4423 | We assume causes, geometry, motion, bodies etc to live, but they haven't been proved [Nietzsche] |
| Full Idea: We have fixed up a world for ourselves in which we can live, with bodies, lines, planes, causes, motion and form; without these articles of faith nobody would endure life. But that does not mean they have been proved. Life is no argument. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §121) | |
| A reaction: It is hard to disagree. A lot of recent thought suggests that they are Hume's 'natural beliefs', like truth and induction, which simply can't be proved. 'Unprovable' does not mean 'incorrect', however. |
| 6579 | Nietzsche's perspectivism says our worldview depends on our personality [Nietzsche, by Fogelin] |
| Full Idea: Nietzsche recommends an extreme version of perspectivism in holding that a person's view of the world is a function of that person's life-affirming (Heraclitean) or life-denying (Parmenidean) personality. | |
| From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882]) by Robert Fogelin - Walking the Tightrope of Reason Ch.3 | |
| A reaction: Fogelin recommends Nehamas on this topic. I am not convinced Nietzsche takes such an individual view as is implied here. See Idea 4420, for example. This view is in tune with Charles Taylor's view that our values shape our understanding of our selves. |
| 24083 | It would be absurd to say we are only permitted our own single perspective [Nietzsche] |
| Full Idea: I think today we are at least far removed from the ridiculous immodesty of decreeing from our corner that one is permitted to have perspectives only from this corner. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §374) | |
| A reaction: He goes on to speculate about the possibility of infinite perspectives, most of them unknowable to us. But Nietzsche was not a simple relativism. The obvious concept needed to accompany a many-perspectives view is consensus. |
| 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. |
| 20115 | All of our normal mental life could be conducted without consciousness [Nietzsche] |
| Full Idea: We could think, feel, will and remember, and we could also 'act', and yet none of this would have to enter our consciousness. The whole of life would be possible without, as it were, seeing itself in a mirror. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: He credits Leibniz with this line of thought. Nowadays the unconscious aspects of thought are a commonplace, not just from Freud, but from neuroscience. We have no idea how conscious other animals are. Nietzsche attributes consciousness to communication. |
| 20117 | Only the need for communication has led to consciousness developing [Nietzsche] |
| Full Idea: I surmise that consciousness has developed only under the pressure of the need for communication; ...consciousness is really only a net of communication between human beings. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: An interesting speculation, well ahead of its time. Given that thought does not require consciousness, as he claims, it is not quite clear why communication needs it. Presumably two robots can communicate. But Idea 20118 is good. |
| 20118 | Only our conscious thought is verbal, and this shows the origin of consciousness [Nietzsche] |
| Full Idea: Only conscious thinking takes the form of words, which is to say signs of communication, and this fact uncovers the origin of consciousness. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: Chicken-and-egg question here. Persinally I take consciousnes to be associated with meta-thought, which bestows huge power, and I take language to arise from meta-thought. |
| 20116 | Most of our lives, even the important parts, take place outside of consciousness [Nietzsche] |
| Full Idea: By far the greatest proportion of our life takes place without this mirroring effect [of consciousness]; and this is true even of our thinking, feeling and willing life, however offensive this may sound to older philosophers. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: Nietzsche didn't just hint at the possibility of a (Freudian) sub-conscious - he was whole-heartedly committed to it, and Freud gave him credit for it. I think philosophers are only just beginning to digest this crucial idea. |
| 20120 | Whatever moves into consciousness becomes thereby much more superficial [Nietzsche] |
| Full Idea: Whatever becomes conscious becomes by the same token shallow, thin, relatively stupid, general, sign, herd signal; all becoming conscious involves a great and thorough corruption, falsification, reduction to superficialities, and generalisation. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §354) | |
| A reaction: Nietzsche would have made a great speech writer for someone. This vision is increasingly how I see people. It is a view reinforced by modern neuroscience, which suggests that we greatly overestimate the conscious part of ourselves. |
| 2932 | 'Know thyself' is impossible and ridiculous [Nietzsche] |
| Full Idea: "Everybody is farthest away - from himself"; and the maxim "know thyself" addressed to human beings by a god, is almost malicious. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) | |
| A reaction: Expressed with characteristcally Nietzschean brio, but I couldn't agree more, and it is a very important truth. You can only require full self-knowledge if the whole mind is available to be known, and that isn't even remotely the case. |
| 24078 | Thoughts cannot be fully reproduced in words [Nietzsche] |
| Full Idea: Even one's thoughts one cannot reproduce entirely in words. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §244) | |
| A reaction: I suppose this is the germ of Derrida, who seems to see little connection between thought and speech. I take this idea to be entirely correct. Our simplistic view of language reduces the fluidity and many dimensions of thought to a pile of lego bricks. |
| 24081 | Most of our intellectual activity is unconscious [Nietzsche] |
| Full Idea: Only now is the truth dawning on us that the biggest part by far of our intellectual activity takes place unconsciously, and unfelt by us. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §333) | |
| A reaction: Note that this is 'intellectual activity', and just the hidden rumblings of instincts and emotions. I think he is right. Philosophers want to verbalise everything, but I don't think the main insights of philosophical thinking are verbal. |
| 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. |
| 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. |
| 2933 | Why do you listen to the voice of your conscience? [Nietzsche] |
| Full Idea: Why do you listen to the voice of your conscience? | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) | |
| A reaction: Nice question. It is perfectly plausible to say that I seem to feel guilty about doing something, but can't see any reason why I should. |
| 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! |
| 20141 | Higher human beings see and hear far more than others, and do it more thoughtfully [Nietzsche] |
| Full Idea: What distinguishes the higher human being from the lower is that the former see and hear immeasurably more, and see and hear thoughtfully - and precisely this distinguishes human beings from animals, and the higher animals from the lower. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §301) | |
| A reaction: Since most people are well equipped with eyes and ears, I take it that this phenomenon, if true, arises from the 'higher' type of person having more interest in what they experience. |
| 24076 | A morality ranks human drives and actions, for the sake of the herd, and subordinating individuals [Nietzsche] |
| Full Idea: Whenever we encounter a morality we find an estimation and order of rank of human drives and actions. These are always the expression of the needs of a community and herd. The individual is valued only as a function of the herd. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §116) | |
| A reaction: A particularly clear summary of Nietzsche's understanding of modern morality (which he rejects). I tend to see values as what is important, but Nietzsche sees them as a ranking. Could be both. I see the individualism here as existentialist. |
| 22471 | Nietzsche thought it 'childish' to say morality isn't binding because it varies between cultures [Nietzsche, by Foot] |
| Full Idea: Nietzsche was not simply a run-of-the-mill moral relativist. He branded as 'childish' the idea that no morality can be binding because moral valuations are necessarily different among different nations. | |
| From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882], §345) by Philippa Foot - Nietzsche's Immoralism p.146 | |
| A reaction: Relativists about knowledge and morality are inclined to take quotations from Nietzsche out of context. The existence of this database probably exacerbates such intellectual wickedness. Get a feeling for the whole thinker! |
| 2935 | No two actions are the same [Nietzsche] |
| Full Idea: There neither are nor can be actions which are the same. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) |
| 20198 | Many virtues are harmful traps, but that is why other people praise them [Nietzsche] |
| Full Idea: Virtues like industriousness, obedience, chastity, filial piety and justice are usually harmful to those who possess them. When you have a real, whole virtue you are its victim. But your neighbour praises your virtue precisely on that account. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §021) | |
| A reaction: This is the conspiracy theory of virtue. We want people to do menial or undesirable jobs, so we dress them up as wonderful virtues, and make people feel good for possessing them. There must be some truth in this. |
| 4275 | You cannot advocate joyful wisdom while rejecting pity, because the two are complementary [Scruton on Nietzsche] |
| Full Idea: Pity and good cheer are complementary, ..so there is something contradictory in a philosophy that advocates joyful wisdom, while slandering pity as the enemy of the higher life. | |
| From: comment on Friedrich Nietzsche (The Gay (Joyful) Science [1882]) by Roger Scruton - Animal Rights and Wrongs p.35 | |
| A reaction: A good objection to Nietzsche. He has a rather solipsistic view of joyful exuberance etc., and fails to realise how social such things must be. In that, Nietzsche was caught in the romantic tradition of Wordsworth and co. |
| 2934 | To see one's own judgement as a universal law is selfish [Nietzsche] |
| Full Idea: It is selfish to experience one's own judgement as a universal law. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §335) |
| 24080 | We should give style to our character - by applying an artistic plan to its strengths and weaknesses [Nietzsche] |
| Full Idea: One thing is essential - 'giving style' to one's character. It is practised by the one who surveys everything that his nature offers in strengths and weaknesses, and subjects it to an artistic plan until each thing appears as art and reason. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §290) | |
| A reaction: Clearly existentialist, in its proposal to change one's own character. I invite the reader to consider applying this to themselves - and I submit that it is an impossible project. Nice thought, though. |
| 20125 | The ethical teacher exists to give purpose to what happens necessarily and without purpose [Nietzsche] |
| Full Idea: That what happens necessarily, spontaneously and without any purpose, may henceforth appear to be done for some purpose, and strike man as rational and an ultimate commandment, the ethical teacher comes on stage, as teacher of the purpose of existence. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §001) | |
| A reaction: This doesn't look like much of a solution to the problem of nihilism, unless the teacher plants an idea in us which endures and grows. Nietzsche's 'eternal recurrence' was supposed to be just such an idea. |
| 9306 | To ward off boredom at any cost is vulgar [Nietzsche] |
| Full Idea: To ward off boredom at any cost is vulgar. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §042) | |
| A reaction: Ignoring 'vulgar', this is a nice thought. Do affluent retired people now travel so much because they are terrified of boredom? What would they end up doing if they stayed at home and lived through the boredom to something else? |
| 24079 | The best life is the dangerous life [Nietzsche] |
| Full Idea: The secret of harvesting the greatest fruitfulness and the greatest enjoyment from existence is: live dangerously! | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §283) | |
| A reaction: I treasured this quotation when I was 17, but failed to live up to it. |
| 2936 | Imagine if before each of your actions you had to accept repeating the action over and over again [Nietzsche] |
| Full Idea: Suppose a demon were to say to you, "This life as you have lived it, you will have to live once more and innumerable times more". …Then the question in each thing, "Do you desire this once more and innumerable times more?" would lie across your actions. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §341) | |
| A reaction: If you were stuck in nihilistic indifference, this thought might not be enough to rouse you from your torpor. If all possibilities in life are boring, repetition cannot pep it up, or make it any worse. But I still love this idea! |
| 6842 | Nietzsche says facing up to the eternal return of meaninglessness is the response to nihilism [Nietzsche, by Critchley] |
| Full Idea: Nietzsche is overwhelmingly concerned with how to respond to nihilism, and he offers the concept of eternal return; the Overman is one who can affirm over and over that one is equal to meaninglessness, without turning to despair or idols. | |
| From: report of Friedrich Nietzsche (The Gay (Joyful) Science [1882], §342) by Simon Critchley - Interview with Baggini and Stangroom p.192 | |
| A reaction: I agree with Critchley that this is not much of a recipe for ordinary people's lives, and I don't even find it very congenial for a tough-minded philosopher. We should make the best of the cards we are dealt, however feeble they may appear. |
| 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. |
| 2931 | God is dead, and we have killed him [Nietzsche] |
| Full Idea: God is dead. God remains dead. And we have killed him. | |
| From: Friedrich Nietzsche (The Gay (Joyful) Science [1882], §125) |
| 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). |