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All the ideas for 'fragments/reports', 'Can Mechanisms Replace Laws of Nature?' and 'Penguin Dictionary of Philosophy'

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43 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Linguistic philosophy approaches problems by attending to actual linguistic usage [Mautner]
     Full Idea: Linguistic philosophy gives careful attention to actual linguistic usage as a method of dealing with problems of philosophy, resulting in either their solution or dissolution.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.318)
     A reaction: This approach is now deeply discredited and unfashionable, and, I think (on the whole), rightly so. Philosophy should aim a little higher in (say) epistemology than merely describing how people use words like 'know' and 'believe' and 'justify'.
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Analytic philosophy studies the unimportant, and sharpens tools instead of using them [Mautner]
     Full Idea: Critics of analytic philosophers accuse them of excessive attention to relatively unimportant matters, and of being more interested in sharpening tools than in using them.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.111)
     A reaction: The last part is a nice comment. Both criticisms seem to me to contain some justice, but recently things have improved (notably in the new attention paid by analytical philosophy to metaphysics). In morality analytic philosophy seems superior.
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
The 'hermeneutic circle' says parts and wholes are interdependent, and so cannot be interpreted [Mautner]
     Full Idea: The 'hermeneutic circle' consists in the fact that an interpretation of part of a text requires a prior understanding of the whole, and the interpretation of the whole requires a prior understanding of its parts.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.247)
     A reaction: This strikes me as a benign circle, solved the way Aristotle solves the good man/good action circle. You make a start somewhere, like a child learning to speak, and work your way into the circle. Not really a problem.
2. Reason / D. Definition / 4. Real Definition
'Real' definitions give the essential properties of things under a concept [Mautner]
     Full Idea: A 'real definition' (as opposed to a linguistic one) is a statement which gives the essential properties of the things to which a given concept applies.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], 'definition')
     A reaction: This is often seen as old-fashioned, Aristotelian, and impossible to achieve, but I like it and aspire to it. One can hardly be precise about which properties are 'essential' to something, but there are clear cases. Your 'gold' had better not be brass.
2. Reason / D. Definition / 7. Contextual Definition
'Contextual definitions' replace whole statements, not just expressions [Mautner]
     Full Idea: Usually in a definition the definiens (definition) can replace the definiendum (expression defined), but in a 'contextual definition' only the whole statement containing the definiens can replace the whole statement containing the definiendum.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], 'definition')
     A reaction: These definitions are crucial to Frege's enterprise in the 'Grundlagen'. Logicians always want to achieve definition with a single neat operation, but in ordinary language we talk around a definition, giving a variety of possibilities (as in teaching).
2. Reason / D. Definition / 9. Recursive Definition
Recursive definition defines each instance from a previous instance [Mautner]
     Full Idea: An example of a recursive definition is 'y is an ancestor of x' is defined as 'y is a parent of x, or y is a parent of an ancestor of x'.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], 'definition')
     A reaction: From this example I guess that 'ancestor' means 'friend'. Or have I misunderstood? I think we need to define 'grand-parent' as well, and then offer the definition of 'ancestor' with the words 'and so on...'. Essentially, it is mathematical induction.
2. Reason / D. Definition / 10. Stipulative Definition
A stipulative definition lays down that an expression is to have a certain meaning [Mautner]
     Full Idea: A stipulative definition lays down that a given linguistic expression is to have a certain meaning; this is why they cannot be said to be correct or incorrect.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], 'definition')
     A reaction: These are uncontroversial when they are explicitly made in writing by a single person. The tricky case is where they are implicitly made in conversation by a community. After a century or two these look like facts, their origin having been lost.
2. Reason / D. Definition / 11. Ostensive Definition
Ostensive definitions point to an object which an expression denotes [Mautner]
     Full Idea: Ostensive definitions explain what an expression means by pointing to an object, action, event, etc. denoted by the expression.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], 'definition')
     A reaction: These will need some context. If I define 'red' simply by pointing to a red square, you might conclude that 'red' means square. If I point to five varied red objects, you have to do the work of spotting the common ingredient. I can't mention 'colour'.
2. Reason / F. Fallacies / 5. Fallacy of Composition
The fallacy of composition is the assumption that what is true of the parts is true of the whole [Mautner]
     Full Idea: The fallacy of composition is an inference relying on the invalid principle that whatever is true of every part is also true of the whole; thus, we cannot assume that because the members of a committee are rational, that the committee as a whole is.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.102)
     A reaction: This is a very common and very significant fallacy, which is perpetrated by major philosophers like Aristotle (Idea 31), unlike most of the other informal fallacies.
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic is based on the notion that there can be membership of a set to some degree [Mautner]
     Full Idea: Fuzzy logic is based upon fuzzy set-theory, in which the simple notion of membership of a set is replaced by a notion of membership to some degree.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.214)
     A reaction: The idea that something could be to some degree a 'heap of sand' sounds plausible, but Williamson and Sorensen claim that the vagueness is all in us (i.e. it is epistemological), and not in the world. This will scupper fuzzy logic.
5. Theory of Logic / B. Logical Consequence / 6. Entailment
Entailment is logical requirement; it may be not(p and not-q), but that has problems [Mautner]
     Full Idea: Entailment is the modern word saying that p logically follows from q. Its simplest definition is that you cannot have both p and not-q, but this has the problem that if p is impossible it will entail every possible proposition, which seems unacceptable.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.169)
     A reaction: The word 'entail' was introduced by G.E. Moore in 1920, in preference to 'imply'. It seems clear that we need terms for (say) active implication (q must be true if p is true) and passive implication (p must be false if q is false).
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Strict implication says false propositions imply everything, and everything implies true propositions [Mautner]
     Full Idea: Strict implication [not(p and not-q)] carries the paradoxes that a false proposition (p) implies any proposition (q), and a true proposition (q) is materially implied by any proposition (p).
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.270)
     A reaction: This seems to show that we have two drastically different notions of implication; one (the logician's) is boring and is defined by a truth table; the other (the ordinary interesting one) says if you have one truth you can deduce a second.
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner]
     Full Idea: 'Material implication' is a term introduced by Russell which is defined as 'the conjunction of p and not-q is false', but carries a strong implication that p implies q, and so there must be some kind of connection between them, which is misleading.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.270)
     A reaction: Mautner says statements of the form 'if p then q' are better called 'conditionals' than 'material implications'. Clearly there is a need for more precise terminology here, as the underlying concepts seem simple enough.
A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner]
     Full Idea: 'Implying' is different from 'inferring', because a person who infers draws the conclusion, but a person who implies leaves it to the audience to draw the conclusion.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.279)
     A reaction: I had always taken it just that the speaker does the implying and the audience does the inferring. Of course a speaker may not know what he or she is implying, but an audience must be aware of what it is inferring.
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Vagueness seems to be inconsistent with the view that every proposition is true or false [Mautner]
     Full Idea: Vagueness is of great philosophical interest because it seems to be inconsistent with the view that every proposition is true or false.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.585)
     A reaction: This would explain why Williamson and Sorensen are keen to argue that vagueness is an epistemological (rather than ontological) problem. In ordinary English we are happy to say that p is 'sort of true' or 'fairly true'.
5. Theory of Logic / G. Quantification / 1. Quantification
Quantifiers turn an open sentence into one to which a truth-value can be assigned [Mautner]
     Full Idea: In formal logic, quantifiers are operators that turn an open sentence into a sentence to which a truth-value can be assigned.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.464)
     A reaction: The standard quantifiers are 'all' and 'at least one'. The controversy is whether quantifiers actually assert existence, or whether (as McGinn says) they merely specify the subject matter of the sentence. I prefer the latter.
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals presuppose a belief (or a fact) that the condition is false [Mautner]
     Full Idea: A conditional is called counterfactual because its use seems to presuppose that the user believes its antecedent to be false. Some insist that the antecedent must actually be false.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.114)
     A reaction: I am inclined to favour the stricter second version. "If I am on Earth then I have weight" hardly sounds counterfactual. However, in "If there is a God then I will be saved" it is not clear whether it is counterfactual, so it had better be included.
Counterfactuals are not true, they are merely valid [Mautner]
     Full Idea: One view of counterfactuals says they are not true, but are merely valid.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.114)
     A reaction: This makes counterfactuals a branch of logic rather than of metaphysics. I find the metaphysical view more exciting as they are part of speculation and are beyond the capacity of computers (which I suspect they are).
Counterfactuals are true if in every world close to actual where p is the case, q is also the case [Mautner]
     Full Idea: Another view of counterfactuals (Lewis, Pollock, Stalnaker) is that they are true if at every possible world at which it is the case that p, and which is otherwise as similar as possible to the actual world, it is also the case that q.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.114)
     A reaction: This seems a good way if putting if, like Lewis, you actually believe in the reality of possible worlds, because then you are saying a counterfactual is made true by a set of facts. Otherwise it is not clear what the truth-maker is here.
Counterfactuals say 'If it had been, or were, p, then it would be q' [Mautner]
     Full Idea: A counterfactual conditional (or 'counterfactual') is a proposition or sentence of the form 'If it had been the case that p, then it would have been the case that q', or 'If it were the case that p, then it would be the case that q'.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.114)
     A reaction: The first statement refers to the past, but the second (a subjunctive) refers to any situation at any time. We know more about inferences that we could have made in the past than we do about what is inferable at absolutely any time.
Maybe counterfactuals are only true if they contain valid inference from premisses [Mautner]
     Full Idea: One view of counterfactuals (Chisholm, Goodman, Rescher) is that they are only true if there is a valid logical inference from p and some other propositions of certain kinds (controversial) to q.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.115)
     A reaction: The aspiration that counterfactual claims should reduce to pure logic sounds a bit hopeful to me. Logic is precise, but assertions about how things would be is speculative and imaginative.
10. Modality / C. Sources of Modality / 6. Necessity from Essence
Essentialism is often identified with belief in 'de re' necessary truths [Mautner]
     Full Idea: Many writers identify essentialism with the belief in 'de re' necessary truths
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.179)
     A reaction: I like essentialism, but I cautious about this. If I accept that I have an essential personal identity as I write this, but that it could change over time, the same principle might apply to other natural essences.
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
Fallibilism is the view that all knowledge-claims are provisional [Mautner]
     Full Idea: Fallibilism is the view, proposed by Peirce, and found in Reichenbach, Popper, Quine etc that all knowledge-claims are provisional and in principle revisable, or that the possibility of error is ever-present.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.194)
     A reaction: I think of this as footnote to all thought which reads "Note 1: but you never quite know". Personally I would call myself a fallibilist, and am surprise at anyone who doesn't. The point is that this does not negate 'knowledge'. I am fairly sure 2+3=5.
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
'Sense-data' arrived in 1910, but it denotes ideas in Locke, Berkeley and Hume [Mautner]
     Full Idea: The term 'sense-data' gained currency around 1910, through writings of Moore and Russell, but it seems to denote at least some of the things referred to as 'ideas of sense' (Locke), or 'ideas' and 'sensible qualities' (Berkeley), or 'impressions' (Hume).
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.518)
     A reaction: See also Hobbes in Idea 2356 for an even earlier version. It looks as if the concept of sense-data is almost unavoidable for empiricists, and yet most modern empiricists have rejected them. You still have to give an account of perceptual illusions.
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
Observing lots of green x can confirm 'all x are green' or 'all x are grue', where 'grue' is arbitrary [Mautner, by PG]
     Full Idea: Observing green emeralds can confirm 'all emeralds are green' or 'all emeralds are grue', where 'grue' is an arbitrary predicate meaning 'green until t and then blue'. Thus predictions are arbitrary, depending on how the property is described.
     From: report of Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.225) by PG - Db (ideas)
     A reaction: This increasingly strikes me as the sort of sceptical nonsense that is concocted by philosophers who are enthralled to language instead of reality. It does draw attention to an expectation of stability in induction, both in language and in nature.
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
'All x are y' is equivalent to 'all non-y are non-x', so observing paper is white confirms 'ravens are black' [Mautner, by PG]
     Full Idea: If observing a white sheet of paper confirms that 'all non-black things are non-ravens', and that is logically equivalent to 'all ravens are black' (which it is), then the latter proposition is confirmed by irrelevant observations.
     From: report of Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.105) by PG - Db (ideas)
     A reaction: This seems to me more significant than the 'grue' paradox. If some observations can be totally irrelevant (except to God?), then some observations are much more relevant than others, so relevance is a crucial aspect of induction.
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Generalisations must be invariant to explain anything [Leuridan]
     Full Idea: A generalisation is explanatory if and only if it is invariant.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §4)
     A reaction: [He cites Jim Woodward 2003] I dislike the idea that generalisations and regularities explain anything at all, but this rule sounds like a bare minimum for being taken seriously in the space of explanations.
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
Biological functions are explained by disposition, or by causal role [Leuridan]
     Full Idea: The main alternative to the dispositional theory of biological functions (which confer a survival-enhancing propensity) is the etiological theory (effects are functions if they play a role in the causal history of that very component).
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §3)
     A reaction: [Bigelow/Pargetter 1987 for the first, Mitchell 2003 for the second] The second one sounds a bit circular, but on the whole a I prefer causal explanations to dispositional explanations.
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan]
     Full Idea: Nothing can count as a mechanism unless it produces some macro-level regular behaviour. To produce macro-level regular behaviour, it has to rely on micro-level regularities.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §5)
     A reaction: This is the core of Leuridan's argument that regularities are more basic than mechanisms. It doesn't follow, though, that the more basic a thing is the more explanatory work it can do. I say mechanisms explain more than low-level regularities do.
Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan]
     Full Idea: To model a mechanism one must incorporate pragmatic laws. ...As valuable as the concept of mechanism and mechanistic explanation are, they cannot replace regularities nor undermine their relevance for scientific explanation.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1)
     A reaction: [See Idea 12786 for 'pragmatic laws'] I just don't see how the observation of a regularity is any sort of explanation. I just take a regularity to be something interesting which needs to be explained.
We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan]
     Full Idea: Summary: mechanisms depend on regularities, there may be regularities without mechanisms, models of mechanisms must incorporate pragmatic laws, and pragmatic laws do not depend epistemologically on mechanistic models.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1)
     A reaction: See Idea 14382 for 'pragmatic' laws. I'm quite keen on mechanisms, so this is an arrow close to the heart, but at this point I say that my ultimate allegiance is to powers, not to mechanisms.
Mechanisms are ontologically dependent on regularities [Leuridan]
     Full Idea: Mechanisms are ontologically dependent on the existence of regularities.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §3)
     A reaction: This seems to be the Humean rearguard action in favour of the regularity account of laws. Wrong, but a nice paper. This point shows why only powers (despite their vagueness!) are the only candidate for the bottom level of explanation.
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan]
     Full Idea: I see nothing metaphysically wrong in an infinite ontological regress of mechanisms and regularities.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §5)
     A reaction: This is a pretty unusual view, and I can't accept it. My revulsion at this regress is precisely the reason why I believe in powers, as the bottom level of explanation.
19. Language / C. Assigning Meanings / 9. Indexical Semantics
The references of indexicals ('there', 'now', 'I') depend on the circumstances of utterance [Mautner]
     Full Idea: Indexicals are expressions whose references depend on the circumstances of utterance, such as 'here', 'now', 'last month' 'I', 'you'. It was introduced by Peirce; Reichenbach called them 'token-reflexive', Russell 'ego-centric particulars'.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.272)
     A reaction: Peirce's terminology seems best. They obviously create great problems for any theory of reference which is rather theoretical and linguistic, such as by the use of descriptions. You can't understand 'Look at that!' without practical awareness.
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
Double effect is the distinction between what is foreseen and what is intended [Mautner]
     Full Idea: The doctrine of double effect is that there is a moral distinction between what is foreseen by an agent as a likely result of an action, and what is intended.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.150)
     A reaction: Abortion for a pregnancy threatening the mother's life. What always intrigues me is the effects which you didn't foresee because you couldn't be bothered to think about them. How much obligation do you have to try to foresee events?
Double effect acts need goodness, unintended evil, good not caused by evil, and outweighing [Mautner]
     Full Idea: It is suggested the double effect act requires 1) the act is good, 2) the bad effect is not intended, and is avoided if possible, 3) the bad effect doesn't cause the good result, 4) the good must outweigh the bad side effect.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.151)
     A reaction: It is suggested that these won't work for permissibility of an action, but they might be appropriate for blameworthiness. Personally I am rather impressed by the four-part framework here, whatever nitpicking objections others may have found.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
'Essentialism' is opposed to existentialism, and claims there is a human nature [Mautner]
     Full Idea: In philosophical anthropology, the view that there is a human nature or essence is called 'essentialism'. It became current in 1946 as a contrast to Sartre's existentialist view.
     From: Thomas Mautner (Penguin Dictionary of Philosophy [1996], p.179)
     A reaction: Being a fan of Aristotle, I incline towards the older view, but you cannot get away from the fact that the human brain has similarities to a Universal Turing Machine, and diverse cultures produce very different individuals.
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
     Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes.
     From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078
     A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book.
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan]
     Full Idea: The dispositional theory of biological functions is not unquestioned. The main alternative is the etiological theory: a component's effect is a function of that component if it has played an essential role in the causal history of its existence.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §3)
     A reaction: [He cites S.D. Mitchell 2003] Presumably this account is meant to fit into a theory of evolution in biology. The obvious problem is where something comes into existence for one reason, and then acquires a new function (such as piano-playing).
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan]
     Full Idea: A generalization is a 'pragmatic law' if it allows of prediction, explanation and manipulation, even if it fails to satisfy the traditional criteria. To this end, it should describe a stable regularity, but not necessarily a universal and necessary one.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1)
     A reaction: I am tempted to say of this that all laws are pragmatic, given that it is rather hard to know whether reality is stable. The universal laws consist of saying that IF reality stays stable in certain ways, certain outcomes will ensue necessarily.
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Strict regularities are rarely discovered in life sciences [Leuridan]
     Full Idea: Strict regularities are rarely if ever discovered in the life sciences.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §2)
     A reaction: This is elementary once it is pointed out, but too much philosophy have science has aimed at the model provided by the equations of fundamental physics. Science is a broad church, to employ an entertaining metaphor.
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan]
     Full Idea: By 'law of nature' or 'natural law' I mean a generalization describing a regularity, not some metaphysical entity that produces or is responsible for that regularity.
     From: Bert Leuridan (Can Mechanisms Replace Laws of Nature? [2010], §1 n1)
     A reaction: I take the second version to be a relic of a religious world view, and having no place in a naturalistic metaphysic. The regularity view is then the only player in the field, and the question is, can we do more? Can't we explain regularities?
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
     Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness.
     From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42
     A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them.