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Aristotle applies his method of running through the phainomena and collecting the endoxa widely, in nearly every area of his philosophy. To take a typical illustration, we find the method clearly deployed in his discussion of time in Physics iv 10— We begin with a phainomenon : we feel sure that time exists or at least that time passes. So much is, inescapably, how our world appears: we experience time as passing, as unidirectional, as unrecoverable when lost. Yet when we move to offer an account of what time might be, we find ourselves flummoxed.

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For guidance, we turn to what has been said about time by those who have reflected upon its nature. It emerges directly that both philosophers and natural scientists have raised problems about time. As Aristotle sets them out, these problems take the form of puzzles, or aporiai , regarding whether and if so how time exists Phys. If we say that time is the totality of the past, present and future, we immediately find someone objecting that time exists but that the past and future do not. According to the objector, only the present exists.

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If we retort then that time is what did exist, what exists at present and what will exist, then we notice first that our account is insufficient: after all, there are many things which did, do, or will exist, but these are things that are in time and so not the same as time itself. We further see that our account already threatens circularity, since to say that something did or will exist seems only to say that it existed at an earlier time or will come to exist at a later time.

Then again we find someone objecting to our account that even the notion of the present is troubling. After all, either the present is constantly changing or it remains forever the same. If it remains forever the same, then the current present is the same as the present of 10, years ago; yet that is absurd. If it is constantly changing, then no two presents are the same, in which case a past present must have come into and out of existence before the present present.

Either it went out of existence even as it came into existence, which seems odd to say the least, or it went out of existence at some instant after it came into existence, in which case, again, two presents must have existed at the same instant. In setting such aporiai , Aristotle does not mean to endorse any given endoxon on one side or the other.

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Rather, he thinks that such considerations present credible puzzles, reflection upon which may steer us towards a deeper understanding of the nature of time. In this way, aporiai bring into sharp relief the issues requiring attention if progress is to be made. Thus, by reflecting upon the aporiai regarding time, we are led immediately to think about duration and divisibility, about quanta and continua , and about a variety of categorial questions.

That is, if time exists, then what sort of thing is it? Is it the sort of thing which exists absolutely and independently? Or is it rather the sort of thing which, like a surface, depends upon other things for its existence?

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When we begin to address these sorts of questions, we also begin to ascertain the sorts of assumptions at play in the endoxa coming down to us regarding the nature of time. Consequently, when we collect the endoxa and survey them critically, we learn something about our quarry, in this case about the nature of time—and crucially also something about the constellation of concepts which must be refined if we are to make genuine philosophical progress with respect to it. What holds in the case of time, contends Aristotle, holds generally.

This is why he characteristically begins a philosophical inquiry by presenting the phainomena , collecting the endoxa , and running through the puzzles to which they give rise.

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Whereas science relies upon premises which are necessary and known to be so, a dialectical discussion can proceed by relying on endoxa , and so can claim only to be as secure as the endoxa upon which it relies. This is not a problem, suggests Aristotle, since we often reason fruitfully and well in circumstances where we cannot claim to have attained scientific understanding.

Minimally, however, all reasoning—whether scientific or dialectical—must respect the canons of logic and inference. Among the great achievements to which Aristotle can lay claim is the first systematic treatment of the principles of correct reasoning, the first logic. Of course, philosophers before Aristotle reasoned well or reasoned poorly, and the competent among them had a secure working grasp of the principles of validity and soundness in argumentation.

No-one before Aristotle, however, developed a systematic treatment of the principles governing correct inference; and no-one before him attempted to codify the formal and syntactic principles at play in such inference. Aristotle somewhat uncharacteristically draws attention to this fact at the end of a discussion of logic inference and fallacy:. Generally, a deduction sullogismon , according to Aristotle, is a valid or acceptable argument.

His view of deductions is, then, akin to a notion of validity, though there are some minor differences. For example, Aristotle maintains that irrelevant premises will ruin a deduction, whereas validity is indifferent to irrelevance or indeed to the addition of premises of any kind to an already valid argument. Moreover, Aristotle insists that deductions make progress, whereas every inference from p to p is trivially valid.

In general, he contends that a deduction is the sort of argument whose structure guarantees its validity, irrespective of the truth or falsity of its premises. This holds intuitively for the following structure:. This particular deduction is perfect because its validity needs no proof, and perhaps because it admits of no proof either: any proof would seem to rely ultimately upon the intuitive validity of this sort of argument.

Aristotle seeks to exploit the intuitive validity of perfect deductions in a surprisingly bold way, given the infancy of his subject: he thinks he can establish principles of transformation in terms of which every deduction or, more precisely, every non-modal deduction can be translated into a perfect deduction. He contends that by using such transformations we can place all deduction on a firm footing. The perfect deduction already presented is an instance of universal affirmation: all A s are B s; all B s C s; and so, all A s are C s. Now, contends Aristotle, it is possible to run through all combinations of simple premises and display their basic inferential structures and then to relate them back to this and similarly perfect deductions.

It turns out that some of these arguments are deductions, or valid syllogisms, and some are not. Those which are not admit of counterexamples, whereas those which are, of course, do not. There are counterexamples to those, for instance, suffering from what came to be called undistributed middle terms, e. There is no counterexample to the perfect deduction in the form of a universal affirmation: if all A s are B s, and all B s C s, then there is no escaping the fact that all A s are C s.

So, if all the kinds of deductions possible can be reduced to the intuitively valid sorts, then the validity of all can be vouchsafed. To effect this sort of reduction, Aristotle relies upon a series of meta-theorems, some of which he proves and others of which he merely reports though it turns out that they do all indeed admit of proofs.

His principles are meta -theorems in the sense that no argument can run afoul of them and still qualify as a genuine deduction. They include such theorems as: i no deduction contains two negative premises; ii a deduction with a negative conclusion must have a negative premise; iii a deduction with a universal conclusion requires two universal premises; and iv a deduction with a negative conclusion requires exactly one negative premise.

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He does, in fact, offer proofs for the most significant of his meta-theorems, so that we can be assured that all deductions in his system are valid, even when their validity is difficult to grasp immediately. In developing and proving these meta-theorems of logic, Aristotle charts territory left unexplored before him and unimproved for many centuries after his death. Aristotle approaches the study of logic not as an end in itself, but with a view to its role in human inquiry and explanation.

Logic is a tool, he thinks, one making an important but incomplete contribution to science and dialectic. A deduction is minimally a valid syllogism, and certainly science must employ arguments passing this threshold. By this he means that they should reveal the genuine, mind-independent natures of things. That is, science explains what is less well known by what is better known and more fundamental, and what is explanatorily anemic by what is explanatorily fruitful.

We may, for instance, wish to know why trees lose their leaves in the autumn. We may say, rightly, that this is due to the wind blowing through them. Still, this is not a deep or general explanation, since the wind blows equally at other times of year without the same result.

A deeper explanation—one unavailable to Aristotle but illustrating his view nicely—is more general, and also more causal in character: trees shed their leaves because diminished sunlight in the autumn inhibits the production of chlorophyll, which is required for photosynthesis, and without photosynthesis trees go dormant. Importantly, science should not only record these facts but also display them in their correct explanatory order.

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That is, although a deciduous tree which fails to photosynthesize is also a tree lacking in chlorophyll production, its failing to produce chlorophyll explains its inability to photosynthesize and not the other way around. This sort of asymmetry must be captured in scientific explanation. Science seeks to capture not only the causal asymmetries in nature, but also its deep, invariant patterns.

Consequently, in addition to being explanatorily basic, the first premise in a scientific deduction will be necessary. So, says Aristotle:. For this reason, science requires more than mere deduction. Altogether, then, the currency of science is demonstration apodeixis , where a demonstration is a deduction with premises revealing the causal structures of the world, set forth so as to capture what is necessary and to reveal what is better known and more intelligible by nature APo 71b33—72a5, Phys.

If we are to lay out demonstrations such that the less well known is inferred by means of deduction from the better known, then unless we reach rock-bottom, we will evidently be forced either to continue ever backwards towards the increasingly better known, which seems implausibly endless, or lapse into some form of circularity, which seems undesirable.

The alternative seems to be permanent ignorance. Aristotle contends:.