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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: All As are Bs.
All Bs are Cs. Hence, all As are Cs. 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 As are Bs; all Bs Cs; and so, all As are Cs. 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 As are Bs, and all Bs Cs, then there is no escaping the fact that all As are Cs. 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.
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.
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.
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: We think we understand a thing without qualification, and not in the sophistic, accidental way, whenever we think we know the cause in virtue of which something is—that it is the cause of that very thing—and also know that this cannot be otherwise.
After all, both those with knowledge and those without it suppose that this is so—although only those with knowledge are actually in this condition. Hence, whatever is known without qualification cannot be otherwise. APo 71b9—16; cf. APo 71b33—72a5; Top. 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: Some people think that since knowledge obtained via demonstration requires the knowledge of primary things, there is no knowledge.
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Others think that there is knowledge and that all knowledge is demonstrable. Neither of these views is either true or necessary.
The first group, those supposing that there is no knowledge at all, contend that we are confronted with an infinite regress. They contend that we cannot know posterior things because of prior things if none of the prior things is primary. Here what they contend is correct: it is indeed impossible to traverse an infinite series. Yet, they maintain, if the regress comes to a halt, and there are first principles, they will be unknowable, since surely there will be no demonstration of first principles—given, as they maintain, that only what is demonstrated can be known.
But if it is not possible to know the primary things, then neither can we know without qualification or in any proper way the things derived from them. Rather, we can know them instead only on the basis of a hypothesis, to wit, if the primary things obtain, then so too do the things derived from them. The other group agrees that knowledge results only from demonstration, but believes that nothing stands in the way of demonstration, since they admit circular and reciprocal demonstration as possible.
Indeed, the necessity here is apparent; for if it is necessary to know the prior things, that is, those things from which the demonstration is derived, and if eventually the regress comes to a standstill, it is necessary that these immediate premises be indemonstrable. In Posterior Analytics ii 19, he describes the process by which knowers move from perception to memory, and from memory to experience empeiria —which is a fairly technical term in this connection, reflecting the point at which a single universal comes to take root in the mind—and finally from experience to a grasp of first principles.
This final intellectual state Aristotle characterizes as a kind of unmediated intellectual apprehension nous of first principles APo. Scholars have understandably queried what seems a casually asserted passage from the contingent, given in sense experience, to the necessary, as required for the first principles of science. Perhaps, however, Aristotle simply envisages a kind of a posteriori necessity for the sciences, including the natural sciences.
In any event, he thinks that we can and do have knowledge, so that somehow we begin in sense perception and build up to an understanding of the necessary and invariant features of the world. As he recognizes, we often find ourselves reasoning from premises which have the status of endoxa, opinions widely believed or endorsed by the wise, even though they are not known to be necessary.
Still less often do we reason having first secured the first principles of our domain of inquiry. This method he characterizes as dialectic. In fact, in his work dedicated to dialectic, the Topics, he identifies three roles for dialectic in intellectual inquiry, the first of which is mainly preparatory: Dialectic is useful for three purposes: for training, for conversational exchange, and for sciences of a philosophical sort.
That it is useful for training purposes is directly evident on the basis of these considerations: once we have a direction for our inquiry we will more readily be able to engage a subject proposed to us. It is useful for conversational exchange because once we have enumerated the beliefs of the many, we shall engage them not on the basis of the convictions of others but on the basis of their own; and we shall re-orient them whenever they appear to have said something incorrect to us.
It is useful for philosophical sorts of sciences because when we are able to run through the puzzles on both sides of an issue we more readily perceive what is true and what is false. Further, it is useful for uncovering what is primary among the commitments of a science. For it is impossible to say anything regarding the first principles of a science on the basis of the first principles proper to the very science under discussion, since among all the commitments of a science, the first principles are the primary ones.
This comes rather, necessarily, from discussion of the credible beliefs endoxa belonging to the science. This is peculiar to dialectic, or is at least most proper to it. For since it is what cross-examines, dialectic contains the way to the first principles of all inquiries. By contrast, the third is philosophically significant. In these contexts, dialectic helps to sort the endoxa, relegating some to a disputed status while elevating others; it submits endoxa to cross-examination in order to test their staying power; and, most notably, according to Aristotle, dialectic puts us on the road to first principles Top.
If that is so, then dialectic plays a significant role in the order of philosophical discovery: we come to establish first principles in part by determining which among our initial endoxa withstand sustained scrutiny.
Here, as elsewhere in his philosophy, Aristotle evinces a noteworthy confidence in the powers of human reason and investigation. Essentialism and Homonymy However we arrive at secure principles in philosophy and science, whether by some process leading to a rational grasping of necessary truths, or by sustained dialectical investigation operating over judiciously selected endoxa, it does turn out, according to Aristotle, that we can uncover and come to know genuinely necessary features of reality.
He relies upon a host of loosely related locutions when discussing the essences of things, and these give some clue to his general orientation. In speaking this way, Aristotle supposes that if we wish to know what a human being is, we cannot identify transient or non-universal features of that kind; nor indeed can we identify even universal features which do not run explanatorily deep.
Rather, as his preferred locution indicates, he is interested in what makes a human being human—and he assumes, first, that there is some feature F which all and only humans have in common and, second, that F explains the other features which we find across the range of humans.
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Aristotle rejects this approach for several reasons, including most notably that he thinks that certain non-essential features satisfy the definition. Thus, beyond the categorical and logical features everyone is such as to be either identical or not identical with the number nine , Aristotle recognizes a category of properties which he calls idia Cat.
Propria are non-essential properties which flow from the essence of a kind, such that they are necessary to that kind even without being essential. For instance, if we suppose that being rational is essential to human beings, then it will follow that every human being is capable of grammar.
Being capable of grammar is not the same property as being rational, though it follows from it.
Aristotle assumes his readers will appreciate that being rational asymmetrically explains being capable of grammar, even though, necessarily, something is rational if and only if it is also capable of grammar. Thus, because it is explanatorily prior, being rational has a better claim to being the essence of human beings than does being capable of grammar. Accordingly, this is the feature to be captured in an essence-specifying account of human beings APo 75a42—b2; Met.
Aristotle believes for a broad range of cases that kinds have essences discoverable by diligent research. He in fact does not devote much energy to arguing for this contention; still less is he inclined to expend energy combating anti-realist challenges to essentialism, perhaps in part because he is impressed by the deep regularities he finds, or thinks he finds, underwriting his results in biological investigation.
On the contrary, he denies essentialism in many cases where others are prepared to embrace it. One finds this sort of denial prominently, though not exclusively, in his criticism of Plato. Indeed, it becomes a signature criticism of Plato and Platonists for Aristotle that many of their preferred examples of sameness and invariance in the world are actually cases of multivocity, or homonymy in his technical terminology.
In the opening of the Categories, Aristotle distinguishes between synonymy and homonymy later called univocity and multivocity. All these locutions have a quasi-technical status for him. In cases of univocity, we expect single, non-disjunctive definitions which capture and state the essence of the kinds in question. Let us allow once more for purposes of illustration that the essence-specifying definition of human is rational animal.
Then, since human means rational animal across the range of its applications, there is some single essence to all members of the kind.
By contrast, when synonymy fails we have homonymy. Very regularly, according to Aristotle, this sort of reflection leads to an interesting discovery, namely that we have been presuming a univocal account where in fact none is forthcoming.
This, according to Aristotle, is where the Platonists go wrong: they presume univocity where the world delivers homonymy or multivocity. In one especially important example, Aristotle parts company with Plato over the univocity of goodness: We had perhaps better consider the universal good and run through the puzzles concerning what is meant by it—even though this sort of investigation is unwelcome to us, because those who introduced the Forms are friends of ours.
Yet presumably it would be the better course to destroy even what is close to us, as something necessary for preserving the truth—and all the more so, given that we are philosophers. For though we love them both, piety bids us to honour the truth before our friends.
Rather, goodness is different in different cases.
Now, Mark is back to discuss his new book Everything He works as an economist at the U. Bureau of Labor Statistics. He also earned a B. Donald is a cognitive-behavioral psychotherapist, trainer, and writer. Robertson has been tirelessly researching Stoicism and applying it in his work for twenty years. Athena and Circe and Hermes all worked to help Odysseus.
Apollo guided Achilles. Zeus and Jupiter were always getting involved in this squabble or that one.
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Sort of weird, right? They were Be Severe Only With Yourself One of the things that separates us from other people—indeed that has been responsible for our success—is our ability to be strict and self-disciplined.It can thus be argued that the search for the sophist and distinction between philosophy and sophistry are not only central themes in the Platonic dialogues, but constitutive of the very idea and practice of philosophy, at least in its original sense as articulated by Plato.
Minimally, however, all reasoning—whether scientific or dialectical—must respect the canons of logic and inference. When introducing this puzzle, Aristotle pauses to reflect upon a precept governing his approach to philosophy: As in other cases, we must set out the appearances phainomena and run through all the puzzles regarding them.
Perhaps, however, Aristotle simply envisages a kind of a posteriori necessity for the sciences, including the natural sciences.
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. Technical artifacts, then, are made to serve some purpose, generally to be used for something or to act as a component in a larger artifact, which in its turn is either something to be used or again a component. Clipping is a handy way to collect important slides you want to go back to later.
The 20th century deals with the upheavals produced by a series of conflicts within philosophical discourse over the basis of knowledge, with classical certainties overthrown, and new social, economic, scientific and logical problems.
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. It is equally problematic whether a unified account of the notion of function as such is possible, but this issue has received considerably more philosophical attention.
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