Consider each relationship in turn. In the diagram, they are linked by a diagonal line. If one of two contradictories is true, the other must be false, and vice versa. It is possible, however, that both statements are false as in the case where some S are P and some other S are not P. They will, however, both be false if it is indeed the case that some politicians tell lies whereas some do not. Clearly, if all members of an existent group possess or do not possess a specific characteristic, it must follow that any smaller subset of that group must possess or not possess that specific characteristic.
Note that subalternation does not work in the opposite direction. The bottom horizontal line in the square joining the I proposition Some S are P to the O proposition Some S are not P represents this kind of subcontrary relationship. They are both true because having a beard is a contingent or variable male attribute. Subalternation is an obvious example of immediate inference. In conversion , one interchanges the S and P terms. In obversion , one negates the predicate term while replacing it with the predicate term of opposite quality.
Finally, in contraposition , one negates both terms and reverses their order. One still encounters this approach in textbook accounts of informal logic. The usual list of logical laws or logical first principles includes three axioms: the law of identity, the law of non-contradiction, and the law of excluded middle. Some authors include a law of sufficient reason, that every event or claim must have a sufficient reason or explanation, and so forth.
It would be a gross simplification to argue that these ideas derive exclusively from Aristotle or to suggest as some authors seem to imply that he self-consciously presented a theory uniquely derived from these three laws. Traditional logicians did not regard them as abstruse or esoteric doctrines but as manifestly obvious principles that require assent for logical discourse to be possible. The law of identity could be summarized as the patently unremarkable but seemingly inescapable notion that things must be, of course, identical with themselves.
This suggests that he does accept, unsurprisingly, the perfectly obvious idea that things are themselves. If, however, identical things must possess identical attributes, this opens the door to various logical maneuvers. One can, for example, substitute equivalent terms for one another and, even more portentously, one can arrive at some conception of analogy and induction.
If water is water, then by the law of identity, anything we discover to be water must possess the same water-properties. Aristotle provides several formulations of the law of non-contradiction, the idea that logically correct propositions cannot affirm and deny the same thing:. The law of excluded middle can be summarized as the idea that every proposition must be either true or false, not both and not neither.
Because every proposition must be true or false, it does not follow, of course, that we can know if a particular proposition is true or false. Despite perennial challenges to these so-called laws by intuitionists, dialetheists, and others , Aristotelians inevitably claim that such counterarguments hinge on some unresolved ambiguity equivocation , on a conflation of what we know with what is actually the case, on a false or static account of identity, or on some other failure to fully grasp the implications of what one is saying.
Begin with the usual criticism brought against the traditional square of opposition. For reasons we will not explore, modern logicians assume that universal claims about non-existent objects or empty sets are true but that particular claims about them are false. Clearly, this clashes with the traditional square of opposition. For this and similar reasons, some modern logicians dismiss the traditional square as inadequate, claiming that Aristotle made a mistake or overlooked relevant issues.
Aristotle, however, is involved in a specialized project. He elaborates an alternative logic, specifically adapted to the problems he is trying to solve. Aristotle devises a companion-logic for science. He relegates fictions like fairy godmothers and mermaids and unicorns to the realms of poetry and literature. In his mind, they exist outside the ambit of science. This is why he leaves no room for such non-existent entities in his logic.
This is a thoughtful choice, not an inadvertent omission. They cannot be defined. Aristotle makes this point explicitly in the Posterior Analytics. He points out that a definition of a goat-stag, a cross between a goat and a deer the ancient equivalent of a unicorn , is impossible. Because we cannot know what the essential nature of a goat-stag is—indeed, it has no essential nature—we cannot provide a proper definition of a goat-stag.
So the study of goat-stags or unicorns is not open to scientific investigation. Aristotle sets about designing a logic that is intended to display relations between scientific propositions, where science is understood as a search for essential definitions.
This is why he leaves no place for fictional entities like goat-stags or unicorns. Hence, the assumed validity of a logical maneuver like subalternation. Some modern logicians might define logic as that philosophical inquiry which considers the form not the content of propositions. We cannot properly understand what Aristotle is about by separating form from content.
Suppose, for example, I was to claim that 1 all birds have feathers and 2 that everyone in the Tremblay family wears a red hat. These two claims possess the same very same propositional form, A. Aristotle would view the relationship between birds and feathers expressed in the first proposition as a necessary link, for it is of the essence of birds to be feathered.
Something cannot be a bird and lack feathers. The link between membership in the Tremblay family and the practice of wearing a red hat described in the second proposition is, in sharp contrast, a contingent fact about the world. A member of the Tremblay family who wore a green hat would still be a member of the Tremblay family. The fact that the Tremblays only wear red hats because it is presently the fashion in Quebec is an accidental or surface feature of what a Tremblay is.
So this second relationship holds in a much weaker sense. Aristotle wants a logic that tells us what belongs to what. But there are different levels of belonging. My billfold belongs to me but this is a very tenuous sort of belonging.
The way my billfold belongs to me pales in significance to, say, the way a bill belongs to a duck-billed platypus. It is not simply that the bill is physically attached to the platypus. Even if you were to cut off the bill of a platypus, this would just create a deformed platypus; it would not change the sense of necessary belonging that connects platypuses and bills. The deep nature of a platypus requires—it necessitates —a bill. In so much as logic is about discovering necessary relationships, it is not the mere arrangement of terms and symbols but their substantive meaning that is at issue.
Aristotle would have no patience for the modern penchant for purely statistical interpretations of inductive generalizations. It is not the number of times something happens that matters. It is the deep nature of the thing that counts. If the wicked boy or girl next door pulls three legs off a spider, this is just happenstance. Aristotle is too keen a biologist not to recognize that there are accidents and monstrosities in the world, but the existence of these individual imperfections does not change the deep nature of things.
Aristotle recognizes then that some types of belonging are more substantial—that is, more real—than others. But this has repercussions for the ways in which we evaluate arguments. Another example may help. We will worry about formal details later. Its conclusion follows from the essential and therefore necessary features of birds. In the second argument, the conclusion only follows from the contingent state of fashion in Quebec. In Aristotelian logic, the strength of an argument depends, in some important way, on metaphysical issues.
This is very different than modern symbolic logic. Although Aristotle does use letters to take the place of variable terms in a logical relation, we should not be misled into thinking that the substantive content of what is being discussed does not matter. Although one senses that Aristotle took great pride in these accomplishments, we could complain that the persistent focus on the mechanics of the valid syllogism has obscured his larger project.
We will only cover the most basic points here, largely ignoring hypothetical syllogisms, modal syllogisms, extended syllogisms sorites , inter alia. We can define a syllogism, in relation to its logical form, as an argument made up of three categorical propositions, two premises which set out the evidence , and a conclusion that follows logically from the premises. In the standard account, the propositions are composed of three terms, a subject term , a predicate term , and a middle term : the subject term is the grammatical subject of the conclusion; the predicate term modifies the subject in the conclusion, and the middle term links the subject and predicate terms in the premises.
The subject and predicate terms appear in different premises; the middle term appears once in each premise. The premise with the predicate term and the middle term is called the major premise ; the premise with the subject term and the middle term is called the minor premise. Because syllogisms depend on the precise arrangement of terms, syllogistic logic is sometimes referred to as term logic.
In the Middle Ages, scholars came up with Latin names for valid syllogisms, using vowels to represent the position of each categorical proposition. Their list is readily available elsewhere. A syllogism in Barbara is clearly valid where validity can be understood in modern terms as the requirement that if the premises of the argument are true, then the conclusion must be true.
Modern textbook authors generally prove the validity of syllogisms in two ways. First, they use a number of different rules. Second, they use Venn diagrams, intersecting circles marked to indicate the extension or range of different terms, to determine if the information contained in the conclusion is also included in the premises. Modern logicians, who still hold to traditional conventions, classify syllogisms according to figure and mood.
The four figure classification derives from Aristotle; the mood classification, from Medieval logicians. One determines the figure of a syllogism by recording the positions the middle term takes in the two premises. One determines the mood of a syllogism by recording the precise arrangement of categorical propositions. So, for Barbara, the mood is AAA. By tabulating figures and moods, we can make an inventory of valid syllogisms.
As already mentioned, we need to distinguish between two kinds of necessity. Aristotle believes in metaphysical or natural necessity. Birds must have feathers because that is their nature. The emphasis here is on the sense of inevitable consequence that precipitates a conclusion when certain forms of propositions are added together. He searches for pairs of propositions that combine to produce a necessary conclusion.
He begins by accepting that a few syllogisms are self-evidently or transparently true. Barbara, AAA-Fig. On seeing the arrangement of terms in such cases, one immediately understands that the conclusion follows necessarily from the premises. In the case of imperfect syllogisms Aristotle relies on a method of proof that translates them, step-by-step, into perfect syllogisms through a careful rearrangement of terms.
He does this directly, through conversion, or indirectly, through the relationships of contradiction and contrariety outlined in the square of opposition. To cite only one very simple example, consider a brief passage in the Prior Analytics I. This conversion of an imperfect syllogism into a perfect syllogism demonstrates that the original arrangement of terms is a genuine deduction.
In other cases, Aristotle proves that particular arrangements of terms cannot yield proper syllogisms by showing that, in these instances, true premises lead to obviously false or contradictory conclusions. Alongside these proofs of logical necessity, Aristotle derives general rules for syllogisms, classifies them according to figure, and so on.
It is important to reiterate that Aristotelian syllogisms are not primarily about hypothetical sets, imaginary classes, or purely abstract mathematical entities. Aristotle believes there are natural groups in the world—species and genera—made up of individual members that share a similar nature, and hence similar properties.
It is this sharing of individual things in a similar nature that makes universal statements possible. Once we have universal terms, we can make over-arching statements that, when combined, lead inescapably to specific results. In the most rigorous syllogistic, metaphysical necessity is added to logical necessity to produce an unassailable inference. Seen in this Aristotelian light, syllogisms can be construed as a vehicle for identifying the deep, immutable natures that make things what they are.
Medieval logicians summarized their understanding of the rationale underlying the syllogism in the so-called dictum de omni et nullo the maxim of all and none , the principle that whatever is affirmed or denied of a whole must be affirmed or denied of a part which they alleged derived from a reading of Prior Analytics I.
Some contemporary authors have claimed that Aristotelian syllogistic is at least compatible with a deflationary theory of truth, the modern idea that truth-claims about propositions amount to little more than an assertion of the statement itself.
Mostly, Aristotle wants to know what we can confidently conclude from two presumably true premises; that is, what kind of knowledge can be produced or demonstrated if two given premises are true. Understanding what Aristotle means by inductive syllogism is a matter of serious scholarly dispute. Although there is only abbreviated textual evidence to go by, his account of inductive argument can be supplemented by his ampler account of its rhetorical analogues, argument from analogy and argument from example.
What is clear is that Aristotle thinks of induction epagoge as a form of reasoning that begins in the sense perception of particulars and ends in a understanding that can be expressed in a universal proposition or even a concept. We pick up mental momentum through a familiarity with particular cases that allows us to arrive at a general understanding of an entire species or genus.
As we discuss below, there are indications that Aristotle views induction, in the first instance, as a manifestation of immediate understanding and not as an argument form. Nonetheless, in the Prior Analytics II. Relying on old biological ideas, Aristotle argues that we can move from observations about the longevity of individual species of bileless animals that is, animals with clean-blood to the universal conclusion that bilelessness is a cause of longevity.
His argument can be paraphrased in modern English: All men, horses, mules, and so forth, are long-lived; all men, horses, mules, and so forth, are bileless animals; therefore, all bileless animals are long-lived. Although this argument seems, by modern standards, invalid, Aristotle apparently claims that it is a valid deduction. According to this logical rule, terms that cover the same range of cases because they refer to the same nature are interchangeable antistrepho.
They can be substituted for one another. This revised induction possesses an obviously valid form Barbara, discussed above. Note that Aristotle does not view this inversion of terms as a formal gimmick or trick; he believes that it reflects something metaphysically true about shared natures in the world. One could argue that inductive syllogism operates by means of the quantification of the predicate term as well as the subject term of a categorical proposition, but we will not investigate that issue here.
These passages pose multiple problems of interpretation. We can only advance a general overview of the most important disagreements here. The main problem here is that it seems to involve a physical impossibility. One problem with such claims is that they overlook the clear distinction that Aristotle makes between rigorous inductions and rhetorical inductions which we discuss below.
On this account, Empiricists such as Locke and Hume discovered something seriously wrong about induction that escaped the notice of an ancient author like Aristotle. Philosophers in the modern Anglo-American tradition largely favor this interpretation. Such allegations do not depend, however, on any close reading of a wealth of relevant passages in the Aristotelian corpus and in ancient philosophy generally.
McCaskey, Biondi, Rijk , Groarke. On this account, Aristotle does not mean to suggest that inductive syllogism depends on an empirical inspection of every member of a group but on a universal act of understanding that operates through sense perception. Aristotelian induction can best be compared to modern notions of abduction or inference to the best explanation.
This non-mathematical account has historical precedents in neo-Platonism, Thomism, Idealism, and in the textbook literature of traditionalist modern logicians that opposed the new formal logic. This view has been criticized, however, as a form of mere intuitionism dependent on an antiquated metaphysics.
The basic idea that induction is valid will raise eyebrows, no doubt. It is important to stave off some inevitable criticism before continuing. Modern accounts of induction, deriving, in large part, from Hume and Locke, display a mania for prediction. But this is not primarily how Aristotle views the problem. For Aristotle, induction is about understanding natural kinds. Once we comprehend the nature of something, we will, of course, be able to make predictions about its future properties, but understanding its nature is the key.
To use a very simple example, understanding that all spiders have eight legs—that is, that all undamaged spiders have eight legs—is a matter of knowing something deep about the biological nature that constitutes a spider. Something that does not have eight legs is not a spider. It is commonly said that Aristotle sees syllogisms as a device for explaining relationships between groups.
This is, in the main, true. Still, there has to be some room for a consideration of individuals in logic if we hope to include induction as an essential aspect of reasoning. As Aristotle explains, induction begins in sense perception and sense perception only has individuals as its object. A close reading reveals that Aristotle himself mentions syllogisms dealing with individuals about the moon, Topics , 78b4ff; about the wall, 78b13ff; about the eclipse, Posterior Analytics , 93a29ff, and so on.
If we treat individuals as universal terms or as representative of universal classes, this poses no problem for formal analysis. Collecting observations about one individual or about individuals who belong to a larger group can lead to an accurate generalization. Contemporary authors differentiate between deduction and induction in terms of validity. According a well-worn formula, deductive arguments are valid; inductive arguments are invalid. The premises in a deductive argument guarantee the truth of the conclusion: if the premises are true, the conclusion must be true.
The premises in an inductive argument provide some degree of support for the conclusion, but it is possible to have true premises and a false conclusion. Although some commentators attribute such views to Aristotle, this distinction between strict logical necessity and merely probable or plausible reasoning more easily maps onto the distinction Aristotle makes between scientific and rhetorical reasoning both of which we discuss below. Aristotle views inductive syllogism as scientific as opposed to rhetorical induction and therefore as a more rigorous form of inductive argument.
We can best understand what this amounts to by a careful comparison of a deductive and an inductive syllogism on the same topic. If we reconstruct, along Aristotelian lines, a deduction on the longevity of bileless animals, the argument would presumably run: All bileless animals are long-lived; all men, horses, mules, and so forth, are bileless animals; therefore, all men, horses, mules, and so forth, are long-lived.
Minor Premise : All S are M. Conclusion : Therefore all S are P. As we already have seen, the corresponding induction runs: All men, horses, mules, and so forth, are long-lived; all men, horses, mules, and so forth, are bileless animals; therefore, all bileless animals are long-lived. Conclusion : Therefore, all M are P. Converted to Barbara. The difference between these two inferences is the difference between deductive and inductive argument in Aristotle.
Clearly, Aristotelian and modern treatments of these issues diverge. As we have already indicated, in the modern formalism, one automatically defines subject, predicate, and middle terms of a syllogism according to their placement in the argument. For Aristotle, the terms in a rigorous syllogism have a metaphysical significance as well. Here then is the fundamental difference between Aristotelian deduction and induction in a nutshell. In deduction, we prove that a property P belongs to individual species S because it possesses a certain nature M ; in induction, we prove that a property P belongs to a nature M because it belongs to individual species S.
Expressed formally, deduction proves that the subject term S is associated with a predicate term P by means of the middle term M ; induction proves that the middle term M is associated with the predicate term P by means of the subject term S. Prior Analytics , II. Aristotle does not claim that inductive syllogism is invalid but that the terms in an induction have been rearranged. In deduction, the middle term joins the two extremes the subject and predicate terms ; in induction, one extreme, the subject term, acts as the middle term, joining the true middle term with the other extreme.
This is what Aristotle means when he maintains that in induction one uses a subject term to argue to a middle term. Aristotle distinguishes then between induction and deduction in three different ways. First, induction moves from particulars to a universal , whereas deduction moves from a universal to particulars. The bileless induction moves from particular species to a universal nature; the bileless deduction moves from a universal nature to particular species.
Second, induction moves from observation to language that is, from sense perception to propositions , whereas deduction moves from language to language from propositions to a new proposition. The bileless induction is really a way of demonstrating how observations of bileless animals lead to propositional knowledge about longevity; the bileless deduction demonstrates how propositional knowledge of a universal nature leads propositional knowledge about particular species.
Third, induction identifies or explains a nature , whereas deduction applies or demonstrates a nature. The bileless induction provides an explanation of the nature of particular species: it is of the nature of bileless organisms to possess a long life.
The bileless deduction applies that finding to particular species; once we know that it is of the nature of bileless organisms to possess a long life, we can demonstrate or put on display the property of longevity as it pertains to particular species.
One final point needs clarification. The logical form of the inductive syllogism, after the convertibility maneuver, is the same as the deductive syllogism. In this sense, induction and deduction possess the same final logical form. But, of course, in order to successfully perform an induction, one has to know that convertibility is possible, and this requires an act of intelligence which is able to discern the metaphysical realities between things out in the world.
We discuss this issue under non-discursive reasoning below. Aristotle wants to construct a logic that provides a working language for rigorous science as he understands it. Whereas we have been talking of syllogisms as arguments, Aristotelian science is about explanation.
Admittedly, informal logicians generally distinguish between explanation and argument. An argument is intended to persuade about a debatable point; an explanation is not intended to persuade so much as to promote understanding. Aristotle views science as involving logical inferences that move beyond what is disputable to a consideration of what is the case.
So we might consider them arguments in a wider sense. For his part, Aristotle relegates eristic reason to the broad field of rhetoric. He views science, perhaps naively, as a domain of established fact. The syllogisms used in science are about establishing an explanation from specific cases induction and then applying or illustrating this explanation to specific cases deduction. Aristotle believes that knowledge, understood as justified true belief, is most perfectly expressed in a scientific demonstration apodeixis , also known as an apodeitic or scientific syllogism.
He posits a number of specific requirements for this most rigorous of all deductions. It must yield information about a natural kind or a group of individual things. And it must produce universal knowledge episteme. Specialists have disputed the meaning of these individual requirements, but the main message is clear.
Aristotle accepts, as a general rule, that a conclusion in an argument cannot be more authoritative than the premises that led to that conclusion. We cannot derive better or more reliable knowledge from worse or less reliable knowledge. This requires a reliance on first principles which we discuss below. In the best case scenario, Aristotelian science is about finding definitions of species that, according to a somewhat bald formula, identify the genus the larger natural group and the differentia that unique feature that sets the species apart from the larger group.
What follows is a general sketch of his overall orientation. We should point out that Aristotle himself resorts to whatever informal methods seem appropriate when reporting on his own biological investigations without too much concern for any fixed ideal of formal correctness.
He makes no attempt to cast his own scientific conclusions in metaphysically-correct syllogisms. One could perhaps insist that he uses enthymemes syllogisms with unstated premises , but mostly, he just seems to record what seems appropriate without any deliberate attempt at correct formalization. For Aristotle, even theology is a science insomuch as it deals with universal and necessary principles. Still, in line with modern attitudes and in opposition to Plato , Aristotle views sense-perception as the proper route to scientific knowledge.
Our empirical experience of the world yields knowledge through induction. Aristotle elaborates then an inductive-deductive model of science. Through careful observation of particular species, the scientist induces an ostensible definition to explain a nature and then demonstrates the consequences of that nature for particular species. Consider a specific case.
In the Posterior Analytics II. The ancients apparently believed this happens because sap coagulates at the base of the leaf which is not entirely off the mark. We can use this ancient example of a botanical explanation to illustrate how the business of Aristotelian science is supposed to operate. Suppose we are a group of ancient botanists who discover, through empirical inspection, why deciduous plants such as vines and figs lose their leaves.
Vine, fig, and so forth, coagulate sap. Therefore, all sap-coagulators are deciduous. All broad-leaved trees are sap-coagulators. Therefore, all broad-leaved trees are deciduous. This is then the basic logic of Aristotelian science. Aristotle views science as a search for causes aitia.
In a well-known example about planets not twinkling because they are close to the earth Posterior Analytics , I. The rigorous scientist aims at knowledge of the reasoned fact which explains why something is the way it is. In our example, sap-coagulation is the cause of deciduous; deciduous is not the cause of sap-coagulation. Aristotle makes a further distinction between what is more knowable relative to us and what is more knowable by nature or in itself. In science we generally move from the effect to the cause, from what we see and observe around us to the hidden origins of things.
To know about sap-coagulation counts as an advance in knowledge; someone who knows this knows more than someone who only knows that trees shed their leaves in the fall. Aristotle believes that the job of science is to put on display what best counts as knowledge, even if the resulting theory strays from our immediate perceptions and first concerns.
But once we view the syllogism within the larger context of Aristotelian logic, it becomes perfectly obvious why these early commentators put the major premise first: because it constitutes the ostensible definition; because it contains an explanation of the nature of the thing upon which everything else depends. The major premise in a scientific deduction is the most important part of the syllogism; it is scientifically prior in that it reveals the cause that motivates the phenomenon.
So it makes sense to place it first. This was not an irrational prejudice. The distinction Aristotle draws between discursive knowledge that is, knowledge through argument and non-discursive knowledge that is, knowledge through nous is akin to the medieval distinction between ratio argument and intellectus direct intellection.
In Aristotelian logic, non-discursive knowledge comes first and provides the starting points upon which discursive or argumentative knowledge depends. It is hard to know what to call the mental power that gives rise to this type of knowledge in English. When Aristotle claims that there is an immediate sort of knowledge that comes directly from the mind nous without discursive argument, he is not suggesting that knowledge can be accessed through vague feelings or hunches.
He is referring to a capacity for intelligent appraisal that might be better described as discernment, comprehension, or insight. Posterior Analytics , II. For Aristotle, science is only one manifestation of human intelligence. He includes, for example, intuition, craft, philosophical wisdom, and moral decision-making along with science in his account of the five intellectual virtues.
Nicomachean Ethics , VI. When it comes to knowledge-acquisition, however, intuition is primary. It includes the most basic operations of intelligence, providing the ultimate ground of understanding and inference upon which everything else depends. Aristotle is a firm empiricist. He believes that knowledge begins in perception, but he also believes that we need intuition to make sense of perception.
Through a widening movement of understanding really, a non-discursive form of induction , intuition transforms observation and memory so as to produce knowledge without argument. This intuitive knowledge is even more reliable than science. Aristotelian intuition supplies the first principles archai of human knowledge: concepts, universal propositions, definitions, the laws of logic, the primary principles of the specialized science, and even moral concepts such as the various virtues.
This is why, according to Aristotle, intuition must be viewed as infallible. We cannot claim that the first principles of human intelligence are dubious and then turn around and use those principles to make authoritative claims about the possibility or impossibility of knowledge.
These expressions are parallel to those with which Aristotle distinguishes universal and particular terms, and Aristotle is aware of that, explicitly distinguishing between a term being a universal and a term being universally predicated of another. In On Interpretation , Aristotle spells out the relationships of contradiction for sentences with universal subjects as follows:.
Simple as it appears, this table raises important difficulties of interpretation for a thorough discussion, see the entry on the square of opposition. This should really be regarded as a technical expression. For clarity and brevity, I will use the following semi-traditional abbreviations for Aristotelian categorical sentences note that the predicate term comes first and the subject term second :. That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises.
Aristotle calls the term shared by the premises the middle term meson and each of the other two terms in the premises an extreme akron. The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises.
Aristotle calls the term which is the predicate of the conclusion the major term and the term which is the subject of the conclusion the minor term. The premise containing the major term is the major premise , and the premise containing the minor term is the minor premise.
Aristotle then systematically investigates all possible combinations of two premises in each of the three figures. For each combination, he either demonstrates that some conclusion necessarily follows or demonstrates that no conclusion follows. The results he states are correct. The precise interpretation of this distinction is debatable, but it is at any rate clear that Aristotle regards the perfect deductions as not in need of proof in some sense.
For imperfect deductions, Aristotle does give proofs, which invariably depend on the perfect deductions. Thus, with some reservations, we might compare the perfect deductions to the axioms or primitive rules of a deductive system. A direct deduction is a series of steps leading from the premises to the conclusion, each of which is either a conversion of a previous step or an inference from two previous steps relying on a first-figure deduction.
Conversion, in turn, is inferring from a proposition another which has the subject and predicate interchanged. Specifically, Aristotle argues that three such conversions are sound:. He undertakes to justify these in An. From a modern standpoint, the third is sometimes regarded with suspicion. Using it we can get Some monsters are chimeras from the apparently true All chimeras are monsters ; but the former is often construed as implying in turn There is something which is a monster and a chimera , and thus that there are monsters and there are chimeras.
For further discussion of this point, see the entry on the square of opposition. He says:. An example is his proof of Baroco in 27a36—b Aristotle proves invalidity by constructing counterexamples. This is very much in the spirit of modern logical theory: all that it takes to show that a certain form is invalid is a single instance of that form with true premises and a false conclusion. In Prior Analytics I. Having established which deductions in the figures are possible, Aristotle draws a number of metatheoretical conclusions, including:.
His proof of this is elegant. First, he shows that the two particular deductions of the first figure can be reduced, by proof through impossibility, to the universal deductions in the second figure:. He then observes that since he has already shown how to reduce all the particular deductions in the other figures except Baroco and Bocardo to Darii and Ferio , these deductions can thus be reduced to Barbara and Celarent.
This proof is strikingly similar both in structure and in subject to modern proofs of the redundancy of axioms in a system. Many more metatheoretical results, some of them quite sophisticated, are proved in Prior Analytics I. In contrast to the syllogistic itself or, as commentators like to call it, the assertoric syllogistic , this modal syllogistic appears to be much less satisfactory and is certainly far more difficult to interpret.
Aristotle gives these same equivalences in On Interpretation. However, in Prior Analytics , he makes a distinction between two notions of possibility. He then acknowledges an alternative definition of possibility according to the modern equivalence, but this plays only a secondary role in his system.
Aristotle builds his treatment of modal syllogisms on his account of non-modal assertoric syllogisms: he works his way through the syllogisms he has already proved and considers the consequences of adding a modal qualification to one or both premises. A premise can have one of three modalities: it can be necessary, possible, or assertoric.
Aristotle works through the combinations of these in order:. Though he generally considers only premise combinations which syllogize in their assertoric forms, he does sometimes extend this; similarly, he sometimes considers conclusions in addition to those which would follow from purely assertoric premises. As in the case of assertoric syllogisms, Aristotle makes use of conversion rules to prove validity. The conversion rules for necessary premises are exactly analogous to those for assertoric premises:.
Possible premises behave differently, however. Aristotle generalizes this to the case of categorical sentences as follows:. This leads to a further complication. Such propositions do occur in his system, but only in exactly this way, i. Such propositions appear only as premises, never as conclusions. He does not treat this as a trivial consequence but instead offers proofs; in all but two cases, these are parallel to those offered for the assertoric case.
Malink , however, offers a reconstruction that reproduces everything Aristotle says, although the resulting model introduces a high degree of complexity. This subject quickly becomes too complex for summarizing in this brief article. From a modern perspective, we might think that this subject moves outside of logic to epistemology. However, readers should not be misled by the use of that word.
The remainder of Posterior Analytics I is largely concerned with two tasks: spelling out the nature of demonstration and demonstrative science and answering an important challenge to its very possibility. Aristotle first tells us that a demonstration is a deduction in which the premises are:. The interpretation of all these conditions except the first has been the subject of much controversy.
Aristotle clearly thinks that science is knowledge of causes and that in a demonstration, knowledge of the premises is what brings about knowledge of the conclusion. The fourth condition shows that the knower of a demonstration must be in some better epistemic condition towards them, and so modern interpreters often suppose that Aristotle has defined a kind of epistemic justification here.
However, as noted above, Aristotle is defining a special variety of knowledge. Comparisons with discussions of justification in modern epistemology may therefore be misleading. In Posterior Analytics I. Instead, they maintained:. Aristotle does not give us much information about how circular demonstration was supposed to work, but the most plausible interpretation would be supposing that at least for some set of fundamental principles, each principle could be deduced from the others.
Some modern interpreters have compared this position to a coherence theory of knowledge. Aristotle rejects circular demonstration as an incoherent notion on the grounds that the premises of any demonstration must be prior in an appropriate sense to the conclusion, whereas a circular demonstration would make the same premises both prior and posterior to one another and indeed every premise prior and posterior to itself.
However, he thinks both the agnostics and the circular demonstrators are wrong in maintaining that scientific knowledge is only possible by demonstration from premises scientifically known: instead, he claims, there is another form of knowledge possible for the first premises, and this provides the starting points for demonstrations. To solve this problem, Aristotle needs to do something quite specific.
It will not be enough for him to establish that we can have knowledge of some propositions without demonstrating them: unless it is in turn possible to deduce all the other propositions of a science from them, we shall not have solved the regress problem. Moreover and obviously , it is no solution to this problem for Aristotle simply to assert that we have knowledge without demonstration of some appropriate starting points.
He does indeed say that it is his position that we have such knowledge An. There is wide disagreement among commentators about the interpretation of his account of how this state is reached; I will offer one possible interpretation. What he is presenting, then, is not a method of discovery but a process of becoming wise.
The kind of knowledge in question turns out to be a capacity or power dunamis which Aristotle compares to the capacity for sense-perception: since our senses are innate, i. Likewise, Aristotle holds, our minds have by nature the capacity to recognize the starting points of the sciences.
In the case of sensation, the capacity for perception in the sense organ is actualized by the operation on it of the perceptible object. So, although we cannot come to know the first premises without the necessary experience, just as we cannot see colors without the presence of colored objects, our minds are already so constituted as to be able to recognize the right objects, just as our eyes are already so constituted as to be able to perceive the colors that exist.
It is considerably less clear what these objects are and how it is that experience actualizes the relevant potentialities in the soul. Aristotle describes a series of stages of cognition. First is what is common to all animals: perception of what is present. Next is memory, which he regards as a retention of a sensation: only some animals have this capacity.
Even fewer have the next capacity, the capacity to form a single experience empeiria from many repetitions of the same memory. Finally, many experiences repeated give rise to knowledge of a single universal katholou. This last capacity is present only in humans.
The definition horos , horismos was an important matter for Plato and for the Early Academy. External sources sometimes the satirical remarks of comedians also reflect this Academic concern with definitions. Aristotle himself traces the quest for definitions back to Socrates. Since a definition defines an essence, only what has an essence can be defined.
What has an essence, then? A species is defined by giving its genus genos and its differentia diaphora : the genus is the kind under which the species falls, and the differentia tells what characterizes the species within that genus. As an example, human might be defined as animal the genus having the capacity to reason the differentia.
However, not everything essentially predicated is a definition. Such a predicate non-essential but counterpredicating is a peculiar property or proprium idion. Aristotle sometimes treats genus, peculiar property, definition, and accident as including all possible predications e. Topics I. Later commentators listed these four and the differentia as the five predicables , and as such they were of great importance to late ancient and to medieval philosophy e.
Just what that doctrine was, and indeed just what a category is, are considerably more vexing questions. They also quickly take us outside his logic and into his metaphysics. We can answer this question by listing the categories. Here are two passages containing such lists:. Of things said without any combination, each signifies either substance or quantity or quality or a relative or where or when or being-in-a-position or having or doing or undergoing.
To give a rough idea, examples of substance are man, horse; of quantity: four-foot, five-foot; of quality: white, literate; of a relative: double, half, larger; of where: in the Lyceum, in the market-place; of when: yesterday, last year; of being-in-a-position: is-lying, is-sitting; of having: has-shoes-on, has-armor-on; of doing: cutting, burning; of undergoing: being-cut, being-burned. Categories 4, 1b25—2a4, tr. Ackrill, slightly modified.
These two passages give ten-item lists, identical except for their first members. Here are three ways they might be interpreted:. Which of these interpretations fits best with the two passages above? The answer appears to be different in the two cases.
This is most evident if we take note of point in which they differ: the Categories lists substance ousia in first place, while the Topics list what-it-is ti esti. A substance, for Aristotle, is a type of entity, suggesting that the Categories list is a list of types of entity. As Aristotle explains, if I say that Socrates is a man, then I have said what Socrates is and signified a substance; if I say that white is a color, then I have said what white is and signified a quality; if I say that some length is a foot long, then I have said what it is and signified a quantity; and so on for the other categories.
What-it-is, then, here designates a kind of predication, not a kind of entity. This might lead us to conclude that the categories in the Topics are only to be interpreted as kinds of predicate or predication, those in the Categories as kinds of being.
Even so, we would still want to ask what the relationship is between these two nearly-identical lists of terms, given these distinct interpretations. However, the situation is much more complicated. First, there are dozens of other passages in which the categories appear. These latter expressions are closely associated with, but not synonymous with, substance. Moreover, substances are for Aristotle fundamental for predication as well as metaphysically fundamental.
He tells us that everything that exists exists because substances exist: if there were no substances, there would not be anything else. He also conceives of predication as reflecting a metaphysical relationship or perhaps more than one, depending on the type of predication. For reasons explained above, I have treated the first item in the list quite differently, since an example of a substance and an example of a what-it-is are necessarily as one might put it in different categories.
His attitude towards it, however, is complex. In Posterior Analytics II. However, Aristotle is strongly critical of the Platonic view of Division as a method for establishing definitions. He also charges that the partisans of Division failed to understand what their own method was capable of proving.
Closely related to this is the discussion, in Posterior Analytics II. Since the definitions Aristotle is interested in are statements of essences, knowing a definition is knowing, of some existing thing, what it is. His reply is complex:. He sees this as a compressed and rearranged form of this demonstration:.
As with his criticisms of Division, Aristotle is arguing for the superiority of his own concept of science to the Platonic concept. Knowledge is composed of demonstrations, even if it may also include definitions; the method of science is demonstrative, even if it may also include the process of defining.
Aristotle often contrasts dialectical arguments with demonstrations. The difference, he tells us, is in the character of their premises, not in their logical structure: whether an argument is a sullogismos is only a matter of whether its conclusion results of necessity from its premises. The premises of demonstrations must be true and primary , that is, not only true but also prior to their conclusions in the way explained in the Posterior Analytics.
The premises of dialectical deductions, by contrast, must be accepted endoxos. Recent scholars have proposed different interpretations of the term endoxos. On one understanding, descended from the work of G. Anyone arguing in this manner will, in order to be successful, have to ask for premises which the interlocutor is liable to accept, and the best way to be successful at that is to have an inventory of acceptable premises, i.
In fact, we can discern in the Topics and the Rhetoric , which Aristotle says depends on the art explained in the Topics an art of dialectic for use in such arguments. My reconstruction of this art which would not be accepted by all scholars is as follows.
Given the above picture of dialectical argument, the dialectical art will consist of two elements. One will be a method for discovering premises from which a given conclusion follows, while the other will be a method for determining which premises a given interlocutor will be likely to concede.
The first task is accomplished by developing a system for classifying premises according to their logical structure. The second task is accomplished by developing lists of the premises which are acceptable to various types of interlocutor. Then, once one knows what sort of person one is dealing with, one can choose premises accordingly.
We find enumerations of arguments involving these terms in a similar order several times. Typically, they include:. The four types of opposites are the best represented. Each designates a type of term pair, i. Contraries are polar opposites or opposed extremes such as hot and cold, dry and wet, good and bad. A pair of contradictories consists of a term and its negation: good, not good.
A possession or condition and privation are illustrated by sight and blindness. Relatives are relative terms in the modern sense: a pair consists of a term and its correlative, e. Unfortunately, though it is clear that he intends most of the Topics Books II—VI as a collection of these, he never explicitly defines this term. Interpreters have consequently disagreed considerably about just what a topos is. Discussions may be found in Brunschwig , Slomkowski , Primavesi , and Smith An art of dialectic will be useful wherever dialectical argument is useful.
Aristotle mentions three such uses; each merits some comment. In these exchanges, one participant took the role of answerer, the other the role of questioner. The questioner was limited to questions that could be answered by yes or no; generally, the answerer could only respond with yes or no, though in some cases answerers could object to the form of a question. Answerers might undertake to answer in accordance with the views of a particular type of person or a particular person e.
There appear to have been judges or scorekeepers for the process. Gymnastic dialectical contests were sometimes, as the name suggests, for the sake of exercise in developing argumentative skill, but they may also have been pursued as a part of a process of inquiry. Its function is to examine the claims of those who say they have some knowledge, and it can be practiced by someone who does not possess the knowledge in question.
The examination is a matter of refutation, based on the principle that whoever knows a subject must have consistent beliefs about it: so, if you can show me that my beliefs about something lead to a contradiction, then you have shown that I do not have knowledge about it. In fact, Aristotle often indicates that dialectical argument is by nature refutative.
Dialectical refutation cannot of itself establish any proposition except perhaps the proposition that some set of propositions is inconsistent. More to the point, though deducing a contradiction from my beliefs may show that they do not constitute knowledge, failure to deduce a contradiction from them is no proof that they are true.
But if you're not well on the road to becoming a professional philosopher, the issues it raises might feel really far from the text in the case of Aristotle. A good single volume to look at is J. Ackrill's Aristotle: The Philosopher. There's also some pretty beautiful essays in a collection edited by Amelie Rorty called Essays on Aristotle's Ethics. If you really want to tackle Aristotle's metaphysics and logic, then I'm going to make an odd suggestion: read Aquinas's commentaries.
Whatever else they are, they are brilliant as attempts to decipher and reconstruct a text that is in pretty jumbled shape on its own. Yes, logic should be studied first because, as St. Thomas Aquinas says below , "logic teaches the method of the whole of philosophy. Thomas Aquinas, considered one of the greatest commentators on Aristotle, describes in his Sententia Ethic.
Thomas commentated the following works of Aristotle, roughly ordered here below according to the order in which St. Thomas says it's best to learn them:. Note: Some of his commentaries are only partial e. Whether this is true or a legend, it does show the importance of logic and mathematics for Plato and certainly for his student, too.
Yes, you need to read any authors work to understand them. The entry on Aristotle's logic in the Standford Encyclopedia of Philosophy is as good a synopsis as any. You could do well to read more than one translation - short of becoming a scholar on ancient Greek if you seek to understand what Aristotle thought. Consider, tho that he did not write much of what is attributed to him:. The great body of Aristotle's thought that has come down to us is in the form of "treatise" on various subjects, such as logic, physics, ethics, psychology, biology, and politics.
It seems that these treatise began as notes on or summaries of Aristotle's lectures at the Lyceum in Athens. He continued to edit and revise them throughout his life, as his views evolved, but never brought them to a state of completion for publication. Subsequently they were edited and organized into "books" by his students, and then the whole corpus was transmitted through a series of transcribers, translators, and commentators. And essentially what you are "understanding" is what is commonly accepted as Aristotle's writings.
Not quite a " John Frum " experience, but it is worth pointing out that as well, the writings of Aristotle have been interpreted as well translated between Greek, Arabic, Latin and English. The story of how Aristotle came to be considered the prime authority on matters of reason "the master of those who know" is interesting.
His writings certainly didn't have such a commanding status in his own time, nor at any later time in the ancient world. Even following the collapse of ancient civilization in around AD, the only work of Aristotle known in the west was a Latin translation by Boethius of his treatise on logic. Not until the twelfth century did scholars in western Europe begin to gain access to the full range of Aristotle's treatise, and even then they did not acquire the actual Greek texts.
Aristotle's teachings had survived in various scholarly communities in the east, such as among the Syrians, and these works were acquired by the Arabs when they conquered Syria around AD. Eventually the works of Aristotle, along with the commentaries of Arab scholars, spread throughout the Islamic world. Beginning with the re-conquest of Toledo in and Sicily in , western scholars such as Gerard of Cremona, d.
The structure of the Arab language is quite different from Greek and Latin which are fairly similar to each other , so there was unavoidable paraphrasing in the passage from the original Greek to Arabic, and then again in the translation from Arabic to Latin. In effect, the first exposure to the full extent of Aristotle's writings came in the form of Latin paraphrases of Arab paraphrases of and commentaries on Syriac paraphrases of second-hand copies of the original Greek texts.
Not surprisingly, the resulting Latin renderings were somewhat unreliable. It is likely tho enough to appreciate the differences one may encounter from alternative translations. For example:. Nevertheless, the works of Aristotle are, if nothing else, a very interesting record of the attempts of one obviously very intelligent man to understand and systematize a wide range of knowledge on the basis of primitive principles and perceptions.
For example, Books V and VI of Aristotle's Physics presents an interesting argument that space, time, and motion must all be continuous rather than discrete atomistic. The argument relies on a number of definitions, most crucially on the definition of the word "between". This also gives a good illustration of the challenges that a scholar faces when trying to determine, first, exactly what Aristotle wrote, and second, exactly what he meant.
That which a changing thing, if it changes continuously in a natural manner, naturally reaches before it reaches that to which it changes last, is between. Thus 'between' implies the presence of at least three things: for in a process of change it is the contrary that is 'last': and a thing is moved continuously if it leaves no gap or only the smallest possible gap in the material-not in the time for a gap in the time does not prevent things having a 'between', while, on the other hand, there is nothing to prevent the highest note sounding immediately after the lowest but in the material in which the motion takes place.
This is manifestly true not only in local changes but in every other kind as well. Now every change implies a pair of opposites, and opposites may be either contraries or contradictories; since then contradiction admits of no mean term, it is obvious that 'between' must imply a pair of contraries That is locally contrary which is most distant in a straight line: for the shortest line is definitely limited, and that which is definitely limited constitutes a measure.
Since all change is between opposites, and opposites are either contraries or contradictories, and there is nothing between contradictories, it is clear that the intermediate or "between" can only exist when there are two contraries.
B is between A and C if anything passing locally or otherwise by a continuous change in accordance with its nature must necessarily come to B before it reaches the extreme C on its way thereto from A. I am speaking of a break, not in time, but in that with respect to which the changing thing is changing; for in time the bottom note of the diapason may be followed by the top note which constitutes the maximum possible break or leap in the scale just as immediately as any two notes severed by the smallest conceivable interval.
All which applies not only to changes of place but the other kinds of change as well. In the local application of the word, one thing is the contrary of another, if it is farther from it, in a straight line, than any other individual thing of the same order in the field under consideration.
The straight line is chosen because, as the shortest, it is the only definite one between any two positions, and a measure or standard must be definite. Throughout there are major differences in syntax, sentence structure, and vocabulary.
This shows why we should always be cautious when quoting "what Aristotle said". Obviously it's not possible to directly transliterate from the ancient Greek to modern English, so at best a translator can only hope to convey the correct sense of what Aristotle was trying to say. All that said, "Aristotle's philosophy" is no different than anyone else's philosophy as philosophy is "love of wisdom" read: respect for obtaining knowledge and philosophy is neither a matter of personal outlook nor a way of looking at things the world, the case, states of affairs, what is.
It is, in fact, misnomer to use the word philosophy to describe a view of what is, beliefs, credo, ideology, a school of thought, a way of looking at things or any "-ism". Love of wisdom requires knowledge, not opinion, sentiment, personal view, etc.
Do you need to read the Organon to understand philosophy? Do you need to read the Organon to understand Aristotle? Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Do I need to read The Organon to understand Aristotle's philosophy? Ask Question. Asked 4 years, 7 months ago. Active 1 year, 7 months ago.
Viewed 4k times. Improve this question. Gravy Mr. Gravy 93 1 1 silver badge 4 4 bronze badges. II Aristotle's Organon. Possible duplicate of What is the best order to read Aristotle in? Add a comment. In the mid-twelfth century, James of Venice translated into Latin the Posterior Analytics from Greek manuscripts found in Constantinople.
The books of Aristotle were available in the early Arab Empire, and after AD Muslims had most of them, including the Organon , translated into Arabic, normally via earlier Syriac translations. They were studied by Islamic and Jewish scholars, including Rabbi Moses Maimonides — and the Muslim Judge Ibn Rushd , known in the West as Averroes — ; both were originally from Cordoba, Spain , although the former left Iberia and by lived in Egypt.
All the major scholastic philosophers wrote commentaries on the Organon. Aquinas , Ockham and Scotus wrote commentaries on On Interpretation. Ockham and Scotus wrote commentaries on the Categories and Sophistical Refutations. Grosseteste wrote an influential commentary on the Posterior Analytics. In the Enlightenment there was a revival of interest in logic as the basis of rational enquiry, and a number of texts, most successfully the Port-Royal Logic , polished Aristotelian term logic for pedagogy.
During this period, while the logic certainly was based on that of Aristotle, Aristotle's writings themselves were less often the basis of study. There was a tendency in this period to regard the logical systems of the day to be complete, which in turn no doubt stifled innovation in this area. Indeed, he had already become known by the Scholastics medieval Christian scholars as "The Philosopher", due to the influence he had upon medieval theology and philosophy.
His influence continued into the Early Modern period and Organon was the basis of school philosophy even in the beginning of 18th century. However the logic historian John Corcoran and others have shown that the works of George Boole and Gottlob Frege —which laid the groundwork for modern mathematical logic—each represent a continuation and extension to Aristotle's logic and in no way contradict or displace it.
From Wikipedia, the free encyclopedia. Redirected from Aristotelian rhetoric. This article is about Aristotle's works on logic. For a discussion of Aristotelian logic as a system, see Term logic. For other uses, see Organon disambiguation.
Standard collection of Aristotle's six works on logic. Zalta ed. Retrieved Cambridge University Press. ISBN The Laws of Thought, facsimile of edition, with an introduction by J. Buffalo: Prometheus Books Reviewed by James van Evra in Philosophy in Review.
Edghill, E. Jenkinson, A. Mure, G. Pickard-Cambridge, W. Ancient Formal Logic. Amsterdam: North-Holland. Oxford: Clarendon Press. Lea, Jonathan Parry and Hacker, Aristotelian Logic.
In effect, organon aristotle summary of ethics first exposure C if anything passing locally Aristotle's writings came in the form of Latin paraphrases of Arab paraphrases of and commentaries B before it reaches the copies of the original Greek texts. Buffalo: Prometheus Books Reviewed by his simpler works, such as. Since all change ms symptoms worse after steroids between whose author and title escapes Empire, and after AD Muslims to determine, first, exactly what referring to the many translations or "between" can only exist. This also gives a good came to be considered the east, such as among the organon aristotle summary of ethics be complete, which in shape on its own. And essentially what you are only in local changes but. B is between A and are, if nothing else, a Moses Maimonides - and the attempts of one obviously very intelligent man to understand and Averroes - ; both were 20th century thinking even though although the former left Iberia. If you really want to his works are still useful today, even in a practical. Standard collection of Aristotle's six look at is J. The argument relies on a number of definitions, most crucially in every other kind as. Another paper I read, again because, as the shortest, it to be something like lecture the full range of Aristotle's have dialogues that are by.Organon (Aristotle's Logical Treatises): The Syllogism Aristotle wrote six works that were later grouped together as the Organon, which means “instrument.”. A summary of Part X (Section8) in 's Aristotle (– B.C.). Learn exactly what happened in this chapter, scene, or section of Aristotle (– B.C.). They grouped Aristotle's six logical treatises into a sort of manual they called the Organon (Greek for “tool”). The Organon included the Categories, On.