Scholars have noticed that the first category, substance or essence, seems to be fundamentally different than the others; it is what something is in the most complete and perfect way. Aristotle does not believe that all reasoning deals with words. Moral decision-making is, for Aristotle, a form of reasoning that can occur without words.
Still, words are a good place to begin our study of his logic. Logic, as we now understand it, chiefly has to do with how we evaluate arguments. But arguments are made of statements, which are, in turn, made of words. In Aristotelian logic, the most basic statement is a proposition, a complete sentence that asserts something.
There are other kinds of sentences—prayers, questions, commands—that do not assert anything true or false about the world and which, therefore, exist outside the purview of logic. Still, it makes perfect sense to predicate properties of anger. We can say that anger is unethical, hard to control, an excess of passion, familiar enough, and so on.
Aristotle himself exhibits some flexibility here. Of course, it is not enough to produce propositions; what we are after is true propositions. Aristotle believes that only propositions are true or false. Truth or falsity at least with respect to linguistic expression is a matter of combining words into complete propositions that purport to assert something about the world.
Individual words or incomplete phrases, considered by themselves, are neither true or false. It is to repeat words without making any claim about the way things are. In other words, a true proposition corresponds to way things are. But Aristotle is not proposing a correspondence theory of truth as an expert would understand it.
He is operating at a more basic level. What does it mean to say that this claim is true? If we observe spiders to discover how many legs they have, we will find that except in a few odd cases spiders do have eight legs, so the proposition will be true because what it says matches reality. Aristotle suggests that all propositions must either affirm or deny something. Every proposition must be either an affirmation or a negation; it cannot be both.
He also points out that propositions can make claims about what necessarily is the case, about what possibly is the case, or even about what is impossible. His modal logic, which deals with these further qualifications about possibility or necessity, presents difficulties of interpretation. We will focus on his assertoric or non-modal logic here. In one famous example about a hypothetical sea battle, he observes that the necessary truth of a mere proposition does not trump the uncertainty of future events.
Because it is necessarily true that there will be or will not be a sea battle tomorrow, we cannot conclude that either alternative is necessarily true. De Interpretatione , 9. Note that we must not confuse the necessary truth of a proposition with the necessity that precipitates the conclusion of a deductively-valid argument. Having fixed the proper logical form of a proposition, he goes on to classify different kinds of propositions. He begins by distinguishing between particular terms and universal terms.
We may claim that all spiders have eight legs or that only some spiders have book-lungs. In the first case, a property, eight-leggedness, is predicated of the entire group referred to by the universal term; in the second case, the property of having book-lungs is predicated of only part of the group. So, to use Aristotelian language, one may predicate a property universally or not universally of the group referred to by a universal term.
Each different categorical proposition possesses quantity insomuch as it represents a universal or a particular predication referring to all or only some members of the subject class. It also possesses a definite quality positive or negative insomuch as it affirms or denies the specified predication. Note that these four possibilities are not, in every instance, mutually exclusive.
More on this, with qualifications, below. One caveat: Although we cannot linger on further complications here, keep in mind that this is not the only way to divide up logical possibility. Aristotle examines the way in which these four different categorical propositions are related to one another. As it turns out, we can use a square with crossed interior diagonals Fig. 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.
Following the collapse of the Western Roman Empire in the fifth century, much of Aristotle's work was lost in the Latin West. The Categories and On Interpretation are the only significant logical works that were available in the early Middle Ages. These had been translated into Latin by Boethius. The other logical works were not available in Western Christendom until translated into Latin in the 12th century.
However, the original Greek texts had been preserved in the Greek -speaking lands of the Eastern Roman Empire aka Byzantium. 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. 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.