What is Aristotle’s theory of logic? Why is it important? This article aims to suggest answers to these questions. It begins with a discussion of Aristotle’s place in the history of philosophy, of logic in particular, and the relationship between his logic and logic as it is practiced today. We explain the idea of the deduction before certain important differences between Aristotle’s philosophy of logic and the projects of contemporary logicians are set out. This article concludes with a discussion of the syllogism and of the distinction between perfect and imperfect deductions.
Aristotle’s Life and Legacy
Aristotle was a Greek philosopher of the 4th century BC, who was taught by Plato, was a tutor to Alexander the Great, and was in charge of the Academy, which was founded by Plato and was the most famous and prestigious academic institution of the Ancient World (certainly in Europe).
Along with Plato, Aristotle is almost inarguably one of the two most important philosophers ever. There is a very simple reason for this: Aristotle has had an extraordinary influence on almost every area of philosophy. We continue to discuss many philosophical problems and topics in a way that is substantially analogous to his method of reasoning. Even in this context, the debt which the discipline of philosophical logic owes to him is exceptional.
Although other logical schools—notably that of the Stoics—had periods of pre-eminence in the Ancient World. However, by later antiquity, and certainly by the medieval period, the dominant form of logical analysis was Aristotelian. Aristotle remained the dominant figure in philosophical logic well into the 19th century. Immanuel Kant famously claimed that Aristotle had discovered all that there was to discover in the subject.
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Even given the significant development of logic in the modern period, owing to the work of Gottlob Frege and subsequent developments in formal logic, the practice of logic still owes a great debt to Aristotle. Indeed, we can follow Robin Smith (as we will at various points throughout this article) in observing that there are significant similarities in the approach uniting modern logicians with Aristotle. In particular, they share a concern with metatheory—studying the theory of logical theories themselves, which means studying the properties of logical systems rather than simply constructing them.
What is Logic?
Given that Aristotle’s is the earliest study of logic that we know of, his system seems remarkably developed and sophisticated. But what is logic, really? Logic can be considered a formal or informal language by which we develop a deductive system. If a language is formal or artificial, then there must be some way in which that language translates into or corresponds to natural languages (those are the languages we actually speak and write with normally).
The purpose of a logical system of this kind is to capture, codify, and record certain features of arguments. In particular, modern logicians focus on validity. Aristotle’s logical works were compiled into what is known as the Organon, or ‘Instrument.’ This is an artificial classification, which reflects a controversy in ancient philosophy over whether logic should be conceived of as a tool to be applied to existent theories or whether it should be seen as a discipline that produces its own theories.
In any case, the classification of the Organon has stuck around. The works contained within it are: Categories, On Interpretation (De Interpretatione), Prior Analytics, Posterior Analytics, Topics, and On Sophistical Refutations. It is worth emphasizing that this is not a structure that Aristotle would have recognized himself. For instance, Prior Analytics and Posterior Analytics were originally part of the same work.
The basis of Aristotle’s logical system is the method of deduction. Aristotle defines deduction as follows:
“A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so.”
The ‘thing supposed’ here is the premise, and the ‘results of necessity’ is the conclusion. This is Aristotle’s way of articulating quite a modern notion, which is that of logical consequence, and is therefore offering a general description of a ‘valid argument.’
Aristotle and Modern Logic
The notion that pairs with that of deduction is induction, which is the pattern of reasoning that relies on observation. Aristotle has much less to say about induction in the context of logic, but he does indicate that inductive reasoning constitutes the basis of the natural sciences.
There are some important differences between Aristotle’s logic and that which modern logicians use today which are worth keeping in mind. First, there are basic differences in terms of execution and style. The underlying methodological differences are the following. A result of necessity implies that the conclusion of a logical argument must be different from that which was presupposed, which implies that the conclusion of an argument cannot be replicated in one of the premises. The phrase ‘certain things having been supposed’ suggests that Aristotle is ruling out arguments with only one premise, which modern logic does not do.
Lastly, there is a problem to do with quantification, hinging on the phrase “because of their being so.” This appears to rule out arguments in which the conclusion is not related to the premises. For instance, arguments in which the premises are inconsistent or arguments with conclusions that would follow from any premise.
It seems to follow that although Aristotle comes close to defining validity in something like the terms we would ourselves, not all valid arguments are captured by Aristotle’s definition of deduction. One gets the sense that this is an error, and that, were Aristotle presented with certain arguments that he might not have thought of (understandably, since they are quite useless for anyone other than a logician), he might well have modified his concept of deduction.
The Syllogism and Truth
The central logical procedure for Aristotle is that of the syllogism, which is the logical procedure that follows the following form:
if A then B; if B then C; therefore, if A then C.
This pattern of reasoning is so important for Aristotle because it allows us to draw a relation that is not immediately observable by way of a ‘middle term’ (which is equivalent to term B in the above). This is very important, in part due to the relationship between knowledge and logical demonstration in Aristotle’s work:
“If knowing is what we have laid it down to be, demonstrative knowledge must be based upon things which are true and primary and immediate, and more known than and prior to and causes of the conclusion; for thus the principles will be appropriate to what is being proved. There can be an inference without these conditions, but there cannot be a proof; for it will not yield knowledge.”
An important distinction in Aristotle’s logical system exists between perfect and imperfect deductions. This distinction is a little bit obscure to us—as with certain things in Aristotle’s philosophy, we aren’t given as many worked examples as we might like.
A New Conception of Language
Much of the work we have inherited from Aristotle was intended to serve as lecture notes. It seems a reasonable conjecture to suggest that certain ambiguities might be resolved by examples provided as Aristotle gave his lectures, which—along with a certain kind of formal debate practice—seems to be one of the chief methods of philosophical teaching and practice in the Academy.
It seems sensible enough to take the distinction between perfect and imperfect deductions as at least functionally analogous to that which exists between axioms and other elements of logical or mathematical systems. In other words, whereas perfect deductions require no proof—there is no elaboration required to show them to be true—imperfect deductions do require demonstration of this kind.
Clearly, for a logical system to be self-contained and self-vindicating in the way Aristotle would like, imperfect deductions must be inferred from a (or several) perfect ones: “the conclusion of such a proof must be eternal—therefore there is no proof or knowledge about things which can be destroyed.”
The purpose of logic, at least for many modern philosophers, is either to test arguments, to understand language better, and (perhaps) to provide a solid foundation for philosophy to build on. On any conception of the place of logic in philosophy, it owes a substantial debt to the philosopher who developed it first.