Aristotelian logic and syllogism
Get a deeper understanding of Aristotelian logic! Follow our comprehensive guide on Aristotle's Theory of Logic and learn about its key principles such as syllogistic & categorical reasoning.
Aristotle's Theory of Logic is one of the most influential intellectual legacies in western civilization. It introduced concepts such as syllogistic and categorical reasoning, which have been used and adapted by philosophers for centuries. In this comprehensive guide, we'll explore the theory and its implications on modern thought.
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| Aristotle on logic |
The Fascinating History Behind Aristotle's Logic
This supremacy was largely lost after the Renaissance, but his supremacy in logic survived. Even at the present day, all Catholic teachers of philosophy and many others still obstinately reject the discoveries of modern logic, and adhere with a strange tenacity to a system which is as definitely antiquated as Ptolemaic astronomy.
This makes it difficult to do historical justice to Aristotle. His present-day influence is so inimical to clear thinking that it is hard to remember how great an advance he made upon all his predecessors (including Plato), or how admirable his logical work would still seem if it had been a stage in a continual progress, instead of being (as in fact it was) a dead end, followed by over two thousand years of stagnation.
In dealing with the predecessors of Aristotle, it is not necessary to remind the reader that they are not verbally inspired; one can therefore praise them for their ability without being supposed to subscribe to all their doctrines. Aristotle, on the contrary, is still, especially in logic, a battle-ground, and cannot be treated in a purely historical spirit.
It is helpful to know something about Aristotle’s logic because important developments in later philosophy either turned upon it or were sparked by extensions and developments of it, especially in the work of Gottlob Frege, Bertrand Russell and others in twentieth-century ‘Analytic philosophy’
What is Aristotle's Theory of Logic?
Aristotle's Theory of Logic is a philosophical approach to understanding how humans can draw logical conclusions from given information. It proposes that logical reasoning is based on certain patterns, such as syllogisms and categorical propositions, which are then synthesized into broader arguments. Aristotle believed that logic could be used to uncover the truth about the world around us, and his thought has been fundamental to the development of western philosophy.
What is Aristotle's Syllogism?
Aristotle's syllogism is one of the pivotal components of his logical theory, representing the first formal method for argumentation that has stood the test of time and can still be applied to our present day reasoning. A syllogism is a three-part logical argument composed of a major premise, a minor premise, and a conclusion. When arranged correctly and supported by evidence, this logical format can be used to make soundly reasoned decisions or draw accurate conclusions from given facts.
Syllogistic Reasoning
Syllogistic reasoning is a central concept in Aristotelian logic. It involves three parts: a major premise, a minor premise, and a conclusion. A syllogism provides the logical connection between two statements, known as premises, which then lead to an inference or conclusion. For example, one syllogism might go like this: All men are mortal (Major Premise); Socrates is a man (Minor Premise); Therefore, Socrates is mortal (Conclusion). With such an understanding of logical reasoning it’s possible to make accurate deductions from given information.
Aristotelian logic and syllogism
Aristotelian syllogism examples
Other forms are: No fishes are rational, all sharks are fishes, therefore no sharks are rational. (This is called "Celarent.").
All men are rational, some animals are men, therefore some animals are rational. (This is called "Darii.")
No Indians are black, some men are Indians , therefore some men are not black. (This is called "Ferio.")
These four make up the "first figure"; Aristotle adds a second and third figure, and the schoolmen added a fourth. It is shown that the three later figures can be reduced to the first by various devices.
There are some inferences that can be made from a single premiss. From "some men are mortal" we can infer that "some mortals are men." According to Aristotle, this can also be inferred from "all men are mortal." From "no gods are mortal" we can infer "no mortals are gods," but from "some men are not Indians" it does not follow that "some Indians are not men."
Apart from such inferences as the above, Aristotle and his followers thought that all deductive inference, when strictly stated, is syllogistic. By setting forth all the valid kinds of syllogism, and setting out any suggested argument in syllogistic form, it should therefore be possible to avoid all fallacies.
Categories of Syllogisms
Aristotle identified four categorical forms of syllogism which each consist of a major premise, a minor premise, and a conclusion. These are affirmative (A), negative (E), universal (I) and particular (O). The three vowels are used to remember the order of the premises in a syllogism; A comes before E, I comes before O. An affirmative syllogism affirms that something is true while a negative syllogism denies it. A universal statement asserts that something pertains to all members of a certain category whereas a particular statement says it only applies to some members.
Examples of proposition
Aristotle took it that the fundamental unit of logical interest is the proposition, the ‘what is said’ by an utterance, this ‘what is said’ being either true or false. A proposition is not a sentence: the sentences ‘snow is white,’ ‘Schnee ist weiss,’ ‘la neige est blanche,’ ‘xue shi baide,’ respectively in English, German, French and Mandarin, all express the same proposition. So do the sentences ‘snow is white,’ ‘whiteness is a property exemplified by snow,’ ‘precipitated ice crystals nucleated around atmospheric particles typically scatter all the visible wavelengths of light.’ Likewise ‘I have a stomach ache’ as said by me might be false but as said by you might be true; here therefore the same sentence expresses different propositions.
The structure of propositions is analysed by Aristotle into two chief components, the subject and the predicate. The subject is that about which something true or false is asserted; the predicate is what is asserted about the subject. So in ‘snow is white’ the subject term is ‘snow’ (and the subject is snow) and the predicate term is ‘is white’ (and whiteness is ‘predicated of’ – said about – the subject). These terms are the focus of his attention. His logical writings contain two slightly different accounts of how they are to be classified. One is the scheme of categories (sometimes known as the predicaments) and the other is what came to be known as the five words or five predictable.
Aristotle's categories explained
The intention behind the notion of the categories is to reveal what we are saying when we make an assertion of the forms ‘A is B,’ ‘A is a B,’ ‘As are Bs.’ For example, if I say ‘A is white,’ the predicate is in the category of ‘quality’ – that is, it tells us what A is like. If I say ‘A is a snowflake’ the predicate falls into the category of ‘substance’, that is, it tells us what thing it is. If I say ‘there are five snowflakes’ the predicate falls into the category of ‘quantity’, how many there are. If I say ‘one snowflake fell after another snowflake’ the predicate is in the category of ‘relation’, how they were related to each other (in this case, in time. ‘Mehul is Sunil’s father’ is another example of the category of relation, in this case, in genetics).
Substance, quality, quantity and relation are the four main categories. Aristotle adds six others: place, time, position, condition, activity, passivity. He does not claim that this list is complete or exhaustive, and because there are pre figurings of this classification in Plato it is likely that Aristotle took his starting point from there.
Aristotle’s investigation of how such classes relate to each other as representable in these ways gave him the concept of a classification into genus, species, difference, property and accident. These are the ‘five words’ (quinque voces) as later logicians called them, and they list the ways in which a predicate can relate to a subject – or, alternatively put, the ways in which we can speak about something. You can speak about something specifically, or generally; that is species and genus. You can talk about the differences between species of things that separate them from each other; that is difference. You can talk about the characteristics of something that are found in all instances of the class of things it belongs to – these are properties. Or you can speak of a characteristic that something happens to have but which it could just as likely not have – which it has accidentally, so to speak; these are accidents, like the shape of a shoe or the colour of a shirt.
What is species according to Aristotle?
The ‘species’, or as Aristotle first called it the ‘definition of a thing relates to its essence, the ‘what makes it what it is’ factor. It is specific to the thing in question. The genus is that part of the thing’s essence which is not unique to it, but is shared with other things of the same kind in general. So ‘lion’ is a species of the genus ‘animal’. (Biological taxonomy differs from this classification, having a more detailed hierarchy in descending order: domains, kingdoms; phyla, classes, orders, families, genera and species.)
The differentia distinguish one species from another within a genus; they are what make circles different from squares though they are both instances of ‘shape. These concepts gave Aristotle his fundamental view about how we categorize or define anything: we do it ‘by genus and difference’.
Aristotle's three laws of thought
Aristotle developed three fundamental laws of thought: the law of identity, the law of non-contradiction, and the law of excluded middle. The law of identity states that a thing is what it is; it states that “A” is “A”. The law of non-contradiction states that something cannot be both true and false at the same time; if something is true then its opposite cannot also be true. Finally, the law of excluded middle stipulates that either one statement or another must be true - there can’t be two contradictory statements between which reality lies undecided.
Logic according to Aristotle
What Aristotle wished to achieve was understanding that is, he wished to give explanations of things and ultimately of the universe itself. The Greek word for explanation, aitia, also means ‘cause’, and Aristotle framed the task of explaining things as ascertaining their causes: to know or understand something, he said, is to know its cause. Now, causes themselves have causes, and there is a risk that the chain of explanation by causes might run back for ever. This is where definition enters the picture.
Suppose you explain A by saying it was caused by B, and that B was caused by C; you will reach a point, say D (or perhaps eventually Z), where the explanation stops because at that point we say ‘because it is what it is’; we have reached the definition of the thing, an account of its nature, from which explanations of C and B and A follow.
Aristotelian or Syllogistic Logic is a form of logical reasoning developed by the Ancient Greek philosopher Aristotle. It consists of two premises which relate to each other in some way and lead to a logical conclusion. Its main principles are based on syllogistic reasoning, where one statement is used to arrive at another, as well as categorical reasonings, where the relationships between sets of classes are examined.
The Modern-Day Impact of Aristotelian Logic
The impact of Aristotle's logical works can still be seen in modern-day life and institutions. Aristotle's logic has been integrated into modern analyses of the scientific method; they remain an essential framework for evaluating information and making decisions. Aristotelian logic also remains an important foundation of legal argumentation and language, as seen in the use of syllogisms, a type of deductive reasoning where a conclusion is gleaned based on two or more propositions that are asserted or assumed to be true.
By the time that logical orginality revived, a reign of two thousand years had made Aristotle very difficult to dethrone. Throughout modern times, practically every advance in science, in logic, or in philosophy has had to be made in the teeth of the opposition from Aristotle's disciples.
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