During the Islamic Golden Age, there was a logical debate among Islamic philosophers and jurists whether the term Qiyas refers to analogical reasoning, inductive reasoning or categorical syllogism.

He demanded strict dialectical training as the means of distinguishing the true from the false, and asserted that logic ( or the syllogism ) furthered the knowledge of catholic verities ; ignorance of logic was the reason why men misunderstood Scripture, since men overlooked the connection – the distinction between idea and appearance.

Before this emergence, logic was studied with rhetoric, through the syllogism, and with philosophy.

However, the enthymeme based upon logic ( especially, based upon the syllogism ) was viewed as the basis of rhetoric.

The syllogism was at the core of traditional deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations.

* as basically a transformation of a deductive categorical syllogism ( but in 1903 he offered a variation on modus ponens instead, and by 1911 he was unconvinced that any one form covers all hypothetical inference ).

Another systematic refutation of Greek logic was written by Ibn Taymiyyah ( 1263 – 1328 ), the Ar-Radd ' ala al-Mantiqiyyin ( Refutation of Greek Logicians ), where he argued against the usefulness, though not the validity, of the syllogism and in favour of inductive reasoning.

Avicenna's system of logic was responsible for the introduction of hypothetical syllogism, temporal modal logic and inductive logic.

Later during the Islamic Golden Age, there was a logical debate among Islamic philosophers, logicians and theologians over whether the term Qiyas refers to analogical reasoning, inductive reasoning or categorical syllogism.

Another systematic refutation of Greek logic was written by Ibn Taymiyyah ( 1263 – 1328 ), the Ar-Radd ' ala al-Mantiqiyyin ( Refutation of Greek Logicians ), where he argued against the usefulness, though not the validity, of the syllogism and in favour of inductive reasoning.

In the third part, Watts discusses reasoning and argumentation, with particular emphasis on the theory of syllogism, which was a centrally important part of the classical logic which Watts ' was treating in his work.

For Aristotle, who defined it in his Rhetoric, an enthymeme was a " rhetorical syllogism " which was based on probable opinions, thus distinguishing it from a scientific syllogism.

The importance of the statistical syllogism was urged by Henry E. Kyburg, Jr., who argued that all statements of probability could be traced to a direct inference.

The statistical syllogism was used by Donald Cary Williams and David Stove in their attempt to give a logical solution to the problem of induction.

Aristotelian logic was the first type of logic to attempt to categorize every valid syllogism.

Before the Middle Ages there was a logical debate among Islamic logicians, philosophers and theologians over whether the term qiyas refers to analogical reasoning, inductive reasoning or categorical syllogism.

This is a reference to Aristotle's work Organon, which was his treatise on logic and syllogism.

The syllogism was too much for Ted.

The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, even the prejudices which judges share with their fellow men, have had a good deal more to do than the syllogism in determining the rules by which men should be governed.

However, by exposing the unparallel structure in the original syllogism, the reader is now able to supply the logical conclusion:

In the explanation of Locke, for example, reason requires the mental use of a third idea in order to make this comparison by use of syllogism.

The premises and conclusion of a syllogism can be any of four types, which are labeled by letters as follows.

The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another.

* Ockham ends ( chapter 18 ) by showing how all these fallacies err against the syllogism.

This logical fallacy is neatly demonstrated by the joke syllogism that contains a fallacy of four terms:

He rejects the medieval apparatus of the syllogism ; but is precluded by his standpoint from understanding the active, spiritual character of thought ; nor had he that interest in natural science and appreciation of inductive reasoning which form the chief merit of JS Mill.

* Barbara, a mnemonic devised by mediaeval scholasticism for a particular syllogism

A problem in meaning arises in the study of Prior Analytics for the word " syllogism " as used by Aristotle in general does not carry the same narrow connotation as it does at present ; Aristotle defines this term in a way that would apply to a wide range of valid arguments.

At present, " syllogism " is used exclusively as the method used to reach a conclusion which is really the narrow sense in which it is used in the Prior Analytics dealing as it does with a much narrower class of arguments closely resembling the " syllogisms " of traditional logic texts: two premises followed by a conclusion each of which is a categorial sentence containing all together three terms, two extremes which appear in the conclusion and one middle term which appears in both premises but not in the conclusion.

Each proposition ( statement that is a thought of the kind expressible by a declarative sentence ) of a syllogism is a categorical sentence which has a subject and a predicate connected by a verb.

The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, and even the prejudices which judges share with their fellow-men, have had a good deal more to do than syllogism in determining the rules by which men should be governed.

Dialethesists solve this problem by rejecting the principle of explosion, and, along with it, at least one of the more basic principles that lead to it, e. g. disjunctive syllogism or transitivity of entailment, or disjunction introduction.

#: from ( 3 ) and ( 4 ) by disjunctive syllogism

Rescher further introduces his specific study of the apory by qualifying the term as “ a group of individually plausible but collectively incompatible theses ,” a designation he illustrates with the following syllogism or “ cluster of contentions ”:

However it can be rewritten as a standard form AAA-1 syllogism by first substituting the synonymous term " humans " for " people " and then by reducing the complementary term " immortal " in the first premise using the immediate inference known as obversion ( that is, " No humans are immortal.

Although Aristotle's logic is almost entirely concerned with the theory of the categorical syllogism, there are passages in his work that are now seen as anticipations of temporal logic, and may imply an early, partially developed form of first-order temporal modal binary logic.

In syllogism, the middle term, which is found in both the subject ( minor term ) and is invariably connected with the predicate ( major term ), is seen as the cause of knowledge.

Heyting algebra -- Higher-order predicate -- Horn clause -- Hypothetical syllogism

The major term is the predicate term of the conclusion of a categorical syllogism.

In logic, a middle term is a term that appears ( as a subject or predicate ) in both premises but not in the conclusion of a categorical syllogism.

In classical logic disjunctive syllogism ( historically known as modus tollendo ponens ) is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.

In propositional logic, disjunctive syllogism ( also known as disjunction elimination and or elimination, or abbreviated ∨ E ), is a valid rule of inference.

* Sir Francis Bacon ( 1561 – 1626 ) published Novum Organum in 1620, which outlined a new system of logic based on the process of reduction, which he offered as an improvement over Aristotle's philosophical process of syllogism.

Although the Ancient Greeks had no separate word for logic as distinct from language and reason, Aristotle's newly coined word " syllogism " ( syllogismos ) identified logic clearly for the first time as a distinct field of study.

( Sanskrit ny-āyá, literally " recursion ", used in the sense of " syllogism, inference ") is the name given to one of the six orthodox or astika schools of Hindu philosophy — specifically the school of logic.

The logic of Aristotle, and particularly his theory of the syllogism, has had an enormous influence in Western thought.

* In logic, the hetu or middle term in a syllogism

In classical logic, hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises.

In propositional logic, hypothetical syllogism is the name of a valid rule of inference ( often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication ).

Hypothetical syllogism is one of the rules in classical logic that is not always accepted in certain systems of non-classical logic.