Quaternio terminorum: The fallacy of four

Near the Fraser River, yesterday

PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.

Quaternio terminorum

This is the fallacy of four terms. (171). The standard three line argument requires that one term be repeated in the first two lines, and not be within the conclusion. (171). This is in the context of syllogistic reasoning. (171).

Common example within philosophy:

All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.

Pirie reasons that 'we cannot deduce new relationships between terms by using a middle term common to both-there isn't one.'

Blackburn explains that a syllogism is the presentation of one proposition from two premises. (368). In other words, two premises (propositions) and then a conclusion.

Logically fallacious

'Description: This fallacy occurs in a categorical syllogism when the syllogism has four terms rather than the requisite three (in a sense, it cannot be a categorical syllogism to begin with!) If it takes on this form, it is invalid.'

However, not all valid and sound argumentation holds to syllogism

University of Kentucky

From the University of Kentucky:

'argument

An Argument is a group of statements including one or more premises and one and only one conclusion. The point of an argument is to give the receiver of the argument good reason to believe new information.'

Premises are not limited, in every case.

University of Windsor 2011

Cited

'G.C. GODDU Department of Philosophy University of Richmond'

'ABSTRACT: Is it possible for an argument to have either zero premises or an infinite number of premises? I shall argue that regardless of how you conceive of arguments you should accept that an argument could have an infinite number of premises. The zero case is more complicated since the matter seems to depend not only on the metaphysics of arguments, but also the nature and function of arguing. I shall argue that at least a plausible case can be made for the possibility of zero premise arguments.'

'How many premises can an argument have?'

'If what I have argued here is correct, then everyone should accept the possibility of infinite premise arguments. On the other hand, whether we should accept zero-premise arguments seems to depend upon the resolution of other highly controversial options in argumentation theory such as—does every argument need a corresponding act of arguing? Does defining argument require an appeal to function? Trying to resolve these issues is a project for another time. At the very least, however, I hope that I have sketched out a position according to which it is straightforwardly possible for there to be zero-premise arguments.'

End citations

I can embrace the idea of many premises and one conclusion. I would present any other conclusion, within another argument. I would prefer this to the rarely used argument with more than one conclusion.

In humility, this material is more within the disciplines of classical/ancient philosophy. I am still a student in regard to fallacies. I am educated at a PhD level in philosophical theology and philosophy of religion. Philosophy of Religion is within the discipline of philosophy, as are my specialties, theodicy, the problem of evil, free will and determinism, but I worked within Religion and Theology departments in the United Kingdom. These disciplines are also under the umbrella of philosophical theology and within that the nature of God can be added as an academic specialty of mine.

I am not a classical/ancient philosopher. I have consistently claimed to only be a philosopher of religion. This also explains why I am reviewing page by page the philosophical texts of Pirie and Langer. To gain more knowledge of classical/ancient philosophy which does overlap with theology and philosophy of religion.

Argumentation presented within my Canadian, Christian, academic career and my secular United Kingdom, MPhil and PhD theses degrees was not by definition, syllogistic. Syllogistic argumentation would be allowed as exception only.

While validity and soundness was required, three or more premises were often provided (and academically required) in arguments, in support of a conclusion, within written text. This is also the case on my websites. I have not attempted to write syllogistic arguments, although I do attempt to present logical and sound arguments.

Non-syllogistic, deductive arguments were used within my academic work and are presented on my websites. When providing four or more premises, I am not attempting a strict syllogistic presentation.

BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy).

PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.

Slight update for an entry on academia.edu on May 27, 2023