# Logical quality

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Logical_quality
> Markdown URL: https://mediated.wiki/source/Logical_quality.md
> Source: https://en.wikipedia.org/wiki/Logical_quality
> Source revision: 1194546892
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

In many [philosophies](/source/Philosophy) of [logic](/source/Logic), [statements](/source/Statement_(logic)) are categorized into different **logical qualities** based on how they go about saying what they say. Doctrines of logical quality are an attempt to answer the question: "How many qualitatively different ways are there of saying something?" [Aristotle](/source/Aristotle) answers, two: you can affirm something of something or deny something of something. Since [Frege](/source/Frege), the normal answer in the West, is only one, [assertion](/source/Logical_assertion), but what is said, the content of the claim, can vary. For Frege asserting the [negation](/source/Negation) of a claim serves roughly the same role as denying a claim does in Aristotle. Other Western logicians such as [Kant](/source/Immanuel_Kant) and [Hegel](/source/Hegel) answer, ultimately three; you can affirm, deny or make merely limiting affirmations, which transcend both affirmation and denial. In [Indian logic](/source/Indian_logic), four logical qualities have been the norm, and [Nāgārjuna](/source/N%C4%81g%C4%81rjuna) is sometimes interpreted as arguing for five.

## Aristotle's two logical qualities

In [Aristotle](/source/Aristotle)'s [term logic](/source/Term_logic) there are two logical qualities: affirmation (kataphasis) and denial (apophasis). The logical quality of a proposition is whether it is affirmative (the predicate is affirmed of the subject) or negative (the predicate is denied of the subject). Thus "every man is a mortal" is affirmative, since "mortal" is affirmed of "man". "No men are immortals" is negative, since "immortal" is denied of "man".[1]

## Making do with a single logical quality

Logical quality has become much less central to logical theory in the twentieth century. It has become common to use only one logical quality, typically called [logical assertion](/source/Logical_assertion). Much of the work previously done by distinguishing affirmation from denial is typically now done through the theory of [negation](/source/Negation).[2] Thus, to most contemporary logicians, making a denial is essentially reducible to affirming a negation. Denying that Socrates is ill, is the same thing as affirming that it is not the case that Socrates is ill, which is basically affirming that Socrates is not ill. This trend may go back to [Frege](/source/Frege) although his notation for negation is ambiguous between asserting a negation and denying.[3] [Gentzen](/source/Gentzen)'s notation definitely assimilates denial to assertion of negation, but might not quite have a single logical quality, see below.

## Third logical qualities

Logicians in the western traditions have often expressed belief in some other logical quality besides affirmation and denial. [Sextus Empiricus](/source/Sextus_Empiricus), in the 2nd or 3rd century CE, argued for the existence of "nonassertive" statements, which indicate suspension of judgment by refusing to affirm or deny anything.[4] [Pseudo-Dionysius the Areopagite](/source/Pseudo-Dionysius_the_Areopagite) in the 6th century, argued for the existence of "non-privatives", which transcend both affirmation and denial. For example, it is not quite correct to affirm that God is, nor to deny that God moves, but rather one should say that God is beyond-motion, or super-motive, and this is intended not just as a special kind of affirmation or denial, but a third move besides affirmation and denial.[5]

For [Kant](/source/Immanuel_Kant) every judgment takes one of three possible logical qualities, Affirmative, Negative or Infinite. For Kant, if I say “The soul is mortal” I have made an affirmation about the soul; I have said something contentful about it. If I say “The soul is not mortal,” I have made a negative judgment and thus “warded off error” but I have not said what the soul is instead. If, however, I say “The soul is non-mortal,” I have made an infinite judgment. For the purposes of “General logic” it is sufficient to see infinite judgments as a sub-variety of affirmative judgments, I have said something of the soul, namely that it is not mortal. But from the standpoint of “[Transcendental Logic](/source/Critique_of_Pure_Reason#Transcendental_Logic)” it is important to distinguish the infinite from the affirmative. Although I have taken something away from the possibilities of what the soul might be like, I have not thereby said what it is or clarified the concept of the soul, there are still an infinite number of possible ways the soul could be. The content of an infinite judgment is purely limitative of our knowledge rather than ampliative of it.[6] [Hegel](/source/Hegel) follows Kant in insisting that, at least transcendentally, affirmation and negation are not enough but require a third logical quality sublating them both.[7]

## The Indian tradition

See also: [Catuṣkoṭi](/source/Catu%E1%B9%A3ko%E1%B9%ADi)

In [Indian logic](/source/Indian_logic) it has long been traditional to claim that there are four kinds of claims. You can affirm that X is so, you can deny that X is so, you can neither-affirm-nor-deny that X is so, or you can both-affirm-and-deny that X is so. Each claim can also take one of four [truth-values](/source/Truth-values) true, false, neither-true-nor-false, and both-true-and-false. However the tradition is clear that the four kinds of statements are distinct from the four values of statements.[8] [Nāgārjuna](/source/N%C4%81g%C4%81rjuna) is sometimes interpreted as teaching that there is a fifth logical quality besides the four typical of Indian logic, but there are disputing interpretations.[9]

## More than one quality today

Although the distinction between affirmation and denial is rarely supported today, you might try to argue that some other distinctions in the structure of assertion could be thought of as differences of logical quality. One might argue, for instance, that the distinction between [sequents](/source/Sequent) with empty and non-empty antecedents amounts to a distinction between [logical consequences](/source/Logical_consequence) and [logical assertions](/source/Logical_assertion). Alternately one might claim that both forms are really just [logical assertions](/source/Logical_assertion) in the [metalanguage](/source/Metalanguage), and are not statements at all in the object language, since the [turnstile](/source/Turnstile_(symbol)) isn't in the object language. Similarly you might argue that a modern language that includes both an assertion mechanism, and a "retraction" mechanism (such as [Diderik Batens](/source/Diderik_Batens)' "Adaptive Logics")[10] could be thought of as having two logical qualities "assertion" and "retraction."

## Notes

1. [Aristotle](/source/Aristotle) [De Interpretatione](/source/De_Interpretatione) section 6

1. Patrick Hurley, A Concise Introduction To Logic. Thomson-Wadsworth, ninth edition 2006 p. 323

1. Zalta, Edward. "Frege's Logic, Theorem and Foundations for Arithmetic" online at [http://plato.stanford.edu/entries/frege-logic/](http://plato.stanford.edu/entries/frege-logic/)

1. [Sextus Empiricus](/source/Sextus_Empiricus), Outlines of Pyrrhonism. [R.G. Bury](/source/Robert_Gregg_Bury) (trans.) (Buffalo: Prometheus Books, 1990). ISBN 0-87975-597-0 Book I Section XX and following.

1. Pseudo Dionysius: The Complete Works, 1987, Paulist Press, ISBN 0-8091-2838-1 Especially clear at end of Mystical Theology.

1. [Immanuel Kant](/source/Immanuel_Kant) [Critique of Pure Reason](/source/Critique_of_Pure_Reason) A71/B96 and following available at ["Kant's Critique of Pure Reason (Translation by Norman Kemp Smith)"](https://web.archive.org/web/20090707011421/http://humanum.arts.cuhk.edu.hk/Philosophy/Kant/cpr/). Archived from [the original](http://humanum.arts.cuhk.edu.hk/Philosophy/Kant/cpr/) on 2009-07-07. Retrieved 2009-07-07.

1. [G. W. F. Hegel](/source/G._W._F._Hegel) The Encyclopedia Logic, trans. Geraets, Suchting, and Harris, Hackett Publishing 1991, Sections 86-98.

1. The Perfection of Wisdom in Eight Thousand Lines and its Verse Summary. ed. Edward Conze. Fifth ed. San Francisco: Four Seasons Foundation, 1995. Also known as the Astasahasrika Prajnaparamita, pp. 176-7.

1. See for example Nāgārjuna's [Mūlamadhyamakakārikā](/source/M%C5%ABlamadhyamakak%C4%81rik%C4%81) 18:10-11.

1. Bremer, Manuel. An Introduction to Paraconsistent Logics. Peter Lang, 2005, pp. 91-106

---
Adapted from the Wikipedia article [Logical quality](https://en.wikipedia.org/wiki/Logical_quality) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Logical_quality?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.