The standard form statement no s are p is a

I. What is a categorical proposition?

Some politicians are persons who embroider the truth.

Some politicians are not honest people.

A ff i rmo and N e g o .

In this fashion, A and I statements are seen to be affirmative, E and O are remembered as negative.

“All (unfledged floithoisters) are (things apt to become unflaggled)”

… the logical subject is composed of all of the words between the quantifier “All” and the copula ”are,” and the logical predicate is composed of all of the words after the copula “are” until the end of the statement.

So the logical subject of this statement is “unfledged floithoisters” and the logical predicate is “things apt to become unflaggled.”

For example, the statement “Some women are physicists at CERN is considered true if there is at least one woman physicist at CERN. (Additionally this statement would be true even if it turned out that all except one person were women physicists at CERN.)

II. Analysis of the Categorical Proposition: Quality, Quantity, and Distribution

E. In sum, thorough knowledge of the following table is absolutely essential to do well in categorical logic:

3. For the predicate of the O proposition, consider the following analogy. If we know that there is a book not in a bookcase, then we know something about each and every shelf in that bookcase—namely, we know that the book is not on that shelf.

1. Traditional logic and the logic of the syllogism descended from Aristotelian logic. Bocheński writes, “[Aristotle] exercised a decisive influence on the history of logic for more than two thousand years, and even today much of the doctrine is traceable back to him.” I. M. Bocheński, A History of Formal Logic , (New York: Chelsea,1961), 40.↩

‘[I]n [the] use of schematic letters like ‘S’ and ‘P’ you find, for example, in one and the same context the phrase ‘every S’, which requires that ‘S’ be read as a general term like ‘man’ and the phrase ‘the whole of S’, which requires that ‘S’ be a singular designation of a class taken collectively, like ‘the class of men’ obviously ‘man’ and ‘the class of men’ are wholly different sorts of expression.↩

“[T]he extreme grammatical oddity” of “All S is P” being translated from “Omne S est P” of the historical Latin texts which ought be, according to him, “Every S is P,” so that the whole class of the subject term is universally quantified and no distribution error occurs.

[P.T. Geach, Logic Matters (University of California Press, 1980), 69.]

However, we follow the usual practice of using “All S is P” for the A statement, recognizing that the statement form need not be necessarily understood as following English grammar prose rules for sentences and can be understood as “All Ss.” ↩

“All S is not P”

“No S is P”

“Some S is not P.”

“No lodestones are non-magnetic ore”

because lodestones (i.e., magnetite) are naturally occurring magnets — all of them, by definition, are magnetic.

But the statement “All swans are not white” in standard form means

“Some swans are not white”

because in nature swans are observed to exist in several other colors also.

To take another example, the statement “All that glitters is not gold” would be conservatively translated into standard form as

“Some things that glitter are not gold.”

not “No things that glitter are gold” because gold things can glitter.

Consequently, statements of the form “All S is not P” are not always the same thing as the E standard form proposition “No S is P.”. To translate properly, one must be aware of the meaning of the terms in the statements.

If specific information about the subject class of a statement is not known, the usual translation of statements of the form “All S is not P” is

“Some S is not P.”

“Not all honey badgers are solitary hunters”

“Some honey badgers are not solitary hunters.”

(and one would not know whether or not it was also true that “Some honey badgers are not solitary hunters”)↩

After studying these notes, try the Chart Quiz where you can practice listing the quantity, quality, distribution of standard from categorical propositions.

Relay corrections, suggestions or questions to
webmaster [at] philosophy.lander.edu
Please see the disclaimer concerning this page.
This page last updated 2021.08.02
Licensed under the GFDL and the
Creative Commons License Version 3.0 or later.