A proposition that says: " The product of the sum and the difference of a and b should give us the difference of the squares of a and b " does express a normative proposition, but this normative statement is based on the theoretical statement "( a + b )( a-b )= a²-b² ".

The earliest known formulation is Aristotle's principle of non-contradiction, first proposed in On Interpretation, where he says that of two contradictory propositions ( i. e. where one proposition is the negation of the other ) one must be true, and the other false.

What proposition 6. really says is that any logical sentence can be derived from a series of nand operations on the totality of atomic propositions.

We can communicate such a game of chess in the exact way that Wittgenstein says a proposition represents the world.

However, the three propositions have different domains: the first proposition says something about " Every object ", while the second says something about " Every raven ".

Diogenes Laërtius says that he declined to identify the Good with the Useful, and that he denied the value of the negative proposition on the ground that affirmation alone can express truth.

Once that is done, Adler says that the reader should find and work to understand each proposition that the author advances, as well as the author's support for those propositions.

But attempting to directly eliminate " is true " from this sentence, on the standard first-order interpretation of quantification in terms of objects, would result in the ungrammatical formulation For all P, if John says P, then P. It is ungrammatical because P must, in that case, be replaced by the name of an object and not a proposition.

* I proposition says, " Some S is P ."

The first view, which might be termed the proof-theoretic or Gentzen-style interpretation of propositions, says that the meaning of a proposition arises from its introduction and elimination rules.

Russell says that if there are no entities X with property F, the proposition " X has property G " is false for all values of X.

I also accept the proposition that if a woman says to a man, ' I want this man murdered ; you promise me to do it ,' and he then promises her ( she believing that he is going to keep his promise as soon as he gets an opportunity ) and goes out and murders someone, then she also is guilty of murder.

Spinoza takes this proposition to follow directly from everything he says prior to it.

This theory of judgment dominated logic for centuries, but it has some obvious difficulties: it only considers proposition of the form " All A are B.

: The categorical proposition " All men are mortal " has the same meaning as the existential proposition " An immortal man does not exist " or " there is no immortal man ".

An " extensional stance " and restriction to a second-order predicate logic means that a propositional function extended to all individuals such as " All ' x ' are blue " now has to list all of the ' x ' that satisfy ( are true in ) the proposition, listing them in a possibly infinite conjunction: e. g. x < sub > 1 </ sub > V x < sub > 2 </ sub > V.

In his proposed resolution, Maher implicitly made use of the fact that the proposition " All ravens are black " is highly probable when it is highly probable that there are no ravens.

It is impossible for the observation of a black raven to increase the probability of the proposition " All ravens are black " without causing exactly the same change to the probability that " All non-black things are non-ravens ".

All bleaching and maturing agents ( with the possible exception of ascorbic acid ) have been banned in the EU, making cake baking a difficult proposition as heat treated flours that mimic the effects of chlorination are to date available only to bulk bakeries.

An Aristotelian proposition may take the form " All men are mortal " or " Socrates is a man.

For the implication P → Q, the converse is Q → P. For the categorical proposition All S is P, the converse is All P is S. In neither case does the converse necessarily follow from the original statement.

All versions of Epistemological Moral Skepticism hold that we are unjustified in believing any moral proposition.

Popper himself used the now famous example of, " All swans are white ," and proposed that just one observation of a single black swan would falsify this proposition and in this way have general significance and stimulate further investigations and theory-building.

UNICEF, in a study entitled Basic Services for All: Public Spending and the Social Dimensions of Poverty, laid out moral, consensual, instrumental and historical grounds, in support of the proposition that state provision of basic services is mandatory regardless of circumstance.

" Hall dedicated The Secret Teachings of All Ages to " the proposition that concealed within the emblematic figures, allegories and rituals of the ancients is a secret doctrine concerning the inner mysteries of life, which doctrine has been preserved in toto among a small band of initiated minds.

For instance, the A proposition (" All S is P ") is affirmative since it states that the subject is contained within the predicate.

All that can be inferred from the original proposition is that " If oxygen is not present, then there cannot be fire ".

In the categorical proposition " All S is P ", the subject term ' S ' is said to be distributed, that is, all members of its class are exhausted in its expression.

Thus, the type ' A ' proposition " All P is S " cannot be inferred by conversion from the original ' A ' type proposition " All S is P ".

All that can be inferred is the type " A " proposition " All non-P is non-S " ( Note that ( P → Q ) and (~ Q → ~ P ) are both ' A ' type propositions ).

This proposition was immediately rejected by the U. S. Shortly afterward, the same day, United States and British forces initiated military action against the Taliban, bombing Taliban forces and al-Qaeda terrorist training camps.

In the above, P is the proposition we wish to disprove respectively prove ; and S is a set of statements, which are the premises — these could be, for example, the axioms of the theory we are working in, or earlier theorems we can build upon.

In more formal terms, a subject < var > S </ var > knows that a proposition < var > P </ var > is true if and only if:

The structural induction proof is a proof that the proposition holds for all the minimal structures, and that if it holds for the immediate substructures of a certain structure S, then it must hold for S also.

225: This article analyzes the definition of publication in the U. S. Copyright Act of 1976 and finds strong support for the proposition that electronic dissemination ( e. g., " Internet publishing ") of works does not result in publication under American copyright law.

: A subject < var > S </ var > knows that a proposition < var > P </ var > is true if and only if:

* The so-called ' A ' proposition, the universal affirmative ( universalis affirmativa ), whose form in Latin is ' omne S est P ', usually translated as ' every S is a P '.

* The ' E ' proposition, the universal negative ( universalis negativa ), Latin form ' nullum S est P ', usually translated as ' no S are P '.

* The ' I ' proposition, the particular affirmative ( particularis affirmativa ), Latin ' quoddam S est P ', usually translated as ' some S are P '.

* The ' O ' proposition, the particular negative ( particularis negativa ), Latin ' quoddam S non est P ', usually translated as ' some S are not P '.

A proposition first offered by Boethius and later by Thomas Aquinas and C. S. Lewis, it suggests that God's perception of time is different, and that this is relevant to our understanding of our own free will.

An Oxford Union debate shown live on New Zealand television in March 1985 showcased Lange, a skilled orator, arguing for the proposition that " nuclear weapons are morally indefensible ", in opposition to U. S. televangelist Jerry Falwell.

# H * A * S * H ( November 29, 1992 ) – Alan, now MEP for the constituency of Obersaxony, is approached by his old patron Sir Greville with a proposition: Sir Greville, acting in the employ of Big Tobacco, wishes for Alan to manipulate Piers into getting the European Commission to legalize cannabis, which the tobacco companies will then make a fortune on.

" This is expressed by saying that a proposition A is logically equivalent to not not-A ), or by the formula A ≡ ~(~ A ) where the sign ≡ expresses logical equivalence and the sign ~ expresses " not " or " negation ".< ref > Or alternate symbolism such as A ↔ ¬(¬ A ) or Kleene's * 49 < sup > o </ sup >: A ∾ ¬¬ A ( Kleene 1952: 119 ; in the original Kleene uses an elongated tilde ∾ for logical equivalence, approximaed here with a " lazy S ".

Formulating evidentialism in terms of the doxastic attitude of belief its most-defended form comes from Conee and Feldman: Belief, B, toward proposition, p, is epistemically justified for Subject, S, at time, t, if and only if B fits the evidence which S has at t.