Whether you experienced the passion of desire I have, of course, no way of knowing, nor indeed have I wished with even the most fleeting fragment of a wish to know, for the fact that one constitutes by one's mere existence so to speak the proof of some sort of passion makes any speculation upon this part of one's parents' experience more immodest, more scandalizing, more deeply unwelcome than an obscenity from a stranger.

A credulousness, a distaste for documentation, an uncritical reliance on contemporary accounts, and a proneness to assume a theory as true before adequate proof was provided were all evidences of his failure to comprehend the use of the scientific method or to evaluate the responsibilities of the historian to his reading public.

The first is the strictly scientific, which demands concrete proof and therefore may err on the conservative side by waiting for evidence in the flesh.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

Attorneys for the eight other defendants said only that there was no proof of their clients' guilt.

( A formal proof for all finite sets would use the principle of mathematical induction to prove " for every natural number k, every family of k nonempty sets has a choice function.

Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.

There are several results in category theory which invoke the axiom of choice for their proof.

A grant application to build a proof of concept prototype was submitted in March 1939 to the Agronomy department which was also interested in speeding up computation for economic and research analysis.

* Drinking songs: According to the grammarian Athenaeus, Alcaeus made every occasion an excuse for drinking and he has provided posterity several quotes in proof of it.

The grammarian Athenaeus quoted some verses about perfumed ointments to prove just how unwarlike Alcaeus could be and he quoted his description of the armour adorning the walls of his house as proof that he could be unusually warlike for a lyric poet.

Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades.

Among his major accomplishments were the 1940 proof, of the Riemann hypothesis for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result ( from 1942 to 1946, most intensively ).

This key result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne.

The " heuristic " approach of the Logic Theory Machine tried to emulate human mathematicians, and could not guarantee that a proof could be found for every valid theorem even in principle.

For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.

* Alan Bundy, University of Edinburgh, meta-level reasoning for guiding inductive proof, proof planning and recipient of 2007 IJCAI Award for Research Excellence, Herbrand Award, and 2003 Donald E. Walker Distinguished Service Award.

* Metamath-a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems ; while the Metamath language is not accompanied with an automated theorem prover, it can be regarded as important because the formal language behind it allows development of such a software ; as of March, 2012, there is no " widely " known such software, so it is not a subject of " automated theorem proving " ( it can become such a subject ), but it is a proof assistant.

An objection against the theist implication of the proposition is that even if one accepts the argument as a proof of a First Cause, it does not identify that First Cause with God.

In propositional logic, disjunction elimination ( sometimes named proof by cases or case analysis ), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.

The basis of this argument is to establish that the creation-evolution controversy is essentially one of interpretation of evidence, without any overwhelming proof ( beyond current scientific theories ) on either side.

His proof is more complex than the more elegant diagonal argument that he gave in 1891.

Gödel's ontological proof is a formal argument for God's existence by the mathematician Kurt Gödel.

Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument.

This is why we cannot naively use the argument appearing at the comment which precedes the proof.

While it is one of the most commonly used concepts in logic it must not be mistaken for a logical law ; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the " rule of definition " and the " rule of substitution " Modus ponens allows one to eliminate a conditional statement from a logical proof or argument ( the antecedents ) and thereby not carry these antecedents forward in an ever-lengthening string of symbols ; for this reason modus ponens is sometimes called the rule of detachment.

" As Objectivist philosopher Leonard Peikoff argued, Rand's argument for axioms " is not a proof that the axioms of existence, consciousness, and identity are true.

Descartes argued further that this knowledge could lead to a proof of the certainty of the existence of God, using the ontological argument that had been formulated first by Anselm of Canterbury.

As anthropologist David Daegling writes, " he skeptics have not felt compelled to offer much of a detailed argument against the film ; the burden of proof, rightly enough, should lie with the advocates.

The phrase is traditionally placed in its abbreviated form at the end of a mathematical proof or philosophical argument when what was specified in the enunciation — and in the setting-out — has been exactly restated as the conclusion of the demonstration.

Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem.

For other examples, see proof that the square root of 2 is not rational and Cantor's diagonal argument.

In the third and fifth Meditation, he offers an ontological proof of a benevolent God ( through both the ontological argument and trademark argument ).

He proposed that the argument from design does not take into consideration future events which may serve to undermine the proof of God's existence: the argument would never finish proving God's existence.

The proof of a mathematical theorem is a logical argument demonstrating that the conclusions are a necessary consequence of the hypotheses, in the sense that if the hypotheses are true then the conclusions must also be true, without any further assumptions.

Evans's argument appears to show that there can be no vague identities ( e. g. " Princeton = Princeton Borough "), but as Lewis ( 1988 ) makes clear, Evans takes for granted that there are in fact vague identities, and that any proof to the contrary cannot be right.

Maher's proof appears to contradict the result of the Bayesian argument, which was that the observation of a non-black non-raven provides much less evidence than the observation of a black raven.

I must confess that I prefer the Liberal who is personally affected, who is willing to send his own children to a mixed school as proof of his faith.

In any event, the critical productivity of that time is abundant proof that if he was taking laudanum, it was never in command of him to the extent that it had been during his vagrant years.

The appointment of U Thant of Burma as the U.N.'s Acting Secretary General -- at this writing, the choice appears to be certain -- offers further proof that in politics it is more important to have no influential enemies than to have influential friends.

The idea of the proof is this.

so that the absence of the hymen is by no means positive proof that a girl has had sex relations.

Most of them, the world over, operate on the same principle by which justice is administered in France and some other Latin countries: the customer is to be considered guilty of abysmal ignorance until proven otherwise, with the burden of proof on the customer himself.

Schwab also declared there is no proof of Weinstein's entering a conspiracy to use the U.S. mails to defraud, to which federal prosecutor A. Lawrence Burbank replied:

level ( when the standard of proof is high, the chances of overlooking

Chaitin prefaces his definition with: " I'll show you can't prove that a program is ' elegant '"— such a proof would solve the Halting problem ( ibid ).

Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers ' common measure is in fact the greatest.

When one attempts to solve problems in this class, it makes no difference whether ZF or ZFC is employed if the only question is the existence of a proof.

It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.

There is some documentary proof that the Romans named the hot sulfur springs of Aachen Aquis-Granum, and indeed to this day the city is known in Italian as Aquisgrana, in Spanish as Aquisgrán and in Polish as Akwizgran.