A standard non-constructive strategy-stealing argument proves that the first player has a winning strategy as follows:

John Nash proved in 1952 that a game of Hex cannot end in a tie, and that for a symmetric board there exists a winning strategy for the player who makes the first move ( by the strategy-stealing argument ).

In CGT there has been less emphasis on refining practical search algorithms ( like the alpha-beta pruning heuristic, included in most artificial intelligence textbooks today ), but more emphasis on descriptive theoretical results, like measures of game complexity or proofs of optimal solution existence without necessarily specifying an algorithm ( see strategy-stealing argument for instance ).

In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many games, that the second player cannot have a winning strategy ( i. e., a strategy that will always win the game for them, no matter what moves the first player makes ).

The strategy-stealing argument applies to any symmetric game ( one in which either player has the same set of available moves with the same results, so that the first player can " use " the second player's strategy ) in which an extra move can never be a disadvantage.

Because of this, the strategy-stealing argument cannot be applied to chess.

The `` Essex Journal '' says that he `` delivered an oration on the bridge, which for elegance of style, propriety of speech or force of argument, was truly Ciceronian ''.

Only George Santayana seemed to understand and appreciate the film when he wrote: `` Miss Poitrine has perpetrated the most eloquent argument for the Protestant faith yet unleashed by Hollywood ''.

Therefore, for any value of T the number of values of f{t} is equal to the ( finite ) number of tangent points corresponding to the argument T plus an odd number.

Changes in the basic wage rate are cost-raising, and they constitute an argument for raising prices.

Obviously, a satisfactory answer to the third question is imperative, if the argument is to get under way at all, for if there is any possibility of doubt whether the patient's tactual sensitivity had been impaired by the occipital lesion, any findings whatsoever in regard to the first question become completely ambiguous and fail altogether, of course, as evidence to establish the desired conclusion.

If the argument is accepted as essentially sound up to this point, it remains for us to consider whether the patient's difficulties in orienting himself spatially and in locating objects in space with the sense of touch can be explained by his defective visual condition.

`` The trouble, '' explained Loy Henderson, then Deputy Undersecretary for Administration, `` is that when we get into an argument with him about this thing, it always turns out that Rooney knows more about our budget than we do ''.

She'd say she didn't feel good on Sunday, couldn't go to church -- there'd be a little argument, but she could be stubborn -- and when the old woman had gone, quick pack the things she'd need to take, all but the dress she'd wear Monday, and take the bag down to that place in the station where you could put things in a locker overnight, for a dime.

Added to the argument was the fact that while she might have tasted the coffee if it had been still hot, she might even have drunk some of it, she wouldn't have taken enough to kill her, for she would have been warned by its taste.

But this argument cannot be pushed very far because the Communist system makes up for any shortcomings of its leaders in respect to corrosion.

Hence, such an appellate court will not consider an appellant's argument if it is based on a theory that is raised for the first time in the appeal.

In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.

Swift goes to great lengths to support his argument, including a list of possible preparation styles for the children, and calculations showing the financial benefits of his suggestion.

This is often the case, for example, with idiomatic expressions whose definitions are rarely or never well-defined, and are presented in the context of a larger argument that invites a conclusion.

The Bohr model for a short time could be seen as a classical model with an additional constraint provided by the ' wavelength ' argument.

However, for quasi-equilibrium systems ( e. g. spins out of equilibrium with the electromagnetic field ) this argument does not apply, and negative effective temperatures are attainable.

An argument for peace with Sparta.

However, more vital propositions, such as Hume's argument for the role of habit in a theory of knowledge, are retained.

He shows how a satisfying argument for the validity of experience can be based neither on demonstration ( since " it implies no contradiction that the course of nature may change ") nor experience ( since that would be a circular argument ).

The argument from morality is an argument for the existence of God.

Portrait of Immanuel Kant, who proposed an argument for the existence of God from morality

In his Critique of Pure Reason, German philosopher Immanuel Kant stated that no successful argument for God's existence arises from reason alone.

Parkinson challenges the argument from moral objectivity by arguing that, for the argument to be successful, it must be shown that morality is objective and commanded by God, rather than just a human invention.

In other words, the higher-dimensional, multi-player, n-in-a-row generalization of game of tic-tac-toe cannot end in a draw, no matter how large n is, no matter how many people c are playing, and no matter which player plays each turn, provided only that it is played on a board of sufficiently high dimension H. By a standard strategy stealing argument, one can thus conclude that if two players alternate, then the first player has a winning strategy when H is sufficiently large, though no constructive algorithm for obtaining this strategy is known.

Quite clearly the anti-trust laws are neither effective nor rational -- and yet the argument goes that they should be extended to the labor union.

They regard a " crime malum in se " as inherently criminal ; whereas a " crime malum prohibitum " ( the argument goes ) counts as criminal only because the law has decreed it so.

Kempe's argument goes as follows.

The usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function and the name was first used in Hadamard's 1910 book on that subject.

Herbert G. Winful argues that the train analogy is a variant of the " reshaping argument " for superluminal tunneling velocities, but he goes on to say that this argument is not actually supported by experiment or simulations, which actually show that the transmitted pulse has the same length and shape as the incident pulse.

If truly irreducible systems are found, the argument goes, then intelligent design must be the correct explanation for their existence.

The argument is not only sound on Tuesdays ( when John goes to work ), but valid on every day of the week.

( It is conceivable that there may have been an intruder that the dog did not detect, but that does not invalidate the argument ; the first premise goes " if the watch-dog detects an intruder.

It is impossible to imagine a man, the argument goes, unless one has in mind a very specific picture of one who is either tall or short, European or Asian, blue-eyed or brown-eyed, et cetera.

His work is notable for the use of the zeta function ζ ( s ) ( for real values of the argument " s ", as are works of Leonhard Euler, as early as 1737 ) predating Riemann's celebrated memoir of 1859, and he succeeded in proving a slightly weaker form of the asymptotic law, namely, that if the limit of π ( x )/( x / ln ( x )) as x goes to infinity exists at all, then it is necessarily equal to one.

The basic argument goes as follows: if the coupling constant were negative, this would be equivalent to the Coulomb force constant being negative.

Scott goes as far as stating that if a man believes in an ultimate truth and argues it, he is only fooling himself by convincing himself of one argument among many possible options.

Combined with the fact that open-source is dominated by a culture of volunteering, the argument goes, security sometimes receives less thorough treatment than it might in an environment in which security reviews were part of someone's job description.

The argument goes as follows:

Correspondingly, the argument goes, the former requires as evidence ravens which turn out to be black and the latter requires non-black things which turn out to be non-ravens.

On the other hand, if such reasoned conclusions are only built originally upon a foundation of sense perceptions, then, the argument being considered goes, our most logical conclusions can never be said to be certain because they are built upon the very same fallible perceptions they seek to better.

Informed consent in this instance goes to the argument of competency on the part of the minor.

His argument rested primarily on the Tenth Amendment: that all rights not endowed to Congress goes right to the States ( or the people ) exclusively.

Hence, this line of argument goes, the objectively dominant effect would be the moral and economic damage due to the massive fear and panic such an incident would spur.

Therefore, the argument goes, the passage of time is nonsensical.

Furthermore, the argument goes, if people choose to work for low wages and in unsafe conditions because it is their only alternative to starvation or scavenging from garbage dumps ( the " preexisting options "), this cannot be seen as any kind of " free choice " on their part.

As the parties are friendly states with an open border, the argument goes no further than an agreement to disagree.

Separate rabbinical schools and separate rabbinic organizations, the argument goes, reflect the reality of a community divided.