However, as in Cantor's argument ( above ), this idea leads to difficulties.

However, in CL it is necessary to explicitly refer to the function namespace when passing a function as an argument — which is also a common occurrence, as in the example above.

" This form of the argument is far more difficult to separate from a purely first cause argument than is the example of the house's maintenance above, because here the First Cause is insufficient without the candle's or vessel's continued existence.

Given the definition of above, we might fix ( or ' bind ') the first argument, producing a function of type.

The above definition implies this one: the upper bound of the empty subset is any existing element of A, because A is nonempty ; furthermore, as provable with an induction argument over the size of nonempty finite subsets, the upper bound of a finite subset may be obtained by finding upper bounds of pairs iteratively.

Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

In this notation, the use of a vertical bar as delimiter indicates that the argument following it is the " parameter " ( as defined above ), while the backslash indicates that it is the modular angle.

Heawood noticed Kempe's mistake and also observed that if one was satisfied with proving only five colors are needed, one could run through the above argument ( changing only that the minimal counterexample requires 6 colors ) and use Kempe chains in the degree 5 situation to prove the five color theorem.

The argument above began by giving an unavoidable set of five configurations ( a single vertex with degree 1, a single vertex with degree 2, ..., a single vertex with degree 5 ) and then proceeded to show that the first 4 are reducible ; to exhibit an unavoidable set of configurations where every configuration in the set is reducible would prove the theorem.

The argument above may not hold for the universe as a whole, since travel times may well explain the lack of physical presence on Earth of alien inhabitants of far away galaxies.

An illustration of Cantor's diagonal argument for the existence of uncountable set s. The sequence at the bottom cannot occur anywhere in the infinite list of sequences above.

However, when k ≥ 3, the expected value is well-defined, and by the above argument, it is

Yet he attacks the idealism of Schopenhauer and Descartes with an argument similar to Kant's critique of the latter ( see above );

In the above argument, the assertion " this number is either rational or irrational " invokes the law of excluded middle.

If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.

Though some points above may be arguable, but some key points seemingly aren't giving that it would require one to abide by many of the premises to even make an argument to begin with.

In the Leipzig disputation with Martin Luther, 1519, Johann Eck used the Corpus, specifically the Angelic Hierarchy, as argument for the apostolic origin of papal supremacy, pressing the Platonist analogy, " as above, so below ".

Since E < sub > 2 </ sub >-E < sub > 1 </ sub > ≫ kT, it follows that the argument of the exponential in the equation above is a large negative number, and as such N < sub > 2 </ sub >/ N < sub > 1 </ sub > is vanishingly small ; i. e., there are almost no atoms in the excited state.

Paedobaptists point to a number of passages in the New Testament which seem to corroborate the above argument.

( In the above symbolic argument, " x is the smallest rational number " would be R and " r < sub > 0 </ sub > ( which is different from x ) is the smallest rational number " would be ¬ R.

It is common to use this first type of argument with propositions such as the one above, concerning the non-existence of some mathematical object.

Thus, as per Draper's argument above, the theory that there is an omniscient and omnipotent being who is indifferent requires no hidden reasons in order to explain evil.

The criterion, given above for the solvability of the word problem in a single group can be extended to a criterion for the uniform solvability of the word problem for a class of finitely presented groups by a straightforward argument.

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.