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.

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.

In the argument above, for any and, whenever and are true, necessarily is true.

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 Mathematical Appendix presents the rigorous argument, but is best read after Part 1, in order that the assumptions underlying the equations may be explicit.

Yet, if the argument is turned awry, there may be found a great deal in Bryan's view, after all.

This is the only valid, and extenuating, argument that may be advanced in defense of the reprehensible attitude of the common wine waiter.

In order to make the implications of our position as clear as possible, we may develop this argument at greater length.

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 ).

Whether a relation of an object is one of its properties may complicate such an argument.

But other thinkers sympathetic to his basic argument have suggested that the necessary ( though perhaps still not sufficient ) extra conditions may include the ability to pass not just the verbal version of the Turing test, but the robotic version, which requires grounding the robot's words in the robot's sensorimotor capacity to categorize and interact with the things in the world that its words are about, Turing-indistinguishably from a real person.

The experiment is the centerpiece of Searle's Chinese room argument which holds that a program cannot give a computer a " mind ", " understanding " or " consciousness ", regardless of how intelligently it may make it behave.

The argument is directed against the philosophical positions of functionalism and computationalism, which hold that the mind may be viewed as an information processing system operating on formal symbols.

( It may require occasional maintenance, but that is beyond the scope of the first cause argument.

I am glad that he has been courageous enough and logical enough to admit that his argument, if pushed as far as it must go, if worth anything, would prove that men may have come from the Ourang-Outang.

However, this argument may be inverted by realists in arguing that since the sentence " Socrates is wise " can be rewritten as " Socrates has wisdom ", this proves the existence of a hidden referent for " wise ".

This argument was a type favoured by the ancient Greek skeptics, and may have been wrongly attributed to Epicurus by Lactantius, who, from his Christian perspective, regarded Epicurus as an atheist.

A claim or defense may be frivolous because it had no underlying justification in fact, or because it was not presented with an argument for a reasonable extension or reinterpretation of the law.

This may mean that the argument is not a good one, or it may show something interesting about northern European culture as compared to Celtic and southern European culture.

This explanation may imply that IQ tests do not necessarily measure a general intelligence factor, especially not Raven's as often argued, but instead may measure different types of intelligence that are developed by different experiences ( this argument is against the notion of an underlying general intelligence, or g factor ).

For example, an ethical argument may claim that if a thing has certain properties, then that thing is ' good.

A minority argument for a date between AD 37 and AD 61 for the Gospel typically suggests that Luke's address to " Most Excellent Theophilus ," may be a reference to the Roman-imposed High Priest of Israel between AD 37 and AD 41, Theophilus ben Ananus.

Now the argument may go against this inference, finding some law that applies to that case but not to ours.