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argument and above
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.
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.

argument and still
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 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.
Saint Thomas Aquinas ’ argument from contingency applies even if the universe had no beginning, but it would still have to be sustained in being at any particular moment by God.
This is an argument still accepted in principle by many psychometricians.
His main line of argument was that the tremendous displacements and changes he was seeing did not happen in a short period of time by means of catastrophe, but that processes still happening on the Earth in the present day had caused them.
Similarly the question of whether a Turing machine T terminates on an initially empty tape ( rather than with an initial word w given as second argument in addition to a description of T, as in the full halting problem ) is still undecidable.
In this work, Bernoulli posited the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel, and that what we experience as heat is simply the kinetic energy of their motion.
Their consummation problems have now been attributed to other factors, around which controversy and argument still continue today.
The three-state strategy is an argument made by some ERA supporters that the earlier 35 state ratifications are still valid and therefore only three more are needed in order to add the ERA to the Constitution, without Congress resubmitting it to state lawmakers.
Hubert has a furious argument with John, during which he reveals that Arthur is still alive.
An argument against this states the notion that such manipulation may be possible but barred from the conscious self via the subconscious self, a ' locked ' portion of the mind that is still nevertheless the same mind.
This argument is still a fallacy even if the conclusion is true.
This argument is still a fallacy even if the conclusion is true.
This argument is still a fallacy even if the conclusion is true.
Even if this argument is valid, the term " extranet " is still applied and can be used to eliminate the use of the above description.
Most of these experts still supported Flourens argument, but Aubertin was persistent in presenting new patients to counter their views.
Professional historians still often use the term " antiquarian " in a pejorative sense, to refer to historical studies which seem concerned only to place on record trivial or inconsequential facts, and which fail to consider the wider implications of these, or to formulate any kind of argument.
But now that the Tortoise accepts premise C, it still refuses to accept the expanded argument.
Since a Taylor series evaluated with a Laurent series as its argument is still a Laurent series, the system can be used to do calculus on transcendental functions if they are analytic.
He hated ignorance, but he hated still more half-learning, and most of all dishonesty in argument or in quotation.
Common Sense presented the American colonists with an argument for freedom from British rule at a time when the question of seeking independence was still undecided.
This argument on the grounds of time still occurs and has caused many defendants, particularly women, to lose their cases on this ground, as they will often wait ( in wife-battering cases ) until the husband is asleep.
Only the latter class of charge seems to have seriously worried the Privy Council, and here Picton's argument that either the laws of Trinidad, then still the laws of the former Spanish colonial power, or ' the state of the garrison ' justified the immediate execution in the cases specified eventually carried the day.
A fallacious argument, just as with a false antecedent, can still have a consequent that happens to be true.
But showing how one argument in a complex thesis is fallaciously reasoned does not necessarily invalidate the proof ; the complete proof could still logically imply its conclusion if that conclusion is not dependent on the fallacy:

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