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proposition and says
The earliest known formulation is Aristotle's principle of non-contradiction, first proposed in On Interpretation, where he says that of two contradictory propositions ( i. e. where one proposition is the negation of the other ) one must be true, and the other false.
What proposition 6. really says is that any logical sentence can be derived from a series of nand operations on the totality of atomic propositions.
We can communicate such a game of chess in the exact way that Wittgenstein says a proposition represents the world.
However, the three propositions have different domains: the first proposition says something about " Every object ", while the second says something about " Every raven ".
Diogenes Laërtius says that he declined to identify the Good with the Useful, and that he denied the value of the negative proposition on the ground that affirmation alone can express truth.
Once that is done, Adler says that the reader should find and work to understand each proposition that the author advances, as well as the author's support for those propositions.
But attempting to directly eliminate " is true " from this sentence, on the standard first-order interpretation of quantification in terms of objects, would result in the ungrammatical formulation For all P, if John says P, then P. It is ungrammatical because P must, in that case, be replaced by the name of an object and not a proposition.
* A proposition says, " All S is P ."
* I proposition says, " Some S is P ."
The first view, which might be termed the proof-theoretic or Gentzen-style interpretation of propositions, says that the meaning of a proposition arises from its introduction and elimination rules.
Russell says that if there are no entities X with property F, the proposition " X has property G " is false for all values of X.
I also accept the proposition that if a woman says to a man, ' I want this man murdered ; you promise me to do it ,' and he then promises her ( she believing that he is going to keep his promise as soon as he gets an opportunity ) and goes out and murders someone, then she also is guilty of murder.
Spinoza takes this proposition to follow directly from everything he says prior to it.

proposition and product
Because this geometrical interpretation of multiplication was limited to three dimensions, there was no direct way of interpreting the product of four or more numbers, and Euclid avoided such products, although they are implied, e. g., in the proof of book IX, proposition 20.
* Revenue model innovation-Innovate how the company makes money by changing the value proposition ( product / service / value mix ) and the pricing model.
We went to Microsoft on the proposition that we wanted this to be their product.
# The proposition must be so strong that it can move the mass millions, i. e., pull over new customers to your product ...!
As was shown in the Cambridge capital controversy, this proposition about the marginal product of capital cannot generally be sustained in multicommodity models in which capital and consumption goods are distinguished.
His ads were focused around what he called the unique selling proposition, the one reason the product needed to be bought or was better than its competitors.
After the Mexican Revolution of 1910, the state officially constructed a Mexican national identity policy on the proposition that Mexicans are the product of a creative mixing of Indians and Europeans — that is, about a fusing together of cultures.
So, proposition is true if it is the " product of political struggle " for the " emancipation of the workers " ( Adorno ).
An elevator pitch, elevator speech, or elevator statement is a short summary used to quickly and simply define a product, service, or organization and its value proposition.
This vision produces a core proposition in textbook neoclassical economics, i. e., that the income earned by each " factor of production " ( essentially, labor and " capital ") is equal to its marginal product.
:( 1 ) the postulate of the principle, or the Cogitatio natural universalis ( good will of the thinker and good nature of thought ); ( 2 ) the postulate of the ideal, or common sense ( common sense as the concordia facultatum and good sense as the distribution which guarantees this concord ); ( 3 ) the postulate of the model, or of recognition ( recognition inviting all the faculties to exercise themselves upon an object supposedly the same, and the consequent possibility of error in the distribution when one faculty confuses one of its objects with a different object of another faculty ); ( 4 ) the postulate of the element or of representation ( when difference is subordinated to the complimentary dimensions of the Same and the Similar, the Analogous and the Opposed ; ( 5 ) the postulate of the negative, or of error ( in which error expresses everything which can go wrong in thought, but only as the product of external mechanisms ); ( 6 ) the postulate of logical function, or the proposition ( designation is taken to be the locus of truth, sense being no more than the neutralized double or the infinite doubling of the proposition ); ( 7 ) the postulate of modality, or solutions ( problems being materially traced from propositions or indeed, formally defined by the possibility of their being solved ); ( 8 ) the postulate of the end, or result, the postulate of knowledge ( the subordination of learning to knowledge, and of culture to method.
It defines high level concepts and the intrinsic value proposition of the product.

proposition and sum
The celebrated Pythagorean theorem ( book I, proposition 47 ) states that in any right triangle, the area of the square whose side is the hypotenuse ( the side opposite the right angle ) is equal to the sum of the areas of the squares whose sides are the two legs ( the two sides that meet at a right angle ).
The sum and whole cause of the writings of this epistle, is, to prove that a man is justified by faith only: which proposition whoso denieth, to him is not only this epistle and all that Paul writeth, but also the whole scripture, so locked up that he shall never understand it to his soul's health.
* Book 1 contains Euclid's 10 axioms ( 5 named postulates — including the parallel postulate — and 5 named axioms ) and the basic propositions of geometry: the pons asinorum ( proposition 5 ), the Pythagorean theorem ( Proposition 47 ), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are " equal " ( have the same area ).
* Book 9 applies the results of the preceding two books and gives the infinitude of prime numbers ( proposition 20 ), the sum of a geometric series ( proposition 35 ), and the construction of even perfect numbers ( proposition 36 ).
His most famous proposition is I think, therefore I am, or Cogito ergo sum.
Dubuat, therefore, assumed it as a proposition of fundamental importance that, when water flows in any channel or bed, the accelerating force which obliges it to move is equal to the sum of all the resistances which it meets with, whether they arise from its own viscosity or from the friction of its bed.

proposition and difference
The constituents of this proposition are simply A, difference and B.
* Early test generation algorithms such as boolean difference and literal proposition were not practical to implement on a computer.

proposition and b
:“ If an integer n is greater than 2, then has no solutions in non-zero integers a, b, and c. I have a truly marvelous proof of this proposition which this margin is too narrow to contain .”
In predicate logic, the truth-value of the proposition expressed above in a formal language does not depend on the particular value of the variable, b. This matches our natural language understanding.
Hempel rejected this as a solution to the paradox, insisting that the proposition ' c is a raven and is black ' must be considered " by itself and without reference to any other information ", and pointing out that it "... was emphasized in section 5. 2 ( b ) of my article in Mind ... that the very appearance of paradoxicality in cases like that of the white shoe results in part from a failure to observe this maxim.
For example, the introductory signal " See " tells the reader that the cited authority either ( a ) supports the stated proposition implicitly, or ( b ) contains dicta that support the proposition.
" But see ," on the other hand, tells the reader that the cited authority either ( a ) contradicts the stated proposition implicitly, or ( b ) contains dicta that contradict the stated proposition.
In mathematics, a Heyting algebra, named after Arend Heyting, is a bounded lattice ( with join and meet operations written ∧ andand with least element 0 and greatest element 1 ) equipped with a binary operation ab of implication such that ( ab )∧ ab, and moreover ab is the greatest such in the sense that if c ∧ ab then c ≤ ab. From a logical standpoint, A → B is by this definition the weakest proposition for which modus ponens, the inference rule A → B, A ⊢ B, is sound.
This may be made clearer by supposing for a moment that only one form of proposition is in question, say the relational form aRb ; then ' He is always right ' could be expressed by ' For all a, R, b, if he asserts aRb, then aRb ', to which ' is true ' would be an obviously superfluous addition.
It is, perhaps, also immediately obvious that if we have analysed judgment we have solved the problem of truth ; for taking the mental factor in a judgment ( which is often itself called a judgment ), the truth or falsity of this depends only on what proposition it is that is judged, and what we have to explain is the meaning of saying that the judgment is a judgment that a has R to b, i. e. is true if aRb, false if not.
The rest is a defense of ( a ) what we now call the principle of contradiction, the principle that it is not possible for the same proposition to be ( the case ) and not to be ( the case ), and ( b ) what we now call the principle of excluded middle: tertium non datur-there cannot be an intermediary between contradictory statements.

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