A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions.
The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.
History is filled with examples of men and women who rendered highly effective performance without the conventional badges of accomplishment in terms of certificates, diplomas, or degrees. Diplomas and tests are useful servants, but Congress has mandated the commonsense proposition that they are not to become masters of reality.
All myth is an enriched pattern, a two-faced proposition, allowing its operator to say one thing and mean another, to lead a double life.
I was trying to show colour, but I realized at the private view that the public were prisoners of a preconceived point of view and that, confronted with all these surfaces of different colours, they responded far more to the inter-relationship of the different propositions, they reconstituted the elements of a decorative polychromy.
The proposition of Mr. Ricardo, which states that a rise in the price of labour lowers the price of a large class of commodities, has undoubtedly a very paradoxical air; but it is, nevertheless, true, and the appearance of paradox would vanish, if it were stated more naturally and correctly.
I think there is a potential civic culture in Arab countries that can lead to democratic institutions and I think Iraq is probably the best place to put that proposition to the test Well, you're going to find a disproportionate number of Jews in any sort of intellectual undertaking.
And how we become like our parents! How their scorned advice - based, we felt in our superiority, on prejudices and muddled folk wisdom - how their opinions are subsequently borne out by our own discoveries and sense of the world, one after one. And as this happens, we realise with increasing horror that proposition which we would never have entertained before: our mothers were right!
If one denies that, when the meaning is true, then the meant is what is so, one rejects propositional truth. If the rejection is universal, then it is the self-destructive proposition that there are no true propositions. If the rejection is limited to the dogmas, then it is just a roundabout way of saying that all the dogmas are false.
The dissemination of the individual's opinions on matters of public interest is for us, in the historic words of the Declaration of Independence, an 'unalienable right' that 'governments are instituted among men to secure.' History shows us that the Founders were not always convinced that unlimited discussion of public issues would be 'for the benefit of all of us' but that they firmly adhered to the proposition that the 'true liberty of the press' permitted 'every man to publish his opinion'.
God is omnipotent; God is wholly good; and yet evil exists. There seems to be some contradiction between these three propositions, so that if any two of them were true the third would be false. But at the same time all three are essential parts of most theological positions: the theologian it seems, at once must adhere and cannot consistently adhere to all three.
A scholar like myself who is not a Sinologist and yet ventures the proposition that Chinese languages should be rewritten in the Greek alphabet (or "Romanized", to use the current term) is treading on uncharted territory (for him) and does so at his peril.
Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.
There'd been studies over the years supporting the proposition that groups composed exclusively of women usually made intelligent decisions, that exclusively male groups did a bit less well, and that mixed groups did most poorly of all, by a substantial margin. It appeared that, when women were present, testosterone got the upper hand and men took greater risks than they might otherwise. Correspondingly, women in the mixed group tended to revert to roles, becoming more passive, and going along with whatever misjudgment the males might perpetrate.
The proposition that economist Ludwig von Mises was a feminist is an apodictic impossibility.
A lot of issues were on the ballots. In New York City there was Proposition 14. That would put a ceiling on the number of late-night talk shows. And California passed Proposition 21. That would change guacamole officially to guac.
While we all could agree that the Zionist ideal is alive and well, there is serious doubt whether the Zionist movement can be said to be an ongoing proposition, fragmented as its components are in ideology and in practice.
If the assertion that there is a god is nonsensical, then the atheist's assertion that there is no god is equally nonsensical, since it is only a significant proposition that can be significantly contradicted.
My son, I do not say these are foals and those asses, these little monkeys and those great baboons, as you would have me do. As I told you from the first, I regard them as earth's heroes. But I do not wish to believe them without cause, nor to accept those propositions whose antitheses (as you must have understood if you are not both blind and deaf) are so compellingly true.
Minds fettered by this doctrine no longer inquire concerning a proposition whether it is attested by sufficient evidence, but whether it accords with Scripture; they do not search for facts as such, but for facts that will bear out their doctrine. It is easy to see that this mental habit blunts not only the perception of truth, but the sense of truthfulness, and that the man whose faith drives him into fallacies treads close upon the precipice of falsehood.
If it is to be established that there is a God, then we have to have good grounds for believing that this is indeed so. Until and unless some such grounds are produced we have literally no reason at all for believing; and in that situation the only reasonable posture must be that of either the negative atheist or the agnostic. So the onus of proof has to rest on the proposition of theism.
It is wrong for a man to say that he is certain of the objective truth of any proposition unless he can produce evidence which logically justifies that certainty. This is what Agnosticism asserts; and, in my opinion, it is all that is essential to Agnosticism. That which Agnostics deny and repudiate, as immoral, is the contrary doctrine, that there are propositions which men ought to believe without logically satisfactory evidence; and that reprobation ought to attach to the profession of disbelief in such inadequately supported propositions.
As Stephen Jay Gould pointed out in Time, in no other Western country is the teaching of Evolution regarded as controversial. Throughout the world, one way or another, most Christian denominations have managed to reconcile belief in God with belief in the mechanisms of natural selection. A French or German or Scandinavian politician who called for students to entertain as a reasonable deduction from existing evidence the proposition that Earth is at most 10,000 years old would be bundled off to a mental hospital.
A willingness to engage in the give and take of argument displays a commitment to cognitive egalitarianism - the proposition that all people should be treated as intellectual equals, and that no individual can legitimately claim a privileged immunity from the burden of proof.
The graphic emphasis placed on those first lines is rather hard to square with the proposition that the monument expresses no particular religious preference.
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