A proof is a proof. What kind of a proof? It's a proof. A proof is a proof. And when you have a good proof, it's because it's proven.
... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself ... A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.
Fraud is fraud. And consumers of any product - whether you want to buy a car, participate in fantasy football - our laws are very strong in New York and other states that you can't commit fraud.
We're going after the possibilities of tax fraud, insurance fraud, securities fraud. We're going to look at this stuff very closely. We have the jurisdiction, we have the resources, and we have the will.
If anything, a message back to [Donald] Trump is, if you have proof, if you have evidence, please bring it forward. Procedures are in place to investigate any real voter fraud.
A mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.
To reason from analogy is often dangerous, but to illustrate by a fanciful analogy is sometimes a means by which we light an idea, as it were, into the understanding of another.
Poems - crystallizations of the universal play of analogy, transparent objects which, as they reproduce the mechanism and the rotary motion of analogy, are waterspouts of new analogies.
I think it's important to reason from first principles rather than by analogy. The normal way we conduct our lives is we reason by analogy. [With analogy] we are doing this because it's like something else that was done, or it is like what other people are doing. [With first principles] you boil things down to the most fundamental truths…and then reason up from there.
If you see fraud and do not say fraud, you are a fraud.
A proof only becomes a proof after the social act of "accepting it as a proof".
What God declares the believing heart confesses without the need of further proof. Indeed, to seek proof is to admit doubt, and to obtain proof is to render faith superfluous.
Proof is boring. Proof is tiresome. Proof is an irrelevance. People would far rather be handed an easy lie than search for a difficult truth, especially if it suits their own purposes.
You constantly hear about voter fraud... but you don't see huge amounts of vote fraud out there.
I tried to explain as much as I could," Poppet says. "I think I made an analogy about cake." "Well, that must have worked," Widget says. "Who doesn't like a good cake analogy?