I have been reading the recent discussion about whether "facts" can be "rational" or "irrational" http://www.askphilosophers.org/question/2829). Professor Rapaport suggests that philosophers use facts differently than most non-philosophers. Facts, he says, "simply 'are'". They are not like beliefs, which are more like sentences. His statements have left me very confused.
The Earth is round. Is that a fact?
We all die. Is that a fact? Seems to me that it is. And it's simultaneously a sentence. I don't see how a fact can be anything but a sentence.
But suppose facts are not sentences. They are situations. One big fact would be the way the world is, I suppose. A smaller fact might be the way my room is right now. Fine, why can't situations be "rational" or "irrational"? I think very often we come upon a situation and say things like "This situation is totally crazy", by which we mean, it is irrational. As the questioner said, dictionary.com defines "rational" as "agreeable to reason". ...
I attempted to define 'Truth' today and so far the best I can come up with is:
In order to really understand and analyse exactly what truth is; we first need to explore the idea of truth in its purest form. The Compact Oxford English dictionary suggests that Truth is 'that which is fact or can be accepted as true.' In this sense, I would first suggest that, philosophically, truth falls more aptly into the area of faith and belief as opposed to anything definitive. This is due to the fact that nothing can be proven to be precisely accurate without error for an infinite amount of time. In fact, even if something were theoretically created at a point in time that was, at that point in time, precisely accurate it cannot be proven to be accurate for an infinite amount of time as, by definition, you would need to test the theory or creation infinitely. We can thus resolve that, despite common definition, truth is a label given to an abstract, repetitive belief specifically in relation to the human condition...
I'm a mathematician looking at some of the work of Leonhard Euler on the "pentagonal number theorem". My question is about how we can know some statement is true. Euler had found this theorem in the early 1740s, and said things like "I believed I have concluded it by a legitimate induction, but at the same time I haven't been able to find a demonstration" (my translation), and that it is "true even without being demonstrated" (vraies sans etre demontrees).
This got me thinking that "knowing" something is not really a mathematical question. A proof lets us know a statement is true because we can work through the proof. But a mathematical statement is true whether we know it or not, and if you tell me you know that a statement is true, and then in fact someone later proves it, I can't show mathematically that you didn't know it all along.
This isn't something I have thought about much before, and my question is are there any papers or books that give some ideas about this that would be approachable by...
Are statements about resemblances objectively true/false, or are they merely statements about the way things seem to us, hence subjective? Is it "objectively" true that pentagons are more like hexagons than circles? Is it objectively true that the paintings of Monet are more like those of Renoir than those of Picasso?
John Carey has written a book called "What good are the arts?" His central idea is that our evaluation of the visual arts and music is completely subjective and relativistic. Art and art creation are seen as an important part of being human but no one can make a case for a work being of higher value because this is just opinion. Fine. However, he goes on to argue the case for the higher value of literature. Predicting the obvious objections one might have after his previous relativist argument he says: "let me emphasize that all the judgements made in this part including the judgment of what 'literature' is are inevitably subjective". Here and in live debates he has stated this as a means of getting himself off his own hook.
So my question is, surely there is some contradiction involved in arguing a position while at the same time stating that it is just subjective? Aren't we trying to lay claim to some objective truth as soon as we begin arguing?