moving finger said:
Of course we can imagine a world where bodies might travel faster than light; there is no logical contradiction in this[/color]. And we can imagine a world where bodies gravitate towards one another according to the inverse of the distance, or the inverse cube, and so on. Newton in fact did envisage these possibilities since there is no logical contradiction in assuming any of them[/color]. It is just that our world does not work in any of these ways.
Ah but there is a logical contradiction! It is just that people don't examine the consequences as carefully as they should. Your post brings up an issue close to my heart.
moving finger said:
What the above shows is that there is often an intuition of a certain kind of "necessity" about the laws of nature as they operate in this world. Nature it seems is inescapably committed to behaving in accordance with its laws and cannot behave otherwise. But is this a correct view of the laws of nature?
I think you are confusing two very different modes of thought.
In essence, there are two very different ways of "understanding" anything. There is that emotional feeling that something makes sense; that you understand what is going on and have no doubts as to the validity of your expectations. Then again there is a very different kind of understanding which allows you to logically defend some set of analytical expectations in intimate detail; even in cases where no emotional feeling exists to defend the validity of those expectations (here I am talking about all those totally counter intuitive deductions so common in analytical work).
In my head, both meanings are very important. When someone says that they "think" something is true, they can have either of the two meanings in mind and they seldom make it clear as to which phenomena they mean to convey. I believe that it is very important that these two different phenomena should be carefully identified and kept in mind whenever rational discussion is attempted.
I like to use the adjective "logical" to classify a specific kind of thought commonly believed, particularly by intellectuals, to be the only possible variety of rational thought (I suspect they believe rational and logical are merely different words for the same phenomena). In my head, the term "rational thought" implies the idea being expressed makes sense: i.e.,
it does not generate emotional doubts as to its validity[/color]. Under that view, the adjective rational does not always imply "logical" (and neither does it imply easy believability but rather only that the presenter believes it). The view also makes it apparent that "rational statements" (though they seem to make sense)
are not necessarily valid[/color], a point anyone familiar with the development of science should be aware. That is, very bright people have made errors in their beliefs from time to time; but that does not mean that those beliefs were irrational.
If one holds that only logical thoughts are rational, then scientific progress becomes impossible since any deductions must be based on things presumed to be valid without reason (those axioms one starts with) and that is certainly irrational. However, I hold that there is a second kind of rational thought which needs to be clearly understood. Call it intuition, Zen or my favorite "squirrel thought"; whatever you prefer.
Squirrels are great in the treetops but they lack a bit of skill on the streets. All my life I have heard those smears you see on the street (and I think you know what I mean) humorously referred to as "poor squirrel decisions". Well, they were actually results of real decisions and I think "squirrel" is an excellent adjective to use. I doubt anyone would classify those decisions, whether they are in the tree tops or in the streets, as "logical"; "intuitive" seems much more reasonable .
So all thought is divided into two categories, each with its own strengths and weaknesses. The great strength of logical thought is that the conclusions reached through logical thought are guaranteed to be as valid as the premises upon which they are based. The weakness of logical thought is that it is limited to a very small number of premises: i.e., the specific number of factors which can be included in the analytical statement of the problem. This is usually a seriously small number when compared to the volumes of information available to us through our senses.
A further problem with logical thought is that the number of specific steps in the process cannot be excessive as we must be consciously aware of each step. If we are to be truly logical, each and every step must be consciously validated. Anyone who has carefully thought anything out is very well aware of the fact that considerable time is consumed in such an analysis. If a logical process were to involve a few billion steps, I doubt many here would attempt to follow that logic. Now mathematics and formal logic provide us with a certain respite from that last constraint but, even so, logical thought is of very limited applicability.
Intuitive thought, on the other hand, has its own strengths and weaknesses. Its strength lies in the astonishing number of factors which can be taken into account (seemingly beyond counting though as Paul points out, it cannot be "infinite"). Its weakness is the fact that the process can not be validated: i.e., there is no way to prove your intuitive conclusions are correct. Nevertheless, most of them will be good decisions. Why is that? The answer should be clear. Whatever the mechanisms are, by which those decisions are reached, they have been honed and polished through millions of years of survival; failure to make
good[/color] "squirrel" decisions has been cleaned from the gene pool by the shear consequences of making really bad decisions.
What I am getting at is the fact that logical thought is actually a rather worthless endeavor when it comes to life and death decisions. It is often much better to "go with your gut". In fact, in the absence of mathematics, logical decisions are so limited as to be almost entirely inapplicable to any day to day activities. This is why many students can not understand a purpose to learning mathematics. Actually they are quite right, neither math nor logic serve much of a purpose to important problems. I have known very successful people who have never made a logical decision in their entire life.
However, when a problem can be approached with math and logic, one can be quite sure of the absolute validity of their conclusions. Well, "absolute" to a certain extent: it is always possible that an important factor was omitted or that some axiom thought to be true was, in fact, false. Thus it is important that we understand how those factors came to be established. There is but one answer; intuition (pure "squirrel" decisions). I have come to the fundamental conclusion that these intuitive decisions are the single most important part of thinking; logical thought is not even possible in the absence of intuition. But the problem is that almost everyone has a great tendency to presume their intuition is infallible.
This is, in fact, the single biggest problem in trying to understand the universe. Most everyone believes the ideas they have arrived at via their personal "squirrel" decisions are the only possible conclusions which can be reached (see my post to the thread:
"is computability an empirical fact of the universe?"). The reader should understand that "belief" of anything is a squirrel decision. The ability to communicate (language itself) was acquired through "squirrel" thought. Accept your squirrel decisions as your best bet when it comes to any serious question, but don't ever think that those squirrel decisions are infallible. You don't have to believe they are infallible to follow them; when it comes to life, "you pays your money and you takes your chances" and worrying about it is a waste of time.
On the other hand, if you want to do science, you should remember that even your most cherished "squirrel" decisions could be wrong. Even you guys who are not "crackpots" should remember that. A lot of science is done in the total absence of logical thought and that has to be so; but scientists should not forget that fact. If they do, science folds over to religion. It may seem to work great, but that does not mean it is valid. Think about that next time you see a "poor squirrel decision".
Have fun -- Dick