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Permalink Reply by Radu Andreiu on October 26, 2010 at 10:11am

As I understand it, logic means studying fundamental truths. Logic is split into inductive and deductive reasoning. The former is based on deriving general conclusions from specific examples and it can't lead to certainty. The latter means reaching a conclusion based on definitions and axioms. These are specifically defined to be true, like non-A is the negation of A, which, in some cases, means everything that is not A. The question here is "if we accept this, what conclusions can we draw?". However, as we're starting from concepts defined by us, it is not a real representation of the truth.

When we're using logic in abstract matters, it's all fair and simple. We are basically creating a virtual world where we postulate some fundamental truths and then use deductive reasoning to deduce (obviously) other general truths. However, when we're analyzing the real world, we ought to use inductive reasoning too. That means that we have to observe the world and postulate what we think are fundamental truth (laws) and only then use deductive reasoning (like in theoretical physics) to search for more complicated truths. But the generalizations that we make are based on a limited amount of examples and so, they can be false, thus leading to false conclusions. That's why theoretical physics always has to be supported by experiments. For instance, until not too long ago, we thought that nothing can be in more places at once. We accepted that as a fundamental truth about the world because it worked so well for such a long period of time. But then quantum mechanics came along and we had to revisit that "truth".

What I'm trying to get at is that truths may not be general truths, but local ones, like those that apply to our universe. If we step out of it, then everything is possible, because there are no restrictions. We're back to the virtual world where some truths are just defined as such and there can be any number of possible axioms. For example, if we change some of the axioms of mathematics, then 2 is equal to 76, or to -2 and so on. sin ( x ) = cos^2 ( x/3) if I change a thing or two in the basic rules of mathematics.

Anyway, that's how I view logic and truth. Also, I hope I wasn't too confusing with my explanation.

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Permalink Reply by Loop Johnny on October 26, 2010 at 1:50pm

Wonderful explanation Radule. I understood everything you have said. I always have thought that everything has a certain uncertainty ( paradox? )

I love the ramification into deductive and inductive. I have never thought about it that way. It reorganized my mind.

If we know all the factors in the system, using deductive logic, we can form a resulting, more complex conclusion which is based on the validity of the initial factors ( true or false )

Inductive is the same thing, different only because of our measuring instruments errors. If a certain instrument could provide a 100% result then that would be 0 uncertainties, thus a true statement. Our instruments, as they advance, can only narrow down the uncertainties.

All our "real" reasoning is based on uncertainties an probabilities.

It all depends on where we are located. If we are inside a system ( reality ) we can only use inductive reasoning. If we create a system that is within us ( our mind ) deductive reasoning provides the resulting answer. The key thing is that all the data within that system is also based on the bigger one ( reality - our mind imagines only what it is capable of - 8 dimensional cubes would be hard )

It is important now that science can narrow down the doubt and that it can infuse our mind with more precise data to chew on.

In the end, inductive and deductive are basically the same. Inductive gets data from reality using some instruments with a given uncertainty. Deductive uses that data to create abstractions.

Thanks Radu and Adriana ( first in line gets the credit ;) ). This was insightful.

By the way. I think what my friend was trying to prove is the uncertainties of logic that make logic "wrong". I just deduced that it's not the logic that's wrong. It's the data from our imperfect instruments.

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Permalink Reply by Loop Johnny on October 26, 2010 at 2:55pm

Uncertainties can be in mathematics too.

solve a + b = 9

a and b has an infinity of solutions in pairs and, i maybe wrong, you can't be certain to what a or b is.

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Permalink Reply by Radu Andreiu on October 26, 2010 at 3:26pm

I think that, if there aren't any more factors involved, the correct and certain answer is:

a ∈ (-∞,∞) and b = 9 - a

This is so because when you are asked to solve and equation, like that above, you are basically asked to say for which values it is true. That doesn't mean that, if you get more than one value, you haven't solved the equation. In this case, the equation is true for all the real numbers represented by a and b (assuming they are real) which have the correlation written above.

There are actually uncertainties in math (i.e. statistics and probabilities), but we can state with absolute certainty what these uncertainties are. However, these uncertainties arise also from the real world. They are there to analyze all the possibilities of a real situation before it happens. For example, if we flip a coin 10 times, we don't know how many times we'll have heads and tails. But we can calculate, for instance, that the probability of there being 9 heads and 1 tails is 10/1024 (of course, this is for a perfectly balanced coin, which can't possibly end up on the side, but more complex calculation can deal with the real coins too). What I'm trying to say is that I haven't come across any uncertainty that doesn't originate in the real world. Maybe they are out there, but it would seem odd at first to find out about them.

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Permalink Reply by Loop Johnny on October 26, 2010 at 3:45pm

So we are certain about the uncertainties of a certain equation. Nice.

Mind = blown

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Permalink Reply by Radu Andreiu on October 26, 2010 at 3:08pm

I didn't know you were from Romania too. The definite article you used for my name gave you up :). It's nice to finally not be the only active user from Romania.

Anyway, getting back to our business, I thank you for the appreciation and I also agree with everything you've just said. Uncertainty is everywhere, thus I can't seem to understand how some people have such strong certainties. Truth, in our case, is only a matter of probabilities. In certain situations we can even approximate the degree of certainty that we have. Of course, this degree also has a degree of uncertainty and so on.

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Permalink Reply by Svendsen on October 27, 2010 at 10:17am

What makes sense on a fundamental instinctive level of understanding.

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Permalink Reply by Radu Andreiu on October 29, 2010 at 7:47am

This way, theists might argue that they're stance is based on logic, because, for them, it "makes sense on a fundamental instinctive level of understanding." I would argue that we need a more objective and organized way of thinking logically. In fact, that's why we have science and math. Even when facts disagree with all our instincts, they still win... like in modern physics. Here, it is not logical to think that space and time can't be modified, even if that's pretty much how things work on our scale, ergo our instincts tell us this is so.

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