Science of Causal Inference

[Drregaleagle]

On another thread entitle "The true nature of religion in civilization's development", Black Wolf raised a good point.

I'm not so sure about this.

For example, I can't just go up and say "Hey did you know that sin(x) can be solved by x - x^3/fact(3) + x^5/fact(5) - x^7/fact(7) + x^9/fact(9) - x^11/fact(11) ..... ". I would have to provide a mathematical proof for it, using derivatives, L'Hopital's rule, and all that other crazy shit. "It works because it's right every time you try it" wouldn't work.

Now, I know mathematics has more demands for non-contradiction than other sciences, but it would be very unsafe to assume that a correlation implies causation until there is absolute certainty

This thought should cause us to ponder the nature of absolute certainty. The critical characteristic of absolute certainty is that certainty develops from the definition of one's terms. Relating to Black Wolf's example, how would you ever notice a correlation of the Maclaurin series with sine values in the first place? If one took a protractor and drew many right triangles, the side ratios of the triangles could be measured with a ruler and the sine values could be calculated. These calculations are not based off of pure deductive reasoning, but the presumably inductive reasoning of the protractor and ruler markings. The measuring instruments are not necessarily accurate.

The Maclaurin series values could be infinitely calculated until one noticed that it didn't agree with the empirically observed values. Obviously, one of the methods is wrong. The reason the observed values must be wrong is because the Maclaurin series determines the sine values by definition. Before Maclaurin series, we didn't have precise values for trigonometric functions.

Also, mathematical objects only exist, however objectively, in the mind. We define and represent objects such as point, line, circle, angle, etc with what we sense in the real world but we don't sense the objects themselves. We develop the concepts of geometric and mathematics objects by thinking about the nature of what we perceive.

[Vik]

This thought should cause us to ponder the nature of absolute certainty. The critical characteristic of absolute certainty is that certainty develops from the definition of one's terms.

Checking differentia of "certain"...

"Certain" represents an assessment of the evidence for a conclusion. What other types of assessments are there? "probable", "possible", "impossible", "arbitrary", etc.

"Probable" means that there is statistical evidence for generalizing from a sample of data. this is very abstract so it's dependent on the certainty of definitions.

"Possible" means that although definitions allow it, and it doesn't contradict anything we know, we don't know enough to "fully affirm" it.

"Impossible" means that it implies a contradiction to something we already know.

I would say that definition is *incidental*, not essential.

McLaurin series values

This is a good example of how definitions can be used to rule out certain types of errors.

The application of definitions to the assessment of particular conclusions is a deductive process.

I'm not sure how this is related to induction or causal inference though. It is my understanding that mathematical induction is actually a type of deduction.

Could you provide more background on what you're trying to say?

Also, mathematical objects only exist, however objectively, in the mind. We define and represent objects such as point, line, circle, angle, etc with what we sense in the real world but we don't sense the objects themselves. We develop the concepts of geometric and mathematics objects by thinking about the nature of what we perceive.

Would you say that there is no mathematics apart from attributes abstracted from reality?