# Math and science

1. Oct 4, 2005

### Imparcticle

what is the difference between mathematical determinism and scientific determinism?

2. Oct 4, 2005

I give up.

Tell me.

3. Oct 4, 2005

### neurocomp2003

expermentation vs theory.

4. Oct 4, 2005

### jimmie

Oh.

Thanks.

Uhh... am I correct in thinking that the "theory" is the "scientific" part?

5. Oct 5, 2005

Staff Emeritus

No, both of them (experimentation and theory) working together make up the "scientific part".

6. Oct 5, 2005

### HallsofIvy

Staff Emeritus
I can think of several different ways of interpreting the word 'determinism'. It would help if you would define the meaning here.

7. Oct 5, 2005

### saltydog

Well, I think "scientific determinism" embodies empirical evidence whereas mathematical determinism involves deductive evidence. However different, empirical and deductive evidence are made from the same cloth it seems to me and is the reason mathematics is so successful in describing nature. Thus maybe there is some intimate connection between empirical (what's really out there), and deductive evidence. Perhaps this is related to the difference between continuous and non-continuous functions: As long as phenomena are "continuous", then deductive reasoning in some form "matches" empirical evidence. However, as discontinuities and critical points emerge, they diverge.

8. Oct 5, 2005

### jimmie

Oh.

Thanks.

that sounds good to me. lets go with that.

9. Oct 6, 2005

### Imparcticle

Can you elaborate on that? What do you mean they diverge?

You are using "deductiive reasoning" and "empirical evidence" together as though they were equivalent...which they are not. Either "deductive reasoning" diverges (whatever you meant by that) with "empirical reasoning" or "deductive evidence" with "empirical evidence". Or does it make a difference, however slight?
note that:
reasoning
The basis or motive for an action, decision, or conviction.

evidence:
A thing or things helpful in forming a conclusion or judgment.

Courtesy of dictionary.com

10. Oct 6, 2005

### Imparcticle

I mean it in the sense of Laplace determinism.

11. Oct 6, 2005

### saltydog

Jesus, I was afraid someone might challenge me on that.

Deduction is based on first-principles, something known beforehand: if it worked before and this is similar to it, then it should work the same way. That's fine for continuous phenomena in which the past is "connected" to the future in some analytical way. We can extrapolate with some confidence into the future based on behavior in the past.

However, deduction cannot predict "emergent" behavior. Wait, let me get my definition out . . .here: Emergence referes to a process by which a system of interacting subunits acquires qualitatively new properties that cannot be understood as the simple addition of their individual contributions.

But the world is massively emergent! I look out of my window . . . ok I've said that one enough in here. Thus if I'm correct in my statement about deduction being incapable of predicting emergence, then deduction limits out grasp on the world. That is where empirical investigation comes in: We let the world tell us and not deduction.

But qualitative change occurs at a singularity or critical point of a system. So therefore, if emergent change represents qualitative change, then somewhere I suppose, must exists a discontinuous, abrupt, critical point in the system.

Thus I suggest deduction is applicable to describing the world only up to a critical point, e.g., a discontinuity.