Using Math to defend scientific method?

Factual Questions
1

Hi all! On another message board, a global warming discussion somehow led into a creationism discussion. But my question to you all is using Mathematics to defend “absolute proof” of science. Someone asked the defender of Creationist:

“Simple question, is the earth 25,000 years old or 4.3 billion?”

To which he replied:

“Simple Answer: Prove either one. I said prove. Not conjecture. Not theory. Absolute Proof. I’ll answer it for you. You simply can’t.”

To which the original questioner stated:

“the entirety of scientific knowledge is unprovable in the way that you’ve just requested.”

To which the Creationist replied:
"False.

2+2=4

Mathematical method
1 Understanding
2 Analysis
3 Synthesis
4 Review/Extend

Scientific method
1 Characterization from experience and observation
2 Hypothesis: a proposed explanation
3 Deduction: prediction from the hypothesis
4 Test and experiment

Can’t be tested so can’t be proven 100%. Lots can be proven just not that. Sorry."

Get all that? His final response sounds ridiculous to me, but Id like some expert opinions on it. Is it fair to apply “truth” of mathematics to scientific theory?

2

IANAM but it seems to me that math is founded on definitions created by human beings.

2+2=4 isn’t a hypothesis arrived at by looking at the universe around us, it comes from some core rules created by mathematicians.

That isn’t strictly speaking “science” so you can’t compare the scientific method and the mathematical method as your creationist laid them out. Perhaps he should add a 0th step to his mathematical method which is “Definition of terms”.

If I get to define my terms then I’ll say “1 year is a unit of time equal to one 4.3 billionth the age of the earth” and voila! I’ve proved that the earth is 4.3 billion years old! Woohoo!

Of course it doesn’t work that way.

Getting offtrack just a hair, science always admits the possibility that a theory is wrong. That’s one of the neat things about it. Nobody will say that the earth is 4.3B years old absolutely, 100%, case-closed, it’s been proven beyond any possible doubt.

However if you’ve got two competing theories and one of them (YEC) has approximately zero evidence while the other one (derived from actual science) has a heap of evidence bigger than Mount Everest, it’s understandable why people would consider one of those theories much more likely to be true.

3

2+2=4 is a self-imposed rule in a fictional environment. If I was to pick up a rock say, “This rock is named Edmond.” It becomes Edmond not because there’s some proof, but because it’s a fiction that everyone around agrees to assume. Fictions can be as absolute as anyone is willing to give them credence for.

4

This probably belongs in GD.

Your Creationist friend is confused. One can apply the truths of mathematics to a mathematical model underlying a scientific theory. But this doesn’t make the truths any less contingent on the empirical data from which the theory was formed. For instance, the Heisenberg Uncertainty principle is a consequence of the mathematics used to describe quantum mechanics, but we would hardly say it has the same status of truth as 2+2=4, since it’s truth is still clearly contingent on the empirical data from which quantum mechanics was formulated.

However, I should mention there have been some philosophers, like Kant, who have argued that some fundamental truths about space and time should be put on the same level as the truths of mathematics. So in other words, some truths of science can be proven using deductive reasoning. Kant’s philosophy is kind of involved, but you can read about it here: Immanuel Kant - Wikipedia .

I’m no philosopher, but it’s my impression that this view is marginal at best today, especially among scientists.

5

I’d say that it’s absolutely unfair, and looking for absolute truths from mathematics isn’t even possible anyway.

For example, if I take a triangle and take the sum of its three angles, what do I get? Those of us who remember our grade-school geometry will answer 180 degrees. However, it’s perfectly possible to develop geometric systems where the sum of the angles in a triangle is never 180 degrees. Such a geometry might seem useless but one such geometry applies to the surface of a sphere!

Mathematics is a very different thing from science. In mathematics we get to make up all of the rules and then we work to see what their consequences are. In science, we see the consequences of the rules and we have to work out what the rules are.

6

To play devil’s advocate, I should point out that you are expressing one view among many regarding the ontogological status of mathematical entities–something philosophers are by no means unanimous about. Different schools of thought would contend that 2+2=4 is a necessary truth since it follows from necessary conditions for experience (Kant again) or that 2+2=4 is an empirical truth (Mill, revised by Quine and Putnam).

More about the various schools of thought here: Philosophy of mathematics - Wikipedia

7

He seems to be saying something like this:

I can’t figure out what the point is supposed to be. Possibly, the missing part of the argument is supposed to be

The proper response to this is to point out that by his own lights, some scientific knowledge is uncertain, so the uncertainty of Earth’s age is not evidence for its being outside the bounds of science.

Another way it might be that the missing part of the argument is supposed to go:

This would make the poster’s demand for “absolute proof” somewhat mysterious, however. He should have only asked for “reasonable proof based on induction from present-day experiments and other tests.” Of course then he’d be in danger of actually being provided with such and his whole argument would (more clearly and explictly) collapse.

-FrL-

8

2+2=4 looks simple, but it’s not.

When reading all of those philosophy of mathematics links, don’t forget about folks like David Deutsch, who argue convincingly that maths follow from physics.

9

It’s always tricky arguing with people whose core beliefs are based on faith.

Tell him the Devil wrote the Bible, which makes the ‘Earth is 6,000 years old’ automatically false.

10

Someone else posted in that thread with the following link, that I beleive provides the answer:

whereby:
"In mathematics, an axiom is any starting assumption from which other statements are logically derived. It can be a sentence, a proposition, a statement or a rule that enables the construction of a formal system. **Unlike theorems, axioms cannot be derived by principles of deduction, nor are they demonstrable by formal proofs—simply because they are starting assumptions—there is nothing else they logically follow from (otherwise they would be called theorems). ** In many contexts, “axiom,” “postulate,” and “assumption” are used interchangeably.

As seen from definition, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results."

So, Mathematics cannot be proven, only assumed through logic.

11

I am not a philosopher, but let me tell how I see these questions. First, let me say that 2 + 2 = 4 is a theorem that follows by the application of logical inference to the definitions of “2”, “4”, and “+”. This much is clear. What about those rules of logical inference? To me they are an article of faith and I cannot see any other way of dealing with this.

Then there is the physical observation (baby physics, but physics for all that) that if you put 2 oranges in an empty box and then add 2 more, and nothing has happened in the meantime (no one has come in and removed an orange, the box has no orange-sized holes, etc.) then the box will contain 4 oranges. And not just oranges, but apples, tennis balls,… This is an observational fact ahd leads to a theory that 2 of anything plus another 2 will give you 4 of them. It cannot be proven, it is just a theory, of the same status as evolution. It is somewhat, but not a whole lot, better supported than evolution.

So in the end, mathematics is also based on faith in logic. This faith is tested against experience every time I prove something using mathematics and the result turns out to be true whenever tested (as with the oranges above).

Now consider creationism (intelligent design, whatever). Also based on faith. However unsupported by facts. For instance, why did I used to have an appendix that was expensive to remove and, in earlier centuries probably fatal? Why do babies have to travel through a hole in one of the major bones in the body that supports upright locomotion? These questions can be raised indefinitely, with only one all-purpose answer: we mortals cannot know the mind of God. Fine, but you claim to know that God is against murder but is all in favor of the invasion of Iraq. Obviously, I could multiply these examples indefinitely, but it would add nothing to the discussion.

Incidentally, what I said about 2 + 2 = 4 gets a bit problematic when it comes to something like 1,000,000,000 + 1,000,000,000 = 2,000,000,000. We believe that would work the same way as 2 + 2 = 4, but it is totally unfeasible to actually do it.

12

I didn’t want or intend this to be a creationist vs science debate, to me the real sticking point is trying to use Mathematics as an “absolute proof.” The Creationist is saying science can have “absolute proofs”, and uses a mathematical equation as his reason why. That doesn’t fly at all in my mind, and I was looking for a mathematical/science “truth bomb” to dump on him :slight_smile:

13

I’d agree: no matter the ontological status of mathematical models and algebras, the ones that actually apply to our world are based on physics. That is to say, if another world “existed”* where the model that fits to that “universe” the closest is the one based on the feeling that egmondo implies bracken forgero, which is not necessarily an inconsistent model in our world, but invalid for our physical circumstances.

*keeping in mind that even metaphysically speaking we might not recognize it as “existence”.

14

There are self-consistent systems which aren’t commutative. Demonstrate to your creationist that a + b is not equal to b + a in one such system and try to get him to disprove it.
The bottom line is that you can obtain absolute proof in mathematics within the system defined, but that doesn’t necessarily map onto the real everyday world. It’s hard to imagine how you could "prove’ something about the real world in the same fashion. Even using Creationist methods and sources.

15

I don’t think the creationist is saying he can prove creationism is true in an absolute sense. Notice he says the age of the earth can not be absolutely demonstrated to be old or young.

-FrL-

16

Wikipedia link: Age of the Earth

Note that even Lord Kelvin’s calculation of the age of the earth was millions of years, not thousands as in the Bible. And he missed important things that hadn’t been discovered when he crunched his numbers, like radioactivity.

The OP’s YEC pal is definitely missing the point about the philosophy of science, especially about Falsifiability.

For crying out loud, tree-ring dating has gone back 10,000 years!

17

There is no way to demonstrate the universe was not created 1 minute ago with all our memories and fossil records and all that created at the same time, along with our beliefs in the age of the universe. Of course, I don’t believe this and doubtless none of you do, but I might point out that from a strictly probabilistic point of view, such a scenario is more probable that one that began with a big bang since a higher entropy system is always more probable than a lower entropy system. Somehow, I do not find this convincing, but it is true for all that.

18

Right, all it would require is an omnipotent being, and that’s not asking much, is it? As a thought experiment, the idea that everything was created an instant ago at every instant is “interesting.” However, all the evidence points to the contrary, the “theory” is unfalsifiable, it generates no predictions, it is not scientific, and it follows that it is not even wrong. It follows that your misguided attempts to use the concept of entropy are also not even wrong, and since we are in GQ: cite?

19

Why is it that people here always get so unhappy when someone points out the simple fact that the “evidence” of evolution (a theory I happen to suspect is most likely to be an accurate explanation of our origins) is not proof of anything regarding the origin of the species, but rather is something we try to explain using the theory of evolution? You cannot prove one way or the other what the origin of the Earth, or of the species hereon was; we weren’t there when it happened, most likely, so all we can do is try to interpret what we have.

FAITH has no business in science, since FAITH is the acceptance as true of things that evidence seems to indicate aren’t true. Adopting as a tenet of faith the proposition that the Earth resulted from the myriad of physical interactions following a “Big Bang” is hardly taking a risk, given what we see around us. But those who try to explain what we see with theory should not in any way be bothered by an expression of faith in some alternate explanation, any more than those who have faith in the alternate explanation should be shaken by the evidence they see around them.

Which is why the whole debate over so called creationism is so stupid. Postulating a non-provable external supernatural causation as a “scientific theory” to support a belief based upon a religious tenet makes no sense; it’s an attempt to take faith into the realm of science, where it has no meaning. Similarly, for scientists to get all upset at expressions of faith that deny that currently most plausible theories accurately state the true past occurrences we cannot prove to have happened is stupid; the scientist should simply say, “if you choose to believe that, be my guest.”

20

But one of those propositions can be disproven; it’s not necessary to prove the truth of one or the other.

Moreover, mathematical knowledge is not scientific knowledge, but rather a language to describe scientific knowledge. It’s like confusing the name of something for the thing itself; what fool, for example, would claim Chicago is not a city in Illinois because he’s been to every city in Illinois, measured them, and failed to find one that is exactly seven letters long.

Probability aside, arguments along these lines are fallacious because for someone to mount such an argument, they must make an assertion. But if you make an assertion about truth that no assertion can meet (and, IMO, descriptions that radically discount how our senses perceive reality fall in this category), one cannot say this assertion about truth itself is true.

One naturally assumes a standard of truth even when making an assertion about truth; that is the whole point of an assertion. Again, the fallacy is confusing the thing being described (“truth”) with the description (“is true”).