Jeremiahcp
Well-Known Jerk
I think after your post number 98 it is clear that you have a strong bias against philosophy. I do not believe you understand it well, and I don't think you know what you are talking about.
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Can the Sciences Prove that Something is True?
- Thread starter Sunstone
- Start date
I think after your post number 98 it is clear that you have a strong bias against philosophy. I do not believe you understand it well, and I don't think you know what you are talking about.
I have a beef with the way philosophers do philosophy. I think there are a LOT of good, philosophical questions that modern science can inspire, but the philosophers simply don't understand the science deeply enough to even ask the questions, let alone have a good discussion on them. In history, when the boundary of knowledge was relatively close and even a lay-person could get to that boundary fairly easily, philosophers made some good contributions. But now it is much more difficult to get to that edge and philosophers are so involved in questions of 'substance' and 'essence' that they simply don't get to the real questions of the day.
I have read enough of it to know that the questions philosophers address are generally irrelevant to the progress of science or mathematics. At least, that is how it has been for the last 100 years or so.
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I'll add that many wallow in arcane quibbling over various obscure philosophical schools of thought.
Philosophers seem gifted at using 1000 words to say what could be summarized in 100.
Perhaps their minds are too highly trained, eh.
Now for something completely different.....
Even that is far from clear. many mathematical results are general ones that cover a very wide range of possibilities. If the cases that can be tested in the real world only select a subset of those possibilities and only test them to a certain accuracy, then why assume the general result is proven?
And I would say that *most* results in math are not affected by 'real world' situations. So, the history of math involves such puzzles as finding integers x and y with x^2 -67*y^2 =1. Not only can such equations be solved, but we can classify their solutions precisely. I have no way to connect such to 'real world' phenomena. But these are *by far* the most common sorts of mathematics.
First, in the use of math as a tool in science nothing is ever proven. The above qualifications do nothing to bring to doubt the accuracy of math in science and practical applications in technology and engineering.
Your proposing to high a fog index for math that is not reality. Jet engines and computers would not reliably work if the above was real.
Huh?!?!?!
This is bizzaro! No scientist claims this foolishness. Math is a descriptive form analytic philosophy, and not effected by anything.
The history of math does involve puzzles, but that is not the purpose of math. Not all math has precise solutions, especially in fractal math with many variables in Chaos theory, but nonetheless this math is very functional and useful in predictive purposes in things like weather forecasting, and climate models.
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Methodological Naturalism evolved as an intuitive deductive philosophy. No, scientist at the time of Newton called the scientific methods they used that, nor do they 'work out' Methodological Naturalism. Scientists do what deductively works, and apply the math from their tool box to their observations.
There is a distinction to be made between the mathematical model of a particular situation and math itself. Math is a formalized study of axiomatic systems. We can make mathematical models for what we see in the real world and those are often quite accurate and useful.
On the contrary, they would work just as well if the underlying mathematics was wrong in detail. All that is required for jet engines and such to work is, say, a 5 decimal place accuracy in prediction. Some areas of science can get to 12 decimal places of accuracy.
But, for example, there is no way to test physically whether a number is irrational. In fact, the irrationality of pi has absolutely no impact on the predictions made: a 20 decimal place, rational approximation would do equally well.
Yes, so the validity or invalidity of any observation cannot affect the truth or falsity of a result in math, nor can such observations serve to justify the mathematical result.
Yes, some areas of mathematics are quite helpful for making models of the real world. But the making of such models is very far from being the 'purpose' of math. In fact, solving the type of problems I mentioned is much more the purpose of math as done by mathematicians than any application.
I was not talking of what the philosophers have come up with regarding the scientific method. Science proceeds by rigorous public investigation of phenomena through
1) Meticulously recorded observation and testing/experimentation/simulation of different aspects of the phenomena in order to
2) Develop a logical or mathematical theoretical model that maps onto the said phenomena thus explaining it and enabling future predictions and technological manipulations
3)All of which is done through a public peer review system to correct for mistakes and biases through cooperative back checking.
The general outline presented above is followed in all sciences I know.
Proof defined as follows
proof | logic
proof, in logic, an argument that establishes the validity of a proposition. Although proofs may be based on inductive logic, in general the term proof connotes a rigorous deduction. In formal axiomatic systems of logic and mathematics, a proof is a finite sequence of well-formed formulas (generated in accordance with accepted formation rules) in which: (1) each formula is either an axiom or is derived from some previous formula or formulas by a valid inference; and (2) the last formula is that which is to be proved.
Things can't be proved in science in the above sense.
Kilgore Trout
Misanthropic Humanist
Indeed. Hence, if referring only to that sense, the question is rhetorical. The question can only be meaningfully discussed if one includes other connotations of the word.
Which are taken over from common usage in English, are full of ambiguities and are not used in scientific papers. Scientific papers never use proof outside of how it's used in mathematics and logic. In science the word proof is used in that sense only. Since science uses math a lot, this avoids disastrous ambiguities. A simple example
Saying that we have "proved" that all plane triangles have sides totaling 180 degrees after observing and constructing thousands of them, noticing that all of these examples do have sides totaling two right angles and hence inductively formulating a law of two right angles that is subject to future refutation by contradictory observations.
Vs
Saying that we have proved that all plane triangles have sides totalling 180 degrees by a formal deductive proof ala Euclid that can never be refuted and does not require the actual observation of even a single actual triangle.
Such very different methods should not be described by the same word. So we don't use the word proof in the first case.
Kilgore Trout
Misanthropic Humanist
I expect you realize that this discussion forum isn't a scientific paper.
I hope I'm not wrong.
I know. I am saying whether science itself sees what it is doing as a form of "proving". It does not.
Kilgore Trout
Misanthropic Humanist
Is there some part of that you perceived I disagree with?
Probably not? I am browsing from a cell phone. Apologize if I have misconstrued something.
Kilgore Trout
Misanthropic Humanist
No worries. Perhaps I misconstrued something.
The idea that the scientific method entails first assuming a metaphysical scheme of "naturalism" is palpable nonsense. That is just the opposite of what Newton did and what he extensively discussed as his method in the Principia. Hypotheses non fingo, he said.
To begin with, the adjective "natural" isn't a scientific term. No scientific discipline defines, tests or depends on it. Nor is the term "naturalism" definable in any meaningful way by any science.
Naturalism (Stanford Encyclopedia of Philosophy)
Perhaps most importantly, if the scientific method were to entail first assuming what is "natural," then no scientific investigation could ever then conclude what is "natural" or that what is "natural" is all that exists, as that would be an example of fallacious reasoning. It would be "affirming the consequent" (If P, then Q. Q. Therefore P.) or some such.
To begin with, the adjective "natural" isn't a scientific term. No scientific discipline defines, tests or depends on it. Nor is the term "naturalism" definable in any meaningful way by any science.
The term “naturalism” has no very precise meaning in contemporary philosophy. Its current usage derives from debates in America in the first half of the last century.
Naturalism (Stanford Encyclopedia of Philosophy)
Perhaps most importantly, if the scientific method were to entail first assuming what is "natural," then no scientific investigation could ever then conclude what is "natural" or that what is "natural" is all that exists, as that would be an example of fallacious reasoning. It would be "affirming the consequent" (If P, then Q. Q. Therefore P.) or some such.
Apparently you've never heard of Noether's Theorems that prove that the conserved quantities are a direct consequence of the differentiable symmetries of a system.
I am very familiar with Noether's Theorems, but you apparently have problems with basic concepts.
Your talking about a math proof, which is different from falsification by scientific method's. If and when you can distinguish between proofs in math and falsification by scientific methods communication will improve.
Noether's Theorems are useful in science as a part of the math tool box. The proofs are on the math, and not the science.
From:Noether's theorem - Wikipedia
Application of Noether's theorem allows physicists to gain powerful insights into any general theory in physics, by just analyzing the various transformations that would make the form of the laws involved invariant. For example:
- the invariance of physical systems with respect to spatial translation (in other words, that the laws of physics do not vary with locations in space) gives the law of conservation of linear momentum;
- invariance with respect to rotation gives the law of conservation of angular momentum;
- invariance with respect to time translation gives the well-known law of conservation of energy
The Noether charge is also used in calculating the entropy of stationary black holes.
Again . . . First, in the use of math as a tool in science, [and in science] nothing is ever proven. I added a clarification to help you understand simple elementary concepts in math and science.
Application of Noether's theorem allows physicists to gain powerful insights into any general theory in physics, by just analyzing the various transformations that would make the form of the laws involved invariant. For example:
More on this will follow
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