Why do people think that we "prove" things in science?

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I don't think I did.

Thanks for an otherwise interesting reply. Your understanding of induction seems to be confined to traditional probabilistic formalism. There is, however, more to it than that.

I see what I did now. You very first sentence there is ambiguous. I read it one way, you intended it another way. Nonetheless, your assertion that 'heliocentrism' is self-evident or fundamental is clear non-sense. It certainly wasn't self-evident to the world prior to the likes of Kepler, Gelileo, Newton and a few other visionaries. Heliocentrism was a concept proven through the techniques of mathematical and logical reasoning. By definition, something can't be proven if it's an axiom (fundamental and self-evident). Therefore, heliocentrism is in no way self-evident. Phenomologically the sun appears to rise and set over the edges of the flat disk earth; a perception which needed to be proven wrong through reason.

On the contrary I'm extremely well versed in the methods of inductive reasoning. While, not all inductive propositions have numerical probabilities explicitly attached to them, ALL propositions do have probabilities attached to them (whether known or not known). Analogy, causal reasoning, and all other methods of induction derive propositions that very rarely have probabilities that are 0 or 1. On the other hand, deduction can only deal with propositions with implied probabilities of 0 or 1. If I assert P, then I claim P has probability of 1 (I claim it's completely 100% true). Similarly, if I assert -P, then I claim P has probability 0 (I claim it's completely 100% false, or 0% true). While the reasoned findings of causal induction (Mill's Methods if you like, though there are newer better systems than Mill) may not have explicit probabilities attached to them they are rarely (if ever) either 100% certain or 0% certain.

In summary:

- Deductive premise has a probability x : (x = 0) or (x = 1). (false or true)
- Deductive conclusion has a probability x : (x = 0) or (x = 1). (false or true)
- Deductive probabilities are always implied.

- Inductive premise has a probability in the range 0.0 <= x <= 1.0.
- Inductive conclusion has a probability in the range 0.0 <= x <= 1.0.
- Inductive probabilities are often implied and nearly always one of the fractional values (anything but 0, or 1).

It most certainly wasn't, but a contemporary context offers a different perspective.


Undoubtedly, and I strongly recommend expanding the insight by including conceptual methods.

Would you mind expanding upon what you mean by 'conceptual methods'? If there's something for more to learn I'm anxious to find out. I've already studied the philosophy of logic such as the various philosophical foundations and controversies of classical vs. non-classical. While are few of the non-classical things are interesting, most seem quite gimmicky in the end (relevance, connexant, fuzzy-systems, etc.). I do enjoy reading about and working on my only theory of truth, which is rather complex for a philosophical theory but I believe reflects the common notion of truth more closely than correspondence, coherence, pragmatic, and even tarski's model theory (if taken as a truth theory). But, why do so many philosophers think any theory with more than three or four axioms is overly complex?

I do tend to reject some of the philosophical controversies as being 'nit picking'. E.g. Issues philosophers have with the formulation of the conditional, and other Truth-Functional operations as being too 'unnatural' is ridiculous. Logic isn't English, which isn't Spanish, which isn't French. Every language does things in its own way. Rephrasing one's English sentence according to the rules and conventions of a target language should be naturally expected. Moreover, excellent techniques have been devised for expanding the expressiveness of logics. Modal logics provide can provide some of that, more experimental formal systems that are still complete and sound provide even greater degrees of expression. Imperative logics are excellent for formalizing ethical theories by extending the definition of a proposition to include maxims. Professor Harry Gensler has an interesting "experiment" where he formulated such a logic and subsequently formalizes the golden rule. While the family of ordered predicate logics where n > 1 (i.e. 2nd order, 3rd order, etc.) are all incomplete, they are at least sound and provide excellent insight into how to reason correctly with their respective codified structures (e.g. variables that reign over predicates rather than objects).

Moving on to applications, while systems like mathematics are not themselves true formal systems. Yes, given that Godel seems to have proven (though small groups of mathematicians are still not convinced of the correctness of his proof) that mathematics has an infinite number of axioms. Hence, mathematics cannot be reduced to a formal system. However, chunks of mathematics lend themselves just fine to formalization. Anyway, mathematicians use only a very small part of logic and yet attempt to claim that logic is a branch of mathematics. It' isn't. It's a sibling discipline of mathematics. Both of which subcategories of the science which studies systems for codifying, manipulating and communicating information. In addition to logic and mathematics, we find linguistics, set theory, model theory, etc...

I think there are many reasons for this naivete. The way science is taught in schools; intellectual laziness or lack of curiosity (some people want others to think for them); the hierarchical place of the white coat 'experts' in society as a whole; a lack of understanding about the scientific process and philosophies of science, like positivism; ignorance about how many times science has got things wrong, badly wrong; the covering up of scientific mistakes; the human desire for simple certainties and belief systems - whether religious or scientific - and easy answers. A lack of understanding about how science is manipulated and mis-reported, and how political science is - the competition for funding has engendered a hidden layer of very dirty tricks.

I think that people tend to see evidence as synonymous with proof. Also, they may take the scientific ideas accepted today as granted, as it is difficult for many people to generalize what has happened in the past and they are inclined to think we know everything.

The general public have not been educated in Type 1 and Type 2 errors, (maybe schools have changed this now) and it's one of the fundamental things you need to understand re scientific findings.

https://explorable.com/type-i-error

I was referring to the book by Harriman (see previously posted link).

Our science education is rather poor. So people have a misconception of what science is and what scientists do.

ruveyn

Thanks. Purchased and now on my Kindle.

Glossing over the intro I see that the ideas presented are based upon Ayn Rand's Objectivism. Interesting approach. I do personally believe that about the best we can do, as far as finding absolute truth is via some pragmatic approach (and as such we can only asymptotically approach absolute truth). The only exceptions are theory-building systems (e.g. linguistics, logic, math, etc.). I think David Hume's Problem of Induction is unsolvable, but I'm not closed to considering proposed solutions.

I find myself actually rather surprised to find anything that builds upon Rand's Objectivism. While I find she seemed a rather likeable person I don't agree with many of her positions, but my position is irrelevant to this. My understanding is that very few philosophers take her works seriously. That position seems to have been mutual as Rand's knowledge of the philosophical works of others seemed quite shallow at best, as if she only read summaries of the philosophers rather than their actual works.

Great. I hope the book offers something of value.

Philosophy is one of my special interests. I'm currently fascinated by the fundamental nature of existence, which I find absurd. I don't think meaninglessness necessarily follows, and I am trying to figure out non-existential implications consistent with logotherapy (for self-therapeutic reasons).

A lot of things discovered by science were just accidental and incidental, rather than hypothesized and proven in rigorous studies, particularly in medicine:

In 1929 a doctor (Philip Hench) noticed that a patient who had arthritis improved suddenly after a bout of jaundice. Intrigued, he noticed this phenomenon in later patients too. In 1950 he shared the Nobel Prize for medicine as his observation led to the discovery of cortisone treatment for severe arthritis.

In 1906, a biochemist was noticed that rats fed a diet of proteins, fats, carbohydrates and minerals failed to thrive. This changed when he added milk - and vitamins were discovered (though they were called "food accessory factors" then.)

Safety glass was discovered by a French chemist (Edouard Benedictus) because he was clumsy and dropped a flask, noticing that the fragments didn't fly apart (the flask had contained collodion in alcohol, which coated the inside. This led to the manufacture of safety glass in cars).

Everyone knows about the discovery of penicillin that came about through one man's careful observation.

The first doctor to suggest that handwashing would cut fatality rates (Semmelweis) also based his idea on observation - and was thrown out of the 'scientific' medical profession for his outrageous idea.

Science isn't always this purist ivory tower enterprise with controlled double blind experiments and artificial laboratory conditions.

http://ilarjournal.oxfordjournals.org/c ... 4/332.long

Sincie I'm stubbon I will attempt this again.

Your claim that heliocentrism is a self-evident axiom demonstrates a lack of understanding of the concepts of both what constitutes self-evidence as well as what an axiom is. I'll take 'axiom' part first.

An axiom is a foundational proposition of a theory. But in which theory is heliocentrism an axiom? An 'axiom' that is not part of a theory is called a 'conjecture', just about the very weakest sort of proposition being neither proven nor self-evident. In NO current theory of physics is heliocentrism an axiom. It's a theorem derived from the axioms of those theories. I cited Newton's Principia in an earlier post, which is where the full theorem of heliocentrism was first proven from Newton's three very simple laws. Since it's proven, it's a theorem.

Two hundred years after NEWTON, Einstein modified Newton's laws of motion. AGAIN, Einstien didn't include Heliocentrism as an axiom of his system. Einstein's theory has a very different theory of gravity but using it one can still derive a proof of heliocentrism. A better proof than Newton's because Einstein's predicts the planet's positions more accurately. But this is the point, heliocentrism is still a consequence of Einstein's axioms NOT one of the axioms. Hence, the state of 'heliocentrism' as a theorem continues to be the state of the art in physics theories.

Now for that 'self-evident' part (but only because I'm a glutton for punishment and I'm bored). Heliocentrism is in NO way self-evident. Stand outside of your home some time and observe the apparent movements of the sun. It is an every-day phenomenological experience that the sun appears to circle a flat-disk earth -- THIS in complete contrast to the NON-self-evident truth of heliocentrism. Self-evident means that something needs no proof. Yet, as I stated above, heliocentrism is a proven theorem of every currently accpeted theory in physics. Hence, it cannot be an axiom of any of those physics. Heliocentrism is proven FROM the axioms of physics. It is a consequence of those laws.

In a specific context, yes, but more generally, an axiom is a self-evident truth. A stone is self-evident. Planets are self-evident. The Sun is self-evident, and so is its position in relation to the planets. This is directly observable; self-evident; a metaphysically given fact; an axiom in itself.

I am new to this forum so I'm sorry if I'm circumventing any introductions I'm supposed to make. I think you guys will find this relevant and helpful. In my opinion nobody has ever understood the role of science more than Feynman. I would recommend watching the entire series to anyone who is truly interested in how science works.

https://www.youtube.com/watch?v=kd0xTfdt6qw

Physics is not built on axioms or absolute truths. There is nothing absolute about the heliocentric model for the solar system. The sun moves (very little but it moves) in response to the gravitational force between it and the planets as well. Heliocentrism is, however, true enough for practical purposes. When you talk about the "truth" in heliocentrism it's really a matter of what framework you are working in. There is absolutely no truth in Newtonian mechanics, but at the same time it's absolutely a valid framework to work within for many systems.

It's not really accurate to use the word axiom when you are talking about a physical law. Axioms are something that can never be explained because they are taken to be true. Physical laws, on the other hand, are still open to explanation. Physical laws are based on repeated observations, and it is in no way apparent whether or not they are consequences of some other phenomena. The distinction is actually something that is really interesting to me.

Absolute truth isn't very useful in science. Making axiomatic statements doesn't even work in the most ideal cases, and in practice it's a lot messier. Almost any interesting problem is fundamentally unsolvable using pure mathematical reasoning. Where the real art comes in is deciding what you can say is "basically true" with negligible or acceptable consequences. Organic chemists push electrons around with arrows from hybrid orbital to hybrid orbital, and while it's blatantly wrong in a physical sense, it works. The concepts of absolute right and wrong are of little use to a scientist.

This is why it is so important that a theory is testable and has a possibility of a distinct negative outcome. That said, every though a scientist has is not specifically crafted with this in mind. I work in an experimental condensed matter lab where much of the work being done is looking for positive evidence of certain phenomena. I don't really agree that in practice, there is a "THE" scientific method. It's more of a scientific ideal.

Absolutely correct.