The role of logic in science

[Paul C. Anagnostopoulos]

In math, the rules of logic are taken as axioms. What about in science? Are the rules of logic among the set of axioms we need in scientific epistemology, or are they somehow more fundamental? Is all of math an axiom of scientific epistemology?

~~ Paul

[Melendwyr]

The belief that the world can be described accurately is a fundamental axiom of science. Math is description - science attempts to show that particular descriptions accurately reflect the natural world.

Logic is the foundation of all thought. Science is merely a subset of thought.

[GreedyAlgorithm]

Logic is the foundation of something, sure, but definitely not thought. Maybe rationality, but not thought. We have plenty of evidence that human thought is not logical by nature*. Should it be? On the one hand, maybe. On the other hand, our intuition is much, much better at many problems than anything else we know. Even if our intuition isn't logical. In science all we need is the Principle of the Uniformity of Nature (which isn't be logically validated).

*Have you ever, say, written a 20 page essay such that after many careful readings you would, given any page, believe that the page should remain as-is, but still believe that the essay should be changed (not every page should remain as-is)? Or that no line of some set of code should be changed but that in some line there is a bug?

[Melendwyr]

Thought is more complex than reaction. Reaction is not founded upon logic - thought is.

[Dymanic]

Reaction is not founded upon logic
Surely it must ultimately reduce to some form of logic.

[Melendwyr]

Surely it must ultimately reduce to some form of logic. The structures responsible for reaction are logical, yes, but reaction is not itself necessarily logical.

[Dymanic]

The structures responsible for reaction are logical, yes, but reaction is not itself necessarily logical.
That's because the structures responsible for reaction were optimized by millions of years of evolution to produce fast answers; not necessarily accurate ones. Making the assumption that every rustling sound coming from a clump of bushes is evidence that a lion is about to pounce is not logically defensible if you examine each instance individually; yet the deer whose policy is to assume otherwise, and stand his ground, can ultimately expect to pay a high price for the luxury of that precision. In a dangerous world, it may be considered logical to err on the side of caution.

[Melendwyr]

No, no: the logical structures involved are neurons, which are elegant summation-and-computation devices following basic laws of physics and chemistry.

[Dymanic]

No, no: the logical structures involved are neurons, which are elegant summation-and-computation devices following basic laws of physics and chemistry.Sounds like the ideal platform for the implementation of a simple logic-crunching virtual machine. Beats that toilet-paper-and-rock thing I heard about all to heck.

[Paul C. Anagnostopoulos]

The belief that the world can be described accurately is a fundamental axiom of science. Math is description - science attempts to show that particular descriptions accurately reflect the natural world. But then why did you argue with Darat about whether logic is an axiomatic assumption of science? Perhaps I didn't understand what you were arguing about.

~~ Paul

[Melendwyr]

But then why did you argue with Darat about whether logic is an axiomatic assumption of science? Perhaps I didn't understand what you were arguing about. Logic is how we generate descriptions. The assumption that the world can be described is why we generate descriptions.

Besides, it's not truly an axiom, since it can be derived from Chaos.

[hammegk]

Perhaps I didn't understand what you were arguing about.
~~ Paul
What's to understand about mis-direction, smoke & mirrors? :)

[Paul C. Anagnostopoulos]

Besides, it's not truly an axiom, since it can be derived from Chaos.
Huh? Could you please elaborate?

~~ Paul

[jj]

In math, the rules of logic are taken as axioms. What about in science? Are the rules of logic among the set of axioms we need in scientific epistemology, or are they somehow more fundamental? Is all of math an axiom of scientific epistemology?

~~ Paul

Only if logic accurately describes observation... Science is emperical.

[jj]

Logic is the foundation of all thought.

I would think that mental illnesses would show that to be otherwise.

[Soapy Sam]

Why would science require axioms at all?

[Dymanic]

Why would science require axioms at all?
It's not that it requires them; it can't avoid them.

[Melendwyr]

Huh? Could you please elaborate? I tried to explain earlier, with the sculpture, how there's an even stronger form of the anthropic principle. You might call it the observer principle.

In a superposition of all possible interactions, only the perspectives in which it's possible for an observer to exist will have observers - thus, according to the experiences of those observers, the universe is always a consistent and ordered place.

That's not a very good explanation, but it's the best I can do. Ever read "The Library of Babel"?

[Soapy Sam]

Dymanic- I agree any reasoning system makes assumptions, but do they need to be axioms?
A reminder from Wikipedia:-
In epistemology (http://en.wikipedia.org/wiki/Epistemology), an axiom is a self-evident (http://en.wikipedia.org/wiki/Self-evidence) truth upon which other knowledge must rest, from which other knowledge is built up. Not all epistemologists agree that any axioms, understood in that sense, exist.
In mathematics (http://en.wikipedia.org/wiki/Mathematics), an axiom is not necessarily a self-evident truth but rather, a formal logical expression used in a deduction to yield further results. Mathematics distinguishes two types of axioms: logical axioms (http://en.wikipedia.org/wiki/Axiom#Logical_axioms) and non-logical axioms (http://en.wikipedia.org/wiki/Axiom#Non-logical_axioms).

[hammegk]

.... Not all epistemologists agree that any axioms, understood in that sense, exist.
In mathematics an axiom is not necessarily a self-evident truth but rather, a formal logical expression used in a deduction to yield further results.
That is, science -- and many epistemologists -- agree that the math defn is the best one can do. :)

[Dymanic]

I agree any reasoning system makes assumptions, but do they need to be axioms?

Only those that cannot be reduced to underlying assumptions.

"An objective universe exists" would be an example.

[Paul C. Anagnostopoulos]

In a superposition of all possible interactions, only the perspectives in which it's possible for an observer to exist will have observers - thus, according to the experiences of those observers, the universe is always a consistent and ordered place.
Ah, that sort of consistent. I assumed that in Stimpy's Axiom 1:

Axiom 1: Everything real can be described according to some set of consistent logical rules (Naturalism).

consistent meant timewise consistent, not logically consistent. Timewise consistent so that you could learn things and make predictions under the assumption that things remain consistent over time. Perhaps I misunderstood him.

~~ Paul

[Melendwyr]

Ah, that sort of consistent. I assumed that in Stimpy's Axiom 1:

Axiom 1: Everything real can be described according to some set of consistent logical rules (Naturalism).

consistent meant timewise consistent, not logically consistent. They have to be logically consistent anyway - otherwise observers could not exist within the system they describe.

[Paul C. Anagnostopoulos]

For those who did not read the thread from which this was born, let me repeat Stimpy's scientific epistemological framework:


Definition 1: The term "real" is defined to refer to everything which has any kind of effect on something else which is real. This self-referential definition is completed with the definition that I am real.

Axiom 1: Everything real can be described according to some set of consistent logical rules (Naturalism).

Axiom 2: The natural laws describing real events can be determined through observation of the effects those events have.

Definition 2: The term "physical" is defined to refer to anything which is, in principle, observable. If axioms 1 and 2 are true, then everything which can meaningfully be said to exist is physical.


Darat and Melendwyr were discussing whether the rules of logic had to be taken as an axiom. Darat said they did. I'm still not sure what Mel is saying, although it seems to be that the world has no choice but to be logical from the observer's viewpoint.

Is that right, Mel?

~~ Paul

[Paul C. Anagnostopoulos]

They have to be logically consistent anyway - otherwise observers could not exist within the system they describe.
Indeed, which is why I took the word consistent to mean timewise consistent.

Ah, so given that the world has to be logically consistent, you're saying that the rules of logic really are deeper than axioms. We don't have to assume they are true, we know they are true. What is that sort of thing called?

~~ Paul

[Soapy Sam]

Seems to me , mathematics is a system of deductive reasoning. There must be consistency or the whole enterprise falls apart. We make the rules.
Science is a system of studying what is. There is no a priori guarantee of consistency or of rules. The fact that we find these is handy, but we should not presume they must exist.

[Melendwyr]

We know the rules that describe our reality are consistent for the same reason we know the "lines" of a magnetic field cannot cross.

[epepke]

In math, the rules of logic are taken as axioms. What about in science? Are the rules of logic among the set of axioms we need in scientific epistemology, or are they somehow more fundamental? Is all of math an axiom of scientific epistemology?

~~ Paul

In a word, no.

Science is first and foremost a practice. It's older than second-order predicate logic, so it can't be based on second-order predicate logic. But some things in science use second-order predicate logic.

I think that when people talk about axioms of science or scientific epistemology, they're missing the point. Most of the things that philostophers consider so basic to science fall into one of two categories:

1) Things that seem to have worked out pretty well in the past, and so we might as well try them out and see where we get.

2) Job descriptions.

[Just thinking]

Logic is the foundation of all thought.

I always regarded logic as the science of reason ...

The ability to assertain (by using the rules of logic) whether conclusions based on previous information were valid or not.

True, reasoning is thought, or part of the thinking process, but it is only a subset of thought. It is not at all impossible to think of things without reason or analysis.

[kuroyume0161]

I agree with the line that we draw our 'assumptions' or 'axioms' of science from observation and that they are not quite as idealistic as those of logic - definitely removed from pure logic. Pure logic constructs a system based on axioms and that is all. After that, it has little concern for empiricity.

Science constructs a system based on observable axioms which are not quite as rigorous. If observations were to change the axiomatic principles, then so would our entire view of science change (say it with me: Eintstein's Theories of Relativity). His theories don't obliterate previous axiomatic principles, but they are certainly shed into a new light and sidelined by them to become 'special or limited cases'.

This is not to say that one doesn't, on occassion, rely upon the other. That would be absurdity. But the final arbiter of scientific knowledge is empirical data and not logical reasoning. One supports the other but does not embrace the other.

[Paul C. Anagnostopoulos]

Science is first and foremost a practice. It's older than second-order predicate logic, so it can't be based on second-order predicate logic. But some things in science use second-order predicate logic.
Say what? I think logic has been around since, well, the beginning of time. The formal study of it may be a recent development, but whether it's an axiom of science doesn't depend on that.

~~ Paul

[Melendwyr]

We shouldn't confuse the study of the thing with the thing itself. Logic is timeless. The study of logic, commonly known as logic, only goes back a few hundred years.

[Paul C. Anagnostopoulos]

And how appropriate for the study of logic to be called logic. That has a, well, ... inherent logic to it.

~~ Paul

[Just thinking]

And how appropriate for the study of logic to be called logic. That has a, well, ... inherent logic to it.

~~ Paul

Perhaps that's why I define it as the science (study) of reason. (See post 29.)

Less circular ...

[lenny]

We know the rules that describe our reality are consistent for the same reason we know the "lines" of a magnetic field cannot cross.
do rules which merely describe reality really have to be consistent?

for that matter, would rules which govern have to be consistent?

and do you really believe "lines of a magentic field" actually exist? or is your point that they are mathematical constructs which, by construction, cannot cross?

[Melendwyr]

do rules which merely describe reality really have to be consistent? Does a logical argument really have to be free of contradictions?

and do you really believe "lines of a magentic field" actually exist? or is your point that they are mathematical constructs which, by construction, cannot cross? I say they're real, but don't take my word for it - ask some iron fillings.

[lenny]

Does a logical argument really have to be free of contradictions?.
i am not sure where you want to go here, but i am keen to find out. do you believe that rules which merely describe reality have to be consistent?
I say they're real, but don't take my word for it - ask some iron fillings.iron filings are not the best conversationalists.

what experiment would you design to establish the existence of a field?