Incompleteness, Undecidability, and Uncertainty

[essentialsaltes]

An example being?

Well, just that Euclidean space is *not* an axiom of Science.

Axioms of science would be more like methodological naturalism.

 

[J_B_]

It seems you are establishing a direct equivalence of theory and scientific object. ... What am I missing?

The term isn't mine, as I've noted. It came from Noble. I'm using it per the impression I got from his text, but he gave no explicit definition. Therefore, it seems silly for me to suddenly pull an explicit definition from thin air ... and somewhat unfair to you.

The original message was that Noble, Longo, Soto, et. al. seem to be saying (and I agree) that without a theory, science has no grounding. There is no arbiter for what the data means, for working out the implications of one conclusion vs. another, what is proper data and what is not, what causes a phenomena and what doesn't. They cite specific examples of the problems they have had in their own research because of the lack of theory. Therefore, it is best to read them firsthand rather than trying to squeeze it out of me.

IMHO, the idea that the data is enough - that data obviously says what it says - that meaning can precede theory - is nonsense. I believe people who make such statements are simply not acknowledging (or aren't even aware) of the theory they're using.

I don't think @FrumiousBandersnatch and I are using "axiom" in the same way. As I said, it seems like a semantic battle.

This all began with the question: Does biology have a fundamental theorem or first principle? My reaction (erroneous though it may be) was, "No, but it should." But then I paused and asked myself, "What is a first principle?" I couldn't answer that question, but Ana Soto did, and I love her answer:

A first principle defines the default (unconstrained) state of a system.

I think that's brilliant. It does, however, introduced Mach's dilemma (I think it was Mach who made this observation about "force"). We never see this pure, default, unconstrained state in nature. This state is, therefore, only conceptual. Given the first principle is based on a concept, we would never be able to refute it. Suppose we account for all the forces on an object, yet still fail to fully describe its motion. We wouldn't say, "Nuts. I guess something other than forces are involved." No, we would say, "There must be an as yet undiscovered force involved."

Sorry. More rambling. I'll go look for a 12-step program and leave you alone.

 

[J_B_]

Axioms of science would be more like methodological naturalism.

OK. Are you saying science does have axioms, then? Because it seemed to me others were saying it does not ... though, again, I'm not sure I know what various people mean when they use that term.

Well, just that Euclidean space is *not* an axiom of Science.

Are you trying to clarify that it is not an axiom of science, but is an axiom of space-time theory (and wouldn't Minkowski space be the better term?)? Or, are you trying to say it's not an axiom of any sciency thing whatsoever?

 

[Ophiolite]

The term isn't mine, as I've noted. It came from Noble. I'm using it per the impression I got from his text, but he gave no explicit definition. Therefore, it seems silly for me to suddenly pull an explicit definition from thin air ... and somewhat unfair to you.

In what follows it is my intention to be critical in an objective sense, regarding your approach. It is not my intention to sound critical in a personal sense.

I am surprised you think it appropriate and productive to use a term, in a discussion about science, on a science forum that you don't properly understand. A term that, nevertheless, is used within your arguments and within your responses to attemtpted refutations of those arguments.

I shall reflect on your other comments and may respond at a later date.

 

[J_B_]

In what follows it is my intention to be critical in an objective sense, regarding your approach. It is not my intention to sound critical in a personal sense.

I am surprised you think it appropriate and productive to use a term, in a discussion about science, on a science forum that you don't properly understand. A term that, nevertheless, is used within your arguments and within your responses to attemtpted refutations of those arguments.

I shall reflect on your other comments and may respond at a later date.

I quoted him, paraphrased him at one point, and when the term emerged with a life of its own, tried to clarify that I didn't think it some widely known and generally accepted scientific concept. Since it seems I'm the only one who's read the text, we're obviously discussing my interpretation of that text. But I have also encouraged everyone, as much as it is possible, to read it for themselves. As noted in post #57, my intent was to introduce this material to people so they could investigate it as they saw fit. It was not my intention to hold court and set myself up as the only judge.

As such, I tried to answer you in my own words, without using the term "scientific object".

Again, you know geology (and your subsequent engineering work) far better than I ever will. If my comments don't describe those things, I defer to you. My apologies for anything else.

 

[SelfSim]

People observe all kinds of things with no idea what it means. Those observations can't be the object of a theory if the theory did not yet exist. It is only when meaning is assigned that it becomes a scientific object.

Formally speaking, some declaration of scientific objective reality, (ie: some 'object' exists as part of science's view of reality), can only be agreed once some tentative hypothesis has been consistently, repeatedly (and independently) verified by formal observations.

An 'observation' in science (loosely) includes the 'what', the 'where' and the 'when'.

The usage of a tentative 'hypothesis' is done deliberately to overcome the issue you mention above, where a formal theory has not yet been developed.

Meaning is what humans add and requires a clearly stated context. The closest to some 'meaning' added by science, would be some reference to a consistent, independently repeated, verification of some clearly bounded (contextualised) hypothesis, theoretical prediction, or the theory itself (once its developed).

Science is defined by its process. Logic is defined by its posited axioms. Science tests axioms (because that's what its process calls for).

 

[Speedwell]

OK. Are you saying science does have axioms, then? Because it seemed to me others were saying it does not ... though, again, I'm not sure I know what various people mean when they use that term.



Are you trying to clarify that it is not an axiom of science, but is an axiom of space-time theory (and wouldn't Minkowski space be the better term?)? Or, are you trying to say it's not an axiom of any sciency thing whatsoever?

The problem is, there is not a single definition of axiom. The tautological axioms of abstract formal systems will not be quite the same kind of beast as the axioms of science, which are falsifiable.

 

[J_B_]

The problem is, there is not a single definition of axiom. The tautological axioms of abstract formal systems will not be quite the same kind of beast as the axioms of science, which are falsifiable.

Then someone should offer up a definition.

 

[Speedwell]

Then someone should offer up a definition.

Because we don't know exactly what you are driving at, that "someone" should be you.

 

[FrumiousBandersnatch]

Indeed, but what's the point being made?

By J_B_ ? I don't know - we seem to be talking past each other...

 

[FrumiousBandersnatch]

Some are arguing science has no axioms. They seem to equate empirical observation with truth. If we see it and name a principle after it, that's a truth, not an axiom.

If that's a veiled reference to me, it's way off beam.

 

[J_B_]

Because we don't know exactly what you are driving at, that "someone" should be you.

I wasn't the one who added a discussion of axioms into the conversation. If my search was correct, it first came from @durangodawood and @FrumiousBandersnatch in posts #23/#24. It only seems fair to let them define what they meant.

 

[J_B_]

I wasn't the one who added a discussion of axioms into the conversation. If my search was correct, it first came from @durangodawood and @FrumiousBandersnatch in posts #23/#24. It only seems fair to let them define what they meant.

Correction. I guess it was @Speedwell in post #4. The search function for CF isn't very good. Axiom, axioms, and axiomatic have to be typed explicitly in separate searches ... or am I doing something wrong?

 

[essentialsaltes]

Are you trying to clarify that it is not an axiom of science, but is an axiom of space-time theory (and wouldn't Minkowski space be the better term?)?

Right, not an axiom of science, but assumptions, stated or not, in a particular model.
I wouldn't quite call them axioms, but they are assumptions used in building a particular model.

Euclidean space is an assumption of Newtonian mechanics.
'flat' Minkowski space is an assumption of special relativity.
Riemannian space is an assumption of general relativity.

I guess jumping back to #4 if that's where it started, Gödel's Theorem is never going to be relevant to science. Mathematical axiomatic systems are nothing but their axioms. Everything else follows as a necessary logical consequence. That's not what science is, even if it has assumptions.

 

[Speedwell]

Correction. I guess it was @Speedwell in post #4. The search function for CF isn't very good. Axiom, axioms, and axiomatic have to be typed explicitly in separate searches ... or am I doing something wrong?

I only pointed out that science is not an axiomatic formal system--which is true whether it has axioms of its own or not..

 

[J_B_]

Right, not an axiom of science, but assumptions, stated or not, in a particular model.
I wouldn't quite call them axioms, but they are assumptions used in building a particular model.

Euclidean space is an assumption of Newtonian mechanics.
'flat' Minkowski space is an assumption of special relativity.
Riemannian space is an assumption of general relativity.

Sure. Could you clarify the difference you see between an assumption and an axiom?

I'm more interested in the specifics of biology, geology, or physics - not the procedural axioms of a general method you noted. Others can, of course, discuss those if they wish.

 

[J_B_]

I only pointed out that science is not an axiomatic formal system--which is true whether it has axioms of its own or not..

OK. Still, feel free to offer what you think an axiom is.

 

[FrumiousBandersnatch]

Likewise, I'm not equipped to argue biology. Neither of us are biologists (I believe), and so this has already devolved into a semantic debate.

I am a biologist (graduate + career, now retired). But this isn't a question of biology or geology, it's a question about the necessary foundations of science.

What is an axiom vs. a foundational empirical observation?

"An axiom, postulate or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments." Wikipedia

This began when I responded to comment #23 in which durangodawood said, "I think science does rest on certain unprovable but intuitively precious axioms. Like: this stuff is real and Im not a brain in a vat. Etc." On reflection (#24), it seemed to me that science need not rest on such axioms - that they are not a necessary basis for or foundation of science. I wanted to get some opinions on this.

I'm not sure we have any scientific common ground upon which we can discuss your proposed question of axioms. If we discuss something from your specialty, it most certainly won't be mine, and if we discuss something from my specialty, it most certainly won't be yours.

Specialities are not relevant, I'm talking about the philosophy of science.

But if you want me to throw something out for discussion, how about "force"? It would be interesting for me to see it discussed by you (@FrumiousBandersnatch ), @Ophiolite , and @Speedwell , but I imagine you're not going to let me sit on the sidelines and observe.

Force is inferred from observation, part of a scientific model, i.e. a result of the application of science.

 

[durangodawood]

Right, not an axiom of science, but assumptions, stated or not, in a particular model.
I wouldn't quite call them axioms, but they are assumptions used in building a particular model.

Euclidean space is an assumption of Newtonian mechanics.
'flat' Minkowski space is an assumption of special relativity.
Riemannian space is an assumption of general relativity.

I guess jumping back to #4 if that's where it started, Gödel's Theorem is never going to be relevant to science. Mathematical axiomatic systems are nothing but their axioms. Everything else follows as a necessary logical consequence. That's not what science is, even if it has assumptions.

OK. Still, feel free to offer what you think an axiom is.

I would offer this again. For science to operate it requires certain assumptions that are deeper than any one fields reigning paradigm. I think its fair to call those assumptions "axioms".

One I offered previously was: the laws of nature are stable across accessible time and space. Dispense with that and theres no way to generalize from repeat observations at all.

(There's our uncertainty. I dont think there's a way for scientific investigation to demonstrate the validly of that axiom with certainty).

 

[J_B_]

I am a biologist (graduate + career, now retired).

I didn't realize that. Or maybe I forgot. Regardless, my apologies. Given you are a biologist, I'd be curious about your thoughts on the two papers referenced.

But this isn't a question of biology or geology, it's a question about the necessary foundations of science.

"An axiom, postulate or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments." Wikipedia

This began when I responded to comment #23 in which durangodawood said, "I think science does rest on certain unprovable but intuitively precious axioms. Like: this stuff is real and Im not a brain in a vat. Etc." On reflection (#24), it seemed to me that science need not rest on such axioms - that they are not a necessary basis for or foundation of science. I wanted to get some opinions on this.

Thank you for the definition. It makes axiom, postulate, and assumption the same thing. It will be all the more interesting, then, to hear @essentialsaltes thoughts on their differences.

Everyone is free to discuss your issue - in this thread even. I don't care. But it's not of interest to me, and wasn't the focus of what prompted me to start the thread. Further, it seems my example of force does not apply. I was asking about the foundations of specific sciences: biology, geology, physics. So, I'll leave you to it.