The assumptions of science

[Mister Agenda]

Hi all. Long time no post on this forum.

I'm currently taking a formal Philosophy of religion class for fun and units.
The professor usually appreciates my skepticism and atheist viewpoint, but we seemed to have a disagreement when it came to the fundamental assumptions of science.

I made the claim that the only time most people exercise strict faith (belief without evidence) is special pleading for the existence of god. I thought it was sort of common sense that science rejects faith in favor of testable hypothesis and empirical evidence. Moreover, I said that faith is not an adequate pathway to truth and that all belief should be rooted in rational justification or evidenciary support (that is if your goal is to form an accurate as possible perception of existential reality as possible) . My professor seemed to disagree stating that it takes faith to "believe" in science as well because of the basic assumptions involved. Here are some basic examples: http://undsci.berkeley.edu/article/basic_assumptions

There must be a difference between the type of assumptions required for the belief in God and those utilized by science, but I'm having a hard time formally expressing the difference. Any takers?

Since when is it an assumption to use the only tools you have to work with? Science doesn't assume the world is consistent and predictable, else it would never have hit on quantum mechanics. Evidence from the natural world is used to investigate causes because that's the only kind of evidence there is. Science works just the same investigating effects supposedly caused by ghosts, it's not an assumption that ghosts aren't real that has led most scientists to note that they keep finding natural causes when they're looking for ghosts. There are no assumptions intrinsic to science, it starts with evidence and follows it, full stop.

Looking further into the site, I see the example of substance A stopping bacterial growth being based on assumptions like 'bacteria can grow on the growth medium' 'Substance B is inert to bacterial growth' that 'one day is long enough for colonies to grow' and so forth. Those aren't assumptions. They're things we've already learned. You don't just suppose that substance B is inert regarding bacteria, you select a substance that has already been tested and demonstrated to be inert.

They seem to use a peculiar definition of 'assumption' that is not this one: a thing that is accepted as true or as certain to happen, without proof. It seems to be more like 'if you don't start science from the beginning every single time you do an experiment, you're assuming everything'.

The site seems to be sincere, but it's an awful message. It's like they're trying to discredit science in the section on assumptions.

[SubcontinentalKiwi]

They seem to use a peculiar definition of 'assumption' that is not this one: a thing that is accepted as true or as certain to happen, without proof.

I only did a basic Theory of Knowledge course in high school, but it actually seems to me like they are using that definition. The assumptions aren't proven because they are not conclusively shown); they are only evidenced through induction. In other words, because our reasons for believing in the assumptions are founded on induction, there will always be some miniscule uncertainty that the assumptions might not hold true in the future.
However, to compare assumptions that are backed up very strongly by inductive evidence and therefore have very small uncertainties attached (such as those in science) with assumptions that are not (such as the existence of God) is logically fallacious, much in the same way that claiming theories are weaker than facts because they are not provable by observation is logically fallacious.

[Plu]

In other words, because our reasons for believing in the assumptions are founded on induction, there will always be some miniscule uncertainty that the assumptions might not hold true in the future.

I've always learned that there is no miniscule uncertainty involved because of the underlying assumption that natural processes are consistent. That assumption basically seals off all the miniscule uncertainties and turn the rest of the inductioned reasoning from assumption to certainty, and as long as "natural processes are consistent" holds as an assumption (which it does, obviously) all of the other lines of reasoning require no assuming at all.

[SubcontinentalKiwi]

In other words, because our reasons for believing in the assumptions are founded on induction, there will always be some miniscule uncertainty that the assumptions might not hold true in the future.

I've always learned that there is no miniscule uncertainty involved because of the underlying assumption that natural processes are consistent. That assumption basically seals off all the miniscule uncertainties and turn the rest of the inductioned reasoning from assumption to certainty, and as long as "natural processes are consistent" holds as an assumption (which it does, obviously) all of the other lines of reasoning require no assuming at all.

You're probably right. What I was trying to get across is that while the assumptions are inductively reasoned and therefore have an intrinsic uncertainty attached, that uncertainty is so small that it's negligible. In other words, we might as well say that there is no uncertainty at all.
(I only think that there's uncertainty attached to inductive reasoning because of what I learned in science class... My teacher was a little incompetent so I might've learned the wrong thing though.)

[entropy]

In other words, because our reasons for believing in the assumptions are founded on induction, there will always be some miniscule uncertainty that the assumptions might not hold true in the future.

I've always learned that there is no miniscule uncertainty involved because of the underlying assumption that natural processes are consistent. That assumption basically seals off all the miniscule uncertainties and turn the rest of the inductioned reasoning from assumption to certainty, and as long as "natural processes are consistent" holds as an assumption (which it does, obviously) all of the other lines of reasoning require no assuming at all.

You're probably right. What I was trying to get across is that while the assumptions are inductively reasoned and therefore have an intrinsic uncertainty attached, that uncertainty is so small that it's negligible. In other words, we might as well say that there is no uncertainty at all.
(I only think that there's uncertainty attached to inductive reasoning because of what I learned in science class... My teacher was a little incompetent so I might've learned the wrong thing though.)

You may find this article interesting:

http://plato.stanford.edu/entries/logic-inductive/

The very first sentence to that article states, "An inductive logic is a system of evidential support that extends deductive logic to less-than-certain inferences." As to the level of uncertainty, that is a huge issue and one most of the rest of the lengthy and involved article deals with.

[entropy]

Looking further into the site, I see the example of substance A stopping bacterial growth being based on assumptions like 'bacteria can grow on the growth medium' 'Substance B is inert to bacterial growth' that 'one day is long enough for colonies to grow' and so forth. Those aren't assumptions. They're things we've already learned. You don't just suppose that substance B is inert regarding bacteria, you select a substance that has already been tested and demonstrated to be inert.

http://plato.stanford.edu/entries/logic-inductive/

Duhem (1906) and Quine (1953) are generally credited with alerting inductive logicians to the importance of auxiliary hypotheses. They point out that scientific hypotheses often make little contact with evidence claims on their own. Rather, most scientific hypotheses only make testable predictions relative to background claims or auxiliary hypotheses that tie them to that evidence. Typically auxiliaries are highly confirmed hypotheses from other scientific domains. They often describe the operating characteristics of various devices (e.g., measuring instruments) used to make observations or conduct experiments. They are usually not at issue in the testing of h[sub:27rw0q28]1[/sub:27rw0q28] against its competitors, because h[sub:27rw0q28]1[/sub:27rw0q28] and its alternatives usually rely on the same auxiliary hypotheses to tie them to the evidence. But even when an auxiliary hypothesis is already well-confirmed, we cannot simply assume that it is unproblematic, or just known to be true. Rather, the evidential support or refutation of a hypothesis h[sub:27rw0q28]1[/sub:27rw0q28] is relative to whatever auxiliaries and background information (in b) is being supposed.

[Mister Agenda]

Looking further into the site, I see the example of substance A stopping bacterial growth being based on assumptions like 'bacteria can grow on the growth medium' 'Substance B is inert to bacterial growth' that 'one day is long enough for colonies to grow' and so forth. Those aren't assumptions. They're things we've already learned. You don't just suppose that substance B is inert regarding bacteria, you select a substance that has already been tested and demonstrated to be inert.

http://plato.stanford.edu/entries/logic-inductive/

Duhem (1906) and Quine (1953) are generally credited with alerting inductive logicians to the importance of auxiliary hypotheses. They point out that scientific hypotheses often make little contact with evidence claims on their own. Rather, most scientific hypotheses only make testable predictions relative to background claims or auxiliary hypotheses that tie them to that evidence. Typically auxiliaries are highly confirmed hypotheses from other scientific domains. They often describe the operating characteristics of various devices (e.g., measuring instruments) used to make observations or conduct experiments. They are usually not at issue in the testing of h[sub:3fon9prn]1[/sub:3fon9prn] against its competitors, because h[sub:3fon9prn]1[/sub:3fon9prn] and its alternatives usually rely on the same auxiliary hypotheses to tie them to the evidence. But even when an auxiliary hypothesis is already well-confirmed, we cannot simply assume that it is unproblematic, or just known to be true. Rather, the evidential support or refutation of a hypothesis h[sub:3fon9prn]1[/sub:3fon9prn] is relative to whatever auxiliaries and background information (in b) is being supposed.

We're not assuming it. We're recognizing that it is not humanly possible to re-test the wheel every time we do an experiment. We can recognize the limitations of induction and still move forward, or we can stop doing science. Yes, the evidential support or refutation of a hypothesis is relative to whatever auxiliaries and background is being supposed. But we do the experiment anyway. It's not the 'proof' part of the definition that doesn't apply, it's the 'accepted as true or certain to happen' part. We know there's a chance that Substance B isn't neutral to bacterial growth after all, and that that chance affects the validity of the experiment. For all we know the laws of physics changed slightly since Substance B was last tested and now it's bacteria fertilizer. But we accept that we can't be 100% certain of all factors and do the experiment anyway because we can't do science, or really, anything else, on the assumption that we can't trust the auxiliaries and background information because induction isn't 100% certain. Justified trust doesn't require 100% certainty.

[josephpalazzo]

Perhaps looking at how QM is developped might shed some light on what are assumptions, and what role they play in science.
 
Here are the fundamental postulates of QM:

Postulate 1: For every state of a quantum system there exist a set of vectors to represent them.

                                                 States  ?  |A>  

Postulate 2: Observables correspond to a set of hermitian operators.

                                                 Observables  ?  H

Postulate 3: The measurable values of the observables are the eigenvalues of the hermitian operators.

                                                 H |?[sub:1ejmf3pd]i[/sub:1ejmf3pd]>  =  ?[sub:1ejmf3pd]i[/sub:1ejmf3pd] |?[sub:1ejmf3pd]i[/sub:1ejmf3pd]>            
                                               
                                                measurable values ?  ?[sub:1ejmf3pd]i[/sub:1ejmf3pd]


Postulate 4: The states for which the observables of H are definite are themselves eigenvectors.  

                                                eigenvectors  ?  |?[sub:1ejmf3pd]i[/sub:1ejmf3pd]>            

Postulate 5: If the system is an arbitrary state |A>, then the probability that it is in one of the eigenvectors |?[sub:1ejmf3pd]i[/sub:1ejmf3pd]> is given by,

                                   P(?[sub:1ejmf3pd]i[/sub:1ejmf3pd])  = < ?[sub:1ejmf3pd]i[/sub:1ejmf3pd] |A> [sup:1ejmf3pd]2[/sup:1ejmf3pd]  =  < ?[sub:1ejmf3pd]i[/sub:1ejmf3pd] |A> <A | ?[sub:1ejmf3pd]i[/sub:1ejmf3pd] >            

Note: definite values are values that involve no statistical fluctuations when they are measured.

From here, to get any experimental validation, one must go through several hundred pages of theory before we can look at particles colliding in  a typical accelerator like the LHC. None of these postulates are observed directly. They cannot be tested. Their only validity is that assuming them to be true, we get to measure such things as the electron anomalous magnetic dipole moment to a precision of 10[sup:1ejmf3pd]-8[/sup:1ejmf3pd], the prediction of the Higgs boson, the Casimir effect, the Lamb shift, anti-matter, and many, many other things.

The basic structure of science is a small number of postulates ? theory ? observable predictions ? empirical verification.

[Jason78]

I got as far as hermitian operators....

Then wolfram.com gave me a headache

[entropy]

Looking further into the site, I see the example of substance A stopping bacterial growth being based on assumptions like 'bacteria can grow on the growth medium' 'Substance B is inert to bacterial growth' that 'one day is long enough for colonies to grow' and so forth. Those aren't assumptions. They're things we've already learned. You don't just suppose that substance B is inert regarding bacteria, you select a substance that has already been tested and demonstrated to be inert.

http://plato.stanford.edu/entries/logic-inductive/

Duhem (1906) and Quine (1953) are generally credited with alerting inductive logicians to the importance of auxiliary hypotheses. They point out that scientific hypotheses often make little contact with evidence claims on their own. Rather, most scientific hypotheses only make testable predictions relative to background claims or auxiliary hypotheses that tie them to that evidence. Typically auxiliaries are highly confirmed hypotheses from other scientific domains. They often describe the operating characteristics of various devices (e.g., measuring instruments) used to make observations or conduct experiments. They are usually not at issue in the testing of h[sub:1mnae1fu]1[/sub:1mnae1fu] against its competitors, because h[sub:1mnae1fu]1[/sub:1mnae1fu] and its alternatives usually rely on the same auxiliary hypotheses to tie them to the evidence. But even when an auxiliary hypothesis is already well-confirmed, we cannot simply assume that it is unproblematic, or just known to be true. Rather, the evidential support or refutation of a hypothesis h[sub:1mnae1fu]1[/sub:1mnae1fu] is relative to whatever auxiliaries and background information (in b) is being supposed.

We're not assuming it. We're recognizing that it is not humanly possible to re-test the wheel every time we do an experiment. We can recognize the limitations of induction and still move forward, or we can stop doing science. Yes, the evidential support or refutation of a hypothesis is relative to whatever auxiliaries and background is being supposed. But we do the experiment anyway. It's not the 'proof' part of the definition that doesn't apply, it's the 'accepted as true or certain to happen' part. We know there's a chance that Substance B isn't neutral to bacterial growth after all, and that that chance affects the validity of the experiment. For all we know the laws of physics changed slightly since Substance B was last tested and now it's bacteria fertilizer. But we accept that we can't be 100% certain of all factors and do the experiment anyway because we can't do science, or really, anything else, on the assumption that we can't trust the auxiliaries and background information because induction isn't 100% certain. Justified trust doesn't require 100% certainty.

I guess I should have made more clear why I posted that quote. You said, "Those aren't assumptions. They're things we've already learned." I posted the quote to amplify what you were saying and put some context to "things we've already learned." I did that because the term, "learned", is vague in this context. How much certainty is implied by the word "learned"? The bit about auxiliaries was to show that though we may be applying things that we "learned" in the past, those "learned" things have their own uncertainties and those uncertainties should be accounted for in determining the uncertainty of the current experiment - that is, we should not assume that the auxiliaries are certain though they have been "learned" about in the past. I wasn't sure what your statement "those aren't assumptions" was about and you put that statement together with one about "already learned" things, so I posted the quote and link in hopes that that would clarify the issue of how "aren't assumptions" relates to "things we have learned".

[josephpalazzo]

I got as far as hermitian operators....

Then wolfram.com gave me a headache

It also goes by the name of self-adjoint operators.

Basically, you want the theory to give you real numbers when you calculate probabilities. In QM, the functions (vectors in Hilbert space) are complex. So if f(x) = e[sup:1t3plr9q]ikx[/sup:1t3plr9q], the complex conjugate is f*(x) = e[sup:1t3plr9q]-ikx[/sup:1t3plr9q]( the* indicates complex conjugate). The product will give you a real number, in this case f(x)f*(x) = 1. But operators could be matrices. In this case, you  take the complex conjugate of every element of the matrix, then transpose each row for a column. The new matrix carries this dagger sign † instead of the star *. Now two matrices (operators) are said to be hermitian if A[sup:1t3plr9q]†[/sup:1t3plr9q] = A[sup:1t3plr9q]-1[/sup:1t3plr9q], where A[sup:1t3plr9q]-1[/sup:1t3plr9q] is the inverse of matrix A ( that is, A[sup:1t3plr9q]-1[/sup:1t3plr9q]A =1, simple rule of math: a number times its inverse equals the identity). Not all matrices gives you this result. So you always want hermitian operators in QM, otherwise, you get weird results.

[entropy]

I got as far as hermitian operators....

Then wolfram.com gave me a headache

It also goes by the name of self-adjoint operators.

Basically, you want the theory to give you real numbers when you calculate probabilities. In QM, the functions (vectors in Hilbert space) are complex. So if f(x) = e[sup:19v2dk6y]ikx[/sup:19v2dk6y], the complex conjugate is f*(x) = e[sup:19v2dk6y]-ikx[/sup:19v2dk6y]( the* indicates complex conjugate). The product will give you a real number, in this case f(x)f*(x) = 1. But operators could be matrices. In this case, you  take the complex conjugate of every element of the matrix, then transpose each row for a column. The new matrix carries this dagger sign † instead of the star *. Now two matrices (operators) are said to be hermitian if A[sup:19v2dk6y]†[/sup:19v2dk6y] = A[sup:19v2dk6y]-1[/sup:19v2dk6y], where A[sup:19v2dk6y]-1[/sup:19v2dk6y] is the inverse of matrix A ( that is, A[sup:19v2dk6y]-1[/sup:19v2dk6y]A =1, simple rule of math: a number times its inverse equals the identity). Not all matrices gives you this result. So you always want hermitian operators in QM, otherwise, you get weird results.

Is this related to what you are saying?:

http://www.cobalt.chem.ucalgary.ca/zieg ... rmit1o.htm

Proof that the eigenvalues of Hermitian Operators are Real
Set up in Operator Notation

[josephpalazzo]

I got as far as hermitian operators....

Then wolfram.com gave me a headache

It also goes by the name of self-adjoint operators.

Basically, you want the theory to give you real numbers when you calculate probabilities. In QM, the functions (vectors in Hilbert space) are complex. So if f(x) = e[sup:13jhu502]ikx[/sup:13jhu502], the complex conjugate is f*(x) = e[sup:13jhu502]-ikx[/sup:13jhu502]( the* indicates complex conjugate). The product will give you a real number, in this case f(x)f*(x) = 1. But operators could be matrices. In this case, you  take the complex conjugate of every element of the matrix, then transpose each row for a column. The new matrix carries this dagger sign † instead of the star *. Now two matrices (operators) are said to be hermitian if A[sup:13jhu502]†[/sup:13jhu502] = A[sup:13jhu502]-1[/sup:13jhu502], where A[sup:13jhu502]-1[/sup:13jhu502] is the inverse of matrix A ( that is, A[sup:13jhu502]-1[/sup:13jhu502]A =1, simple rule of math: a number times its inverse equals the identity). Not all matrices gives you this result. So you always want hermitian operators in QM, otherwise, you get weird results.

Is this related to what you are saying?:

http://www.cobalt.chem.ucalgary.ca/zieg ... rmit1o.htm

Proof that the eigenvalues of Hermitian Operators are Real
Set up in Operator Notation

[ Image ]

It's along the same line, though I was looking at matrices as operators ( years of studying QFT gets you to think in more abstract objects). What you have there is a generic operator ( A-hat). In that case the hermiticity is in the line:

??[sub:13jhu502]?[/sub:13jhu502]*(A-hat)?[sub:13jhu502]?[/sub:13jhu502]d? = {??[sub:13jhu502]?[/sub:13jhu502]*(A-hat)?[sub:13jhu502]?[/sub:13jhu502]d?}*  

this is like saying, object = object*, IOW, the object equals to its complex conjugate. This is ok for ordinary objects in calculus. But with matrices, you need to not only complex conjugate the elements of the matrix, but transpose each row to a column. But the idea is the same, you get a real number when you do the calculation ( last line, a[sub:13jhu502]?[/sub:13jhu502] = a[sub:13jhu502]?[/sub:13jhu502]*, therefore a[sub:13jhu502]?[/sub:13jhu502] is real) .

[Solitary]

There is a big difference between assuming the world is real and knowable and gathering evidence from it than assuming there is more to it than that and there is an invisible supernatural world and is only to be known from a fairy tail assumed to be written from men listening to an invisible God or visible angels, or in one's mind or feelings and emotions  only. Give me a break!  This is insane.  :roll:    Solitary

[the_antithesis]

Science is based upon observation, hypethesizing based on those observations, and then testing that hypethesis to confirm if it's true.

Faith is based on jumping to a conclusion and assuming it's true despite any any future observations to the contrary.

Tell your professor to eat more dick.