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 (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?
First of, testifiable, meaning you can repeat an experiment under the same conditions and get the same result is an important factor for the scientific method.
Next, observable, something you can observe in nature, preferably more than once and give the same results from observation. It's deduction, yes, but even though it doesn't guarantee certainty, it does guarantee certifiability, that something can be shown to be the way it is.
Last, but not least, falsefiability. That there, for any theory or hypothesis or even guess, exists an antithesis that will prove a proposition false.
That's at least the starting point for formalization of "basic assumptions" in science that faith lacks.
Quote from: "LexxM1985"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 (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?
In a way he is correct. When presented to the ignorant like me, science indeed must be taken as "faith" as I cannot do the science myself and must trust science tellimg me the truth. However, since science has a very proven and reliable track record, "faith" such as it is not such a great leap. Those who are not ignorant and do the science do not need the so-called faith.
Whoa! Whoa! Science isn't based on assumptions or faith, it is based on empirical facts and sound reasoning and trust. Of course there are assumptions, but those assumptions aren't based on superstitious nonsense but reality, and then tested to disprove the assumptions. Mathematics is based on assumptions too, but it works just like science does. Religion is pragmatic and works too for some, but it is not a source for the truth or fact if it doesn't work.
Science is self correcting and evolving to make it better to know the world we live in. Religion evolves too but is funda"mental"ly flawed because there is no empirical reliable evidence to support it, and only subjective evidence that is not a reliable search for the truth. It also is not self correcting like science is. He is confusing faith with trust! When I fly I trust the plane won't crash, but I don't have faith it won't which demands a deity. :roll: Find a different teacher that knows the difference between faith and trust. :roll: :rolleyes: Solitary
Quote from: "LexxM1985"I made the claim that the only time most people exercise strict faith (belief without evidence) is special pleading for the existence of god.
People believe all sorts of things based on faith - existence of ghosts, spirits, paranormal phenomenon, righteousness of their nation's reasons for going to war, etc., etc.
QuoteThere must be a difference between the type of assumptions required for the belief in God and those utilized by science...
Two words: Occam's Razor. The assumptions of science are much more parsimonious than those of any religion.
Three more words: Begging the question. The assumptions of religion very often assume their conclusions.
What assumptions do I need to hold to "believe" that we got here through evolution? I must assume that the laws of nature we know now were the laws of nature in the past.
What assumptions do I need to hold to "believe" in something like young earth creationism? I must assume the eternal existence of a deity possessing omnipotence, omniscience, a personality, emotions, and a reason to bother creating us. I must further assume that the laws of nature have changed dramatically over time. In short, I must
assume my conclusion, which is begging the question.
What's the difference between a real thing and fantasy? Empirical evidence.
Quote from: "LexxM1985"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 (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?
Your professor is correct, which it seems like you realize - I say that because it seems to be an implication from your statement that there must be a difference between the types of assumption required. So, it seems that the question you are wondering is if atheists and theists both must start with sets of assumptions (you have to, otherwise the argument for your position devolves into infinite regress of justifications or circular reasoning), then do the differences in the kinds of assumptions each makes provide good reason to be more skeptical of theist assumptions than atheist assumptions. (I hope that made sense.)
It might be worthwhile to say what assumptions almost all theists and atheists have in common. Let me start with both of their assumptions with respect to the question of whether or not solipsism is true. [Solipsism is "the philosophical idea that only one's own mind is sure to exist" ~ Wikipedia - http://en.wikipedia.org/wiki/Solipsism (http://en.wikipedia.org/wiki/Solipsism)] I think it is generally safe to say that both theists and atheists assume that solipsism is false, they both assume that there is a reality beyond "my" own individual mind. (Note that for both the theist and atheist, this a essentially a leap of faith. There is no way to prove that reality isn't solipsistic - you must just assume it isn't.) Further, I think both theists and atheists would generally agree that our senses provide us with information about the reality beyond our minds. I think both theists and atheists would generally agree that there are occasions where our perception of reality that we gather from our senses is "out of whack"; e.g., hallucinations. There are times when our guesses about how the world works are wrong; e.g., thinking the world is flat. I think both reasonable theists and atheists agree that it's pragmatically worthwhile to have a method for determining when it is likely that our perceptions are erroneous and our guesses about how the world works are wrong. I think both reasonable theists and atheists agree that science provides an excellent framework for such a practical methodology.
So what assumptions
don't reasonable theists and atheists share? There are always semantic minefields within semantic minefields in questions like that. You have to carefully define the term "theism" so you can more apparently see what assumptions are essential to theism that an atheist would reject. IOW, the answer to your question may depend on what the term "theism" is taken to mean. Ultimately, it's probably going to come down to what is intended to be meant by the term "god" - that is, what is the essential quality or nexus of qualities that a god has or gods have? I would posit that one of the most common assumptions that you find amongst theists that atheists would not accept is the idea that there is something that is supernatural. By "supernatural", I mean the capacity to effect change in physical reality by a cause or causes that are not bound by physical laws. I think that theists make the assumption that there is such a supernatural agent and atheists do not is perhaps the primary assumption that divides theists from atheists. Of course, there are all kinds of ramifications that follow from the theists belief in other qualities of their believed deity, but they tend to collapse down to the difference between assuming there are supernatural agencies and not assuming that.
I think too often atheists try to look to science to validate their rejection of the assumption of supernatural agency. It does seem like that is what science implies. But I don't think it does. I think what science implies is that IF the observed event(s) are the result of patterned laws to how reality works, then by the scientific method we can determine to the best of our knowledge at the moment, which hypothesized patterns are actual patterns (there is also usually a causal theoretical framework to explain the pattern). But does science imply that there are no supernatural events? I don't think so because I think that the proper way to view science is by using the conditional statement I did above - "IF the observed event(s) are the result of patterned laws..." Within the logic of science itself there are no grounds to dismiss the possibility that there are supernatural events - all that science can say is that if there are such events as supernatural events, science can have nothing to say about them because science is only about patterned physical laws (and their theoretical causal explanations). Again, there is nothing intrinsic to science that implies that it is not possible that there are supernatural events.
But... here's where the seeming symmetry of justification between theists and atheists breaks down. The theist is making an additional claim - that there
are supernatural events/agents. It is totally kosher for an atheist to ask a theist to justify her/his claim that there are supernatural events/agents. Some theists will claim that they can show convincing evidence that there are supernatural events/agents. The nature of the evidence they want to present is often quite in dispute. The types of things they provide as evidence can be extremely broad - from the fact that a large majority of the people in the world accept that there are supernatural events/agents to personal revelations.
So, yes, atheists make basic assumptions about the world just like theists, but theists also assume that there is or are supernatural event(s)/agent(s). I think that is the key difference in basic assumptions between theists and atheists. I don't think the resolution to the question of whether or not theistic assumptions about the supernatural are justified can be found in science. If a theist believes in the supernatural, then she/he believes in something that science can't test and they accept that untestability. It would be nice if science could answer these kinds of questions but it can't. If someone is prepared to accept the existence of something that can't be empirically verified, then they are just starting out from a fundamentally different view of how things are compared to someone who assumes that that which is real is empirical.
Edit: I just reread your question (and its context) and I think my response wandered off from what you were looking for. If so, sorry about that. Maybe there's something in it worth the read anyway, though.
Quote from: "LexxM1985"My professor seemed to disagree stating that it takes faith to "believe" in science as well because of the basic assumptions involved.
I'm no expert, but aren't the basic assumptions supportable through inductive reasoning? I mean, we can reproducibly and consistently observe that these assumption are true, and thus (with a small degree of uncertainty) extrapolate that they will continue to be true in the future.
I don't think the same could be said about God.
The points about testability and falsifiability that came up earlier in this thread are also really good! :)
Quote from: "LexxM1985"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 (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?
I suppose you always have to make some basic assumptions behind any kind of reasoning. So yes, there are basic assumptions in science. But I think you are on the right track... That is, they are different from the assumptions in religious belief. To my mind, the differences are like night and day.
Religious arguments continually try to equate spiritual bullshit to science, and I think your prof might be doing that: "Look here! Religion and Science both make assumptions. Therefore, they must be equally valid." But they are not the same kind of assumptions. They simply don't equate.
Here is an assumption: "Any thought that farkles through my brain is as valid as something purely rational." There I just stated an assumption. If someone equates that with a basic assumption of science (which is exactly what the spiritual argument in question is doing), you can't even begin a reasonable discussion, because reason is obviously not even on the table.
Your prof might be attempting to stimulate some philosophical thought process in you, but don't mistake bullshit for reason. Any empty claim remains just that, no matter how much bullshit you back it up with.
Another thing to clarify with your professor is to ask him to explain what he means. He kind of dumped a load in your lap and is expecting you to swim your way out of a sea of confusion he created. That might have some value as an educational tool, but it's not out of line for you to ask him to justify his claim. You don't have to be confrontational, just conversational. You want to understand what he's talking about. But that's not the same thing as accepting his reasoning. There should be no expectation that you must accept what he says, but it would be helpful to at least understand what he's saying.
Quote from: "Sal1981"First of, testifiable, meaning you can repeat an experiment under the same conditions and get the same result is an important factor for the scientific method.
But that's not an assumption. That's a pre-requisite for a consistent reality. If reality wasn't consistent, then it wouldn't matter what experiments you carried out, because tomorrow you could be a pineapple.
The difference in assumptions is that the response to a scientific assumption is "this is trivial, why do you ever bother to write that down?" and the reaction to a religious assumption is "you need how many books to explain this assumption to me?".
Basically.
Quote from: "entropy"So, yes, atheists make basic assumptions about the world just like theists, but theists also assume that there is or are supernatural event(s)/agent(s). I think that is the key difference in basic assumptions between theists and atheists. I don't think the resolution to the question of whether or not theistic assumptions about the supernatural are justified can be found in science. If a theist believes in the supernatural, then she/he believes in something that science can't test and they accept that untestability. It would be nice if science could answer these kinds of questions but it can't. If someone is prepared to accept the existence of something that can't be empirically verified, then they are just starting out from a fundamentally different view of how things are compared to someone who assumes that that which is real is empirical.
*** my underlining.
Indeed this is exactly where theists and atheists differ. Moreover, many atheists, including myself, go an extra length by saying that if there is no empirical evidence for an existential claim, then there is no difference between that claim and fantasy. And therefore one must conclude that the claim IS fantasy.
This applies not only to leprechauns, invisible pink unicorns, Mickey Mouse and Batman and a whole slew of fictional characters but also to demons, angels and gods.
For what it's worth, I also took Philosophy of Religion in college. I was a theist at the time. Well, kind of a half assed theist well into the questioning phase of my life. I thought the course was wonderful, and it probably contributed in a small way to my atheism. I have no idea what the professor's beliefs were. He somehow gracefully avoided giving out cues, although I can't remember anyone outright asking him about it.
QuoteHe somehow gracefully avoided giving out cues, although I can't remember anyone outright asking him about it.
Interestingly enough, I've never seen someone outright ask me about my beliefs either. Especially not theists. They always either assume all manner of stuff or just don't care at all. But they never actually ask. Weird, that.
Quote from: "Plu"QuoteHe somehow gracefully avoided giving out cues, although I can't remember anyone outright asking him about it.
Interestingly enough, I've never seen someone outright ask me about my beliefs either. Especially not theists. They always either assume all manner of stuff or just don't care at all. But they never actually ask. Weird, that.
It's the same for me, even among people who know I'm an atheist. Only one theist has ever asked me why I'm an atheist. I find that kind of strange since I am surrounded by theists and I would expect more people to at least be curious about an obvious exception to the norm.
Quote from: "LexxM1985"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 (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.
Quote from: "Mister Agenda"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.
QuoteIn 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.
Quote from: "Plu"QuoteIn 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.)
Quote from: "SubcontinentalKiwi"Quote from: "Plu"QuoteIn 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/ (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.
Quote from: "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/ (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.
Quote from: "entropy"Quote from: "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/ (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.
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.
I got as far as hermitian operators....
Then wolfram.com gave me a headache
Quote from: "Mister Agenda"Quote from: "entropy"Quote from: "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/ (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".
Quote from: "Jason78"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.
Quote from: "josephpalazzo"Quote from: "Jason78"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 (http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/quanmath/hermit1o.htm)
Proof that the eigenvalues of Hermitian Operators are Real
Set up in Operator Notation
(//http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/quanmath/hermit11.gif)
Quote from: "entropy"Quote from: "josephpalazzo"Quote from: "Jason78"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 (http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/quanmath/hermit1o.htm)
Proof that the eigenvalues of Hermitian Operators are Real
Set up in Operator Notation
[ Image (//http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/quanmath/hermit11.gif) ]
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) .
(//http://i243.photobucket.com/albums/ff277/josephpalazzo/Matriceshc.jpg) (//http://s243.photobucket.com/user/josephpalazzo/media/Matriceshc.jpg.html)
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: :rolleyes: Solitary
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.
Quote from: "entropy"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".
Thanks for clarifying, Entropy.