Science and Reason: Is there an alternative to "faith" for a

Metaphysics and Epistemology
1

On a global warming post, I recently initiated a debate about whether or not amateurs are qualified to have an opinion on such controversies. I took up the position that we couldn’t. Ifairness to the other side, I would like to acknowledge the troublesome implications of my own arguments.

  1. Modern mathematics, physics, biology, astrophysics, climatology, chemistry, etc. is extremely complex. While well-informed amateurs can read and understand the results of the studies in those fields, they can’t really understand the “science” behind the results. To take the most direct reason for such an inability, they can’t understand the math. The math behind most of the models, whether it is of climate change or of sunspot cycles or of the human genome, requires years of advanced study. Saying you understand the results is like saying a non-German speaker can understand the poetics of Goethe: While they can understand the broad-strokes, they can’t really enter into a debate about the details.

But…

  1. Does that mean we just have to accept what the scientists tell us? Does accepting science we don’t understand imply an abdication of reason? Does this turn science into a new religion?

I can read science on global warming, non-Euclidian geometry, or string theory, but I don’t really understand the science and math behind the models, and I certainly don’t have the background to adjudicate between competing scientific claims.

Similarly, this question led me to a somewhat mean-spirited and bitter debate with Dragonmaci about non-Euclidian geometry and Quantum Mechanics. I don’t really have the mathematical background for such a debate, but I took the position that amateurs shouldn’t object on epistemological grounds to scientists following the scientific method.

I nonetheless felt somewhat disarmed by others who claimed I was substituting the “authority” of others for my own reason.

What should be the rational response when confronted with a controversy that one’s own reason can’t adjudicate given one’s inability to understand the math behind the competing claims? (Although one could if one took the time to learn it) Given that most of us aren’t willing to devote years of our life to advanced scientific study, is there an alternative to just accepting what the scientists tell us?

I would be particularly interested in hearing from people with an expertise in science, math, or the philosophy of science.

P.S. Please don’t tell me to learn more math. I will when I can, but the vast majority of us are in the position of having to make do with Calculus and introductory college science as the high-point of our scientific education.

PPS. Please don’t indict my definiton of “faith.” I understand that belief with a rational basis isn’t “faith,” but that kind of gets to the heart of the issues.

PPPS. Please forgive all the PS’s, but I’m well aware of the contentiousness of some on this forum… That’s why I love it!

2
  1. Modern mathematics, physics, biology, astrophysics, climatology, chemistry, etc. is extremely complex. While well-informed amateurs can read and understand the results of the studies in those fields, they can’t really understand the “science” behind the results.

This may or may not be correct – I think it isn’t. If you meant to say that they don’t know the underlying science (facts and logic), I would agree; I don’t agree that they can’t understand. Though I also think that some people are incapable of understanding, but let’s not get involved in that matter. Generaly speaking it’s not true that the inability to understand is really “about the math”, but it may well be the case that a particular scientist is incapable of explaining his knowledge to a person who doesn’t know what he (the scientist) knows. The best scientists do have a deep enough grasp of the subject that they can render it comprehensible to other intelligent people who lack the technical background. I do sympathize, though, with those who splutter exasperatedly “I can’t explain this if you don’t know the math”. Teaching is hard.

  1. Does that mean we just have to accept what the scientists tell us?

You don’t have to accept anything. If you disagree with the law of gravity and don’t want to accept what a scientist tells you, have fun.

Does accepting science we don’t understand imply an abdication of reason?

Wrong question – invalid question. You do understand the difference between science, i.e. the methods of gaining knowledge, and the claimed results of ostensive practicioners, right? Can you rephrase the question so as to actually ask the question that you meant to ask?

I don’t really have the mathematical background for such a debate, but I took the position that amateurs shouldn’t object on epistemological grounds to scientists following the scientific method.

Leaving out the math part, do you recognise the difference between valid and invalid methods; and can you apply that distinction to a particular case? I don’t want to imply any endorsement of the rejection of science – there’s a regrettable tendency for some new students of Objectivism to get all rationalistic when it comes to physics. For example, do you know why the Copenhagen interpretation isn’t a “fact”?

What should be the rational response when confronted with a controversy that one’s own reason can’t adjudicate given one’s inability to understand the math behind the competing claims?

You should request a reduction to the axiomatic. Whether the request will be granted is another issue – often, science fans don’t actually know the science well enough to help you,and they end up just screaming “Modern science teaches that…!”

The underlying problem is that trust is not justified unless it is earned. Why should you trust a scientist? Maybe that’s the best application of epistemology and the scientific method. Tell me, why should you trust a scientist? If you can’t answer that, then you are condemned to faith-hell. If you can answer that, then you can apply the answer concretely to some examples of global warming or other kinds of applied science.

3

Although I generally like your posts DavidOdden, I will have to disagree with you. How can you know whether they are correctly applying the “underlying methodology” unless you can understand the science. And yes math is really, really important. The biggest misapprehension that laypeople have about science is their underestimation of the importance of math, and the math that scientists–especially physcists and mathemeticians–use is well beyond the ability of anyone to understand without quite a bit of study. I tried to post below some formulas for eliptic geometry that would have been relevant in my debate with Dragonmaci about non-Euclidean geometry, although the translation from the web to my post didn’t work out so well. At any rate, you can find for yourself with a quick search of the web lots of “gibberish” which we’ll have to take on “faith” is good science.

My question was an honest one, although I think lots of us have such pride in our reason that we would rather evade this difficult question. I would certaintly be glad if someone had a more satisfying way to resolve the issue.

So here are some formulas…

In the projective model, the points of n-dimensional real projective space are used as points of the model. The points of n-dimensional projective space can be identified with lines through the origin in (n+1)-dimensional space, and can be represented non-uniquely by nonzero vectors in Rn+1, with the understanding that u and λu, for any non-zero scalar λ, represent the same point. Distance can be defined using the metric

d(u, v) = \arccos \left(\frac{u \cdot v}{||u||\ ||v||}\right).

This is homogeneous in each variable, with d(λu, μv) = d(u, v) if λ and μ are non-zero scalars, and so it defines a distance on the points of projective space.

The two models represent different geometries; in the hyperspherical model, two distinct lines intersect exactly twice, at antipodal points, and in the projective model, lines intersect exactly once. By identifying antipodal points the hyperspherical model becomes a model for the same geometry as the projective model. A notable property of the projective model is that for even dimensions, such as the plane, the geometry is nonorientable.

A model representing the same space as the hyperspherical model can be obtained by means of stereographic projection. Let En represent Rn ∪ {∞}, that is, n-dimensional real space extended by a single point at infinity. We may define a metric, the chordal metric, on En by

\delta(u, v)=\frac{2 ||u-v||}{\sqrt{(1+||u||^2)(1+||v||^2)}}.

where u and v are any two vectors in Rn and ||*|| is the usual Euclidean norm. We also define

\delta(u, \infty)=\delta(\infty, u) = \frac{2}{\sqrt{1+||u||^2}}.

The result is a metric space on En, which represents the distance along a chord of the corresponding points on the hyperspherical model, which it maps bijectively to by stereographic projection. To obtain a model of elliptic geometry, we define another metric

d(u, v) = 2 \arcsin\left(\frac{\delta(u,v)}{2}\right).

The result is a model of elliptic geometry.

4

How can you know whether they are correctly applying the “underlying methodology” unless you can understand the science.

I think what you just said reduces to saying “It’s not possible to learn science except as an act of faith”. But let me explain this in a bit more detail. First you have to understand what science is: it is the systematic creation of generalizations that describe existents (entities and relationships). It sets as its standard of validity all such referents in reality (not just description of those actually observed). These generalizations – scientific laws, for example – depend on concept formation, certain axiomatic relations (e.g. “cause”), and logic. The method, which is actually well laid out in OPAR Ch. 5, involves sorting between alternatives in order to reach certainty.

Specific scientific knowledge is not required to understand the logical relations that hold in what we know as “the scientific method”. That’s good, of course, because otherwise, science would be circular, being valid only if the method is valid, but there being no way to validate the method without knowing the distinction between valid and invalid science.

I tried to post below some formulas for eliptic geometry that would have been relevant in my debate with Dragonmaci about non-Euclidean geometry, although the translation from the web to my post didn’t work out so well.

It doesn’t matter, because you could post a link to something off-site, e.g. a page on arXiv. There is no question that such equations exist; but tell me, can you indicate one which you claim is empirically valid? How do you know that it is empirically valid? What are the alternatives to that equation, and how do you know that the alternatives are not empirically valid? I want you to reduce the question to experimental evidence. Point to reality, not imagination. Start by stating what empirical hypothesis you think this symbolic barrage has any bearing on.

If you’re just mad at DragonMaci, that’s your right, but you shouldn’t act out your anger here. Instead, how about this: prove scientifically that OJ did it.

5

To what degree can amateurs have an opinion on science if they can’t understand the science?

I don’t think you understand my question. I’m not saying that one can’t learn science except as an act of faith. You learn science as a scientist. But what about when amateurs want to examine scientific conclusions. They can read the conclusions, learn a bit about the methodology, but once they enter into the details of the “science” there’s a good chance they’ll be lost. I believe in the scientific method, and I tend to think scientists know what they’re talking about–peer review is a good system.

My question isn’t about my anger with Dragonmaci, but I find the fact that no one is willing to confront the problem troubling. There’s a difference between pride and arrogance. Saying you “understand” a scientific concept when you know the conclusion and perhaps a bit about the reasoning (but not, for example, the difficult mathematical formulas) is like saying you “appreciated” a Hugo novel when you just read the cliff notes. I think there’s something intellectually dishonest about it.

Oh, and math isn’t about “empricial” verification… people stopped thinking that once they realized they couldn’t “square the circle.” Mathemathical proof doesn’t happen in a laboratory, but that doesn’t mean it’s arbitrary… it’s extremely rigorous: every step has to follow from the one before. Sometimes they are so complex (e.g., the proof for Fermat’s Last Theorm) that only a handful of people in the world can understand them. It would be ridiculous to claim that I “understand” the proof for FLT, but it would be equally ridiculous for me to be skeptical of the proof just because I can’t understand it.

In case anyone’s confused, here’s my question:

To what degree can amateurs have an opinion on science if they can’t understand the science?

6

To what degree can amateurs have an opinion on science if they can’t understand the science?

They fall into two kinds. Ignorant amateurs can’t, intelligent ones can.

But what about when amateurs want to examine scientific conclusions.

If they are intelligent ones, they should examine the empirical basis for the conclusion. Otherwise, they should become intelligent. If neither is possible, they shouldn’t bother.

I believe in the scientific method, and I tend to think scientists know what they’re talking about–peer review is a good system.

Compared to what? Everything is good, some things are better. BTW, did you read the peer reviews in the Bogdanoff affair? I’d say wow, but I’ve seen too much similar stuff to be shocked. I’m not willing to get very specific about peer-reviewing, but I can identify some real clear problems, not that I have a solution. So that defines the limits of credibility of published articles. The key problem is volume (of stuff to be reviewed).

but I find the fact that no one is willing to confront the problem troubling.

What problem? The problem of publishing standards, or the problem of amateurs not having a grip on the science.

Oh, and math isn’t about “empricial” verification

Right, so that’s part of why math is no substitute for actual empirical proof. Maybe you could re-read what I said and see that I was requesting a proof of.

To what degree can amateurs have an opinion on science if they can’t understand the science?

To the extent that a paper relies on an identifiably invalid method, or is known by the person to be actual counterexemplified, an amateur can have a valid opinion about a scientific claim. So far, I haven’t seen an empirical claim that we could have a scientific or unscientific opinion about.

7

To the extent that a paper relies on an identifiably invalid method, or is known by the person to be actual counterexemplified, an amateur can have a valid opinion about a scientific claim. So far, I haven’t seen an empirical claim that we could have a scientific or unscientific opinion about.

How does an amateur recognize “an identifiably invalid method”? Sure, there will be obvious cases of bad science, but those will be rare. I was thinking of cases (e.g., the global warming debate) where there is “good science” supporting both sides.

In addition, I think you are over-estimating ability of amateurs to evaluate “emprical” claims. Often, even looking at “raw data” requires considerable expertise (e.g., could you recognize a particular virus if given a microscope?). Moreover, much of science is building models and theories based on this data, and evaluating the degree to which a particular model matches data is often a tricky thing. That’s why scientists have disagreements.

How about the empirical claim that there is anthropogenic warming… There are literally thousands of studies offering evidence for and against the claim. I could read the conclusions and try to formulate an opinion, which is in fact what some amateurs interested in the subject do. My question, however, is about whether or not these amatuers are kidding themselves. While they might understand some of the studies (e.g., temperature records), they certainly won’t understand the methodology and data behind others. Moreover, they won’t have a snowball’s chance in hell of understanding the math behind the sophisticated computer models climatologists use to try to understand the interactions between a multitude of variables.

Do you see the difficulty? Will you even acknowledge that this might be a problem? Amateurs who think they “understand” climatology have just read the “cliff notes” version of science. They might be able to talk about some of the broad strokes, but do they really know what they’re talking about?

P.S. I think the Bogdonoff affair proves my point. A minority of referees recognized it to be BS, but other didn’t have sufficient expertise or were just being lazy. This seems a strong indication that there is something very pernicious about pretending to understand something that you don’t fully understand.

8

Will you even acknowledge that this might be a problem? Amateurs who think they “understand” climatology have just read the “cliff notes” version of science.

In what way is that a problem. Or perhaps, the question is, who is it a problem for? It’s not a problem for me. It’s certainly suboptimal that there are idiots in the world, some with PhDs and some without. Are you assuming that everybody needs to be a climatologist? Just explain to me why it should be a “problem”.

9

I laid out the problems in my original post.

  1. How much deference should we give science?

  1. Is accepting science we don’t understand an abdication of reason?

  2. To what extent can non-scientists intervene in scientific debates?

To take another example besides global warming, what about monetary and fiscal policy. Objectivism has a clear position based on political philsosophy, but it also makes claims about the economic effects of those policies. Free market economists (e.g., Greenspan, Friedman) have written both popular and academic economics literature. While I can understand the former, the latter sometimes escapes me…

While I have a tentative answer to my questions…

  1. a lot

  2. no

  3. little to not at all…

I realize that my responses might be troubling to some. I was hoping someone might have some better answers.

10
  1. How much deference should we give science?

Little.

  1. Is accepting science we don’t understand an abdication of reason?

Yes.

  1. To what extent can non-scientists intervene in scientific debates?

Extensively.

I was hoping someone might have some better answers.

My answers are better than yours. Is it a problem that you don’t accept my answers?

Also wanted to mention: those aren’t problems, those are questions. That’s what confused me. Problems are different from questions, even though that distinction is typically muddled in modern science.

11

Little.Yes.Extensively.My answers are better than yours. Is it a problem that you don’t accept my answers?

Do you believe Fermat’s Last Theorm to be true? I do, but I couldn’t tell you why… few people could. It seems you are in the untenable position of:

a. not believing FLT or

b. claiming you understand it

And if you understand the proof of FLT, then I’m the Admiral of the Ocean Sea!

12

Do you believe Fermat’s Last Theorm to be true? I do, but I couldn’t tell you why… few people could.

Any joe-six-pack with an advanced degree in algebraic topology with a particular focus on Galois theory could tell you this!

13

Do you believe Fermat’s Last Theorm to be true?

Do you believe it to be science? I don’t. Did you know that math and science are different? Now stop yapping about math in a thread about science.

14

I do believe math to be a science, but that’s kind of irrelevant to my dilemma. Gvien scientific theory x which you don’t understand, Either

A. You do believe x or

B. You don’t believe x.

Is there a third option I’m missing? Even if I don’t understand FLT, I do understand the law of the excluded middle.

I think the debate about whether math is a science is peripheral to this issue, so I’ll meet you half-way and allow you to substitute for X any scientific theory you don’t understand… say Einstein’s special theory of relativity.

I choose option A. You seem to be saying you’ll go with B, which means that you don’t believe in a great deal of science… a peculiar position for a man of reason.

P.S. If you don’t believe in magnetism (since I don’t think you understand the physics), then maybe you should stop claiming to be the “World’s Northernmost Objectivist” :lol:

15

I do believe math to be a science, but that’s kind of irrelevant to my dilemma.

I don’t: I think that really is the heart of the problem. Science is empirical, math is not. You cannot embrace a contradiction.

A. You don’t believe theory X which you don’t understand or

B. You do believe theory X even though you don’t understand it.

Maybe if you would explain what you think “belief” refers to, what the object of belief is, and what the alternatives to belied are, things would be clearer. Rather than focusing on mathematical proofs, which have no empirical proof and do not necessarily describe reality (though in some cases like integer addition they do), or focusing on dubious broad side of the mountain range science like climatology, you could direct your questions at something in physics or chemistry, where you have a vastly better chance of finding an actually true claim.

Underlyingly, it seems that you’re getting impaled by the True/False problem. I’ll interject that I do advocate reading OPAR ch. 5 to get a good understanding of the issue, and I advocate it three times. This is the second time. You will then see how you are stuck on the horns of a false dichotomy. For a rational man, you must judge that the existence of the referents of a proposition can be reduced to axiomatic status. In order to do that, you have to be able to identify the referents of a proposition – you have to understand the proposition. If you leap to the conclusion that the proposition is true without even knowing what the referents are, you’re not using reason, you are using faith.

Here’s a practical application, and I’ll draw on a bit of my own scientific expertise. I’m telling you that as a matter of scientific fact, beana ii leat boazu. A faith-based citizen would accept the proposition, because it really is a true fact, and I am giving you my authoritative word. I can also tell you that garja lea guolli, and you can easily check that for yourself. By your principle, you should accept my two statements. I eagerly await your compliance.

16
  1. How much deference should we give science?

  1. Is accepting science we don’t understand an abdication of reason?

  2. To what extent can non-scientists intervene in scientific debates?

I think you raised some interesting points, although I think it applies not only to science but in general to anything that you have no first hand practical knowledge of. I think David’s point is true in so far as if you’re intelligent enough and someone is willing and capable of explaining something, eventually you will be able to understand. But in reality it isn’t possible nor practical for a person to learn these things when the investment of time and energy required outweighs his curiosity.

For instance, do you question the capabilities of your pilot when you board a commercial aircraft? Most people don’t, because they take it on faith that the training methods that the pilots completed are sufficient. Do you trust your auto mechanic? Your plumber? So on and so on. Yes, in some cases you may have some knowledge about the subject, and therefore reason your way to a conclusion and decide to repudiate their professional opinions or expertise. But in the instances when you don’t, you trust them to do their job and make your judgment based on the results. Does the fact that you place your trust in a professional constitute an abdication of reason? I don’t think so, because you’re essentially acknowledging your ignorance and forming a rational opinion based on what information you do have. Obviously the more knowledge you have, the more accurate your opinion tend to be, but ignorance does not equal an abdication of reason if you understand what you’re ignorant about.

So how much deference then should we give science? As much as we would any other fields we’re not intimately knowledgeable about. Is it an abdication of reason? Again, no, if you acknowledged your ignorance but apply reason based on what you do know. Being rational doesn’t mean you’re always correct or omniscient, it just means you are using your logical faculties as it applies to your life. Finally, to what extent can an amateur can intervene in a scientific debate – as much as he wishes to. But others are also fully capable of discerning his ignorance, and thereby dismissing or discounting his opinion. It’s not really a question of whether he should or could have an opinion, but a question of how much should the listener value his opinion. That that, can be determined only on a case by case basis by the parties involved based on their judgment of the other.

17

I don’t: I think that really is the heart of the problem. Science is empirical, math is not. You cannot embrace a contradiction.Maybe if you would explain what you think “belief” refers to, what the object of belief is, and what the alternatives to belied are, things would be clearer. Rather than focusing on mathematical proofs, which have no empirical proof and do not necessarily describe reality (though in some cases like integer addition they do), or focusing on dubious broad side of the mountain range science like climatology, you could direct your questions at something in physics or chemistry, where you have a vastly better chance of finding an actually true claim.

Granted that science is empirical and math is not; math is certainly logical. We also know that it’s possible to logically deduce facts without actually having empirical to back it up (for instance in the case of integer addition). Then you get into the problem of, for instance, advanced physics, where a lot of the models are mathematically based and extremely difficult to test empirically. Yet physics is clearly considered a science.

Furthermore, there is also the case where it’s virtually impossible for a layman (even an intelligent one) without a background in, say, statistics, to factually decide whether a scientist had been correct in his regression and conclusion. Granted that if he had the time to take several courses in stat he may understand what is going on, it would be unpractical to do so. In this case the layman is left with only two choices – he either accept that his opinion may be worth very little, or seek more education.

18

We also know that it’s possible to logically deduce facts without actually having empirical to back it up (for instance in the case of integer addition).

I don’t understand what you mean. For example, assuming that I know that A has 7 oranges and B has 12 and I know that they put their oranges into an empty bowl, then I can know for certain that when they do that, there are 19 oranges in the bowl. Okay. That’s because various underlying factual assumptions were empirically proven, and the content of the deduction is trivial. Is that what you’re getting at?

Then you get into the problem of, for instance, advanced physics, where a lot of the models are mathematically based and extremely difficult to test empirically. Yet physics is clearly considered a science.

Right, but physicists don’t deduce facts from the math. They deduce and identify predictions of propositions (the model), and an experimentalist tests whether that is the case (or not, as in string theory).

In this case the layman is left with only two choices – he either accept that his opinion may be worth very little, or seek more education.

To quote from the Ayn Rand Letter 1.7:

  • This does not require omniscience or omnipotence; it is the subconscious expectation of automatic omniscience in oneself and in others that defeats many would-be crusaders (and serves as an excuse for doing nothing). What is required is honesty—intellectual honesty, which consists in knowing what one does know, constantly expanding one’s knowledge, and never evading or failing to correct a contradiction. This means: the development of an active mind as a permanent attribute

and III.10:

  • What objectivity and the study of philosophy require is not an “open mind,” but an active mind—a mind able and eagerly willing to examine ideas, but to examine them critically. An active mind does not grant equal status to truth and falsehood; it does not remain floating forever in a stagnant vacuum of neutrality and uncertainty; by assuming the responsibility of judgment, it reaches firm convictions and holds to them. Since it is able to prove its convictions, an active mind achieves an unassailable certainty in confrontations with assailants—a certainty untainted by spots of blind faith, approximation, evasion and fear.

I understand that many people think it’s impractical to have an active mind because they are very busy. You get two guesses at which approach I advocate.

19

Are you saying there are non-empirical truths (e.g., math), or that math isn’t true? How does this not fall prey to the analytic/synthetic dichotomy (i.e., math consists of analytic truths and science of synethic ones). There is only kind of truth… truth about reality. Different contexts have different standards of evaluating whether something is true. I don’t think math has a different epistemological status than chemistry: they’re both disciplines that purport to describe reality. If you want to say math isn’t a science, I’m willing to concede the point, but math is certainly true in the same sense that chemistry is or philosophy is… they’re all disciplines that attempt to discover truths about reality.

I looked at chapter five .. Were you talking about the idea of the “arbitrary”? Maybe that idea could clarify that dilemma.

Professor Smith, a widely respected chemist with a record of impeccable honesty tells you, “X is true. In fact, it’s been completely accepted in the field of chemistry for fifty years.” He then hands you a book outlining X and why it’s true. You don’t understand it. Is it arbitrary to believe X?

I would say no, since believing people who know what they’re talking about and have no reason to lie isn’t an “arbitrary” basis for belief. We take the word of others for things we can’t verify all the time. It’s not arbitrary if there is a basis for trust, and Occham’s razor would militate believing all the scientists are lying. Moreover, it is rational to believe things even if we can’t be certain of them. For example, I believe the sun will rise tomorrow even though I’m not certain of it.

And I would believe Stephen Hawking if he told me, “beana ii leat boazu.” I don’t think it’s arbitrary, but maybe I’m just a soft touch. Perhaps after we’ve gotten to know each other a little better, I’ll extend you the same courtesy. :lol:

When I say I “believe” something, I’m making a claim that there is a correspondence between the mental concept and reality.

It is possible to say “x” is true even if I don’t know why it’s true. It’s possible for me to “identify the referents” and “understand a proposition” without understanding why the proposition is purported to be true. Here are two reasons…

  1. It is possible for me to grasp a concept (say the conclusions of a scientific report) that is meaningful to me even if I don’t understand the concepts that I would need to verify the truth or falsity of the concept.

  2. To take another example, I understand FLT. If says that there is no integer greater than two for which a to the n power plus b to the n power can equal c to the n power. I understand that. I bet you do too. Look, look, a concept in my mind! But is it true? I’ll say yes, but I’ll never understand Wiles’s proof of it. I don’t think that my belief is arbitrary given the rigor that mathemeticians applied in testing it.

P.S. If you want to debate about the epistemological status of math, I"m game, but please start a new thread.

PPS. Would you please respond to my query about whether of not you believe in magnetism or the special theory of relativity? :slight_smile:

PPPS. Thanks for the post Moebius. I thought it made sense. Just one comment about the issue of scientific debates: I find debates on “global warming” amongst amateurs frustrating because neither side knows enough to prove why the other side is ignorant. They’re essentially lobbing contextless facts at each other without the necessary knowledge to integrate these facts into a meaningful picture of what’s happening.

I wrote the post because I find the arrogance of amateurs who think they understand climate science when they’e just read the cliff notes galling.

20

I don’t understand what you mean. For example, assuming that I know that A has 7 oranges and B has 12 and I know that they put their oranges into an empty bowl, then I can know for certain that when they do that, there are 19 oranges in the bowl. Okay. That’s because various underlying factual assumptions were empirically proven, and the content of the deduction is trivial. Is that what you’re getting at?

I’m saying, because I know that one and one equals two, two and two equals four, so on and so forth, I can deduce multiplication, and therefore I can deduce division, so on and so forth, without further empirical evidence. But you’re right, the initial assumptions of integer addition were grounded in empirically proven facts. But then if you take this line of reasoning further, you end up with the conclusion that the entire field of mathematics ARE in fact empirically proven, and therefore a science according to your original statement. However let’s be clear that although the actual mathematics in and of itself are facts, it does not follow that the conclusions that you draw by applying the math to something else are necessarily facts as well.

Right, but physicists don’t deduce facts from the math. They deduce and identify predictions of propositions (the model), and an experimentalist tests whether that is the case (or not, as in string theory).

You are absolutely right in spirit. But take for example, when Einstein had developed the special theory of relativity. At the time it was published, it was entirely grounded in mathematics – or at least, only understood in terms of its mathematics. Yet since math is in essence logic, you can deduce its correctness by applying it first to the assumptions that were previously proven. At the time there weren’t really any way to test his theory experimentally, yet the math was correct (albeit unproven). It wasn’t until the past decade or so when we’re able to build mile long machines that shoot out subatomic particles at incredible speeds that we’re able to actually design these sort of experiments.

Another obvious example of deducing facts from math would be the ancient astrologer’s ability to calculate the distance from the earth to the moon, or the radius of earth through mathematics, without having to actually measure.

The point is, given that mathematics is essentially a logical progression, if you can definitely deduce facts if the initial assumptions you used was correct. The whole point of the experiments is to ensure the correctness of your math.

I understand that many people think it’s impractical to have an active mind because they are very busy. You get two guesses at which approach I advocate.

I’m not sure what you’re trying to say. I agree with the sentiment of having an active mind, but that doesn’t contradict the fact that it is simply impossible for you to know everything there possibly is to know, and therefore must sometimes accept your ignorance and defer some tasks to others.