Cheers!

And no, physics is not based on mathematics. It only seems to be, because you have to use mathematics in order to do physics. Yes, mathematical knowledge may be a prerequisite to understanding physics, but physics is in no way “built upon” mathematics. It’s theoretically possible (though very unrealistic) for someone to devote their whole life to studying math, and come to learn virtually everything about it (that has so far been discovered) and still know absolutely nothing about basic physics or any other area of science. The only reason you might study a little physics in a math class is just to see how math can be applied to real world problems. But you don’t need to understand the physics to understand the math. Physics and all other sciences are based on real world observations. To do science, you have to open your eyes, look around the world, and see what Mother Nature has to offer. Isaac Newton didn’t come up with his laws of motion just by sitting in the armchair and thinking about it. He had to literally use his eyes and see how physical bodies behave in the real world. Math is different. Mathematicians start with concepts, definitions, axioms, and then logically derive theorems from those axioms, as well as from earlier theorems. Mathematicians never have to look around the world and see what Mother Nature has to offer. Theoretically, a blind man sitting in the armchair (if he had an IQ of 100,000) could ascertain the truths of logic and mathematics just by pure thought alone. But he still would know nothing of science.

You said, “It is implied that the fields of logic and math are truths that were discovered, but did not demonstrate a need to be tested. So it is accepted that the field of mathematics never once had an incorrect assumption that had to be vetted out by testing and/or further scrutiny?”

I admit I’m not 100% on this, but I’m going to venture to say that this is more or less the case. Yes many mathematical discoveries have turned out to be surprising and counterintuitive. (E.g. the discovery of irrational numbers, or the different cardinalities of infinity) But none of these surprising discoveries contradicted any previous mathematical knowledge. (There was no ancient mathematical theorem that said that all numbers were rational, that got overturned with the discovery of irrational numbers.) Again, mathematical inquiry just doesn’t work the same way as scientific inquiry. That’s not to say that math is better, or worse, than science. They’re just different methods of inquiry applied to different kinds of subject matter.

You said, “Concerning the field of logic- we accept there are certain logical truths, but how did these come to be discovered? Were they merely thought into existence by some smart dudes and/or dudettes? Or were they the result of observation and hypothesis? Further explanation is needed.”

Do you believe in contradictions? Do you really think that there are any statements of the form “P & ~P” which could possibly be true? If so, reasoning with you would be pointless. But if not, then why not? What makes you so sure that a contradiction could never be true? Did you really need to be told this by some “smart dude”, otherwise you would never have known? Please tell me that it’s intuitively obvious to you that a contradiction can never be true. But here’s another question: Are you 100% certain that a contradiction can never be true? Or are you LESS than 100% certain (99.999%) that a contradiction can never be true? Which is it? If you’re 100% certain about the falsity of contradictions, then where are you getting this certainty from? From science? But the scientific method can never establish anything with absolute certainty, because you never know when a theory may be falsified by a new discovery. To think like a scientist on this matter, you would have to say that you don’t believe in true contradictions, because in your entire life, you’ve never seen one. But that doesn’t mean there are no true contradictions. For all you know, there could be a true contradiction somewhere in the Andromeda galaxy. Speaking for myself, I am 100% certain that there are no true contradictions, because I know that it is impossible for any contradiction to be true. And how do I know this? Because for any proposition P, if P is true, then by definition, ~P is false, and vice versa. So there are only two possible states of affairs: P is true and ~P is false, or P is false and ~P is true. And in order for a conjunction (an “and” statement) to be true, both the conjuncts must be true at once. And since there’s no possible state of affairs in which P and ~P are both true at once, that means that the statement “P & ~P” is necessarily, inevitably, and indubitably false. And that’s how I know with 100% certainty that no contradiction could possibly be true. (This could be more simply demonstrated with a truth table.) And notice that nowhere in this reasoning did I have to use any of my five senses. I never had to see what Mother Nature has to offer. The impossibility of true contradictions is thus knowable by pure thought alone. A blind man sitting in the armchair could figure it out. And similarly for other basic truths of logic.

As for morality. It is an unresolved issue in philosophy as to whether there are any objective moral truths. If there are no objective moral truths, then obviously science cannot test them or ascertain them. (Psychologists and sociologists might be able to investigate why certain people or societies hold the moral beliefs that they do, but that’s a different matter.) If, on the other hand, there are such things as objective moral truths, then it is no easy task to determine what they are. Philosophers for centuries have been proposing competing moral theories to shed some light on this, and every theory has its own unique insights to be brought to bear on the matter. But every moral theory also has its weaknesses. Welcome to philosophy. But there are some moral truths that seem pretty obvious. My favorite example (which I’ve brought up in the past, and some of you are sick of it, but here it is again) is that it seems unquestionably immoral to tie up puppy dogs and burn them alive for the sheer sport of it. I challenge anyone to tell me to my face, in all honesty and sincerity, that you don’t think there would really be anything wrong with such a practice. Granted, I just made this up, but if there really were some monster out there who burned puppy dogs alive for fun, I would be tempted to say that what he/she was doing was morally wrong, regardless of how anyone (including myself) feels about it. I don’t know. Maybe there are no objective moral truths, but it certainly is not irrational to think that there are. And assuming, for the sake of argument, that there are objective moral truths, science cannot tell us anything about them. The eighteenth century philosopher (and a very prominent skeptic!) David Hume raised the famous “is/ought” problem in ethics. In a nutshell, you can’t reason from an “is” to an “ought”. All the information about what IS happening tells us nothing about what OUGHT to happen. And science is very good at telling us what IS the case in the physical world. But this tells us nothing about what OUGHT to be the case in the physical world. If we really want to make the world a better place, and increase the world’s supply of happiness and well-being, then science can certainly be instrumental in telling us how to do this. But science can at best tell us HOW. It cannot tell us that we SHOULD. Are we really obligated to increase the world’s supply of happiness and well-being? Maybe we’re morally obligated to do the opposite, to increase the world’s supply of pain and misery? Science can tell us how to do that, too. But science can’t tell us what we should or should not do. I challenge you to name one scientific discovery that has any implications for how we OUGHT to act. I doubt you’ll be able to find such a thing, because science can only discover the “is’s”. It cannot discover the “oughts”. The gulf between “is’s” and “oughts” is so wide, that some philosophers question whether there really are any “oughts”.

We all know the difference between so-called subjective and objective reality and perhaps Brad should have defined this a little more clearly. However, I don’t think this is a case of scientism rearing its ugly head and needing to be slain (yes I am being facetious here), but merely an attempt to explain to laymen (such as myself) the importance of viewing the world through a scientific (and yes logical) lens.

I think saying that the Andromeda galaxy existed even though the Flintstones were not aware of it is an overly simplistic example. Mankind at the time most likely had a difficult time grasping the things they could not directly observe. Yet we understand the concept of indirect observation to a great degree now. Even though now we accept that things can exist even though we can’t directly observe them, we still have rules about how they can be indirectly observed. Science (and yes by extension logic) helps us discover and tune these rules, they are not assumed out of thin air.

Attempting to compare logic and mathematics to other disciplines of science and then demonstrate a notion of superiority based on the differences seems like a case of putting the cart before the horse. All of these scientific fields are based on an abstraction of the layers below it. Biology is based on chemistry, which is based on macrophysics, which is based on microphysics, which is based on mathematics, which I assume was begatted by logic. These are gross oversimplifications, I know. My point that due to increasing levels of complexity by adding each layer, I don’t think you can imply that a science is inferior because it can’t always make direct correct assumptions (like mathematics can). The requirement for scientific methodology is not an inferiority, but instead a tool to be able to use these complex abstractions without being required to spend years mathematically calculating out each layer of assumptions recursively. Instead we can make educated guesses based on the abstract concepts we do know and then in turn test those guesses out.

Also, to be fair, the field of mathematics has a several thousand year head-start on most other areas of science. Shoot the field of evolutionary biology is what, a hundred years old?

It is implied that the fields of logic and math are truths that were discovered, but did not demonstrate a need to be tested. So it is accepted that the field of mathematics never once had an incorrect assumption that had to be vetted out by testing and/or further scrutiny?

Concerning the field of logic- we accept there are certain logical truths, but how did these come to be discovered? Were they merely thought into existence by some smart dudes and/or dudettes? Or were they the result of observation and hypothesis? Further explanation is needed.

Many people try to discount the realm of science and view it only as one of several competing philosophies for obtaining truths about the world. But they seem to discount the fact that that science yields us far greater real-world results (on everything from Antibiotics to Zoology) than any other ‘competing’ philosophy. Yes, science is still in its infancy and we have a long way to go to even begin to understand a small portion of our existence, but this is no reason to trivialize its methodology. This methodology (when it is properly applied) has a reputation of producing good results while weeding out the bad ones.

It is stated that the scientific method can give us no insight on the concept of “moral truths”. I am not sure I understand what a moral truth is. With a name like “moral truth” I assume it is a concept that is undeniable and external to human existence. Since it is referenced in plural form, I assume there are multiple truths. If there are multiple, undeniable truths and there are more than one I assume that there is a list of them somewhere, kind of like the 10 commandments.

If I search for “moral truths” on wikipedia (the oracle of all human knowledge), I see only a few references. One reference is to an article on moral relativism (which I think is the wrong way to go if we are establishing a truth). Another reference that I found is that moral truths are a tenet of intuitionism, which in turn seems to be an offshoot of ethics. I would imagine being the implied stature of these moral truths would warrant far more attention on the Internet.
My point in all of this is this. This concept of “moral truths” is presented as an undeniable tenet of existence that can’t be touched by the scientific method. But what I am seeing is that this concept of moral truths is nothing more than nomenclature specific to specific areas of philosophy that attempt to make observations on certain aspects of human interaction. Again, further explanation is needed before we can assume that:

1. Moral truths exist and are concrete and infallible (or insert whatever description that makes them a truth here).
2. Scientific method cannot test the claims of moral truths.
3. Therefore scientific method is inadequate and cannot explain everything.

I don’t think it has been demonstrated that we can assume that number 1 is correct. So I’m not sure this is a very persuasive point. Can you elaborate?

If there are any typos or misprints, please forgive. This tiny comment window is kind of irritating to work with. We may have to do something different with it.