Thursday, March the 10th, 2005

Stuff I wrote elsewhere, in response to:

You see, science requires proof and rational explanation behind every statement. There may be certain ‘statements’ (that have no)/(cannot have any) proof in the language called as ‘science’.

I’ve been meaning to say something about this ever since I saw it, but didn’t make the time earlier.

No, science does not require a proof or rational explanation behind every statement. All science tries to do is to explain (more and more complicated things) based on logically sound arguments following from (simpler and simpler) assumptions that most people (can and do) agree on. These axioms form the basic tenets of a theory.

You take a (believable enough) axiom, “time cannot flow backward”, say. You then make rational arguments based on and building upon this fact, you get a theory. If the theory fits most things you see in everyday life, it is a good theory. Whether or not the basic axiom is true, is not important. It sure needn’t be proved, as science does not require it. All science says is if you’re willing to accept it, everything based on it is logically true, and holds. (Which implicitly carries along with it the caveat, true as long as your axioms were.)

Interestingly enough, most things we call laws today were pretty much just statements from very brilliant people, with insanely keen insight into how things might be behaving. Again, the general import here is that they just work, they fit all that we see, there are no obvious counter observations, and therefore, the statement was a building block of science. It didn’t matter if they were stated with proof or not, they worked beautifully, and thus true for all practical purposes.

Case in point, if Newton just said oh, “rate of change of the momentum of a particle is directly proportional to the net external force acting on it”, it doesn’t matter to anyone whether it came with a proof or not. For almost all systems we get to observe in our daily lives, this is a true statement, and thus, we, even as scientists, can “just accept” it. Sure, it can be easily proved today from more general mechanics descriptions making suitable assumptions on the space we live in (space is homogeneous, say). But then again, these other more general mechanics descriptions have their own set of axioms which were arbitrarily chosen (but intelligently argued) to be true.

To conclude, I reiterate — science does not require proof or rational explanation behind every statement. Science takes few building blocks without proof and logically draws conclusions from them. So yes, you were right that there are statements which have no proof in science, but it’s not some secret. Science gladly accepts that.

They’re called axioms, and stated upfront every time a theory is proposed.

This is a printer-friendly version of the journal entry “In response” from actuality.log. Visit to read the original entry and follow any responses to it.

4 Responses to “In response”

  1. Sudeep says:

    I think this is the reasoning behind the original post.There is a result in mathematics(Godels theorem) which says that any system built upon a finite set of axioms and rules is incomplete, in that it contains more true statements than which it can possibly prove according to its own set of rules and axioms.A result of this being, the ideal of science can never be realized- to devise a set of axioms from which all phenomena of the external world can be deduced.

    Perhaps this is what the original post was trying to convey
    “There may be certain ’statements’ (that have no)/(cannot have any) proof in the language called as ’science’.”

    Statements here refering to truths about the system and ‘language of science’ refering to axioms and rules upon which the system is built on.

  2. wahgnube says:

    Firstly, I just went through the theorem and a rough hand-wavey proof, and you have a good point. But I seriously doubt this is the sort of thing the parent poster was referring to. I will defer responding to this until I’ve read up a bit more upon the works of this person. Now I realize I’ve missed out a lot by not having to take any classes on formal mathematical logic, or philosophy. Stuff that I think this event is going to drive me into rectifying.

    Naively though, … well, I can’t frame the question at the moment. I will let you know when I do.

    Unrelated: Employed yet?

  3. pul| says:

    Firstly, I don’t think it was the sort of thing the parent poster was referring to ;) Secondly Harish, I appreciate the simple and lucid explanation you’ve offered. I have to agree with you on the “few building blocks without proof” thing. However, how does one explain using science, ‘statements’ that do not happen to have any logical base. Say something intuitive, something un-expected, un-perceived of. For argument sake, let’s say you saw something totally unphysical and to actually make this support our argument better, only you were able to visualize this among a group of people who were all in the same state of consciousness as you were. (i.e. something equivalent all other conditions remaining constant) All but you refute your claim. You know this is true but you cannot offer any explanation that can possibly add any degree of credibility to your experience. Does science now require that you now call this an axiom in order to enter this observation into its dictionary? (Of course probably subject to the constraint that there have to be several such instances before it is even given a second thought). PS: I love this new comment form. There’s much more width than before.

  4. Sudeep says:

    You may be right about the parent poster, since you have read it in context.

    What got me interested in all this, is actually a book I am reading right now – ‘Godel Escher and Bach’ by Douglas Hofstadter.That book is equal to any course in logic/philosophy, and probably more insightful.

9,975,891 people conned into wasting their bandwidth.