¿Es racional pensar inductivamente?

El razonamiento inductivo es una clase de razonamiento que nos permite concluir cosas generales a partir de observaciones particulares. Por ejemplo, si sabemos que siempre ha sido el caso que al tirar una pelota ésta se cae, entonces por inducción podríamos concluir que la pelota se caerá cada vez que la tiremos.

Es importante notar que a pesar de que este tipo de razonamiento parece tener sentido, no es lógicamente sólido: el hecho de que algo siempre haya ocurrido hasta ahora no significa que continuará ocurriendo. Tomemos un simple ejemplo: mi computadora nunca ha explotado cuando la enciendo, entonces por inducción podría asumir que no explotará tampoco la próxima vez que la encienda; sin embargo, esta conclusión no es necesariamente cierta — una falla eléctrica podría hacer que mi computadora explote la próxima vez que la encienda a pesar de que esto nunca ha pasado.

A pesar de que la inducción no es lógicamente sólida, la usamos todo el tiempo: asumo que mi computadora no explotará la próxima vez que la encienda, asumo que si un coche me atropella resultaré lastimado, asumo que comerme un puño de habaneros tendrá resultados terribles, etc. Ciertamente, no confiar en la inducción nos llevaría a adquirir hábitos bastante extraños (¡tal vez tendría que ponerme un traje anti-bombas para usar mi computadora!). Aún más, la inducción ha probado ser una herramienta extremadamente poderosa para el desarrollo científico. Es difícil imaginar un mundo en donde los científicos no aplicaran el razonamiento inductivo para proponer hipótesis y desarrollar teorías.

La inducción es claramente una forma de razonamiento sumamente útil, pero ¿es posible justificar racionalmente la confianza que la mayoría le tenemos?

David Hume

Pues de acuerdo a David Hume, parece que nel, pastel.

El filósofo escocés llegó a esta controversial conclusión después de notar de que siempre que hacemos inferencias inductivas, parece que asumimos lo que él llama la ‘Uniformidad de la Naturaleza” (UN). En otras palabras, parece que asumimos que los fenómenos naturales se comportan uniformemente.

Pero, ¿cómo podemos saber si la UN es cierta? Es perfectamente posible imaginar un universo en donde las cosas se comporten aleatoriamente, por lo cual estrictamente no es posible probar que la UN es cierta. Pero, ¿podríamos por lo menos reunir evidencia empírica que la respalde? Uno podría estar tentado a decir que el hecho de la UN ha sido cierta hasta ahora es razón suficiente para asumir que es cierta en general, pero este es un razonamiento inductivo ¡que a su vez depende de la UN! Un argumento que asume una proposición A, no puede ser usado para probar que A es cierta. Tratar de probar la UN a través de la experimentación nos lleva a razonar en círculos.

Entonces tenemos que la inducción necesita a la UN, pero no podemos probar que ésta es cierta o reunir evidencia a su favor sin razonar en círculos. Nuestras inferencias inductivas están basadas en una asunción acerca del mundo sobre la cual no tenemos justificación racional; por lo tanto, Hume concluye que nuestra confianza en la inducción es una cuestión de fe.

¿Fe en el corazón de la ciencia? Esa es una conclusión con la cual jamás creí poder estar de acuerdo.

Hekanibru

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10 pensamientos en “¿Es racional pensar inductivamente?

  1. Consider, if you will, the possibility that we do not use induction as we go through life counting on things to be as we imagine they are. Yes, we have a sort of positioning in such affairs. No, it is not induction that we use to position ourselves with these expectations.

    Among the more recent explorations I've seen on this general topic are the writings of David Miller (U. Warwick). He elaborates the radical skeptic perspective on rationality quite nicely, to my eye.

  2. I wanted to think about it before posting something stupid. And I thought about it, so let's see how well it goes.

    First, although we can't tell whether UN is “true”, we could, in principle, provide some sort of “formal proof” using probabilities and assuming that the universe behaves like some kind of Turing Machine. I think, in fact, that this would be very closely related to the “formal proofs” that have been given for Occam's razor.

    This, of course, proves nothing. As now we have even more “unproven” assumptions (i.e. that the universe behaves like something or whatever).

    The real question here is whether we actually have to “prove” UN in order to justify science. And I think the answer is: no.

    UN isn't really an “axiom” of science but, very much like Occam's razor, more of an heuristic. It allows us to “infer” (note the quotes) and propose hypotheses, but we still have to test them and try to falsify them.

    The curx here is that science never tells us anything for sure. At most, science is only able to guarantee us things like “if assumptions then so and so“. But, unlike religions, it doesn't ask us to “have faith” in those assumptions. Science is pretty well aware that our assumptions might be wrong, and more than happy to change those assumptions when this turns out to be the case.

  3. The question would then be, why do we prefer that heuristic? Is it rational to do so?

    I agree with you that “Science is pretty well aware that our assumptions might be wrong, and more than happy to change those assumptions when this turns out to be the case.” The post, however, was not about whether this is the case; it was about trying to find a rational justification for assuming certain things (e.g., UN) over others.

    Clearly, so far it has been more *useful* to assume UN than not to, but, as Hume points out, this doesn't mean it is rational to do so.

  4. Ok, I think that I've already answered your question in my comment. But probably I wasn't very explicit about it.

    “Is UN rational?” The answer is: No.

    “Why do we prefer UN to other ‘heuristics’?” There is no particular reason. We shouldn't really ‘prefer’ it to others. As long as we're able to propose hypothesis to test, it doesn't really matter where do they come from.

    What I was trying to argue, though, is that this doesn't imply that there is “blind faith at the heart of science”.

    Incidentally, your comment made me remember one sort of joke we had when training to solve math problems. For many of the problems, the solution consisted in starting with some strangely looking formula, and then apply a number of straightforward derivation steps until, eventually, you get the proof you were looking for. The latter steps were always very clear and simple, but there was no obvious indication of how were you supposed to come up with the original formula in the first place. We used to call the first step of this method: ‘divine inspiration’.

  5. You say that we shouldn't prefer some heuristics over others to propose hypotheses. Perhaps this is true, but nevertheless many scientists *do* prefer some heuristics over others (typically UN) to do so. Therefore, in this sense, there is blind faith at the heart of science.

  6. Like the blind faith I have for preferring vanilla over strawberry ice-cream?

    In all seriousness, if we can think of scientific claims as being of the form “A -> B”. Then useful scientific claims will probably be the ones where:
    (1) A “seems” to be true in world
    (2) We are actually able to prove “A -> B”
    (3) B tells us something “useful”

    Starting with “A = not UN” is probably not very popular among scientists because: “not UN” doesn't “seem” to be true in the world, and because there is probably not much you can prove starting from that assumption.

    So I don't really see “faith” (not to say “blind”) as being a factor for scientists “preferring” to assume UN.

    And still, not all of our scientific theories start with the UN assumption (at least in a strong sense). Take quantum mechanics for example where, down there, is all pretty much based on randomness and probabilities!

  7. Some scientists assume UN *because* they believe it's true, and then propose hypotheses of the form: UN and A -> B. The faith claim follows since there is no rational justification for believing UN.

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