Posts Tagged ‘inductive reasoning’

Induction Machines

In critical rationalism, induction on 23/08/2011 at 12:26 pm

Imagine that a computer is built to make empirical generalizations with inductive logic (whatever that may be) and that this computer is in a simple universe with a limited number of individuals,number of properties, and relationships between these properties the individuals can have. Furthermore, the universe operates with a limited number of ‘natural laws’. In this universe a computer can be created such that in some reasonable period of time it will discover the ‘natural laws’. If the laws were modified, then the computer would find a new set of laws. If this universe were further complicated, then this computer could be enhanced to be able to formulate hypotheses, to test these hypotheses, and to eliminate those that do not survive testing.

This induction machine is limited insofar as it is limited by its programmer’s intellectual horizon: the programmer decides what is or is not a property or relation; the programmer decides what the induction machine can recognize as repetitions; it is the programmer that decides what kinds of questions the machine should address. All the most important and difficult problems are already solved by the programmer, and this induction machine is little more than a speeding-up process of a room full of bean-counters or punch-card holders.

Here we have today’s work in artificial intelligence, which is precisely limited by this constraint. The theories that these computer programs develop are conditional on the initial conditions that are needed for in an induction machine. Inductive inferences does not then occur within the context of discovery; the programmer provides these. Inductive inferences occur within the context of justification, and even then it still does not satisfactorily solve the problem of induction, for the problem cannot logically be solved. These computers have become problem-solving machines that operate on conjecturing the most parsimonious theory and attempted refutation of that theory.



In critical rationalism, popper on 29/07/2011 at 1:10 am

Peter Singer’s 1974 article in the New York Review of Books, Discovering Karl Popper is extremely favorable of Popper’s philosophy of science–except for three paragraphs in the middle, which are highly informed criticism. I’ve reproduced them below along with some limited comments in light of that criticism.

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Wherefore art thou Induction?

In critical rationalism, induction, quine, underdetermination on 11/07/2011 at 10:12 am

The word ‘induction’ takes on many meanings, always when most convenient. Like a slippery eel, just when a critic of induction has their hands around its neck, it wiggles out once more.

Does induction refer to the ‘context of discovery’ or the ‘context of justification’?

If ‘induction’ refers to the context of discovery, the critic of induction need only point to the greatest historical developments in science. Without blinders on, the critic points out that these theories are birthed in the heat of dealing with significant scientific problems. The framework comes before observation (read: Einstein). How then could enumerative induction work? Theories are then imaginative creations–possible solutions to problems. Even if enumerative induction is permitted during the context of discovery, it does not help the scientist any more than dreaming next to a raging fire (read: Kekul√©’s oroboros), drug use (read: Feynman, Kary Mullis), &c., which is to say that is has no privileged position over even the most arbitrary ‘methods.’

If ‘induction’ refers to the context of justification, is this a process of objective inductive verification¬†√† la Carnap? If so, then this program is defunct, for no number of verifications can increase the probability assigned to a strictly universal statement. Is this the process of subjective certitude after repeated verifications? Then it contradicts the probability calculus and fails to solve the problem of underdetermination.

If ‘induction’ refers to the metaphysical assumption of regularity of systems, which we may approximate if enough inductions of the system are collected, then the inductivist retreats to asserting only that there exists regularities, calling this assumption ‘induction.’ If a proposed regularity should turn out to be false, then this was either a mistaken induction or not induction at all. If it is not an induction, then this is little more than wordplay: we cannot tell this type of induction apart from a conjecture. If it is a mistaken induction, this type of induction should only be known to be mistaken in hindsight: it tells us nothing until we learn that we are wrong.

And what is that but a falsification?


Reduced to Twelve Lines of Dialogue

In critical rationalism, empiricism, induction, popper on 05/07/2011 at 12:32 pm

Logical Positivist: Popper, we know we didn’t let you in our club, but what you do you think of our plan on eliminating metaphysics by reducing all meaningful statements to elementary statements of experience or analytic truths? Isn’t it swell?

Popper: Are you blind?

Logical Positivist: What?

Popper: You define ‘meaningful’ as ‘possible to empirically investigate’ while you define ‘meaningless’ as ‘impossible to empirically investigate,’ but metaphysics has usually been defined as non-empirical. Your use of the word ‘meaningless’ is derogatory, rather than descriptive. I call your very plan into question as merely restricting definitions.

Logical Positivist: No, it’s not!

Popper: Fine, if that will not turn you, put that criticism aside. Does this criticism work? Your very plan is not analytic, nor is it reducible to an elementary statement of experience. Therefore, there exists at least one meaningful metaphysical statement: your plan.

Logical Positivist: … could you try something more … palatable?

Popper: Sure, try this on for size. If we assume that you are successful in eliminating all metaphysics–by that very criterion of meaning, scientific laws cannot be reduced to elementary statements of experience, and ought to be rejected as meaningless.

Logical Positivist: … um … Let me get back to you …

Popper: Take as much time as you want. Put all my previous objections aside and assume for the moment that you have solved them all. How about this? You accept an inductive logic, right?

Logical Positivist: Sure!

Popper: Your proposed inductive logics are not reducible to elementary statements of experience or analytic truths. Your plan is clearly incoherent.