against induction

some of you who know me know that one of my charming quirks is that i don't believe in empirical induction. i don't mean in hume's sense - it's not just that i don't think induction leads to weaker inferences than deduction. my skepticism is this: i don't believe that induction exists as an independent mode of reasoning. i believe that there is nothing gained by adding induction to our reasoning toolbox, because anything that it does is already covered by abduction. since there are things covered by abduction that are not covered by induction, it is induction that is redundant.

my initial formulation of induction is as follows:

for every individual P and attribute X, frequent observation that an instance of P has attribute X, with no observation that P lacks attribute X, licenses the inference that every P has attribute X.

i don't think much of the critique is contingent on this particular formulation; i welcome feedback on it.

i can think of four arguments against induction, but i don't have good names for them at the present. i'm aware from personal experience and from reading feyerabend that good marketing is essential to philosophical and scientific progress, so i will start trying to think up some good names - maybe get burson-marsteller to do some pro bono work on my behalf. in the meantime, here are the names of the arguments.

1. the raven paradox argument
2. the argument from the structure of logic
3. the unvarying datum argument
4. the clash with theory argument

in this post i'll give very quick summaries. i'll plan to elaborate in the future.

1. the raven paradox argument

take the following proposition:

(p) every raven is black

(p) is logically equivalent to (p')

(p') every non-black thing is not a raven

if induction is valid, then observing many black ravens lets us infer (p) (and (p')). so far, so good. but observing many non-black non-ravens also lets us infer (p) (and (p')), and this goes against our understanding of what good evidence is. right now i can see an orange curtain, a greyish ceiling fan and white walls. they are not good evidence that all ravens are black, but induction suggests that they are.

this argument, due to hempel, has generated a number of solutions intended to rescue induction. i don't think they're very good, and i hope to address them in the future. i believe my approach - to dump induction in the harbor - makes more sense.

2. the argument from the structure of logic

logic is about drawing conclusions from premises using formal rules. the rules are rigid, while the premises and conclusions vary. i suggest that this restricts the modes of reasoning to two: given premises, reasoning to conclusions - this is deduction; and given conclusions, hypothesizing premises - this is abduction. there is no room for other modes of reasoning like induction. it is possible, of course, that induction is a submode of abduction; but if induction is to not be redundant, then the burden is on its advocates to show that it has interesting properties that set it apart from ordinary abduction.

3. the unvarying datum argument

suppose P has two subtypes: P' and P''. and suppose we observe, frequently and unvaryingly, that instances of P' have attribute X. does this license an inference that all P have attribute X? by induction, it does. and then it follows that all instances P'', about which we've observed nothing, have attribute X. this is preposterous.

the same situation arises with respect to a P with no subtypes, but which could in principle be observed under different conditions but is observed in only one kind of condition. suppose that in all the observations, P has attribute X. induction would lead us to believe that every P has attribute X, without accounting for the possibility that it is an artifact of the conditions of observation.

4. the clash with theory argument

induction allows us to infer that the sun will rise tomorrow. suppose we have a very good theory of the cosmos which predicts with certainty that before tomorrow, the earth will stop rotating, or else that the sun will explode. it is rational to believe the theory rather than our past experience. but induction allows us to infer that the sun will rise tomorrow. so induction licenses an irrational inference.

feedback welcome.

EDIT: how could i forget the grue argument of nelson goodman?

5. the grue argument

define the attribute grue as follows.

for some time t and all P, P is grue iff it is green if observed before t and blue if not observed before t.

if some P has been observed before t, then induction allows us to infer with equal probability at t that P is green and that P is grue. this means that it predicts with equal force that P will appear green and that P will appear blue next time it is observed.