The Problem with the Problem of Induction
There is a problem with the problem of induction at its very premise. The problem of induction acknowledges identity while simultaneously violating it.
Here is an interesting quote from the evil, secular Wikipedia:
So, for instance, from any series of observations that water freezes at 0°C it is valid to infer that the next sample of water will do the same only if induction works. That such a prediction comes true when tried merely adds to the series; it does not establish the reliability of induction, except inductively. The problem is, then, what justification can there be for making such an inference?
The problem of induction is saying that as time progresses, why should we believe that the identity of an entity (in this example, water) would remain as it is? In the water example, the PoI states that we cannot know that the water will still freeze at the same temperature in the future. The PoI could even go so far as to state that we cannot know that the water will freeze at any temperature in the future. But why stop there? The PoI could go so far as to challenge the existence of the water itself! If we can challenge the freezing temperature of water by challenging induction, why not challenge the continued existence of that water by challenging induction? Whether you challenge a property of the water, or the existence of the water itself, you are still challenging the same thing: the identity of the water. I contend that if the water changes freezing temperature without any other factors involved, then it is no longer water. Its identity has been violated. The PoI assumes identity in its acknowledgement of the water's existence and properties at time T, but it then violates the identity of the water (and therefore existence, because water that doesn’t freeze at 0'c in a normal earth environment/pressure is not water) at T+1. Where is the justification for such an identity violation?
Time is dependent upon axioms such as identity. Axioms are not dependent on anything. But the PoI states that we can violate axioms with the insertion of time into the mix. Where is the justification for such a proposition? How does time cause a violation of the axioms it is dependent on?
Lets take another example from the evil, secular Wikipedia. This is another snip from the same link:
Nelson Goodman presented a different description of the problem of induction in the article "The New Problem of Induction" (1966). Goodman proposed a new color, "grue". Something is grue if it is green up until some given time, and blue thereafter. The "new" problem of induction is, how can one know that grass is indeed green, and not grue?
I don’t know if anyone has challenged Goodman before in the way that I will challenge him, but I hope I can state it clearly enough. I think that Goodman's color issues highlight the misunderstanding of identity that the PoI exhibits. Let's talk about what color is for a second. Color is defined as a particular frequency of light. Light comes to us in waves, and these waves have frequencies. Blue has a different frequency than green. If you mix the two frequencies together, you can get blue-green or green-blue. Green and blue come to our eyes in completely different frequencies of light. They are identified by their distinct frequencies. When you look at colors such as blue-green, what you are seeing is either a combination of two distinct frequencies, or you are seeing a frequency that resides at the cusp of blue and green. Either way, the identities of these colors, and their frequencies, remains constant.
So what is Goodman proposing? He is proposing a color that would change frequency or identity after a given point in time. Goodman is proposing a violation of identity, in that the frequency of the "grue" would change. If someone proposes a blue-green color mix, I imagine a combination of the blue frequency, and the green frequency, or possibly a frequency that resides halfway between blue and green. But that's not what Goodman had in mind! Goodman thinks that we can assign one identity/color value (grue) to an entity (light wave) that will violate it's own identity, and change its light frequency, after a certain point in time has passed!
A color's identity involves the constancy of its light frequency. It is not possible for a color to keep its identity while changing its light frequency. One color (grue) cannot be defined by having two distinct frequencies that exist in different points in time. The only way to do it would be to have two identities(blue and green) and have one replace the other after a given point of time. But then, there would be no PoI because we wouldn’t be talking about one entity changing its identity, instead we would be talking about two entities keeping their identities constant, but merely substituting the place of each other after a given point in time. Goodman grossly misunderstands color, or should I say, the PoI grossly misunderstands identity.
No defense of induction against the PoI is necessary, for we can defeat the PoI on its own premises. The PoI fails to mount a proper attack because it violates identity in its attack. If the PoI has no concept of identity, it cannot attack induction itself, which does have a proper concept of identity.