Internet Goosing the Antithesis

Tuesday, May 17, 2005

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.

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At 5/17/2005 2:43 PM, Blogger Aaron Kinney declaimed...

Oh yea. I didnt refer to any source for my definition of color, so that must be GOOD form! Woohoo!

At 5/17/2005 4:27 PM, Blogger Francois Tremblay declaimed...

I'm afraid I'm going to have to go slightly against my esteemed friend Aaron on this one.

There would be no inductive problem with the colour "grue". That is to say, insofar as we can know the identity of grass, we can know that it is of the colour "grue", i.e. that it will eventually change hue. We can also find the underlying reason why grass is "grue" and identify a biological theory to that effect, because nature is uniform.

To come back to the observations, the so-called problem is circular, since it assumes that we cannot know "grue". The observations are NOT :

1. The grass is green.
2. The grass is green.
3. The grass is green.
X. The grass is blue.
X+1. The grass is blue.

But :

1. The grass is grue. (on green wavelength)
2. The grass is grue. (on green wavelength)
3. The grass is grue. (on green wavelength)
X. The grass is grue. (on blue wavelength)
X+1. The grass is grue. (on blue wavelength)

At 5/17/2005 4:27 PM, Blogger Zachary Moore declaimed...


Very interesting. I never considered the Problem of Induction from that perspective before. Well done.

At 5/17/2005 4:33 PM, Blogger Zachary Moore declaimed...


But doesn't the idea of a color that changes frequency violate the very idea of color in the first place? In other words, if grass did, in reality, alternate between green and blue, wouldn't it be more reasonable to just say, "it is either green or blue," than to say, "it is grue?"

The definition of "grue" in this example doesn't actually give us any information about the color of the grass. I might as well, at the same time, rename myself "Zanc," under the assumption that while I am Zach now, our identities may switch in the future, in which case I will become Franc. Such definitions are meaningless, I think.

At 5/17/2005 5:00 PM, Blogger Aaron Kinney declaimed...

I am actually glad that a fellow atheist disagreed with me. I am the first to admit (and Ive said it before) that the PoI is new to me and Im still learning about it.

I may be totally wrong about everything in my post and Im not afraid to be proven wrong. I will consider it a valuable learning experience either way. This is just the way it appears to me.

I even took the time to read Bertrand Russels chapter 6 in his book Problems on Philosophy (or was it called Problems with Philosophy? I forget exactly) during my lunch break. And I honestly think that Russel's writings on the PoI are subject to my criticisms here.

In regards to the color "grue", what light frequency is it? If its more than one frequency, and those frequencies exist in the grue at different points in time, then I maintain my contention that it is a violation of identity.

How can you assign two light frequencies at two different points in time to one color definition?

Time is temporal. Time is not a constant. What if time were to slow or change or stop before the given point was reached where grue changed from green to blue? Would the color still be grue, or would it change to "green"?

I see your point there Franc regarding the numbered progressions of the grue, but I will still (for now anyway) maintain my stance and state that the grue definition is violating identity. A color is a wavelength or a given range of wavelengths, and it is not time-dependent. A grue as defined in this discussion, would be something other than (or more than) color, although color could be a property assigned to the grue.

For example, look at a chameleon. It can change colors. But is "chameleon" a color? Nope. It is an entity that has color values assigned to it, but chameleon itself is not a color.

The same goes for the water. In the water's case, the boiling point replaces the light wavelength in the color example. If pressure placed on the water remains the same (say the pressure of Earths atmosphere at sea level), and the waters boiling point suddenly changes, then I conted that the water is NOT actually water; it is something else. To assign the definition of "water" to a liquid that has a different boiling point than "water" would be to violate its identity. It would be like assigning two seperate entities the same definition.

And to look at the grue one more time, note that the PoI relies not on "grue" but on the "grass" having the color of "grue". In this case, I contend that "grue" would not be defined as a color itself, but it would be defined as a property of the grass which can change color. The "grue" would NOT be defined as a given light frequency, but instead "grue" would be defined as the changing of light frequncy of grass from one color to another. Again, the identity of color is confused/violated.

At 5/17/2005 5:01 PM, Blogger Francois Tremblay declaimed...

"But doesn't the idea of a color that changes frequency violate the very idea of color in the first place? In other words, if grass did, in reality, alternate between green and blue, wouldn't it be more reasonable to just say, "it is either green or blue," than to say, "it is grue?""

Hmmm. If you define colour as a specific wavelength, sure. I can agree with that you wrote. Either way, it's not a problem for induction because we can find the underlying theory and assume that grass will keep having that property.

At 5/17/2005 5:35 PM, Blogger Aaron Kinney declaimed...

Another intersting thought:

To properly define "grue" for the PoI, we need to stop defining it as a color and instead define it as a property that allows for the change of color. But then, the PoI must shift its attack, because the color changing of the "grue" grass would be consistent with its identity, and the PoI would instead have to attack the grue grass by proposing that at some future point in time, the grass may change to not have the property of grue.

What I think is that, with every example given for the PoI, we can point out the identity confusion and show that the PoI mistakenly defines its terms, such as "grue" and "water" (water that freezes at a non-water temperature).

However, I feel like Im going out on a limb, and Im anxious to see if anyone can show me where Im wrong, or where Im misunderstanding the PoI. But after reading Russells chapter 6, I currently think that the PoI really is nothing more than identity confusion. The PoI is like an argument with no teeth.

Induction can say that it would expect the future to somehow change, with proper causality. but the PoI seems to propose changes in identities without causality. In fact, the PoI depends on it. For when we recognize causality in induction, we can say that contradictions do not exist, and if there is an apparent PoI, its really just ourselves misidentifying the causes or factors invovled.

If anyone wants to provide another scenario where induction can fail (like grue or freezing water etc...) I will be happy to receive it. Im looking for such an example where the violation of identity is not apparent.

At 5/17/2005 5:36 PM, Anonymous Anonymous declaimed...

who has read Goodmans paper?

At 5/17/2005 5:39 PM, Blogger Aaron Kinney declaimed...

Lets imagine that water suddenly changed its freezing point. This would imply a problem of induction. But if we were to check our premises, and see that the change in the freezing point had a CAUSE, and was not uncaused, wouldnt that mean that induction did NOT fail?

Or if bread suddenly became poisonous (to take from Russells chapter 6), if we were to discover a CAUSE for the poison, wouldnt that mean that induction succeeded and the Problem of Induction was simply the failure to identify a cuase for the poison? It just seems to me that, no matter how you cut it, the PoI relies on uncaused causes and identity violations.

Can anyone confirm or refute my assertion that the PoI relies on a violation of causality?

At 5/17/2005 5:40 PM, Blogger Aaron Kinney declaimed...

Anon said:

"who has read Goodmans paper?"

I dont know. Maybe anonymous did?

At 5/17/2005 5:51 PM, Blogger Aaron Kinney declaimed...

More on Goodman's Grue analogy

"grue is, strictly speaking, not a colour but a complex property that is a function of both colour and time of first observation."

Hah! An admission from the evil secular wikipedia.

They are confusing analogies here. You cannot admit that Grue is NOT a color, and expect to compare it with green or blue (both strictly colors) in an analogy. You cant have your cake and eat it too. If gure is not strictly a color, then there is no problem to discuss! But wait, they continue:

"The problem is this. Let t be some moment in the future. Then "All emeralds are green" and "All emeralds are grue" are both true. So long as t has not yet arrived, every green emerald we find agrees with both sentences, but surely a green emerald is evidence only for "All emeralds are green", not evidence for "All emeralds are grue." The problem is to explain why not."

They are asking to explain or prove a negative. They are asking one to refute an unsupported assertion, since the future point of "T" has not yet arrived. How can one even propose that the GRUE color change will occur in the future unless they use induction? Otherwise, its an unsupported assertion.

This reminds me of the whole Invisible Pink Unicorn thing. You havent explored the entire universe, so you cant prove that an Invisible Pink Unicorn doesnt exist. Or you havent gotten to the future yet, so you cant prove that the emeralds are not GRUE.

The burden of proof is not on the Green/blue-er, but on the grue-er. It is the grue-er that asserts the property of grue with the emeralds, so it is the burden of the grue-er to prove that in the future, the emerald will switch to blue.

It looks like I got it right the first time I opened my mouth/keyboard on this topic. Burden of proof, people!

Jesus Christ how insane! Its a burden-of-proof confusion, mixed with an identity violation (strict color spectrum vs. property grue which is not a strict color), and also mixed with a causality violation (the PoI proposes uncaused causes).

At 5/17/2005 5:51 PM, Blogger Francois Tremblay declaimed...

"Lets imagine that water suddenly changed its freezing point. This would imply a problem of induction. But if we were to check our premises, and see that the change in the freezing point had a CAUSE, and was not uncaused, wouldnt that mean that induction did NOT fail?"

Well, that was my general point. Uniformity would only be broken if things changed in a way inconsistent witht their identity.

We're not always correct when we claim inductive reasoning, and that is where the confusion usually comes in. Opponents of induction will say that our mistakes in identifying something as being proper induction is a problem of induction itself. But this is a confusion between epistemology and metaphysics.

Let me illustrate. Suppose that it is the nature of water to change freezing point according to a given equation, because its molecules are clustering with time. The fact itself is observable. We say :

1. The freezing point of water (at sea level, and so on) is zero celsius.
2. The freezing point of water is zero celsius.
3. The freezing point of water is zero celsius.
Therefore the freezing point of water is zero celsius.

This is NOT induction because the property of freezing point is dependent on another variable, which has not been taken into account in observations at times 1, 2 and 3. Induction implies that we have found a property that depends directly on the identification we make (in this case, that we are observing water at sea level). But we haven't. This is same as the grue example.

Okay, I forgot what my point was, but I hope my post is clear enough.

At 5/17/2005 7:21 PM, Blogger Aaron Kinney declaimed...

"This is NOT induction because the property of freezing point is dependent on another variable, which has not been taken into account in observations at times 1, 2 and 3."

Hmmm. Im not sure if I understand exactly what you are saying, but I got an idea at least.

You mention the fact that in this instance we havent taken into account another variable.

The PoI basically supports contradictions in the identity of entities being observed/discussed. But if there is another variable that was unobserved, then there in fact is no contradiction (and the PoI is mistaken). It is simply that we did not take into account all factors, and therefore we didnt properly use induction in the first place.

Am I making any sense here? Am I understanding your statement on any level, or am I mistaking it?

At 5/17/2005 8:45 PM, Blogger Francois Tremblay declaimed...

Yes, basically you got it. Induction is no different than deduction : if you make a mistake and don't include something that is necessary for the property, then you'll get it wrong. This is not properly called a "problem of induction", but "mistakes".

At 5/18/2005 9:46 AM, Blogger Zachary Moore declaimed...


"The burden of proof is not on the Green/blue-er, but on the grue-er."

Ah, now I see. One might be able to conceive of any temporally changing property, but without evidence (damn, that tricky word again), it's just blowing smoke.

At 1/22/2006 3:49 AM, Blogger Brent declaimed...

Induction can be understood as a special case of deduction, but with the assumption of an important premise, called the Uniformity Principle (UP). It says that if two things are similar in 1 way, they are likely to be similar in other ways. The more similar they are, the more likely they are to be similar in more ways. This compounds when you are dealing with multiple objects of comparision. For example, if I have seen 100 birds which are exactly the same, except that 10 of them spit fire, if I see another bird that seems the same otherwise, there is a 1 in 10 chance he spits fire.

The answer to your water problem is actually the same as the grue example. Sure, you could define water as something having properties A, B, and X, X being "having a freezing point of 0 degrees C". If "water" suddenly started freezing at 5 degrees C, then in reality water would have ceased to exist everwhere, having been replaced with "water2", which has properties A, B, and Y, Y being "having a freezing point of -100 degrees C".

The point of the POI, however, is that unless we assume (have faith that) the UP is true, we cannot believe that "water" will likely exist one minute from now, or in a house I haven't been in. If I enter a new house I cannot put something with properties A, and B in the freezer and expect it to freeze (unless I believe the UP). I have absolutely no justification for assuming that this substance is "water" and not "water" unless I believe that the UP is true. Why would I even get a freezer? If I can't say that water will likely exist tomorrow, it seems irrational to buy one.

Let me rephrase the grew problem so it is clearer: At this time, all grass is green. But it is theoretically possible that all grass is also grueous (not a color), meaning that on February 15, 2006 it will turn blue. It is not that green changes to blue, but that the grass changes from green to blue. When looking at grass now, how do we know whether it is grueous or not? I would say that grass is most likely going to stay green (and thus is probably no gruous), because it has been green since it first evolved into its current form. But the only way I can be justified in saying that is if we assume the UP is true, without any empirical evidence or even a logical argument to back it up.

At 6/30/2006 10:44 AM, Blogger Gef declaimed...

Thanks for that, it's great to see a slightly different persepective on the topic.
BTW have you seen my new pup from Darksky Alaskan Malamutes? He's really a great pup.
Have a great day




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