An Arrogant Acerbic Attempt to Acertain and Attack the Axioms found within the Problem of Induction

Bet you thought I'd do that Annoying Alliteration all the way through didn't you?

This week I finished "Language, Truth, and Logic" by Ayer. And I found myself remarking over and over "wow... this guy simultaneously loves and hates Hume." So, after finishing Ayer, I picked "An Enquiry Concerning Human Understanding" back up, wondering if I'd get anything more out of it the second time through. And lo and behold, I did.

So here's my go at critiquing Hume.

In this essay, I intend to do three things:

  1. Introduce Hume's problem of induction to those who aren't familiar with it
  2. Show my proposed solution to the problem
  3. Critique my own position and try to find the holes in my logic(because there's no possible way a 19 year old second year philosophy student could solve the problem of induction, so I've gotta be wrong somewhere)

The Problem of Induction

In this section I intend to summarize the Problem of Induction simply and cogently so that someone who hasn't read Hume can understand it.

Very early on in the Enquiry, Hume differentiates between "Matters of Fact" and "Relations of Ideas."
  • Matters of Fact are claims we make about the world. For instance "David Hume looked like a potato" is a Matter of Fact. Most importantly, Matters of Fact aren't inherently true. For instance, David Hume could just as easily not look like a potato. I will henceforth be calling Matters of Fact a posteriori ideas because I'm a lot more used to that terminology.
  • Relations of Ideas are claims we make about pure logic. For instance, "a statement can't be true and false simultaneously" is a relation of ideas. Relations of Ideas are inherently and eternally true. For instance, it is nonsensical to assert that an idea can be true and false simultaneously. I will henceforth be calling Relations of Ideas a priori ideas because again, I'm more comfortable with that terminology
But how do we justify either kind of reasoning? Why do we think they have any bearing on reality?
  • A-priori knowledge is easiest to justify, it is true because it is literally impossible to deny an a-priori statement.
  • A-posteriori knowledge is a lot harder. How do I justify claims about the world around me? 
    • The answer is experience, for instance I know windows are fragile because they tend to break when I throw stuff at them for instance 
Well ok, that works fine for stuff I've already experienced. But then what justifies making predictions about the future? Why do I think the window will break the next time I throw something at it? Why can I make a claim about something about which I have no experience?
  • I could justify it via a priori logic- But that doesn't work because the opposite of a causally reasoned conclusion is not logically impossible(which a priori truths have to be.) For instance, it is not logically impossible for a window to remain intact when I throw something at it
  • I could justify it via past experience, for instance in the past windows have all broken when rocks were thrown at them. But what makes me think windows will continue to break in the future?
In other words, why do we think similar causes yield similar effects? Well, Hume just decided to run through all the possibilities
  • So could like causes, like effects be justified by:
    • A priori logic? No because like above, it is not logically impossible for tomorrow not to be like today
    • Could it be intuition(in the Cartesian sense)? No, because we don't know anything a posteriori from birth, only some limited a priori truths
    • Could it be past experience? We've seen previously that like causes have like effects, every time I've eaten the bread previously it has nourished me, thus it will nourish me in the future
Hume concluded that the best possible explanation would be grounding induction(the future will be like the past) in experience(historically the future has been like the past.) 

Do you see the problem? We've just grounded inductive reasoning in inductive reasoning! 

In short, the claim we've just made is 

The future will be like the past because the past has been like the future

Which is tautological, you can't ground the validity of experience in experience! 

To put it another way, we are trying to explain why past experience is relevant to future experience. But we cannot do that without grounding our argument in past experience, which we can't assume is relevant because that's what we're trying to prove in the first place!

My Take on the Whole Debacle

My main critique of Hume's logic lies within the definitions and distinctions he makes between induction(a posteriori) and deduction(a priori.)

For my argument we have to take two things as axiomatic:
  1. God does not exist(some of you might have to stop right here)
  2. Natural Laws govern the way the universe functions
If we take those two things as axioms, we can move on.

The crux of my argument lies in the distinction made between deduction and induction. Remember, most importantly deductive truths are impossible to deny cognitively(it is literally impossible to believe the alternative.) For instance, try as you might it is cognitively impossible to believe that 1+1=3.

Induction is the opposite. It is possible to deny inductive truths, for instance it is possible to believe that Donald Trump is not president. The important thing is, inductive claims do not have truth baked into them.

I intend to challenge the distinction.

How can I deny deductive truths?

I will begin as Hume does, with a question. Is it possible, cognitively, to deny that certain deductive truths exist? For instance, is there any scenario where I could believe that 1+1 is 3? If we go a little more complex, it is entirely possible. I'm bad at calculus, thus every time I do a calculus problem wrong I am in effect denying that the outcome is the true one.

Someone defending Hume would reply that I am simply mistaken, and am not denying the truth, I simply have inadequate information. And that by recognizing that I've done something "wrong" I am asserting that there is one truth in the first place.

Keep that in the back of your mind for now, and let's change gears to induction.

Are There Inductive Truths That Cannot be Denied?

Imagine, for a second, that you are an omniscient being. Not all powerful, just all knowing.

Imagine, as stated in our axioms, that you know every natural law and that those laws are the only things governing the universe(because there is no god to break them.)

If we grant that the universe is predictable(because natural laws behave consistently) then you would be able to see every event from the beginning to the end of time(if given adequate time to work out how the laws would interact and play off of one another.) Thus, if someone walked up to you and said "Global Warming is not real" it would be literally cognitively impossible for you to deny it. If you know everything that will occur, then assenting to any other possibility becomes impossible because that possibility is simply impossible!

Normally inductive truths are probabilistic because we have inadequate data. I am 99.99999% sure Donald Trump is(unfortunately) president, but there is always a slim possibility my senses decieve me. But if I knew everything about the universe and all its laws, all of a sudden truths about the world would become undeniable.

So as of now, my probabilistic inductive truths are only really untrue because they might be wrong... They are a probabalistic reflection of an absolute truth(which I could know if I had adequate brainpower and time.)

Tying These Two Together

Does this sound familiar to you? Making a probabilistic reflection of an absolute truth? Almost like doing a... math problem?

Whenever we do math problems there is a possibility that we will be wrong. This is due to inadequate information. Whenever we make a claim about the world there is a possibility that we will be wrong. This too is due to inadequate information.

Since we can be wrong about both induction and deduction because of inadequate information, there seems to be no reason to differentiate between the two. At best we could differentiate based on one dealing with physical reality and the other dealing with logical matters but that's pushing it.

What I Hope to Have Accomplished

I think I have simultaneously demonstrated the flaws of deductive reasoning and the merits of inductive reasoning

Under my revised(very Spinoza-esque) system, our claims about the world around us should be probabalistic, and regarded as math problems. Some math problems are very hard, and some are very easy. The same applies to inductive truths. But the more adequate ideas we have(Spinoza is the man, everything can be tied back to him,) the closer we can come to being 100% sure about our solution to the universe's big math problem.

Potential Problems with my Solution

The biggest hole I see here is I presuppose natural laws exist, which we can't really establish without using induction(which I am trying to prove the viability of in the first place)

I personally don't think this is that big a deal as the alternative is saying that the universe is just random and incomprehensible, which is just an asinine claim.

However, I will grant that I attempt to show the validity of induction by using tools found via induction.

I doubt this is the only flaw, and if any of you see logical errors feel free to point them out?

Also, Hume really does look like a potato. The man had no chin.

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