Monday, December 10, 2007

Induction and Deduction, Segue Into A Priori

The problem of induction has always bothered me. It has never seemed to me like a problem at all.

And now I can prove it.

Deduction works by elucidating the relationships between concepts. The problem is, for creatures;born, there's no way to obtain concepts except through induction. This includes evolving to be born with certain concepts, as the genetic material does not inherently know anything, and must learn entirely through trial and error.

As a result, in practice, deduction is always a sub-discipline of induction. Thus the 'problem of induction' was itself found using induction. As a result, to throw out induction is to throw out the problem of induction, allowing induction once more...and there's a barber I'd like you to meet.

Also as a result of this fact, a priori is clearly an invalid concept. All concepts are a posteriori, including a priori.

No, the only way the problem of induction is an actual problem is if you're actually some kind of infinite consciousness, in which case you'd know things just because you're an infinite consciousness. Presumably, you'd then use your mighty infinitude to solve the problem in an infinitesimal instant.


First Principles

Because deduction is in effect a species of induction, a priori knowledge in the usual definition doesn't exist.

Therefore, I will redefine it.

A conclusion reached from first principles or a priori was reached through the logical consequences of the definitions of the concepts involved.

Such a proof always applies if the concepts apply; this is why a priori proofs are so valuable, which is why they are so prized.

My favorite type of proof is what I call an a priori hammer of Thor. Such a proof is true a priori, and even if you disprove the existence of some of the premise-concepts, you end up at the same conclusion. While the details of the proof will change under various assumptions, the conclusion will not. Such a proof is a thorough examination of a full tree of yes/no questions, where each terminating twig is identical.

Such proofs are transcendentally true. They are true regardless of concepts, and depend only on the rules of logic themselves. Such conclusions are probably true in not only all universes, but all possible universes. (Including that infinite consciousness.)

17 comments:

Andrew Crawshaw said...

You said "the only we can obtain concepts is through induction" my response is that induction is false, so that your "the only way obtaining concepts" by modus tollens is an incorrect premise, we gain knowledge also through guesses and trying to refute those guesses. Induction is not proved wrong by induction it is proved wrong by a simple and elegant (whough inverse to your) argumant, that to justify induction you need recourse to induction (circular argument). Deduction is not aquired through induction, it was aquired by accident like most other knowledge and the reason we kept it was orignally because humans thought it was usefull, but really because it has survived many tests to refute it.

Alrenous said...

You're begging the question. You have to justify deduction before you're allowed to use modus tollens.

Yes, I did just demand you justify justification. Do you see how I'm mimicking your strategy in reverse?

Andrew Crawshaw said...

No, you first have to justify induction before you can assume it is somehow part of reality, in the way that you say it is. Deduction is not an empirical principle but a logical one, if you find something wrong with deduction (no one has ever falsified it), please state your disagreement explicity. and then I will answer it. whereas induction is not justified logically or empiricaly.

ok, here goes, induction cannot lead to knowledge one) because to grasp induction you first have to have induction as part of your tool kit, but that is impossible.

second) no amount of evidence gives you warrant to apply that evidence beyond the data.

you said induction is the only way we can gain concepts, the above warrants my modus tollens therefore your assumption is incorrect; if p then q, not-q, therefore not-p.

if you have to gain concepts through induction, how did we get come across induction?

Alrenous said...

Deduction is no more a non-empirical principle than induction is. Look at it from the other direction: if empirical evidence suggested that deduction didn't work, would you throw out the evidence or deduction?

By contrast,
"second) no amount of evidence gives you warrant to apply that evidence beyond the data."

Empirically, people generalize from raw datasets all the time and it works fine.

"if you find something wrong with deduction"

I believe deduction is useful.

"induction cannot lead to knowledge one) because to grasp induction you first have to have induction as part of your tool kit, but that is impossible."

Deduction/logic cannot lead to knowledge because to grasp deduction/logic you first have to have deduction/logic as part of your tool kit, which contradicts the premise that you're grasping it.

Ergo, logically you cannot know logic. Curious state of affairs, don't you think?

" the above warrants my modus tollens"

Err, no? My point is that it doesn't.

"if you have to gain concepts through induction, how did we get come across induction?"

You get it for free. Brains occur by chance. They are organized by chance. The ones that happen to implement a useful epistemology survive. Gene pools learn as an unavoidable consequences of physics.

Again: gene pools learn to make useful brains, which can then go on to embody more traditionally restricted definitions of learning.

This dynamic certainly isn't deduction. So, by process of elimination...

Drew Zi said...

"Deduction is no more a non-empirical principle than induction is. Look at it from the other direction: if empirical evidence suggested that deduction didn't work, would you throw out the evidence or deduction?"

Deduction is a logical concept. induction has no logical warrant, so tpositivsts tried to look for an emprical warrrant which lead to an inifinte regress. Modus tollens, my friend.


>"By contrast,
"second) no amount of evidence gives you warrant to apply that evidence beyond the data."
Empirically, people generalize from raw datasets all the time and it works fine."<

They do not "generalize from raw data sets", they guess what the data means, and try to apply to data that does not exist yet. this is guess work, and through guess work and criticism we come up with a theory

>""if you find something wrong with deduction"

I believe deduction is useful."<

and logical? Unless you are a pragmatist?

>""induction cannot lead to knowledge one) because to grasp induction you first have to have induction as part of your tool kit, but that is impossible."

Deduction/logic cannot lead to knowledge because to grasp deduction/logic you first have to have deduction/logic as part of your tool kit, which contradicts the premise that you're grasping it.

Ergo, logically you cannot know logic. Curious state of affairs, don't you think?" <

Are you seriously claiming that induction and deduction are attempting to solve the same problem? the way we come across concepts is by conjecture (guesses) all knowledge we have is a guess right down to guessing what our own senses are telling us. that is how we aquire knowledge then we use deduction to build logical implications of our guesses and then criticism to refine them and then science to try to refute them.

?" the above warrants my modus tollens"

Err, no? My point is that it doesn't.

"if you have to gain concepts through induction, how did we get come across induction?"

You get it for free. Brains occur by chance. They are organized by chance. The ones that happen to implement a useful epistemology survive. Gene pools learn as an unavoidable consequences of physics.
"
isn't "by chance" the better explanation for the process you call induction, or have you subtly appropriated a concept and put it under the title "induction" that concept being evolutionary epistemology. Trial and error is not induction.

the fact that you say we get it for free refutes your idea that we get our knowledge from induction. That is two strikes against induction. Usually critical rationalism only allows one; the two are

1) induction leads to an infinite regress
2) we got the knowledge of induction by chance, therefore not all knowledge requires induction.

"Again: gene pools learn to make useful brains, which can then go on to embody more traditionally restricted definitions of learning."

this borders on nonsense. gene pools don't learn to make useful brains, brains survive by being useful.

"This dynamic certainly isn't deduction. So, by process of elimination..."

this dynamic is called chance. You seem to have no idea what problem induction was trying to solve, it tried to solve both where we get our knowledge from and how we apply that knowledge beyond the data set. it can't account for either.

(this is a new account because I wanted to get my blog inline with my youtube).

Andrew Crawshaw

Drew Zi said...

"You're begging the question. You have to justify deduction before you're allowed to use modus tollens.

Yes, I did just demand you justify justification. Do you see how I'm mimicking your strategy in reverse?"

I am not a justificationist I am a fallibalist, who uses criticism and refutation. Induction has been successfully refuted, deduction has not.

the problem with induction is because it is inherently a justificationary tool, whereas deduction in an inferential tool.

Alrenous said...

Do you want to know why you've failed to convince me?

Drew Zi said...

Can we avoid "meta" discussions, please.

have you got any rebuttals to what I said?

Alrenous said...

We can't avoid meta, because the meta is broken.

When I last provided rebuttals, it produced no effect. I am forced to conclude I wasted my time.

Drew Zi said...

Thanks for the discussion.

Shlomo Maistre said...

"Deduction works by elucidating the relationships between concepts. The problem is, for creatures;born, there's no way to obtain concepts except through induction. This includes evolving to be born with certain concepts, as the genetic material does not inherently know anything, and must learn entirely through trial and error.

As a result, in practice, deduction is always a sub-discipline of induction."

False, false, and false.

Deductive reasoning eventually beats inductive every time.

It's hardly off-base to doubt whether inductive reasoning is real at all.

Alrenous said...

Kindly try including information in your comment next time. That was merely annoying.

Shlomo Maistre said...

"The problem is, for creatures;born, there's no way to obtain concepts except through induction."

Man is quite literally born with an implicit understanding of truths. There must be such a thing as a priori knowledge, for if there were not then man would be incapable of learning new information.

But it's deeper than that. Man knows because he knows. New information is merely a reminder of inherently universal truth man is faintly aware of by virtue of his birth.

"This includes evolving to be born with certain concepts, as the genetic material does not inherently know anything, and must learn entirely through trial and error."

Man is indeed born with certain concepts and the genetic material, as it is not a conscious being, does not inherently know anything. But man does not entirely learn through trial and error; man learns mostly - if not entirely - by deductive reasoning. He knows certain things - or is at least made aware of his knowledge through experience- and thereby deduces other things that must be true as a consequence of recombinations of his understanding and experiences.

"As a result, in practice, deduction is always a sub-discipline of induction."

Deductive reasoning trumps inductive reasoning every time - eventually. Mencius Moldbug explains:

"Science, if it means anything, means scientific reasoning. "Scientific" being an adjective, "scientific reasoning" is a subset of "reasoning." Why are certain inductive methods, in certain cases, reliable? Because we deduce that they are so. It's not that reason works because reason is scientific. It's that science works because science is reasonable.

Since science works because science is reasonable, we can distinguish between science that works, and science that doesn't work, by the exercise of reason. Ie, by philosophy. For instance, philosophy tells us: does this science make falsifiable predictions? If so, it probably works. If not, probably not. As the Bible says, the tree is known by its fruit."

Shlomo Maistre said...

I like to think I’m about as extreme a Platonist and rationalist (as opposed to empirist) on epistemology and metaphysics as one can be. I’m a hard dualist on the mind-body problem and believe in a priori knowledge and universals. I think that all true propositions are inherently analytic (not synthetic), that essence is prior to superior to, separate from existence. But most importantly I think that all these views are one and the same (belief in abstract/divine), come from intuition/faith, and lead not to the correct “politics” but to the right understanding of politics.

One way to sum this up would be that theology is the only proper form of philosophy.

Alrenous said...

That's what I was asking for, and I appreciate the consideration.


and thereby deduces other things that must be true as a consequence of recombinations of his understanding and experiences.

Sic et non.
Man can't previously know his sensations. There would be no need to perceive things if it were already known.
However, it is true that these sensations, once they appear, are analyzed entirely through deduction. I had not previously appreciated this. I will consider it at length.



Mencius Moldbug explains:

Moldbug is incomplete.
Science works because it is reasonable. We know reason works through experience. At least, conditional on the above-mentioned consideration.



rationalist (as opposed to empirist)

Properly appreciated these things are the same, not in opposition.



I’m a hard dualist on the mind-body problem

Have you read my latest proof on that subjection? I believe I've finally nailed it.



that essence is prior to superior to, separate from existence.

That's self-contradictory. Existence is a kind of essence. The essences that matter (e.g. are worth knowing) are the ones that exist, meaning existence has to be superior to or more fundamental than essence.



come from intuition/faith

Sounds confused.

That said I'm currently sympathetic to the idea religion as a separate category comes from special pleading. Philosophy is a religion. Science is a religion. Is a Christian who doesn't take their faith out of the Church a real Christian? Take it to work? Take it home?

Shlomo Maistre said...

1. "Man can't previously know his sensations."

Agree, but where did I suggest otherwise? I said that certain truths are faintly understood by man by virtue of birth - not that man knows sensations prior to feeling them.

2. "There would be no need to perceive things if it were already known."

First of all is there really a "need" to perceive anything? More seriously - I think I know what you are getting at - man lives and as a consequence of living must experience. In order to more efficiently/properly interact with his environment it helps to perceive reality as accurately as possible.

3. "However, it is true that these sensations, once they appear, are analyzed entirely through deduction. I had not previously appreciated this. I will consider it at length."

Sounds good.

4. "Science works because it is reasonable."

But how is science assessed as reasonable? The ultimate, final answer must be: via philosophy, which is to say by way of deductive reasoning.

5. "Properly appreciated these things are the same, not in opposition."

How is that?

Rationalism considers knowledge to primarily come via ways other than the senses, while empiricism considers the senses as the primary means by which knowledge is acquired. There are perspectives that may to varying degrees combine both approaches, but ultimately they are divergent viewpoints.

6. "Have you read my latest proof on that subjection? I believe I've finally nailed it."

I have not. Link please?

7. "Existence is a kind of essence."

Existence is an instance of an essence.

8. "The essences that matter (e.g. are worth knowing) are the ones that exist, meaning existence has to be superior to or more fundamental than essence."

The opposite is true. All essences are worth knowing and existence is contingent on essence in every instance of it. Plato was right; Aristotle was wrong.

Human understanding can only ultimately derive from a priori knowledge. Man can only ever know because he knows – i.e., it is in his nature. Man is born with memories (a priori knowledge) that through his experiences he remembers as recollections of the universals by which the mortal domain was formed.

Alrenous said...

1.
Man is born able to perceive, but perception is constructed by trial and error. I would call that induction. A perceptive system works once, therefore it's always used afterward. Similarly, man thinks using a machine that was constructed the same way.

4.
The ultimate assessment is whether it achieves our goals, and thus serves its purpose. This is done empirically: we try science, and if it works for us, we induce we should keep doing it.

Certainly, with sufficient philosophical skill, we can basically guarantee it will work. Which philosophy is done through deduction. However, the ultimate point is to practice science, to try it out, to experience it empirically. It cannot serve us unless we experience using it. Empiricism would be the final test even if we could 100% guarantee we didn't need it.

Further, we learn philosophy in the first place inductively. Either through evolution teaching our genes which teach our brain, or our brain using its basic learning capacities to observe identities and causation.
We know what is philosophical by asking physics to test our theories of logical implication. Physics is quite forthcoming with this information, it turns out, meaning it's so easy to learn we often forget it must be learned. (Hail physics.)

5.
It's rational to test things.
Empirically, rational thought works - Einstein derived Einsteinian relativity from Maxwell's equations, and he was simply correct.

In other words, A => B and B => A, meaning A=B. They are different sides of some more fundamental identity.

This mirrors the subjective/objective relationship, so the fundamental identity is probably existence.

6.
http://alrenous.blogspot.com/2015/09/morality-1-subjectivity-and-objectivity.html

7.
Instance = kind_of

8.
While I'm glad to have a Platonist around, so I hope you'll be stubborn...you are certainly incorrect. All intrinsic kinds of worth have been contradicted. There is only relative worth - worth to, e.g. me in particular. Some essences it does not profit me to know. They are worthless to me. In particular, essences that refer to sensations I will never encounter.

Some will probably be worthless to everyone. Specifically, the essences which refer to entities that cannot be interacted with.

While it was understandable that Plato would posit a priori knowledge, it is now not only possible, but easy, to show how almost all knowledge is a posteriori.

The exception being zeroth level qualia. The immediate sensations of the mind are not knowledge, but that through which things are known.

The previous paragraph seems unclear. Possibly even untrue. I will have to consider it at length.