Limited Non-Trivial Assumption Fallacy

[Kriminal99]

Induction Primer

 

This thread has to do with the limits of induction. For those of you that don't know, induction is the idea that future events will resemble similar past ones.

 

If the Sun rises every day for a million years, then it will probably rise tomorrow as well.

 

People likely have a natural capacity for this type of reasoning that, for example, helps you know where to reach for the alarm clock in the morning without looking for it.

 

As various philosophers have argued, there is no reason to trust induction other than that it usually works.

 

Limits of Induction Primer

 

Consider a grass lawn covered with snow. You roll a snowball across the lawn. As you roll, the ball grabs snow off the grass and the lawn is revealed. You swirl in towards the center from the edges of the lawn. You roll 95% of the snow off of the yard and everywhere you roll grass is revealed. Using inductive reasoning, you decide that removing the rest of the snow will reveal grass as well. You roll over the remaining 5% and find that there is no grass there, but rather a hole in the yard.

 

Consider this: The hole was there the entire time. The only reason we didn't think there would be one is because we didn't roll over the part of the lawn that had one yet.

 

The only reason Induction is useful at all is because metaphorically, the hole isn't usually at the end of our snowballs path. That doesn't mean it can't be, so induction THE PREMISE OF ALL HUMAN KNOWLEDGE can always be doubted.

 

Limited Non-Trivial Assumption Fallacy

 

Suppose earlier today you purchased gum and gave all but one stick to friends. You put the leftover stick in your pocket. Assuming that the man in the trench coat didn't pick pocket you in the subway stick of gum from you when you went through the crowded subway, you reach in your pocket. There is no gum in your pocket.

 

You think to yourself, Proof by negation, my assumption that my gum wasn't pick pocketed by the man in the trench coat is false. Hence you accuse the man in the trench coat of stealing.

 

What is wrong with this picture? It is wrong because there are an infinite number of "hole in the grass scenarios" that you also assumed did not happened. You just didn't recognize these assumptions consciously like you did in the case of the trench coat man pickpocketing you.

 

Other assumptions you REALLY made:

 

1) The person in the yellow coat didn't pickpocket you

2) The person in the red coat didn't pickpocket you

3) A person you did not see pickpocket you (infinite variations)

4) You gum did not fall out in your car

5) Your gum did not fall out at the station

6) Your gum did not fall out at an unknown location

7) The gum did not stick to the bottom of the last one you gave to your friend.

8) A piece of gum did not stick to the bottom of the one you gave to a friend but it is unknown which one

9) You counted wrong

10) An unknown but plausible thing did not occur to cause the stick of gum to not be there (infinite variations)

 

11) The gum ceased to exist because it's sub atomic particles behaved in an unusual manner

12) The gum ceased to exist because we live in a computer program and it was simply deleted to mess with your head.

13) The gum ceased to exist for an unknown reason (infinite variations)

14) The gum was warped out of your pocket by a space alien.

 

15) Any reason we have yet to understand could have caused the gum to not be there (infinite variations)

 

Note that prior to 11 there are still infinite plausible explanations that we did not think of. After 11 we denote explanations that are less plausible.

 

But since we are dealing with the unknown, all implausible means is that "the hole in the grass was at the end of the path". In other words everything we had experienced up to this point gave no indication that what happened now was going to happen.

 

Hence, "Proof by negation" is fallacious because every argument has infinite assumptions. This is necessitated by the limits of induction.

[REASON]

Good introduction to induction. I followed it completely.

 

So what's next? What would you like to discuss? :hihi:

[Kriminal99]

Well... Do you know why for example Bell's experiments only had the 3 assumptions he claims they had, when it seems to me according to the limits of induction he can't know what assumptions he was making?

 

If you like reading summarized philosophy I can summarize a few more topics that I understand. I'll post something tomorrow.

[Thunderbird]

Tell me if this fits into induction theory;

 

When we first started studying dino fossils, the beds were most always found within environmental layers indicating a warm swampy region. The early conclusion were drawn that large dino must have been swap dwellers, when in fact the reason was that’s just happens to be the right conditions for a depositional fossil beds to form.

[Kriminal99]

Exactly!

 

Scientists did not recognize their assumption that ultimately turned out to be false. Their assumption perhaps came from a comparison to some kind of useful technique like finding bat guano in a certain area to indicate where bats are. The assumption failed because of the time and number of events that passed between the bones being deposited and being found.

 

The whole point of the limit of induction, is that you don't know what assumption you are using that could ultimately fail.

 

When you use induction, you group what you think are similar experiences together but in fact no two experiences are ever exactly alike.

 

For instance, When I say that the sun will probably rise tomorrow, I am guessing that today is similar to all the other days that the sun rose. On all those different days, different things were going on in the world and the sun still rose.

 

When we claim the sun will rise tomorrow, we are basically assuming that tomorrow is like all those other days we sampled from in which the sun rose. Alike in every way relevant for the sun rising.

 

If a giant meteor full of foreign materials is going to hit the sun, then any day that wasn't happening is not a good indicator of what will happen when the meteor is there.

 

The funny thing is, to start we don't know what differences are significant or not. We just have to wait to see why our assumptions failed and look back in hindsight for information that can allow us to predict next time.

 

Thus when induction fails, the general assumption that has failed is that the new situation is like the old ones. It can fail, it often does fail, but if we don't make that assumption our choices are limited to nothing. We have no premises to reason from, probability theory breaks down, all human knowledge breaks down.

[Thunderbird]

This addresses an issue I've had with tetrapod evolution.

In current thinking the transition from fish to amphibians is characterized in artist renderings as a swamp dwelling creature grasping submerged branches, then crawling out of an estuary, swamp or lowland river system.

This scenario seems to me unlikely, in the fact that there would not be an sustained adaptive pressure to exit laterally outward from this environment onto land into smooth transitional phases.

 

 

 

A more likely scenario is for the tetrapod to migrate into the upland stream systems to spawn seasonally in a parallel direction with the river system.

This seasonal migratory path would provide a sustained cyclical pressure to advance upland as far as possible into the protected pools in the river bed that would be separated, yet connected by ever smaller streams of water. This upland streambed environment would provide the ideal spawning environment and also a smooth cyclical transitional pressure to migrate further into the highlands to reproduce in the protected pools void of the large predatory fishes.

Utilizing the theory of inductive reasoning Tetrapod evolution may have been misinterpreted because just like in the case of the dinos, fossils of the Tetrapods were only preserve in lowland areas of deposition, While the highlands were in a constant erosional phase leaveing behind a very scant environmental/fossil records.

[Erasmus00]

The only reason Induction is useful at all is because metaphorically, the hole isn't usually at the end of our snowballs path. That doesn't mean it can't be, so induction THE PREMISE OF ALL HUMAN KNOWLEDGE can always be doubted.

 

The exception, is of course mathematics. Here one starts with a specific set of axioms/assumptions and uses DEDUCTIVE reasoning to work out fundamental truths.

 

Now, if we ever start comparing a mathematical evaluation to the real world, we have to be careful about the limits of induction- all we can with experiment is DISPROVE the original mathematical axioms/assumptions. We cannot however prove them true.

-Will

[Kriminal99]

The exception, is of course mathematics. Here one starts with a specific set of axioms/assumptions and uses DEDUCTIVE reasoning to work out fundamental truths.

 

Now, if we ever start comparing a mathematical evaluation to the real world, we have to be careful about the limits of induction- all we can with experiment is DISPROVE the original mathematical axioms/assumptions. We cannot however prove them true.

-Will

 

Yes... Deductive reasoning doesn't provide any premises or do anything on it's own, but you can say "if X then Y" with relative certainty... Of course deductive reasoning itself may be something that we come to value through induction... but if we doubt that then we doubt everything.

[Erasmus00]

Yes... Deductive reasoning doesn't provide any premises or do anything on it's own, but you can say "if X then Y" with relative certainty... Of course deductive reasoning itself may be something that we come to value through induction... but if we doubt that then we doubt everything.

 

So then you've answered your own question about Bell's theorem. Bell starts with assumptions- measurements are local, measurements are deterministic. He then DEDUCTIVELY shows that measurements have certain bounds.

 

Experiments then show that these measurements are actually outside those bounds. Hence, we have to give up either locality, determinism, or deductive logic. Most physicists stick to locality, as a wide variety of experimental data can be explained with locality.

-Will

[Kriminal99]

The question about Bell was how it is believed that proof by negation is valid when a person really doesn't know what assumptions they are making.

[Erasmus00]

The question about Bell was how it is believed that proof by negation is valid when a person really doesn't know what assumptions they are making.

 

Because, as mentioned above, its DEDUCTIVE from a limited set of assumptions. I'm tired of explaining this to you over and over, so unless you bring up something new I'm done with this.

-Will

[Kriminal99]

Because, as mentioned above, its DEDUCTIVE from a limited set of assumptions. I'm tired of explaining this to you over and over, so unless you bring up something new I'm done with this.

-Will

 

You are not explaining anything you are refusing to read the question. The question is how can he know what assumptions he has made.

 

His set of assumptions is not limited nor does he know what they are.

 

If you believe you have some kind of point with this, I think you are misunderstanding the question. The argument shows how proof by negation is invalid when you actually try to use it for anything... It is not deductive reasoning at all.

[ughaibu]

It's sometimes claimed that the complexity of the world indicates a high likelihood for the existence of god and the fact of creation, but without any satisfactory notion of what god is or how creation works. So, we have an unknown substance (god) and an unknown process (creation) forming what we can call 'explanation 1' (x1). We can also suggest x2, which relies on unknown substances (US) and unknown processes (UP) but has nothing in common with x1, and we can suggest xn+1, which has US and UP and nothing in common with x1, x2........xn, thus demonstrating that without specification, god and creation is infinitely unlikely. Why does this inductive proof fail?

[Kriminal99]

It's sometimes claimed that the complexity of the world indicates a high likelihood for the existence of god and the fact of creation, but without any satisfactory notion of what god is or how creation works. So, we have an unknown substance (god) and an unknown process (creation) forming what we can call 'explanation 1' (x1). We can also suggest x2, which relies on unknown substances (US) and unknown processes (UP) but has nothing in common with x1, and we can suggest xn+1, which has US and UP and nothing in common with x1, x2........xn, thus demonstrating that without specification, god and creation is infinitely unlikely. Why does this inductive proof fail?

 

There are a few things wrong with that. For one there is more than one explanation that involves god and creation, in fact there are infinite. Thus if you are reasoning on the basis that the different explanations are equally likely, you would look at the ratio of god/creation explanations to non god/creation explanations. But this is meaningless because you are dealing with ratios of infinity. It is one thing to say that 3X/5X as x -> infinity is 3/5, but this is different. In the X case the two infinities have the same properties, ie they grow at the same rate etc.

 

Next you can only treat them as being equally likely when you have no information to reason upon. We have information regarding both theories so we would have to use that information to evaluate instead.

[ughaibu]

All god/creation explanations are in x1, it doesn't matter if there's an infinite number of them, they're infinitely improbable, as demonstrated.

In any case, what does your objection have to do with assumptions and the failure of induction?

[Kriminal99]

All god/creation explanations are in x1, it doesn't matter if there's an infinite number of them, they're infinitely improbable, as demonstrated.

In any case, what does your objection have to do with assumptions and the failure of induction?

 

You tell me, you brought the argument up?

 

Anyways, you can't squeeze all God/Creation explanations into the first one and then allow other explanations to be infinite in number. There are infinite God/Creation explanations just as there are infinite other types of explanation. The "divide the one explanation by infinite possible" trick only applies if there were really only one explanation involving God.

 

I suppose you could use reason to try and argue that the ratio of infinite god explanations to infinite other explanations was small but that would be pointless since you can only use the "equally likely" model in the absence of information about which is more likely.