Induction, Popper, Falsification

[ZenKitty]

I was reading through some of Language, Truth, & Logic by A.J. Ayers and started to wonder when he talked about empirical hypothesis under the verification theory of science. Ayers pointed out that it was based on the Induction.

"The answer is that (empirical hypotheses) are designed to enable us to anticipate the course of our sensations. The function of a system of hypotheses is to warn us beforehand what will be our experience in a certain field- to enable us to make accurate predictions. The hypotheses may therefore be described as rules which govern our expectation of future experience. There is no need to say why we require such rules. It is plain that our ability to make successful predictions depends the staisfaction even our simplest desires, including the desire to survive."

&

"We remark, then, as a fact that our forecasts of future experience are in some way determined by what we have experienced in the past. And this fact explains why science, which is essentially predictive, is also to some extent a descritpion of our experience...But even if we do not follow past experience slavishly in making our predictions, we are guided by it to a very large extent. And this explains why we do not simply disregard the conclusion of an unfavourable experiement. We assume that a system of hypotheses which has broken down once is likely to break down again...We alter our system because we think that by altering it we shall make it a more efficient instrument for the anticipation of experience. And this belief is derived from our guiding principle that, broadly speaking, the future course of our sensations will be in accordance with the past."

But Popper was against the verificationist theory of science and supported Hume's critique of Induction and said that science did not rely on it or need it. Here is what he said about the problem of Induction in his Logic of Scientific Discovery.

“According to a widely accepted view- to be opposed in this book- the empirical sciences can be characterized by the fact that they use ‘inductive methods’, as they are called. According to this view, the logic of scientific discovery would be identical with inductive logic, i.e. with the logical analysis of these inductive methods.”

“It is usual to call an inference ‘inductive’ if it passes from singular statements (sometimes called ‘particular’ statements), such as accounts of the results of observations or experiments, to universal statements, such as hypotheses or theories. Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white.”

Here is Popper's solution, which is falsification and supposedly deductive and not inductive.

“If this decision is positive, that is, if the singular conclusions turn out to be acceptable, or verified, then the theory has, for the time being, passed its test: we have found no reason to discard it. But if the decision is negative, or in other words, if the conclusions have been falsified, then their falsification also falsifies the theory from which they are logically deduced…I never assume that we can argue from the truth of singular statements to the truth of theories. I never assume that by force of ‘verified’ conclusions, theories can be established as ‘true’, or even as merely ‘probable’.”

Popper appears to have to resort to saying that if we have a theory that makes a false prediction, then it shall make that false prediction in the future as well. So say that I have the theory that says apples will not fall when you let go of them from your hand. You let go of it and it falls to the ground. This would falsify your hypothesis, and so you would reject it. But why would we reject it when it made a false prediction when it can make the same prediction for the next time and it ends up being correct.

The point appears that Popper's idea of elimination by false prediction relies on induction when Ayer said, "And this explains why we do not simply disregard the conclusion of an unfavorably experiment. We assume that a system of hypotheses which has broken down once is likely to break down again." We discard theories because when they make false predictions we come to expect them to continue to still be wrong on the same thing, and have more falsity in it when we find one thing. This is because we know it from past experience that this happens. So it appears that Popper's ideas themselves still rely on a universal idea that appears to be inductive. IF it is not inductive then it is tautological and carries no empirical content. This would appear to mean that Popper still falls for Hume's problem of Induction.

Popper even appears to admit as much when he said, "My proposal is based upon an asymmetrybetween verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements. Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the 'inductive direction'; that is, from singular to universal statements."

So it appears that Popper contradicts himself in saying he has solved the problem of induction. He says that Induction, which his position opposes, moves from singular statements to universal statements, but now he admits that his position eventually falls for moving from singular statements to universal statements. So to solve the problem of induction he uses the problem of induction. So he again falls for Hume's problem of induction.

[Ed3]

Hi Zen Kitty,

As you point out, Hume and Popper both rejected induction as a “proof” of any empirical judgment.

However Popper generally felt that if a hypotheses implied a prediction, and the prediction was falsified then the hypothesis was false.

This springs from a simple valid logical argument.

If A implies B, then not B implies not A.

Here we will set H to be the Hypothesis and P to be the Prediction.

For example if the Hypothesis is: (the Earth rotates counter clockwise as viewed from the North Pole AND (the Sun is stationary AND sufficiently rotated with respect to axis between the North and South Poles)), then the Prediction will be: (the Sun will appear to transit the Earth from the East to the West).

Some freshman philosophical questions were framed around whether or not we could prove that the Sun always rose in the East.

Hume and Popper would say that no matter how many times the Sun appears to transit the Earth from the East to the West you can not conclude: the Earth rotates counter clockwise as viewed from the North Pole AND (the Sun is stationary AND sufficiently rotated with respect to axis between the North and South Poles).

As far as I know, their somewhat counter intuitive analysis has never been discredited.

Popper’s insight was that from the logical implication if A implies B, one could draw the logical inference that Not B implies Not A.

Again looking at this from the point of view of Science, and substituting H for A and P for B, we have that if H implies P then NOT P implies NOT H.

Logically, if we can show any prediction to be false, then the associated Hypothesis must logically be false. If Not P implies Not H then H is false and it needs not rely on any other examples,

We do not need to find any additional samples, or continue to falsify the Hypothesis.

Recapping: a “proof” by induction traditionally requires multiple empirical tests and never is logically valid. Whereas, Falsifying a Hypothesis requires only one empirical test and is always logically valid*.

*Nothing is actually that simple because the Hypothesis may not actually imply the Prediction. Furthermore the empirical test that Falsifies the Prediction must be done rigorously examining not simply for engineering tolerances but also for fundamental biases in our world view.

Thanks Ed

[James S Saint]

This springs from a simple valid logical argument.

If A implies B, then not B implies not A.

Emmm... "valid"??
I don' think so.

..unless you are using "implied" and "valid" in a very loose sense.

But I agree that a single failure disqualifies a hypothesis (except for QM).

[Ed3]

Hi James,

I should have specified that I was assuming a bivalent logic.

If you still disagree, I think that I would like to hear more from you.

Thanks Ed

[Flannel Jesus]

This springs from a simple valid logical argument.

If A implies B, then not B implies not A.

Emmm... "valid"??
I don' think so.

I'm not sure if you're kidding or if you're talking about some obscure form of logic or if you're being uber-pedantic, but in the off chance that you're just making an error (which is my hypothesis), what he said is just Modus Tollens, which is in fact, within the system of formal symbolic logic most commonly used, very valid.

[James S Saint]

I have to guess at what you mean by "bivalent".
If you mean exclusivity, then I would agree.

"If only A->B then !A->!B"

..and "modus tollens" is presumptuously false.

A->B does not equate to B->A

There must be an exclusivity concern stated premising that ONLY A->B.

In other words, something else, perhaps C could imply B as well.
In which case, B would imply EITHER A or C... or some other possible cause of B.

[Flannel Jesus]

*Nothing is actually that simple because the Hypothesis may not actually imply the Prediction. Furthermore the empirical test that Falsifies the Prediction must be done rigorously examining not simply for engineering tolerances but also for fundamental biases in our world view.

Glad you put in this caveat, I was hoping to see something like that.

You're exactly correct, it's not always so cut-and-dry as implied by just the pure Falsification approach. Sometimes a theory implies a prediction, but not with 100% certainty -- ie, if TheoryA is correct, then I could perhaps have 70% chance of making ObservationA in a given experiment. But if ObservationA turns out to not occur, that doesn't mean that TheoryA is false, it just means that TheoryA now has some evidence against it. If, on the other hand, TheoryA being true implied 100% chance of ObservationA, then failing to see ObservationA would completely falsify TheoryA.

Eliezer Yudowsky put it best: Popper's approach to falsification is just a specific instance of the more general theory of Bayesian Probability.

[Flannel Jesus]

James, you're very confused. Very much so. The fact that you think somebody is saying that A -> B equates to B -> A tells me that you really don't understand what Modus Tollens is, because you're certainly not talking about it. Nor do you understand what you're disputing.

I know you're smart enough not to make this mistake, refrain from responding until you've figured it out please. I'm trying to help you here. You're making a big error, one that I think you're smart enough not to make.

[James S Saint]

James, you're very confused. Very much so.

Haha.. yeah right...

The fact that you think somebody is saying that A -> B equates to B -> A tells me that you really don't understand what Modus Tollens is, because you're certainly not talking about it. Nor do you understand what you're disputing.

I know you're smart enough not to make this mistake, refrain from responding until you've figured it out please. I'm trying to help you here. You're making a big error, one that I think you're smart enough not to make.

Gyahd..

Modus Tollens
It is the inference that if

1. P implies Q, and the second premise, Q, is false,
2. Then it can be logically concluded that P must be false.

That is exactly;
If A->B then B->A

[James S Saint]

Oopss.. oopss.. okay, okay... sorry.. brain slip here...

If A implies B, then NOT B implies that A was not present.

Sorry, you guys were right.


..proving once again that even us "Saints" can screw up now and then.

[Flannel Jesus]

I know that from your point of view it's hard to see, but you're making yourself look very silly right now. This is not up for dispute. This is logic 101. You're incorrect, and PROFOUNDLY so. Unless you're trying to dispute the very foundations of logic, then you're making a mistake. Please, please, please take a break from posting and read about it, think about it, you WILL, I promise, discover that you're in error, and you'll blush a bit when you find out. I don't want you to keep going down this road, I respect you too much to see you make such a gross error. Please, I beg of you, stop and figure out exactly why you're wrong before you post again.

[edit] gotcha.

[ZenKitty]

However Popper generally felt that if a hypotheses implied a prediction, and the prediction was falsified then the hypothesis was false.

Right, but the problem I pointed out that this is inductive. In the past we have noticed that if a theory makes a false prediction in the scope of X, then it will continue to make false predictions in the scope of X. So this is an inductive argument. Because it was false in the past it will be false in the future. So this would mean that we beg the question. My point is that Popper wants to escape and "Solve the problem of Induction" by using Induction.

Example: If X then Y; Y; Therefore X. This is inductive in that we think it will be Y next time.
If X then Y; ~Y; Therefore ~X. This is inductive in that we think it will be ~Y next time. This is inductive.

[James S Saint]

However Popper generally felt that if a hypotheses implied a prediction, and the prediction was falsified then the hypothesis was false.

Right, but the problem I pointed out that this is inductive. In the past we have noticed that if a theory makes a false prediction in the scope of X, then it will continue to make false predictions in the scope of X. So this is an inductive argument. Because it was false in the past it will be false in the future. So this would mean that we beg the question. My point is that Popper wants to escape and "Solve the problem of Induction" by using Induction.

Well now that one isn't exactly the way it happens (assuming that I have had enough COFFEE!).

The idea in performing an experiment is to control the setting such as to eliminate any possibility of alternate causation. This sets up the "Equivalence Principle" - Equal Situation yields Equal Result. So in the future if, and only if, the situation is exactly the same then the result will be the same.

So even if you propose that the laws of physics get changed some time in the future (which is logically impossible), the experimental evidence is still valid because assuming that the laws of physics did actually change, then the situation has changed and you no longer have the same experiment.

[ZenKitty]

[The idea in performing an experiment is to control the setting such as to eliminate any possibility of alternate causation. This sets up the "Equivalence Principle" - Equal Situation yields Equal Result. So in the future if, and only if, the situation is exactly the same then the result will be the same.

The problem is that you are relying on Induction for this answer, and Popper rejected Induction, so it follows that this is to be rejected.

So even if you propose that the laws of physics get changed some time in the future (which is logically impossible), the experimental evidence is still valid because assuming that the laws of physics did actually change, then the situation has changed and you no longer have the same experiment.

I see no contradiction in denying the law of physics, so how is it impossible?

[James S Saint]

[The idea in performing an experiment is to control the setting such as to eliminate any possibility of alternate causation. This sets up the "Equivalence Principle" - Equal Situation yields Equal Result. So in the future if, and only if, the situation is exactly the same then the result will be the same.

The problem is that you are relying on Induction for this answer, and Popper rejected Induction, so it follows that this is to be rejected.

No. I am relying on Definition.

If there is anything different about the situation than previously setup such as to cause a different result, then you are not tlaking about the same defined situation.

All entities are defined by their causal affects. So if anything different happens than had previously happened, then by Definition, the setup was different (assuming that the setup actually had eliminated alternative causation).

I see no contradiction in denying the law of physics, so how is it impossible?

That is kind of a complex topic that even the experts have difficulty seeing, not really suited for this thread.

[ZenKitty]

No. I am relying on Definition.

If there is anything different about the situation than previously setup such as to cause a different result, then you are not tlaking about the same defined situation.

All entities are defined by their causal affects. So if anything different happens than had previously happened, then by Definition, the setup was different (assuming that the setup actually had eliminated alternative causation).

So your position has no empirical content and is not about the world. But we also notice that we can imagine otherwise, but we cannot imagine that a bachelor is an unmarried males.

[Ed3]

Hi Zen Kitty,

Speaking strictly from a view of logic, we do not know whether or not the following statement is true:

“In the past we have noticed that if a theory makes a false prediction in the scope of X, then it will continue to make false predictions in the scope of X”

In fact it is, as you claim, an inductive statement.

Assuming that the Prediction is falsified even once, all we know for sure is that the Hypothesis can not logically imply the Prediction.

This is Popper’s contribution, and it is a simple application of bivalent logic.

Thanks Ed

[ZenKitty]

Speaking strictly from a view of logic, we do not know whether or not the following statement is true:

“In the past we have noticed that if a theory makes a false prediction in the scope of X, then it will continue to make false predictions in the scope of X”

In fact it is, as you claim, an inductive statement.

I was pretty sure it was an inductive statement, besides Popper admitting that his ideas relied on induction. I just found it interesting that he said he was pointing out how science does not have an inductive method and says it follows a certain way that is eliminative. He thought this was not inductive in some sense or said that the scientific method doing it eliminatively would not be inductive. But he ends up admitting it was. So it appears he was not really an "Inductive Skeptic".

Assuming that the Prediction is falsified even once, all we know for sure is that the Hypothesis can not logically imply the Prediction.

This is Popper’s contribution, and it is a simple application of bivalent logic.

Thanks Ed

Well, this is not quite true in one sense. From a false theory you may derive infinitely many correct predictions and infinitely many false predictions.

[James S Saint]

No. I am relying on Definition.

If there is anything different about the situation than previously setup such as to cause a different result, then you are not tlaking about the same defined situation.

All entities are defined by their causal affects. So if anything different happens than had previously happened, then by Definition, the setup was different (assuming that the setup actually had eliminated alternative causation).

So your position has no empirical content and is not about the world. But we also notice that we can imagine otherwise, but we cannot imagine that a bachelor is an unmarried males.

No. My position is that the empirical setup is given a definition. As long as that empirical setup is repeated according to that definition, there is no LOGICAL choice but to receive the same empirical result. It has nothing to do with altering the laws of physics or anything else.

The purpose of Science is to verify that the setup causes the result. Science only repeats things so as to help ensure that the setup really was what they thought and not merely an unseen accident. Multiple witnesses to the event are there so as to more ensure that there isn't an issue of misinterpretation of the setup or result. If those things are truly established as accurate, then it is a matter of definition that the empirical setup will cause the empirical result every single time and without fail. It is not an issue of possible future changes of situation.

[ZenKitty]

No. My position is that the empirical setup is given a definition. As long as that empirical setup is repeated according to that definition, there is no LOGICAL choice but to receive the same empirical result. It has nothing to do with altering the laws of physics or anything else.

The purpose of Science is to verify that the setup causes the result. Science only repeats things so as to help ensure that the setup really was what they thought and not merely an unseen accident. Multiple witnesses to the event are there so as to more ensure that there isn't an issue of misinterpretation of the setup or result. If those things are truly established as accurate, then it is a matter of definition that the empirical setup will cause the empirical result every single time and without fail. It is not an issue of possible future changes of situation.

You sound like someone that the problem of induction was specifically meant for. You are defining what you have observed, which is what you found to exist. But how does this entail that you defining what has happened at that particular instance say what is going to happen with the next test?

We may imagine a person who comes to the Earth, and he would describe what he observes when he first shows up. How does that tell him anything new about the world, like what is going to happen tomorrow? They just defined what they observed, but that does not appear to tell them anything beyond that observation, which was defined. But we can imagine it to be otherwise as well, so there appears to be logical choice for it to be the way that it is. It can have been otherwise, or tomorrow can be otherwise than yesterday.

Now you also bring up cause, so how did this come by from the first observation that one makes?

[James S Saint]

No. My position is that the empirical setup is given a definition. As long as that empirical setup is repeated according to that definition, there is no LOGICAL choice but to receive the same empirical result. It has nothing to do with altering the laws of physics or anything else.

The purpose of Science is to verify that the setup causes the result. Science only repeats things so as to help ensure that the setup really was what they thought and not merely an unseen accident. Multiple witnesses to the event are there so as to more ensure that there isn't an issue of misinterpretation of the setup or result. If those things are truly established as accurate, then it is a matter of definition that the empirical setup will cause the empirical result every single time and without fail. It is not an issue of possible future changes of situation.

You sound like someone that the problem of induction was specifically meant for. You are defining what you have observed, which is what you found to exist. But how does this entail that you defining what has happened at that particular instance say what is going to happen with the next test?

That is the point in verifying that "the next test" is validly the same as the first. The only issue is what comes of the situation defined by the first test, "Does A cause B". If you don't have A anymore, you can't have a second test of it and don't care if A causes B.

Now you also bring up cause, so how did this come by from the first observation that one makes?

Once A has been carefully identified, whatever comes forth from A, "B", defines A as the "cause of B".

[ZenKitty]

That is the point in verifying that "the next test" is validly the same as the first. The only issue is what comes of the situation defined by the first test, "Does A cause B". If you don't have A anymore, you can't have a second test of it and don't care if A causes B.

But you could still find B without A. So what good is defining it as A causes B when you did not need A to bring about B?

Once A has been carefully identified, whatever comes forth from A, "B", defines A as the "cause of B".

All you have found that B came from A. So by cause you appear to mean finding one thing follows another. I do not see how a definition shows that one thing follows another like that. You found A, defined A, and happen to see B and define B. You found B to follow A. But that does not appear to show any link, like there is a link between being a bachelor and being an unmarried male. So A is Bachelor and B is unmarried male, from A we know B and from B we know A. But with the empirical situation that you bring up, it does not appear that knowing A means we know B like we did with the Bachelor. So it does not appear to logically entail anything. So you appear to have to rely on something else to bring about this logical entailment.

[James S Saint]

That is the point in verifying that "the next test" is validly the same as the first. The only issue is what comes of the situation defined by the first test, "Does A cause B". If you don't have A anymore, you can't have a second test of it and don't care if A causes B.

But you could still find B without A. So what good is defining it as A causes B when you did not need A to bring about B?

If the postulate was merely that A causes B, you don't care if something else also causes B. That is another issue.

Once A has been carefully identified, whatever comes forth from A, "B", defines A as the "cause of B".

All you have found that B came from A. So by cause you appear to mean finding one thing follows another.

Yep. That's what it means.

I do not see how a definition shows that one thing follows another like that. You found A, defined A, and happen to see B and define B. You found B to follow A. But that does not appear to show any link, like there is a link between being a bachelor and being an unmarried male.

Being a bachelor is not the cause of being an unmarried male. Those are merely two descriptions or words for the same thing. They are a descriptive relationship, not a causative relationship.

The point was to identify a causal relationship with sufficient definition so as to be able to know when it ("A") might again cause the same result, "B". Merely defining A and B as the same thing is not the same thing.

[ZenKitty]

Being a bachelor is not the cause of being an unmarried male. Those are merely two descriptions or words for the same thing. They are a descriptive relationship, not a causative relationship.

The point was to identify a causal relationship with sufficient definition so as to be able to know when it ("A") might again cause the same result, "B". Merely defining A and B as the same thing is not the same thing.

I see no difference between descriptive relationship and causative relationship for "A causes B". And it appears that those thins you brought up all fall for the problem of induction.

[James S Saint]

Being a bachelor is not the cause of being an unmarried male. Those are merely two descriptions or words for the same thing. They are a descriptive relationship, not a causative relationship.

The point was to identify a causal relationship with sufficient definition so as to be able to know when it ("A") might again cause the same result, "B". Merely defining A and B as the same thing is not the same thing.

I see no difference between descriptive relationship and causative relationship for "A causes B".

Yes. I noticed your inability to see that type of thought quite long ago.

Time is the difference.
For "A" to be a "cause", "B" must come after "A".