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New Induction Disproof

Deutsch, Popper, and Feynman aren't inductivists. I could add more people to this list, like me. So here we see a clear pattern of people not being inductivists. There's a bunch of data points with a certain thing in common (a person not being inductivist). Let's apply induction to this pattern. So we extrapolate the general trend: induction leads us to conclude against induction. Oh no, a contradiction! I guess we'll have to throw out induction.

Q&A:

Q: Your data set is incomplete.
A: All data sets are incomplete.

Q: Your data set isn't random.
A: No data sets are entirely random.

Q: I have an explanation of why your method of selecting data points leads to a misleading result.
A: That's nice. I like explanations.

Q: Don't you care that I have a criticism of your argument?
A: I said we should throw out induction. As you may know, I think we should use an explanation-focussed approach. I took your claim to have an explanation, and lack of claim to have induced anything, as agreement.

Q: But how am I supposed to object to your argument using only induction? Induction isn't a tool for criticizing invalid uses of induction.
A: So you're saying induction cannot tell us which inductions are true or false. We need explanation to do that. So induction is useless without explanation, but explanation is not useless without induction.

Q: That doesn't prove induction is useless.
A: Have you ever thought about how much of the work, in a supposed induction, is done by induction, and how much by explanation?

Q: No.
A: Try it sometime.

Elliot Temple on September 16, 2009

Comments (20)

How do you come up with explanations without induction?

Anonymous at 6:48 AM on September 19, 2009 | #1904
Creativity.

Elliot at 10:10 AM on September 19, 2009 | #1905
So you just make things up?

Anonymous at 3:41 PM on September 19, 2009 | #1906
Yeah, sure. Then you criticize them to eliminate errors. More info can be found in _Conjectures and Refutations_ by Karl Popper, or _The Fabric of Reality_ by David Deutsch.

Elliot at 3:44 PM on September 19, 2009 | #1907
But how do you make things up? And how do you criticise them? What processes are you using?

Don't tell me to read thick books. If you understood them, you can answer my questions.

Anonymous at 2:34 AM on September 20, 2009 | #1908
I didn't tell you to read any book.

How one makes things up, *exactly*, is not known. Same for criticism. If we knew that we could write an AI.

However, it is known that people do make things up. For example, people made up Persephone. And it is known that people do think of criticism, e.g. my criticism of induction.

Elliot at 10:39 AM on September 20, 2009 | #1909
If it's not know and the books don't have the information, why were you recommending them?

Anonymous at 5:25 AM on September 24, 2009 | #1911
Surely your data set creates a trend whereby we can say; people who aren't 'inductivists' aren't inductivists.

If we apply induction to that, it allows us to predict that the next person who isn't an inductivist won't be an inductivist.

No contradiction (though your supposed contradiction didn't exist anyway).

Anonymous at 7:36 PM on August 11, 2010 | #2061
what does it mean not to be an 'inductivist' in quotes?

your example of applying induction needs more detail. are you offering a guarantee? where is the inductive method? and you seem to be saying induction can predict that people with attribute X will have attribute X, which is kind of pointless and doesn't tell you how to figure out if they have attribute X in the first place.

Elliot at 10:43 PM on August 11, 2010 | #2062
I apologise for my odd use of quotation marks; I was attempting to express my distaste at the label (and what I believed was an implied sneer). To my mind, inductive reasoning is a powerful, albeit fallible, tool for expanding our knowledge.

Back to my objection. I am pointing out that your data set doesn't have a trend of people not being inductivists; it has a trend of people who aren't inductivists not being inductivists.

As for where the inductive method is; surely it is in the same place as you use it when you say

'Let's apply induction to this pattern. So we extrapolate the general trend...'

I confess I don't really follow your barrage of questions (it seems like a lot of heat but no light) I haven't changed anything from your own argument, save that I suggest you have misrepresented the 'general trend'.

Probably the most scathing criticism of your argument (if indeed you meant it to be a serious argument; I presume from your defence of it that this isn't an elaborate parody) is that my previous point notwithstanding, you don't even have a contradiction.

To illustrate, even if you do have a general trend of people not being inductivists, and even if this does justify you in expecting the next person you meet won't be an inductivist. This tells you nothing about induction itself, save only that it is an unpopular method of justifying belief (which of course it isn't). Quite where you believe the contradiction lies is utterly mysterious to me. All you have done is use an inductive argument to conclude that the next person/philosopher you meet won't be an inductivist. This is perfectly legitimate.

ps. This is totally off topic, but by 'justificationist' do you mean what I would call 'classical foundationalist' (ie. a person who believes knowledge can be grounded in induibitable principles)?

Ben at 7:26 AM on August 12, 2010 | #2063
Ah, some confusion here. I didn't realize the two anonymous comments in a row were different people, and yours was replying to the original post not continuing the discussion in comments. Makes more sense now. Also, FYI, my questions were intended only to clarify (for example b/c there are multiple varieties of induction lately, so someone saying something positive about induction should specify which one they are advocating).

OK let's talk about induction more seriously.

Hume proved induction doesn't, strictly, work. Inductivists then faced a problem: if inductive conclusions might be wrong, how do we figure out when they are right and when wrong?

This got a variety of responses, many along the lines of "induction provides strong but fallible support" or "induction makes conclusions highly likely to be true" or even "induction hints at the truth".

The basic theme here is to admit induction doesn't strictly work (b/c no one managed to find any way to dispute that), but to gloss that over and carry on as before.

These new varieties of induction have also been refuted now. For example, Popper took on the probabilistic stuff in detail (brief summary: you need some system or guidelines or instructions for figuring out how likely stuff is, and how that changes as more evidence is added. But no proposed approaches, when mathematically analyzed, meet very basic criteria for making any sense and being viable. For example, some lead the probabilities over 100% or violate the basic mathematics of probability)

What about the less specific approach which offers "support" instead of probability? There are two main replies:

1) induction doesn't make sense. all finite sets of data are compatible with infinitely many theories. so how can they support one of those theories over another? this is a basic question about induction which goes unanswered.

2) justificationism itself is a mistake.

Justificationism is, roughly, the theory that ideas can be supported. That includes the idea that evidence or arguments can have (more or less) 'weight'. Fallible support is included here.

To take on one aspect of justificationism, there is a regress problem. If I support X with Y, Y itself needs more than 0 support or weight in order for X to gain anything, right? So I have to support Y with Z. But then Z needs support. This is where a "classical foundationalist" approach like you mention could come in -- it's an attempt to escape the regress by declaring some propositions don't need any support but are simply outside critical debate.

This regress problem has no solution, other than transforming it into a different problem also with no solution. (e.g. you can avoid the regress with foundations, but then you have the problem of why you are arbitrarily declaring some ideas true without argument. And of course you can't give arguments for the foundations or they aren't really foundations and your arguments will face the same regress problem we started with).

I hope that clears some things up. I can provide more detail on any of these points.

Elliot at 1:15 PM on August 12, 2010 | #2064
Hmm, it wasn't particularly my intention to discuss induction per se, simply to dispute the merits of the argument you offered. However, if I may take your lack of a defence against the points I raised as implicit agreement with my objections, then I'm happy to debate the wider issue.

That said I wish first to dispute the sentence;

'Hume proved induction doesn't, strictly, work...'

In particular, I wish to challenge the implication of 'work'. Hume showed that induction cannot deliver logically valid arguments (as in any inductive argument it will be possible for the premises to be true, and the conclusion false). Accordingly, if infallibilist knowledge is one's goal; induction will not prove fruitful.

However, failure to deliver logically valid arguments is a trait common to all fallibilist methodologies. Falsification is no better off here. Hence why I find your subsequent comment unfortunate. You say;

'The basic theme here is to admit induction doesn't strictly work (b/c no one managed to find any way to dispute that), but to gloss that over and carry on as before.'

As I say, if your definition of 'strictly work' is 'delivers infallibilist knowledge' then no epistemic methodology 'strictly works' but I cannot see how this attacks induction.

Re. probabilism, I know very little of this particular theory hence will refrain from comment. I am aware that it is still a 'live' theory though, so I conclude Popper's analysis is not regarded as the definitive answer.

Turning to your two subsequent claims, I think both are mistaken. Your point about an infinite number of claims being supported by inductive reasoning from a particular data set seems to rest on a conflation of two different concepts of infinity. Infinite can mean impossible to even count up to the end of the series (as the series is open ended), or it can mean containing everything (eg. the claim that 'space is infinite').

If we consider any finite data set, I agree it supports an uncountably large number of theories (eg. 'I have seen 100,000 swans all white, I have never seen a swan other than white:- the next swan I see will be white' also supports the theory that 'the next swan I see won't be black, or red, or grenn...') Notice however, that it doesn't support the theory 'the next swan I see will be black'. Hence it refers only to the first kind of infinity (as it doesn't contain all possible theories). This said, I fail to see the point of your objection; the data set can support every single valid theory (either as a singular instance, or as a set) precisely because there is no contradiction in it doing so. If a property is true for a consistent set of data, then it is true for each member of that set, regardless of how large the set is. For your objection to succeed, you must show how an inductive argument can justify both a theory, and the negation of that theory. This is not a task I advise you to waste a significant amount of time on!

Re. justificationism. I confess to being utterly bewildered at your claim that no argument carries any more weight than another. Contrast:

1) Socrates is a man
2) All men are mortal
------------
Socrates is mortal

With:

1) Socrates is a man
2) All men are mortal
--------------
Socrates is not mortal

Is you position really that these arguments have no difference regarding their ability to justify their conclusions?

Finally, I both understand and accept the regress problem, however it is only a problem with infallible attempt to justify belief. If you are to srgue for your unorthodox position, you must explain quite why all fallibilist methods of justifying belief fail.

Ben at 9:43 AM on August 13, 2010 | #2065
> Hume showed that induction cannot deliver logically valid arguments (as in any inductive argument it will be possible for the premises to be true, and the conclusion false).

Right. So this raises a problem for inductivists: how are inductive claims better than wild guesses? With both gueses and inductions, the conclusions may or may not be true.

Another way to put the question is: What does induction actually do?

This may sound like an easy problem. Of course they are different, you may say. But what is the difference, precisely? What makes inductions better than guesses? Or if they aren't better, why should we use them?

There have been many attempts to answer these questions, but I don't believe any have succeeded. How about you explain one that you think successful, and I can point out what I think is wrong with it?

One attempt was to say that induction (partially/fallibly) supports or justifies its conclusions, but this has a regress problem (see below).

> I both understand and accept the regress problem, however it is only a problem with infallible attempt to justify belief.

The regress problem applies to any type of support or justification, even partial support.

If we just make up a proposition it starts with zero support, right? Not some fallible support, but absolutely none (unless you start asserting foundations or self-supporting statements or something like that). So then we use a second proposition to give some amount of support to the first. But the second proposition cannot give any support at all unless it, itself, has some amount of support or justification, which will have to come from a third propostion, which will itself need some support.

So I think fallible approaches have the same regress problem.

> Is you position really that these arguments have no difference regarding their ability to justify their conclusions?

Yes, I believe all conclusions have zero justification (justification is a mistake). However, I do accept other things. For example, I accept that a statement can have a status of refuted or non-refuted. This covers the Socrates examples easily enough. I think a more telling example would involve 3 or more arguments. Weights come on a continuum, and I take issue with that. So weighting would be able to take 3+ arguments and put them in order of weight. But I would put them only into two categories. Then I would say if the non-refuted category has exactly one member, we should tentatively accept it. (One good thing about this approach is that no kind of justification or support is needed. If there's no non-refuted rival theory, then accepting the sole contender is easy.)

> Notice however, that it doesn't support the theory 'the next swan I see will be black'.

The evidence is consistent with infinitely many theories in which the next swan will be black. Because of this, inductivists face a hard question: why should the "next swan will be white" theory be favored?

Here are some theories which are consistent with all the evidence, but which predict the next swan will be black:

1) I have been seeing swans sequentially, and the first 100k are all the white ones, and the next 100k are all the black ones.

2) My eyesight was very bad but has recently been repaired and actually all swans are black.

3) Advanced aliens control my life. They will cause the next swan I see to be black. The number of aliens involved in the conspiracy is N. (This one is a template for a theory. By varying N, we can get an infinity of different specific theories. I hope that clarifies what I meant by infinity.)

4) All swans were white, but they turn black on a particular date that just passed.

5) All swans in England where I lived are white, but swans in India where I just moved are black.

You may say these are bad theories. You may be right. Yet they are consistent with the evidence. How does induction object to them? Induction attempts to derive theories from evidence, but how is it to tell apart all the theories compatible with the evidence?

Elliot at 6:11 PM on August 13, 2010 | #2066
> However, if I may take your lack of a defence against the points I raised as implicit agreement with my objections, then I'm happy to debate the wider issue.

I am happy to drop the points in the original post. The target audience was people who already accept multiple arguments against induction. I think the argument can be repaired with modifications that would seem minor to someone who already agrees about induction in general, but which might seem large to someone else.

Elliot at 6:12 PM on August 13, 2010 | #2067
I'll work in reverse order through the points you raise.

I'll begin with your five hypothetical counter examples.

Hmm, I am unimpressed by an alteration to my claim, which 'allows' these five examples to seem to counter me. To illustrate; I claimed

'Notice however, that it doesn't support the theory 'the next swan I see will be black'

Whereas you write in response

'The evidence is consistent with infinitely many theories in which the next swan will be black.'

I'm sure I don't need to elaborate on the difference between evidence supporting a theory, and evidence being consistent with a theory. All your five examples amount to, are instances of reasoning counter-inductively (none better than, some worse than, the Gamblers Fallacy).

Their existence does not cause a problem for inductive methodology, precisely because their existence is a necessary corollary of induction only generating theories that stand in a certain evidential relationship with a data set. Basically, if induction only generates theories that are reinforced by the trends present in a data set, then the negation of induction will generate opposite theories. The very fact that one can reason counter-inductively and still be correct merely shows that induction is a fallible methodology (it also highlights the difference between knowledge & true belief). This is no different from somebody reasoning counter-falsification.

Jumping up to your point about regress. You have a somewhat idiosyncratic notion of justification. Justification is simply a matter of a belief standing in a suitable relationship to justfying principles. You are certainly correct to say that one suggestion for a justifying principle is 'a corollary of a foundational truth' (ie. classical foundationalism) but this is far from the only (or best) game in town.

I'll sketch out two different fallibilist theories of justification, perhaps you'll be so kind as to explain how the regress problem applies to them.

Firstly, Nozick's theory of subjunctives.

S knows that P iff:
1) S believes that P
2) P is true
3) If not P, then S would not believe that P
4) If P, S would still believe P if S's situation was altered.

Each condition is necessary for knowledge, taken together, they are sufficient.

Secondly a basic falsificationist narrative.

S knows that P iff:
1) S believes that P
2) P is true
3) S is unaware of a better explanation for a particular phenomena than P
4) S has taken reasonable steps to criticise P

(Forgive my poor treatment of falsification. I don't mean this as an underhand attack on the theory; I simply want to sketch an outline that a more experienced advocate of such a theory could improve on).

Notice that in both cases (indeed, in all cases) justification is a process of tethering one's belief in a fact, to the truth of that fact (in a modern sense, one does this while allowing for one to be mistaken about the fact). This is to eliminate 'bad/irrational' methods of knowledge 'creation' like the examples of counter-induction you suggested earlier. NB; this point also answers your claim about arguments having 'zero justification'.

Finally, everything I have said allows me to answer your first question;

'how are inductive claims better than wild guesses?'

Simply because (in some sense) induction is a justfying principle. This demands an answer to the question 'in what sense' and here there are many different narratives. One of the most popular (until recently) was the externalist story, whereby a belief being justified, was simply a matter of it possessing a certain property (usually 'being the output of a process that reliably generates correct results'). Induction certainly fulfills that criteria (as Hume himslef was very quick to point out). Unfortunately, this narrative will no longer suffice. Following Goodman & his 'New Riddle of Induction' a paper that introduced the concept of 'Grue' (and to my mind, some of the best recent philosophy).

Goodman agrees that induction generally outputs true belief, but disagree's that the relationship is close enough to amount to 'justification'. He argues that supporters of strong induction need to present criteria that explain what data sets are appropriate to apply induction to, and which ones aren't. Once this has been done, he accepts that for all those in the former category, they are justified by induction, but until a division can be principally supported, he doubts the validity of justification via induction (though he does not dispute its necessity).

Ben at 6:47 AM on August 16, 2010 | #2068
Hi, this is getting pretty long so let's just look at a couple main points at a time, and can come back to the rest (if they don't evaporate from settling these main issues):

> I'm sure I don't need to elaborate on the difference between evidence supporting a theory, and evidence being consistent with a theory.

Yes you do. Please go ahead. I claim there is no difference. (Or put another way: I claim evidence never supports anything, but it can be consistent, i.e. non-contradictory.)

> Firstly, Nozick's theory of subjunctives.
>
> S knows that P iff:
> 1) S believes that P
> 2) P is true
> 3) If not P, then S would not believe that P
> 4) If P, S would still believe P if S's situation was altered.
>
> Each condition is necessary for knowledge, taken together, they are sufficient.

I'll call doing all the steps together an NTS. Suppose Bob claims to have an NTS about some subject Q. This, you say, justifies Q, right? But Bob might be mistaken about whether he has an NTS. How do we know if he has an NTS or not? We better come up with an NTS saying Bob has a correct NTS. Now we have a second NTS, and we will wonder if it's correct (and transitively this still can affect whether the we accept the first is correct). So we create a third NTS about that. And so on. Regress.

So I don't see how this approach helps with the regress problem.

For the "basic falsificationist narrative", if it is intended to offer justification (Popper's philosophy, sometimes called falsificationism, is *not* intended to offer justification), simply replace NTS with BFN above.


FYI the Popperian (non-justificationist) schema of how we make progress is:

problem -> tentative conjectured solutions -> error elimination (criticism) -> replacement of erroneous theories -> new problem(s)

PS I'm familiar with Grue, my (4) above about swans changing color on a date is a variant of it.

Elliot at 9:51 AM on August 16, 2010 | #2069
I agree with you eminently sensible appeal for brevity. That said, I'll focus on three short points.

Firstly, I suggest that your analysis of NTS is inadequate (indeed is misguided). To show this, re-examine the four criteria again, you'll notice that they aren't steps that S must follow, they are simply states of affairs which either hold, or fail to hold. Also notice that their holding (or not) is not a matter of S knowing that they hold (ie. S can be ignorant of all of them-possibly bar (1)-and they will still apply).

To show this, I'll run the analysis with an ordinary knowledge claim; the claim that S has two hands.

S knows that he has two hands if and only if;

1) He believes that he has two hands
2) He does in fact have two hands
3) If he didn't have two hands, he wouldn't believe that he did
4) If he did have two hands, he would still believe it if other details of S's lie were different.

If we imagine that S is a normally functioning human, then we can see that all these criteria obtain; hence on a Nozickian (sp?) analysis S 'knows' (is justified in believing) he has two hands. Note how at no point does S need to reference antecedent knowledge (indeed, in the entire analysis, the word 'know' is used only once-indicating that S does not need to run a second NTS in order to establish pre-existing knowledge). For this, I claim that your regress statement is incorrect.

My second point refers to your Popperian analysis. Justificationist or not, it should be possible to give any epistemic theory in the format of necessary & sufficient conditions (much like I offer Nozick's theory).

Ben at 4:59 AM on August 17, 2010 | #2070

Apologies

Hmm...computer mistake on my part.

...cont.

My question then is; how would you formalise the Popperian analysis (ie. S knows that P iff....). I could be wrong & Popperians deny the possibility of knowledge, but this does not appear to be your position.

Finally, the question of how support differs from consistency. I confess that this is a far more interesting question than prima facie it appeared to be. That said, excuse this answer as preliminary.

It seems to me that any inductive argument would be logically valid, provided one could justify a principle which held that 'all things being the same, the past will resemble the future'. Of course, such a principle doesn't exist (at least as far as we have been able to prove). However, the extent to which it appears to hold in practice (empirically) seems to differ between data sets & theories. Some theories (like the counter-inductive ones you offered previously) depend on such a principle not holding at all (thus are rendered weaker by every instance of the principle seeming to be the case). Other theories (like the thought that the sun will rise in the East tomorrow) benefit from a vast number of instances whereby the principle appears to be correct. I tentatively suggest that though

'The Sun has always risen in the East'

is logically consistent with

'Therefore it will rise in the West tomorrow'

The difference between what is required to make a logically valid argument to the different conclusions (ie. the above conclusion vs. 'Therefore the Sun will rise in the East again tomorrow') is the difference between evidence supporting a theory, and merely being consistent with the theory.

ps. I apologise for missing your reference to grue earlier.

Ben at 5:18 AM on August 17, 2010 | #2071

Lack of an edit button :-(

Triple posting is egregious, but forgive me. I merely wanted to amend a word; please ignore my claim that your analysis of NTS was 'misguided' and instead read 'off target'.

The former seems more offensive than it was my intention to be.

Ben at 5:22 AM on August 17, 2010 | #2072
Regarding regress, as a first point: how do you justify this Nozickian approach itself? I think that is decisive.

But perhaps more usefully, I'm interested in human knowledge. If you say "If some stuff was true, which we can never know, that would be knowledge" ... well, who cares? We can't act on the knowledge unless we know we have it. If we know we have some idea, but we don't know if it's any good, then we need to figure out if it's any good. We can't do that by saying "it's good if some state of affairs hold" unless we can actually figure out if those states of affairs do hold. But if you try to figure out if they do hold, and start making concrete claims about them, then those claims themselves need justifying (if you seek justification), and the regress issue remains.


Regarding necessary & sufficient conditions: the necessary & sufficient conditions to make progress (learn things; create knowledge) are to find problems, conjecture solutions to them, use criticism to improve those solutions, and to not just do this once through but to keep doing it many times in parallel as new problems are found.


> My question then is; how would you formalise the Popperian analysis (ie. S knows that P iff....). I could be wrong & Popperians deny the possibility of knowledge, but this does not appear to be your position.

The Popperian analysis does not answer the question of how to decide if S knows P. It tells us how to learn and improve our ideas, but it doesn't not tell us if/when we have done so.

Popperians do deny the possibility of "knowledge" in the traditional sense of Justified, True Belief. One reason is the regress problem which affects all attempts to justify. The Popperian view is that that kind of epistemology is misguided and can't work, but a fallibilist epistemology seeking conjectural knowledge is possible and sufficient.

Perhaps this statement will help clarify (it's a little similar to "S knows P iff"): we can tentatively accept all ideas which we know no criticism of, and no others. (Be advised the meaning of "criticism" here is taken very broadly.)


Regarding support and consistency, "the future resembles the past" does not help b/c "resembles it how?" Suppose there is a sun that rises in the East for 1 million years, then the West for 1 million years, alternating. Then that's what it's been doing in the past, and if it switches then it resembles the past just fine. Or in other words, I deny there is any difference between "resembles" and "is consistent with".

The point is that when the sun rises in the East, that is an instance of the theory "the sun rises in the east a million times then the west a million times". It is evidence for that theory, just as much as for any other theory, b/c what's happening is exactly what it says should happen. There is nothing counter-inductive about a theory that perfectly matches all the observations under consideration.

This may seem frustrating because it violates common sense. That's true enough. There *are* good arguments against the "million times alternating" theory, and they're pretty obvious. It's a bad theory. However, those arguments are not inductive. Induction itself isn't up to the task (I claim). Criticism and argument in general are up to the task, but those aren't induction.

Elliot at 10:36 AM on August 18, 2010 | #2073

What do you think?

(This is a free speech zone!)