Blame David Hume

[BaalChatzaf]

Whenever this problem of induction comes up, I know it's a cheap shot, but the itch gets to me.

We KNOW that falsifiability has worked perfectly in the past, but if all goes according to "problem of induction" standard, that says nothing about it working in the future. Who knows? It might not work tomorrow. Right?

Michael

Falsifiability is based on a deductive principle (modus tollens) not an inductive principle. As long as we take the law of non-contradiction as absolute then falsifiability is based on sound deductive logic.

Induction is not a valid mode of inference. It is a -heuristic- rule that enables one to get from a finite set of particular/singular (non-quantified) propositions to a general (universally quantified) proposition. The generality is not guaranteed to be true, no matter how many particular statements lead up to it.

it does not matter how many black crows you observe. Unless the domain of crows is totally exhausted then the general statement

"all crows are black" might not be true. As a matter of practical consideration one could not determine if he had seen every last crow that was, is and will be. So exhaustion of the domain is not a practical achievement. However if one finds a non-black crow (most likely an albino), then the general proposition is falsified for sure. All that is required to falsify a generality is a single counter example.

Ba'al Chatzaf

[Michael Stuart Kelly]

As long as we take the law of non-contradiction as absolute... .

Bob,

Now why on earth would we do a fool thing like that? Just because you say so? That means nothing about how it will be tomorrow by your own standard.

Michael

[Nicholas Dykes]

You did say, "There is no way of logically deciding a definition is true or false." I don't know why you put 'logically' in there.

It was in reference to the defective Randian claim that "The truth or falsehood of all of man’s conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions."

I put it there to distinguish Rand's use of "truth" from meaning conventionally true. Recall that Rand derides the idea that meanings of words are simply conventions. Recall she also claims that "The fundamental concept of method, the one on which all the others depend, is logic." Thus she is suggesting that definitions can, and indeed must, be logically decided as to their truth or falsity.

But there is no way of doing this. It does not work as advertised...;-)

Suppose I say, 'an orange is a fruit, it grows on tress, and, depending on variety, it's roundish, yellowish, sweetish and consists of an outer skin with an inner core in segments.' What has ~logic~ got to do with deciding whether that definition is true or false?

Precisely my point.

The problem with Popper, as with Hume, and with Popperians generally, is that they are sceptics who deny the possibility of certain human knowledge. You present them with a lump hammer and say 'hit your thumb with it,' and they reply, 'just because every known instance of belting your thumb with a hammer has resulted in pain does not mean that if I thwack my thumb with this hammer pain will result.' Talk about LOL. If that's what Popperians call logic, good luck to them.

Popperians have no special meaning for logic. We use the same meaning as most logicians. Objectivists, however, do have their own special meaning.

Concepts are open-ended, knowledge grows.

I do not see any basic conflict between this and Popper's position, other than that Rand insists on self-contradictory jargon about "contextual certainty." This amounts to saying all our present knowledge is uncertain. The irony is that she so violently attacks the very position she unwittingly holds!

Popper's point is that if we hold these expectations as to what this identity consists of merely hypothetically, leaving them open to be overthrown by conflicting experience, then there is no logical problem.

That doesn't sound very like Popper. Do you have a citation for it?

It's paraphrased from Objective Knowledge, I will supply a ref later. I am surprised you don't think it sounds like him, I can't see what is unusual about it.

It's half past midnight here, too late for this really. Goodnight. Nick

Good morning!..;-)

'Evenin' Daniel! I hope this finds thee well. The sun is struggling to shine here, which kindles a little optimism -- we've had a truly dreadful summer.

Do you think we could move this exchange to a new thread? Say, "Popper v. Rand"? It's all getting a bit ragged and random. I have to say, I did enjoy the old journal way of debating; when each writer got two cuts at the cat, with plenty of time to consider in between. This quickfire fencing is fun, but I think the old method tended towards greater understanding in the long term.

I don't actually believe we're very far apart. I've often wished to find in a philosopher a blend of Rand's passion and insight with the knowledge and skill of a professional. It couldn't be Popper and Rand, because both are too unyielding. Rand plus Brand Blanshard would have been great. David Kelley has come closest to my ideal but as yet hasn't produced the geat synthesis I yearn for.

I have to go out in 20 mins. So I'll be quick.

First, I don't carry a brief for Ayn Rand. I love her novels; agree with the basics of her philosophy; am sure she's almost entirely right about ethics, but I disagree with her politics, and am embarrassed by her demonising of Kant, etc. I'm also troubled by some technical issues, such as this business of 'contextual' knowledge, which strikes me as bordering on relativism.

As to Popper, I admire his learning, enjoyed his writing, and his combative spirit, and think his critical method is very helpful. But I dislike his scepticism, his reliance on Hume and Kant, and his penchant for sweeping generalisations.

So I'm prepared to debate Popper v. Rand. But my interest is not in defending Rand against Popper, or Popperians, it is in establishing the ~truth~. I won't debate as a 'Randian', but as myself.

Lastly, I'm already encountering the problem on OL that I encountered on OWL: no matter how enjoyable, it simply takes up too much of my time. So if you do want to debate with me, I shall confine myself to one or two posts a week, no more.

For starters, if you want to, why don't you give us/me a succinct description of Hume's 'problem of induction', perhaps if you like from statements you've already made.

Anyhow, I'm off down the pub now for a pint of our local Herefordshire ale, Wye Valley, with my mate Ian, who has paid me the triple compliment of buying a copy of my book, reading it, and enjoying it thoroughly -- tho' he knows nothing about philosophy!

Bye now. Nick

[Mindy Newton]

Therefore we must accept the conclusions of Hume and Kant that we can't know anything and that our senses don't provide evidence about the world? Rand was smarter than that, even if she hadn't studied Hume's problem in detail.

Hume never ever said that we can't know anything.

Read -Enquiry into Human Understanding- part 64. Hume states that we clearly perceive prior and posterior events. What we do not perceive is necessary connection. The necessity connection between the prior event (cause) and the posterior event (effect) is a mental construct, a kind of inference.

Think of it this way. Nature provides the dots (and we come to know them). We draw the lines connecting them.

Ba'al Chatzaf

Hume also said we don't perceive our conscious self.

--Mindy

[Mindy Newton]

Experimentally observed -a finite number of times-. No finite set of observations can establish a general principle, unless the set of observations exhausts the domain of application of the principle, which almost never happens.

It may or may not be possible to exhaust the domain of application. If not, then we have a series of better and better approximations as we explore more and more of the domain. But, each approximation is valid. It holds under the range of conditions that have been explored. The Induction Problem is different. It says that we can never know anything, even approximately.

Nonsense! The induction problem (so-called) is that induction is not a logically valid mode of inference. Induction is a practical way of producing general statements from a finite set of instances. The generalization might be true or it might be false.

We always -know- (or could know) the particulars. It is the generalization that is not guaranteed to be true.

I think you have been reading too much Peikov. Don't. He is more often wrong than right and he is a mathematical and scientific ignoramus.

Ba'al Chatzaf

Math isn't the holy grail you think. Did you know that two and two don't always make four? Take two bananas and add two quarts of swamp gas. What do you get? You don't get four of anything!! You don't get four objects, or four "measures." Would you like to say that what we can't do is "add" these two particular "twos?" But we can. We can add them to a tank, for example.

The point is that numbers are adjectives. "Two" is always two of some kind. We are so accustomed to leaving out the grammatical niceties, we lose sight of their existence. Math is nothing until you get its conceptual context straight.

--Mindy

[Daniel Barnes]

'Evenin' Daniel! I hope this finds thee well.

It does...;-)

Do you think we could move this exchange to a new thread? Say, "Popper v. Rand"?

Possibly, but that might be a bit wide ranging. And truth be told, I'm a bit over induction having done several long threads here on it prior to your arrival. Shall we narrow it down a bit, and start with an area we are in fact quite close on? I like what you say here:

I'm also troubled by some technical issues [with Rand's theories], such as this business of 'contextual' knowledge, which strikes me as bordering on relativism.

Well, me too. I think this is exactly where Rand's theory of knowledge leads, despite her condemnations of relativism.

Lastly, I'm already encountering the problem on OL that I encountered on OWL: no matter how enjoyable, it simply takes up too much of my time. So if you do want to debate with me, I shall confine myself to one or two posts a week, no more.

Right now, that's my speed too. I've got a new business on the go, so I'm all for the pithy.

If that interests you, I'll start a new thread. Maybe "The Accidental Relativist: Does Rand's 'contextual' theory of truth lead to Relativism?"

[Mindy Newton]

Kant's reaction to Hume was shock that religious beliefs had no claim to being reasonable on Hume's terms.

Sez you...;-) There's a very well argued case that Kant was coming to the defence of Newton, for example.

You would be better to address the point at issue, Mindy, which is not "Is Kant evil?", but "why do Objectivists obsess about Kant when it was Hume that set Kant off in the first place?"

My answer to that question is that Rand simply did not understand Hume's problem. Conveniently we have her own testimony to this fact, which one would think would settle the issue. This does raise, however, a second question which is: if Rand didn't understand Hume, how could she be relied on in her judgement of Kant?

My point didn't get across. Hume tried to improve knowledge by eliminating arbitrary, non-empirical ideas. Kant, seeing that religion would lose on this basis, went to extremes to defend religion, in the process discrediting all of human knowledge and even making reality inaccessible to us. Hume tried to rid us of groundless ideas, Kant sacrificed ideas and reality in order to salvage religion.

--Mindy

[tjohnson]

Math isn't the holy grail you think. Did you know that two and two don't always make four? Take two bananas and add two quarts of swamp gas. What do you get? You don't get four of anything!! You don't get four objects, or four "measures." Would you like to say that what we can't do is "add" these two particular "twos?" But we can. We can add them to a tank, for example.

The point is that numbers are adjectives. "Two" is always two of some kind. We are so accustomed to leaving out the grammatical niceties, we lose sight of their existence. Math is nothing until you get its conceptual context straight.

--Mindy

You need to learn the difference between pure mathematics and applied mathematics.

[Michael Stuart Kelly]

You need to learn the difference between pure mathematics and applied mathematics.

GS,

You need to understand what someone is saying and actually verify what they need before telling them what they need. I seriously doubt you gave Mindy's comment more than 20 seconds thought. How do you know what she needs from such a cursory examination? You don't even know her.

Maybe, just maybe, she has examined the idea of "pure mathematics" and found it wanting. If I were you, I would want to know why. At the very worst, she could cause you to think a little. But for that, your value has to be engaging her ideas instead of decreeing what her cognitive needs are.

Try this rhetoric: "I disagree with..." That is so much better than the old spouse nag of "Your problem is that you..."

The first sounds like an intellectual. The second sounds like a control freak bent on bickering.

I love discussion. I really don't like preaching.

Michael

[Nicholas Dykes]

'Evenin' Daniel! I hope this finds thee well.

It does...;-)

Do you think we could move this exchange to a new thread? Say, "Popper v. Rand"?

Possibly, but that might be a bit wide ranging. And truth be told, I'm a bit over induction having done several long threads here on it prior to your arrival. Shall we narrow it down a bit, and start with an area we are in fact quite close on? I like what you say here:

I'm also troubled by some technical issues [with Rand's theories], such as this business of 'contextual' knowledge, which strikes me as bordering on relativism.

Well, me too. I think this is exactly where Rand's theory of knowledge leads, despite her condemnations of relativism.

Lastly, I'm already encountering the problem on OL that I encountered on OWL: no matter how enjoyable, it simply takes up too much of my time. So if you do want to debate with me, I shall confine myself to one or two posts a week, no more.

Right now, that's my speed too. I've got a new business on the go, so I'm all for the pithy.

If that interests you, I'll start a new thread. Maybe "The Accidental Relativist: Does Rand's 'contextual' theory of truth lead to Relativism?"

You're on! You start. However, in view of the tenor of certain posts I've seen on OL, I would like to make emphatically clear that I am not the slightest bit interested in ~attacking~ Ayn Rand, or Popper, or anybody else. What I ~am~ interested in doing is refining and improving my knowledge and understanding of ~philosophy~, a subject I have been interested in since I was sixteen years old. On that basis, let us commence.

All the very best with your business. When my back collapsed, in 1992-3, my wife started a new business which turned out to be a huge success. I sincerely hope yours follows the same path. Nick

Edited August 22, 2008 by Nicholas Dykes

[Dragonfly]

Math isn't the holy grail you think. Did you know that two and two don't always make four? Take two bananas and add two quarts of swamp gas. What do you get? You don't get four of anything!! You don't get four objects, or four "measures." Would you like to say that what we can't do is "add" these two particular "twos?" But we can. We can add them to a tank, for example.

The point is that numbers are adjectives. "Two" is always two of some kind. We are so accustomed to leaving out the grammatical niceties, we lose sight of their existence. Math is nothing until you get its conceptual context straight.

--Mindy

You need to learn the difference between pure mathematics and applied mathematics.

Exactly. In mathematics numbers are not adjectives but abstract objects. In mathematics two plus two is always four, and those numbers are not "of some kind". Now we may apply such mathematical objects and theories to the real world, but whether this works is an empirical question and a bad application doesn't invalidate the mathematical truths.

[Mindy Newton]

In order for the the Induction Problem, as stated by Popper and Hume, to be a serious problem it is necessary to ignore the Law of Identity and its corollary, the Law of Causality.

In fact the Law of Identity is about as relevant to the problem of induction as a fish is to a bicycle.

Here's why: All the LOI states is that in order to exist, a thing has to have an identity.

The LOI is however entirely silent when it comes to what that identity is (that is, its nature), and its corollary is equally silent on how it behaves (that is, its causal relations).

Unfortunately for this line of argument, the what and how is exactly where Hume's problem begins.

The Law of Identity goes much farther than you claim. Identity, or a thing's nature, changes in limited ways, unless the thing is destroyed. The characteristics of, say, swans, vary somewhat, but not wholesale. Some of those characteristics stay the same. That is the basis of inductive certainty. "All swans..." can only refer to what remains a swan. The stability of nature is the basis of inductive certainty. Some characteristics vary, others don't. There are "reasons" as in relations or connections for why the changeable characteristics are so, and why the invariant ones are invariant. Discovering what is what is the nitty-gritty of science.

--Mindy

[Michael Stuart Kelly]

In mathematics numbers are not adjectives but abstract objects. In mathematics two plus two is always four...

Dragonfly,

At least that was the case up to now. Who knows about tomorrow? It might be different then. Right?

Michael

[Dragonfly]

In mathematics numbers are not adjectives but abstract objects. In mathematics two plus two is always four...

At least that was the case up to now. Who knows about tomorrow? It might be different then. Right?

No, mathematical statements are always true, that's the difference with science. Perhaps one day you'll get it, but I won't hold my breath...

[Michael Stuart Kelly]

... mathematical statements are always true...

Dragonfly,

Why?

Michael

[Dragonfly]

The Law of Identity goes much farther than you claim. Identity, or a thing's nature, changes in limited ways, unless the thing is destroyed. The characteristics of, say, swans, vary somewhat, but not wholesale. Some of those characteristics stay the same. That is the basis of inductive certainty. "All swans..." can only refer to what remains a swan. The stability of nature is the basis of inductive certainty. Some characteristics vary, others don't. There are "reasons" as in relations or connections for why the changeable characteristics are so, and why the invariant ones are invariant. Discovering what is what is the nitty-gritty of science.

And the law of identity doesn't tell us anything about that.

[Dragonfly]

... mathematical statements are always true...

Why?

Perhaps you should read the Analytic-Synthetic thread on this forum, where I've written tons of material about that question. I'm not going to do your homework for you.

[Michael Stuart Kelly]

Dragongfly,

You have proclaimed your proclamation about math being different. You have not given reasons why it is so. You should remember that I participated on that thread you mentioned. All I'm saying is that saying doesn't make it so.

I am starting to be curious as to why the double-standard with human knowledge. I am interested in what leads a person to believe in one.

(Just for the record, I obviously do hold that 2 + 2 always equals 4, but I also hold that the concept bear will always mean that big dangerous animal you can find in the woods.)

If one can proclaim that one form of knowledge is absolute but the other form is not, why not go whole hog and proclaim that no knowledge is absolute? That would be consistent, at least. What's the reasoning behind the double standard?

Michael

[merjet]

In mathematics numbers are not adjectives but abstract objects.

This is how to create floating abstractions.

[Mindy Newton]

Math isn't the holy grail you think. Did you know that two and two don't always make four? Take two bananas and add two quarts of swamp gas. What do you get? You don't get four of anything!! You don't get four objects, or four "measures." Would you like to say that what we can't do is "add" these two particular "twos?" But we can. We can add them to a tank, for example.

The point is that numbers are adjectives. "Two" is always two of some kind. We are so accustomed to leaving out the grammatical niceties, we lose sight of their existence. Math is nothing until you get its conceptual context straight.

--Mindy

You need to learn the difference between pure mathematics and applied mathematics.

Yes, in "pure" mathematics, a higher level of abstraction is assumed. Numbers, points, lines, functions, etc., are treated as if they were objects, not characteristics of objects. However, this is a convenience only. It is not a repudiation of the context required to make numbers, and thus arithmetic and mathematics, meaningful. It is just "permission" to leave out the extra language. When people take "science" and/or "mathematics" to be superior, purer, more certain, etc., than philosophy or reason at large, they are mistaking that convenience as lack of encumbrance, which it isn't. There isn't pure mathematics without applied mathematics, and there isn't either without pre-existing concepts.

--Mindy

[Darrell Hougen]

In the swan case, they do not grant full identity and causality to swans. But they do to parts of swans and they use this to claim that it somehow proves that their view of swan is correct and lacking in fundaments.

The irony is in the end result. If you step outside the jargon, you can still have an open-ended category with these dudes that admits new knowledge to be included into it. (And that is one of the fundaments of a concept in Objectivism.) For instance, swan still continues to be a category to them. The only thing is that not all swans are white. I can't think of any Objectivist who would argue with that, either. The emphasis for them is placed on the new knowledge and not the category, but I haven't seen them state that making categories is invalid. In fact, they use categories all the time, especially when playing these word games.

Well said.

Darrell

[Darrell Hougen]

What you say, Darrell, is both very true and very important.

I noticed the Hume/Popper failure to take account of the Law of Identity when I was studying Popper back in the 1990's and drew attention to it in my essay "A Tangled Web of Guesses: A Critical Assessment of the Philosophy of Karl Popper" (1996); and in my "Debunking Popper" (~Reason Papers~ #24, Fall 1999). I also revisit the issue in my recent philosophical novel ~Old Nick's Guide to Happiness~.

If you don't have a copy, it's well worth getting H.W.B. Joseph's ~An Introduction to Logic~ out of the library, for he, of course, solved Hume's imaginary 'problem of induction' in 1916 -- precisely by pointing out that Hume's argument was in 'flat conflict' with the Law of Identity. Joseph was, unsurprisingly, an Aristotelian. Secondhand copies of his book can usually be found in the Philosophy section at Booth Books in Hay-on-Wye if you'd like me to try and track one down for you. I go there frequently, it's only about 40 minutes from where I live.

The encyclopaedically well-read George H. Smith drew attention to Joseph in his 1991 collection ~Atheism, Ayn Rand and Other Heresies~ (p. 200). The latter is a really fun read. I would warmly recommend it for anyone wanting a light-hearted, less po-faced look at Objectivism. Nicholas Dykes

Thanks for the comments and the references. I'll be sure to get a copy of "Old Nick's Guide to Happiness." Believe me, it's high on my list of books to buy.

Darrell

[Brant Gaede]

In mathematics numbers are not adjectives but abstract objects. In mathematics two plus two is always four...

At least that was the case up to now. Who knows about tomorrow? It might be different then. Right?

No, mathematical statements are always true, that's the difference with science. Perhaps one day you'll get it, but I won't hold my breath...

Because there is nothing to be false?

--Brant

[Darrell Hougen]

In order for the the Induction Problem, as stated by Popper and Hume, to be a serious problem it is necessary to ignore the Law of Identity and its corollary, the Law of Causality.

In fact the Law of Identity is about as relevant to the problem of induction as a fish is to a bicycle.

Here's why: All the LOI states is that in order to exist, a thing has to have an identity.

The LOI is however entirely silent when it comes to what that identity is (that is, its nature), and its corollary is equally silent on how it behaves (that is, its causal relations).

Unfortunately for this line of argument, the what and how is exactly where Hume's problem begins.

The law of identity implies certain things. For one, it implies that it takes a finite amount of time for something that exists to be transformed into something else. If that were not true, then it would be impossible to state that a thing had an identity in the first place.

It is also clear that the more massive something is, the longer it takes to transform it and the more energy the transformation requires. These seem like corollaries of the law of identity, though, at this point, I'm sort of going out on a limb. Still, it seems reasonable that to transform something massive, all of its parts must be transformed. So, if it takes a certain amount of time and energy to transform something small, it should take longer and require more energy to transform something large.

Back to the main point; to state that something has a specific nature is to state that the ways in which it can be altered or transformed are limited as are the things that it can do or can be done with it. The law of identity doesn't specify what those limits are --- they must be discovered --- just that there are limits. Again, if there were no limits, then a thing would not have an identity.

At any rate, the above qualities can be seen in every day life. One doesn't leave home in the morning and return to find that one's car has become a giant pumpkin during the day. Cows don't jump over the moon. And, old women don't live in shoes. Such is the stuff of fairy tales.

Darrell

[Brant Gaede]

Dragongfly,

You have proclaimed your proclamation about math being different. You have not given reasons why it is so. You should remember that I participated on that thread you mentioned. All I'm saying is that saying doesn't make it so.

I am starting to be curious as to why the double-standard with human knowledge. I am interested in what leads a person to believe in one.

(Just for the record, I obviously do hold that 2 + 2 always equals 4, but I also hold that the concept bear will always mean that big dangerous animal you can find in the woods.)

If one can proclaim that one form of knowledge is absolute but the other form is not, why not go whole hog and proclaim that no knowledge is absolute? That would be consistent, at least. What's the reasoning behind the double standard?

Michael

I don't think a mathematical statement is knowledge. "2" per se refers to nothing. "2 + 2 = 4" per se refers to nothing. "2X + 2Y" tells us nothing about X or Y. X and Y tell us nothing about 2.

This is as far as I can go with this, assuming I have gone anywhere. However, truth is absolute. We know some of it. We think we know additional stuff but generally the more abstract and complicated the more tentative it is.

--Brant