Deduction and induction

[Speakpigeon]

Apparently Peirce also developed a probabilistic theory of inductive validity. Yes!

See http://www.jstor.org/discover/10.23...id=2129&uid=2&uid=70&uid=4&sid=21104406632873

You can apparently read it on line free...

Or buy the pdf for $13.50, for... 26 pages. That's one buck for two pages! A bargain!

Peirce's Probabilistic Theory of Inductive Validity
Chung-Ying Cheng
Transactions of the Charles S. Peirce Society
Vol. 2, No. 2 (Fall, 1966), pp. 86-112
Published by: Indiana University Press
Article Stable URL: http://www.jstor.org/stable/40319525

EB

 

[fromderinside]

Sorry-sorry, you may disregard my previous link! It's not very good…


This one is better: Stanford Encyclopedia of Philosophy: Logical Consequence

1. Deductive and Inductive Consequence
In inductively valid arguments, the (joint) truth of the premises is very likely (but not necessarily) sufficient for the truth of the conclusion. An inductively valid argument is such that, as it is often put, its premises make its conclusion more likely or more reasonable (even though the conclusion may well be untrue given the joint truth of the premises).

We seem to disagree on what exactly are inductively valid argument but I'm probably right...

And it does say "inductively valid arguments"…
EB

So you will agree that the inductive argument that gravity pulled mass was valid since it explained celestial mechanic observations until it was found that gravity distorted space was confirmed by observations such as light being bent around massive objects so now it is only approximately valid for large objects moving relatively slowly.....

 

[fast]

Sorry-sorry, you may disregard my previous link! It's not very good…


This one is better: Stanford Encyclopedia of Philosophy: Logical Consequence

1. Deductive and Inductive Consequence
In inductively valid arguments, the (joint) truth of the premises is very likely (but not necessarily) sufficient for the truth of the conclusion. An inductively valid argument is such that, as it is often put, its premises make its conclusion more likely or more reasonable (even though the conclusion may well be untrue given the joint truth of the premises).

We seem to disagree on what exactly are inductively valid argument but I'm probably right...

And it does say "inductively valid arguments"…
EB

It's regrettable that the author has chosen to use the term in that fashion, as it does appear to support the notion that inductive arguments are the kinds of arguments that can be said to be valid. Clearly, such usage goes against the mainstream usage which makes it very clear that valid arguments can only apply to deductive arguments because of the necessity (through entailment) of the conclusion.

 

[Speakpigeon]

Sorry-sorry, you may disregard my previous link! It's not very good…


This one is better: Stanford Encyclopedia of Philosophy: Logical Consequence



We seem to disagree on what exactly are inductively valid argument but I'm probably right...

And it does say "inductively valid arguments"…
EB

So you will agree that the inductive argument that gravity pulled mass was valid since it explained celestial mechanic observations until it was found that gravity distorted space was confirmed by observations such as light being bent around massive objects so now it is only approximately valid for large objects moving relatively slowly.....

No.

Obviously not but that simple fact is probably too hard to grasp for you. Clue: your post is well below the standard for a philosophical forum and for me at any rate. I could tell you why but do you want to know? You lazy dog will have to ask anyway.
EB

 

[Speakpigeon]

Sorry-sorry, you may disregard my previous link! It's not very good…


This one is better: Stanford Encyclopedia of Philosophy: Logical Consequence



We seem to disagree on what exactly are inductively valid argument but I'm probably right...

And it does say "inductively valid arguments"…
EB

It's regrettable that the author has chosen to use the term in that fashion, as it does appear to support the notion that inductive arguments are the kinds of arguments that can be said to be valid. Clearly, such usage goes against the mainstream usage which makes it very clear that valid arguments can only apply to deductive arguments because of the necessity (through entailment) of the conclusion.

First, he is not the only one talking about, and accepting the idea of, inductive validity. It goes back at least to Pierce as I already pointed out.

Second, I challenge you to quote any author who stated explicitly that inductive arguments could not possibly be valid in some sense. Clearly, an inductive argument is not valid in the same way that a deductive argument can be but that is completely irrelevant since nobody is claiming this and certainly no me. There is clear blue water between inductive and deductive arguements (or inferences) and that's it.

Finally, it seems to me your brain is playing trick on this issue. You don't seem to have any argument (no ones that would be relevant) and I've provided you with everything you needed to accept this idea. I would call that being very literal-minded, like a security agent at an airport security check.

Anyway, I feel we've said whatever needed to be said on the subject and it's no big deal.
EB

 

[fast]

It's regrettable that the author has chosen to use the term in that fashion, as it does appear to support the notion that inductive arguments are the kinds of arguments that can be said to be valid. Clearly, such usage goes against the mainstream usage which makes it very clear that valid arguments can only apply to deductive arguments because of the necessity (through entailment) of the conclusion.

First, he is not the only one talking about, and accepting the idea of, inductive validity. It goes back at least to Pierce as I already pointed out.

Second, I challenge you to quote any author who stated explicitly that inductive arguments could not possibly be valid in some sense. Clearly, an inductive argument is not valid in the same way that a deductive argument can be but that is completely irrelevant since nobody is claiming this and certainly no me. There is clear blue water between inductive and deductive arguements (or inferences) and that's it.

Finally, it seems to me your brain is playing trick on this issue. You don't seem to have any argument (no ones that would be relevant) and I've provided you with everything you needed to accept this idea. I would call that being very literal-minded, like a security agent at an airport security check.

Anyway, I feel we've said whatever needed to be said on the subject and it's no big deal.
EB

So, let me get this straight.

If I say that no inductive argument is valid, and if I mean "valid" in the same sense you would mean "valid" when using the term, "deductively valid", wouldn't it be incorrect to say that I'm wrong when I say that no inductive argument is valid simply because the term "valid" is apparently ambiguous?

 

[Speakpigeon]

If I say that no inductive argument is valid, and if I mean "valid" in the same sense you would mean "valid" when using the term, "deductively valid", wouldn't it be incorrect to say that I'm wrong when I say that no inductive argument is valid simply because the term "valid" is apparently ambiguous?

I don't see what would be ambiguous as long as we are able to distinguish between inductive and deductive arguments.

And we can always specify: deductively valid or inductively valid.

As shown below, validity applies outside logic so nobody is ever going to accept that it only applies to deductive arguments or conclusions:

1. Well justified: a valid objection.
2. Resulting in the appropriate results: a valid method.
3. Supported by legal force: a valid title.
4. Logic
a. Argument where the conclusion may logically be derived from the premises: a valid argument.
b. Correctly inferred from a premise: a valid conclusion.
5. (Archaic) Of sound health.

EB

 

[Philos]

Me I would certainly say that the following inference it's a valid one:

Most men are no taller than 1.83m;
Jackson is a man;
We don't know anything that would entail that Jackson is taller than 1.83m
Therefore, Jackson is probably no taller than 1.83m.

Doesn't that show that we are not sure of the conclusion?

But, this one wouldn't be valid:

Most men are no taller than 1.83m;
Jackson is a man;
We don't know anything that would entail that Jackson is taller than 1.83m
Therefore, Jackson is no taller than 1.83m.

EB

EB,

Yes, provided that we add the 'probably' disclaimer we are in the realms of contingency.

In philosophical logic the terms valid/invalid and true/false have a formal meaning which is not available outside of deduction.

http://en.wikipedia.org/wiki/Inductive_reasoning

Alex.

 

[fast]

I don't see what would be ambiguous as long as we are able to distinguish between inductive and deductive arguments.

And we can always specify: deductively valid or inductively valid.

As shown below, validity applies outside logic so nobody is ever going to accept that it only applies to deductive arguments or conclusions:

1. Well justified: a valid objection.
2. Resulting in the appropriate results: a valid method.
3. Supported by legal force: a valid title.
4. Logic
a. Argument where the conclusion may logically be derived from the premises: a valid argument.
b. Correctly inferred from a premise: a valid conclusion.
5. (Archaic) Of sound health.

EB

Wait, what? You're using those lexical definitions?

 

[Speakpigeon]

Me I would certainly say that the following inference it's a valid one:

In philosophical logic the terms valid/invalid and true/false have a formal meaning which is not available outside of deduction.

It's good to know that some hatchet men are working on the subject.

Do you think there is some kind of central clearinghouse for philosophical terminology? Members appointed by whom?

I thought I had given examples of respectable sources showing that the expression "inductive validity" was in use.

However, my point is that I think it is interesting to look at how inductive arguments could be valid. Do you refuse to talk about passports being valid? I'm sure not, so you should not shrink from saying that an inductive argument is valid as long as it is clear that you are talking about an inductive argument. Any problem with that?
EB

 

[Speakpigeon]

I don't see what would be ambiguous as long as we are able to distinguish between inductive and deductive arguments.

And we can always specify: deductively valid or inductively valid.

As shown below, validity applies outside logic so nobody is ever going to accept that it only applies to deductive arguments or conclusions:

EB

Wait, what? You're using those lexical definitions?

Listen, it's all very well to have a conversation and poke fun but I think my post was very clear as to what my point was. Do you have something to say about it or not?
EB

 

[fast]

Wait, what? You're using those lexical definitions?

Listen, it's all very well to have a conversation and poke fun but I think my post was very clear as to what my point was. Do you have something to say about it or not?
EB

I appreciate that you're trying to have a serious discussion, but something's amiss. There are times when I think you're failing to allow the context to disambiguate the meaning of the words I'm using.

For example, if I say I'm running low on funds and need to go to the bank, you will insist that I went to the bank, even though you know I never went to the financial institution. Why? Because you saw me at the river bank. I'm not mistaken when I say I never went to the bank, even though I went to the river bank. The proposition expressed when I say no inductive argument is valid is true, not false just because the term, "valid" has other lexical meanings. I never went to the bank. That's true, and just because it just happens to be true that I went to the bank (by the river), it's still false that I went to the bank (financial institution).

When I think there's no need to further disambiguate the issue, I find myself right back where I started, having to explain what I'm not talking about.

And yes, I accept that some inductive arguments are valid, but am I, or am I not correct when I say no inductive argument is valid? Do I really need to explain?

 

[Philos]

Folks,

I think that an inductive argument could be said to be valid if it shows that we cannot be sure of the conclusion.

Alex.

 

[Speakpigeon]

Listen, it's all very well to have a conversation and poke fun but I think my post was very clear as to what my point was. Do you have something to say about it or not?
EB

I appreciate that you're trying to have a serious discussion, but something's amiss. There are times when I think you're failing to allow the context to disambiguate the meaning of the words I'm using.

For example, if I say I'm running low on funds and need to go to the bank, you will insist that I went to the bank, even though you know I never went to the financial institution. Why? Because you saw me at the river bank. I'm not mistaken when I say I never went to the bank, even though I went to the river bank. The proposition expressed when I say no inductive argument is valid is true, not false just because the term, "valid" has other lexical meanings. I never went to the bank. That's true, and just because it just happens to be true that I went to the bank (by the river), it's still false that I went to the bank (financial institution).

When I think there's no need to further disambiguate the issue, I find myself right back where I started, having to explain what I'm not talking about.

And yes, I accept that some inductive arguments are valid, but am I, or am I not correct when I say no inductive argument is valid? Do I really need to explain?

I thought I had already responded to that by pointing out that the context needs to make clear when we're talking about an inductive argument and when I am talking about a deductive argument, which is obviously done if we use the expression "inductive validity" or, when we are obviously talking about an inductive argument, that it is valid.

Inductive and deductive arguments are different in nature so I don't see how inductive and deductive validities could be mistaken one for the other.

I'm also insisting on using "validity" for inductive argument because, current usage notwithstanding, I think it should be the proper word to use and that it is misleading to use a different word. I think current usage is a leftover of past, possibly still linguering, misunderstandings about of the difference between inductive and deductive arguments.

However, if you think that there is still an issue about whether certain inductive arguments could possibly be deductively valid you may be right but then we would need examples to see if that's the case.
EB

 

[Speakpigeon]

Folks,

I think that an inductive argument could be said to be valid if it shows that we cannot be sure of the conclusion.

Alex.

I understand what you mean but I definitely disagree with the way you say it!

In my previous example, I'm definetely pretty sure about the conclusion:

Most men are no taller than 1.83m;
Jackson is a man;
We don't know anything that would entail that Jackson is taller than 1.83m
Therefore, Jackson is probably no taller than 1.83m.

That is to say, I'm pretty sure, given the premises, that Jackson is probably no taller than 1.83m.

You'd be right to say that maybe he is taller than 1.83m, and we should be just as sure that that is also true, but the conclusion is not that he is no taller than 1.83m but that he is probably no taller than 1.83m and that's why we should be pretty sure this conclusion is correct, irrespective of whether, actually, Jackson is or not taller than 1.83m.

Do you see a problem in saying "Jackson is probably no taller than 1.83m AND maybe he is taller than 1.83m"? Me I think it is also a valid conclusion of the premises!
EB

 

[fast]

I appreciate that you're trying to have a serious discussion, but something's amiss. There are times when I think you're failing to allow the context to disambiguate the meaning of the words I'm using.

For example, if I say I'm running low on funds and need to go to the bank, you will insist that I went to the bank, even though you know I never went to the financial institution. Why? Because you saw me at the river bank. I'm not mistaken when I say I never went to the bank, even though I went to the river bank. The proposition expressed when I say no inductive argument is valid is true, not false just because the term, "valid" has other lexical meanings. I never went to the bank. That's true, and just because it just happens to be true that I went to the bank (by the river), it's still false that I went to the bank (financial institution).

When I think there's no need to further disambiguate the issue, I find myself right back where I started, having to explain what I'm not talking about.

And yes, I accept that some inductive arguments are valid, but am I, or am I not correct when I say no inductive argument is valid? Do I really need to explain?

I thought I had already responded to that by pointing out that the context needs to make clear when we're talking about an inductive argument and when I am talking about a deductive argument, which is obviously done if we use the expression "inductive validity" or, when we are obviously talking about an inductive argument, that it is valid.

Inductive and deductive arguments are different in nature so I don't see how inductive and deductive validities could be mistaken one for the other.

I'm also insisting on using "validity" for inductive argument because, current usage notwithstanding, I think it should be the proper word to use and that it is misleading to use a different word. I think current usage is a leftover of past, possibly still linguering, misunderstandings about of the difference between inductive and deductive arguments.

However, if you think that there is still an issue about whether certain inductive arguments could possibly be deductively valid you may be right but then we would need examples to see if that's the case.
EB

There is still something going on that bothers me. I have an appreciation for distinctions, and although I almost always prefer to use lexical definitions over stipulative definitions, I readily accept the stipulative usage of the term, "valid" since it's a technical term in logic.

When I say that no inductive argument is valid, i do so because it's not the kind of argument that can be valid--it's a category error in fact. When I say all that, I'm using the term "valid" in the technical sense ordinarily used by logicians. Meanwhile, I hear you and accept that we can use the term as it is commonly used in our lexicon.

So far so good, but when you speak of another distinction (between that of deductive validity and inductive validity) this is where things get tricky and we have to keep our eye on the ball. By virtue of even uttering the term deductive validity in contrast to inductive validity, there is an underlying issue that goes beyond the fact that there are lexical and stipulative usages of terms.


Look at what you wrote:

I thought I had already responded to that by pointing out that the context needs to make clear when we're talking about an inductive argument and when I am talking about a deductive argument, which is obviously done if we use the expression "inductive validity" or, when we are obviously talking about an inductive argument, that it is valid.

The ambiguity that context needs to clear up hasn't to with whether an argument is deductive or inductive--it has to do with with whether we're using the term validity in a technical sense or lexical sense--unless you're prepared to offer me a commonly used technical definition of "validity" when applied to inductive arguments to the exclusion of deductive arguments, I must insist that the underlying confusion between us hasn't been resolved.

Would you accuse a student using a lexical meaning of the term "valid" when discussing only deductive arguments as speaking about inductive validity?

 

[Philos]

Folks,

I think that an inductive argument could be said to be valid if it shows that we cannot be sure of the conclusion.

Alex.

I understand what you mean but I definitely disagree with the way you say it!

In my previous example, I'm definetely pretty sure about the conclusion:

Most men are no taller than 1.83m;
Jackson is a man;
We don't know anything that would entail that Jackson is taller than 1.83m
Therefore, Jackson is probably no taller than 1.83m.

That is to say, I'm pretty sure, given the premises, that Jackson is probably no taller than 1.83m.

You'd be right to say that maybe he is taller than 1.83m, and we should be just as sure that that is also true, but the conclusion is not that he is no taller than 1.83m but that he is probably no taller than 1.83m and that's why we should be pretty sure this conclusion is correct, irrespective of whether, actually, Jackson is or not taller than 1.83m.

Do you see a problem in saying "Jackson is probably no taller than 1.83m AND maybe he is taller than 1.83m"? Me I think it is also a valid conclusion of the premises!
EB

speakpigeon,

Maybe I was teasing a bit and I think we actually agree. I am saying that the only valid thing we can say about an inductive argument is that it is an inductive argument. As this is a logical tautology we can include it in the category of validity aka deduction. Using the terms 'probably' and 'maybe' is what separates induction from deduction and it is this inconclusiveness which marks out an inductive argument from a deductive argument. The key is that with induction there is always the possibility of more information to undermine our conclusion, although I do agree that 'maybe' is a get out from being undermined. We'll maybe need to look into that part more closely. What kind of conclusion is a maybe?

Of course, with a tautology there is no possibility of more information as that would invalidate the tautology, so a tautology is always valid, in the way that an induction is never valid except to say that it is valid that induction is induction.

Tautologies can seem inductive but it's a trick. For example if I say "If it gets any colder in here it won't be as warm as it is now." That seems like an induction but it's just a joke on tautologies. I'm just saying, "If it gets any colder in here it will get colder in here."

In your Jackson case there is a genuine induction, and a strong one. I think it may be valid to say that the Jackson case is an induction.

Alex.

 

[fast]

I understand what you mean but I definitely disagree with the way you say it!

In my previous example, I'm definetely pretty sure about the conclusion:

Most men are no taller than 1.83m;
Jackson is a man;
We don't know anything that would entail that Jackson is taller than 1.83m
Therefore, Jackson is probably no taller than 1.83m.

That is to say, I'm pretty sure, given the premises, that Jackson is probably no taller than 1.83m.

You'd be right to say that maybe he is taller than 1.83m, and we should be just as sure that that is also true, but the conclusion is not that he is no taller than 1.83m but that he is probably no taller than 1.83m and that's why we should be pretty sure this conclusion is correct, irrespective of whether, actually, Jackson is or not taller than 1.83m.

Do you see a problem in saying "Jackson is probably no taller than 1.83m AND maybe he is taller than 1.83m"? Me I think it is also a valid conclusion of the premises!
EB

speakpigeon,

Maybe I was teasing a bit and I think we actually agree. I am saying that the only valid thing we can say about an inductive argument is that it is an inductive argument. As this is a logical tautology we can include it in the category of validity aka deduction. Using the terms 'probably' and 'maybe' is what separates induction from deduction and it is this inconclusiveness which marks out an inductive argument from a deductive argument. The key is that with induction there is always the possibility of more information to undermine our conclusion, although I do agree that 'maybe' is a get out from being undermined. We'll maybe need to look into that part more closely. What kind of conclusion is a maybe?

Of course, with a tautology there is no possibility of more information as that would invalidate the tautology, so a tautology is always valid, in the way that an induction is never valid except to say that it is valid that induction is induction.

Tautologies can seem inductive but it's a trick. For example if I say "If it gets any colder in here it won't be as warm as it is now." That seems like an induction but it's just a joke on tautologies. I'm just saying, "If it gets any colder in here it will get colder in here."

In your Jackson case there is a genuine induction, and a strong one. I think it may be valid to say that the Jackson case is an induction.

Alex.

The technical term, "valid" applies only to deductive arguments, and there is no technical term, "valid" that applies to non-deductive arguments. An inductive argument is a kind of non-deductive argument;moreover, there is no technical term, "valid" that applies to inductive arguments. So, if there is a term, "valid" that applies to inductive arguments (and I concede to the claim there are), then the term is not a technical term. By technical term, I mean a kind of stipulative term.

If a conclusion to an argument MUST follow from its premises (be it true or not), then 1) the argument is deductive and 2) the form of the argument is valid (and I'm using the technical meaning of the word, "valid"; hence, I'm not using the lexical meaning of the word.

If the conclusion to an argument is not a logical necessity, then 1) the argument is not a deductive argument and 2) the form of the argument is not valid--again, I'm not using any lexical definition of the word, "valid".

Now, let's turn to a few things you said, one being, "I am saying that the only valid thing we can say about an inductive argument is that it is an inductive argument." An inductive argument is an inductive argument. That's true. It's sometimes called a trivial truism because it is a tautology. Your particular use of the word, "valid" in this instance should be avoided. If you think what you're saying is true, then say that. Don't substitute what you mean to express with that word. It's a confusion that's easily avoidable. Incidentally, it's not the only (ONLY) true statement we can say about inductive arguments.

A second remark is, "Using the terms 'probably' and 'maybe' is what separates induction from deduction and it is this inconclusiveness which marks out an inductive argument from a deductive argument." There's a lot to unpack here, but the use of the word, "what" in this instance shows that you are not properly delineating the two kinds of arguments, but yes, if a conclusion must follow from it's premises, then the argument is not an inductive argument.

 

[Philos]

Now, let's turn to a few things you said, one being, "I am saying that the only valid thing we can say about an inductive argument is that it is an inductive argument." An inductive argument is an inductive argument. That's true. It's sometimes called a trivial truism because it is a tautology. Your particular use of the word, "valid" in this instance should be avoided. If you think what you're saying is true, then say that. Don't substitute what you mean to express with that word. It's a confusion that's easily avoidable. Incidentally, it's not the only (ONLY) true statement we can say about inductive arguments.

fast,

I think it is helpful to compare the words 'valid' and 'true'. In formal logic we find that deductive arguments can be valid and statements can be true. However, these arguments and statements are trivial in the sense that they don't tell us anything about the world of contingencies. They are valid or true by the terms within those arguments or statements. In this sense both are 'closed' and (as you say) trivial. Some have said that the whole of mathematics is like this, which is food for much philosophical thought.

Induction is not 'closed'. Inductive arguments are strong or weak, although no inductive argument is as strong as a deductive argument as full strength is validity for an argument and truth for a statement. Inductive arguments can never reach full strength as the arguments' strength does not rely wholly on the terms within it.

The really interesting thing about all this is what it tells us about reasoning and the world around us. We have intellectual tools which also practically limit us in dealing with the world. That's philosophy.

Alex.

 

[Speakpigeon]

I think we actually agree.

Actually, I'm quite sure we don't, at least judging on what you said in your post. However, I already explained in my few recent posts all that you would need to know to understand why and I don't want to reiterate.
EB