Deductive and inductive arguments

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Emil
 
Reply Fri 15 Jan, 2010 05:30 am
First read this. Then skim this discussion and this and pay careful attention to the posts by Kritikos.

How to distinguish them? Do you agree with the author of the above article's distinction method? In short, he thinks that intention of the maker of the argument decides what kind of argument it is. Thus, it is not an mind-independent fact what kind an argument is. That is interesting, maybe even implausible. Who knows. Kennethamy defended the intention theory before.

Kritikos, a critique of Ken argued like this:
Quote:
I am not saying that your position is indefensible; just that you have offered no good defense of it. In fact, for my part, I think that it is hopeless to try to define "deductive" in terms of the intentions of the author of an argument, for three reasons. First, one cannot always ascertain from the form or content of an argument whether its author intended it to be deductively valid; second, a definition in terms of the intentions of the author makes it possible for a deductively valid argument not to be a deductive argument (the author might not have so intended it); and third, the term "deductive" signifies a logical category, while the intentions of an author are not a matter of logic (i.e., it is a logical question whether an argument is deductively valid, but not a logical question whether the author of the argument intended it to be so).
(#92)

Ken also made this analogy:
Quote:
Not distinguishing between deductive arguments, and valid deductive arguments, is just like not distinguishing between addition, and correct addition.
(#95)

Quote:
A deductive argument is one such that if it is correct, then it is impossible for the premises to be true, and the conclusion false. (Logically impossible). But surely, you see there is a difference between an addition, and a correct addition. Why then is it so difficult to see the difference between a deductive argument, and a correct (valid) deductive argument. Just as not all additions are correct, not all deductive arguments are valid.

Just as we use addition to get true answers to sums, so we use deduction to get true conclusions from true premises. And, just as we sometimes fail to get true answers to sums, so we sometime fail to get true conclusions from true premises. But are due to mistakes on the part of the person who does the adding, in the first case; and due to mistakes on the part of the deducer, in the second case. The two are quite parallel.
(#97)

Which I find persuasive. But Ken offers no theory about how to distinguish them, he only argues that they are different.

I wonder if the type/token distinction can help us here.
 
kennethamy
 
Reply Fri 15 Jan, 2010 07:50 am
@Emil,
Emil;120114 wrote:
First read this. Then skim this discussion and this and pay careful attention to the posts by Kritikos.

How to distinguish them? Do you agree with the author of the above article's distinction method? In short, he thinks that intention of the maker of the argument decides what kind of argument it is. Thus, it is not an mind-independent fact what kind an argument is. That is interesting, maybe even implausible. Who knows. Kennethamy defended the intention theory before.

Kritikos, a critique of Ken argued like this:
(#92)

Ken also made this analogy:
(#95)

(#97)

Which I find persuasive. But Ken offers no theory about how to distinguish them, he only argues that they are different.

I wonder if the type/token distinction can help us here.


I am not sure what you think we need a theory of: The difference between correct and incorrect, or between induction and deduction.
 
Emil
 
Reply Fri 15 Jan, 2010 09:54 am
@kennethamy,
kennethamy;120129 wrote:
I am not sure what you think we need a theory of: The difference between correct and incorrect, or between induction and deduction.


Then maybe you too should read the links.

Of course, what is needed is an explanation of what a deductive argument is and what an inductive argument is.
 
Zetherin
 
Reply Fri 15 Jan, 2010 10:00 am
@Emil,
Some conclusions we can assume are only probable. We would not give these conclusions the same guarentee we would with deductive conclusions (as mentioned within the article).

And to ascertain whether a conclusion can be nothing more than probable, I would suspect we must take a look at the conclusion. Anything which falls into the scope of Hume's problem of induction; that is, a future occurence concluded based on past occurences, we can assume is inductive.
 
Emil
 
Reply Fri 15 Jan, 2010 11:11 am
@Zetherin,
Zetherin;120146 wrote:
Some conclusions we can assume are only probable. We would not give these conclusions the same guarentee we would with deductive conclusions (as mentioned within the article).

And to ascertain whether a conclusion can be nothing more than probable, I would suspect we must take a look at the conclusion. Anything which falls into the scope of Hume's problem of induction; that is, a future occurence concluded based on past occurences, we can assume is inductive.


And the relation between this and the question in the thread is... (?)
 
Zetherin
 
Reply Fri 15 Jan, 2010 11:18 am
@Emil,
Emil;120164 wrote:
And the relation between this and the question in the thread is... (?)


I don't understand how you can't see the relation. You're asking how to distinguish between deductive and inductive arguments. I offered one way you can.

Haha, I love how you put the question mark in parenthesis. You could have just as easily typed, "Wat is the relation between this and the thred?".
 
Pyrrho
 
Reply Fri 15 Jan, 2010 11:53 am
@Emil,
I don't understand what you are asking in your opening post.

Are you wanting to be able to distinguish between an argument that is intended to be deductively valid and one that is intended to be inductively valid? (Please note, "valid" means something different with induction than deduction, though, roughly, they mean that there is a kind of support that the premises give for the conclusion; with deduction, the support is absolute, and with induction, it is not).

If you find an argument that is deductively valid, or resembles a deductively valid argument, typically, it will be intended to be an example of deduction, but otherwise, if it is an argument, it is most likely intended to be induction.

There are also clues that can occur, whereby someone tells you how strongly they think the conclusion follows, which generally is an indication of whether it is a deductive argument or an inductive one. If they say, "it is likely" (or something similar) in the conclusion, usually this will mean they intend to have an inductive argument, but if they say "necessarily" or "it is impossible" (or something similar), they almost certainly mean that it is a deductive argument (though some people seem confused by this and imagine this to be a modal fallacy that is being committed, rather than simply the person telling you what kind of argument it is).

Often, people do not fully state an argument, such that there are implicit premises (i.e., premises that are not stated), which are judged to be sufficiently obvious that they don't need to be stated. For example, when speaking with a person schooled in modern theories of the shape the earth, one will normally find it unnecessary to state "the shape of the earth is roughly spherical", even though it may be a required part of the argument. So one is often in a position of needing to understand the intentions of the speaker (or writer) in order to identify what the argument is.

In practice, I think that the article to which you have linked is correct, that one must typically figure out the intentions of the speaker in order to know what the argument is. But the essential nature (I mean that phrase in the ordinary way, not in some metaphysical sense) of a deductively valid argument (or, for that matter, an inductively valid argument) is not determined by someone's intentions.
 
Emil
 
Reply Fri 15 Jan, 2010 12:36 pm
@Zetherin,
Zetherin;120166 wrote:
I don't understand how you can't see the relation. You're asking how to distinguish between deductive and inductive arguments. I offered one way you can.

Haha, I love how you put the question mark in parenthesis. You could have just as easily typed, "Wat is the relation between this and the thred?".


Not exactly. I asked for a theory of what a deductive argument is and what an inductive argument is. That you have not given.

(Stylistically I like to put question marks in parentheses sometimes. Don't know why. Did you intentionally use CS spellings instead of TO? "wat" instead of "what" and "thred" instead of "thread".)

---------- Post added 01-15-2010 at 07:44 PM ----------

Pyrrho;120173 wrote:
I don't understand what you are asking in your opening post.

Are you wanting to be able to distinguish between an argument that is intended to be deductively valid and one that is intended to be inductively valid? (Please note, "valid" means something different with induction than deduction, though, roughly, they mean that there is a kind of support that the premises give for the conclusion; with deduction, the support is absolute, and with induction, it is not).

If you find an argument that is deductively valid, or resembles a deductively valid argument, typically, it will be intended to be an example of deduction, but otherwise, if it is an argument, it is most likely intended to be induction.

There are also clues that can occur, whereby someone tells you how strongly they think the conclusion follows, which generally is an indication of whether it is a deductive argument or an inductive one. If they say, "it is likely" (or something similar) in the conclusion, usually this will mean they intend to have an inductive argument, but if they say "necessarily" or "it is impossible" (or something similar), they almost certainly mean that it is a deductive argument (though some people seem confused by this and imagine this to be a modal fallacy that is being committed, rather than simply the person telling you what kind of argument it is).

Often, people do not fully state an argument, such that there are implicit premises (i.e., premises that are not stated), which are judged to be sufficiently obvious that they don't need to be stated. For example, when speaking with a person schooled in modern theories of the shape the earth, one will normally find it unnecessary to state "the shape of the earth is roughly spherical", even though it may be a required part of the argument. So one is often in a position of needing to understand the intentions of the speaker (or writer) in order to identify what the argument is.

In practice, I think that the article to which you have linked is correct, that one must typically figure out the intentions of the speaker in order to know what the argument is. But the essential nature (I mean that phrase in the ordinary way, not in some metaphysical sense) of a deductively valid argument (or, for that matter, an inductively valid argument) is not determined by someone's intentions.


I am asking:

1. What is a deductive argument and what is a deductively valid argument?
2. What is an inductive argument and what is an inductively valid argument?
3. Are all arguments deductive or inductive?
4. Are some arguments deductive and inductive?

Kritikos' position is that all deductive arguments are deductively valid. So, in his view there is no deductive argument that commits a formal fallacy. Seems implausible to me and it is certainly inconsistent with what most logicians think.
 
Zetherin
 
Reply Fri 15 Jan, 2010 12:46 pm
@Emil,
Emil;120186 wrote:
Not exactly. I asked for a theory of what a deductive argument is and what an inductive argument is. That you have not given.


Then I misunderstood. I didn't know you were asking only for theories. I got this impression because you typed:

Quote:

How to distinguish them?


So, I provided a way to distinguish them. I suppose if we all worked together we could piece together a theory. Or maybe you could piece one together using knowledge you've gathered already on your blog!

Quote:

Did you intentionally use CS spellings instead of TO? "wat" instead of "what" and "thred" instead of "thread".


Yes, of course! :bigsmile:
 
Emil
 
Reply Fri 15 Jan, 2010 12:49 pm
@Zetherin,
Zetherin;120189 wrote:
Then I misunderstood. I didn't know you were asking only for theories. I got this impression because you typed:

So, I provided a way to distinguish them. I suppose if we all worked together we could piece together a theory. Or maybe you could piece one together using knowledge you've gathered already on your blog!


My bad. The problem is not that people cannot distinguish between them in practice. That people can do pretty good. The questions are the four I mentioned above.
 
Pyrrho
 
Reply Fri 15 Jan, 2010 12:58 pm
@Emil,
Emil;120186 wrote:
...

I am asking:

1. What is a deductive argument and what is a deductively valid argument?
2. What is an inductive argument and what is an inductively valid argument?
3. Are all arguments deductive or inductive?
4. Are some arguments deductive and inductive?

Kritikos' position is that all deductive arguments are deductively valid. So, in his view there is no deductive argument that commits a formal fallacy. Seems implausible to me and it is certainly inconsistent with what most logicians think.



I am still a bit puzzled by your questions, particularly coming from you. What is wrong with the responses given in a typical introductory logic textbook?

I do not wish to waste time in writing out those same things that can be so easily found in an ordinary logic textbook (if you want a specific recommendation, try Copi's Introduction to Logic, any edition), and which I suspect you already know or have read. But as it is quick and easy to answer the third and fourth questions, I will do so now:

3. Yes.
4. No, unless you mean that part of a lengthy argument (that is really a series of arguments) is inductive, and part is deductive.

It may be worth mentioning that not everything people say or write is an argument.
 
Zetherin
 
Reply Fri 15 Jan, 2010 01:20 pm
@Emil,
Emil wrote:
1. What is a deductive argument and what is a deductively valid argument?


A deductive argument is an argument where the conclusion follows necessarily from the premises.

A valid deductive argument is a deductive argument where the conclusion follows necessarily from the premises.

A non-valid deductive argument is a deductive argument where the conclusion does not follow necessarily from the premises.

Quote:
2. What is an inductive argument and what is an inductively valid argument?


An inductive argument is an argument where the premises offer a degree of support for the conclusion, but do not necessarily entail it; there is no guarentee (like your article noted).

As for validity, we cannot use the same notion of validity as we do with deductive arguments, because to be valid means it is not possible that the premises can be true and the conclusion false. And premises in an inductive argument can be true and yet the conclusion can be false. So I suppose this is why people use the property "cogency" instead.

Quote:
3. Are all arguments deductive or inductive?


I think it depends how we use the word "argument". But, I think if we use the word formally, the answer is yes.

Quote:
4. Are some arguments deductive and inductive?


Do you see how many ways this question can be interpreted?

1.) Yes, some arguments are deductive, some arguments are inductive.
2.) Yes, some arguments (like Pyrrho noted), can have inductive and deductive parts.
3.) No, if you mean that only some arguments are inductive or deductive. Because all formal arguments are deductive or inductive (and you might mean this since this question comes after the one which specifies "all arguments").
 
kennethamy
 
Reply Fri 15 Jan, 2010 01:22 pm
@Emil,
Emil;120144 wrote:
Then maybe you too should read the links.

Of course, what is needed is an explanation of what a deductive argument is and what an inductive argument is.


That is not difficult. Deductive arguments are intended to be conclusive arguments by the arguer. If the argument is not conclusive, but is intended to be conclusive, it is a failed (invalid) deductive argument. On the other hand, if an argument is not intended to be a conclusive argument by the arguer, it is non-deductive. But if the premises fail to support the conclusion of the non-deductive argument, then it is a failed (weak) non-deductive argument.

However, whatever the arguer intends, deductive or non-deductive, there are some arguments which it would hardly make sense to intend it as deductive, since it is so clearly non-conclusive; or make sense to intend it as non-deductive since it is so clearly conclusive. It would be a good rule (I think) to count a valid deductive argument as deductive, and a strong non-deductive argument as non-deductive.
 
Zetherin
 
Reply Fri 15 Jan, 2010 01:39 pm
@kennethamy,
kennethamy;120199 wrote:
That is not difficult. Deductive arguments are intended to be conclusive arguments by the arguer. If the argument is not conclusive, but is intended to be conclusive, it is a failed (invalid) deductive argument. On the other hand, if an argument is not intended to be a conclusive argument by the arguer, it is non-deductive. But if the premises fail to support the conclusion of the non-deductive argument, then it is a failed (weak) non-deductive argument.

However, whatever the arguer intends, deductive or non-deductive, there are some arguments which it would hardly make sense to intend it as deductive, since it is so clearly non-conclusive; or make sense to intend it as non-deductive since it is so clearly conclusive. It would be a good rule (I think) to count a valid deductive argument as deductive, and a strong non-deductive argument as non-deductive.


But can't we distinguish between inductive and deductive arguments without considering the intent of the arguer at all?
 
kennethamy
 
Reply Fri 15 Jan, 2010 01:50 pm
@Zetherin,
Zetherin;120208 wrote:
But can't we distinguish between inductive and deductive arguments without considering the intent of the arguer at all?


I don't see how, although, as I said, there are pretty clear cases of both kind when it would be implausible for the arguer's intention not to be the one or the other. In those cases we have what, in legal jargon, we might call, "constructive intent". That it was the arguer's intent whether or not it actually was (or the arguer was confused).
 
Zetherin
 
Reply Fri 15 Jan, 2010 01:58 pm
@kennethamy,
kennethamy;120214 wrote:
I don't see how, although, as I said, there are pretty clear cases of both kind when it would be implausible for the arguer's intention not to be the one or the other. In those cases we have what, in legal jargon, we might call, "constructive intent". That it was the arguer's intent whether or not it actually was (or the arguer was confused).


But we can distinguish an inductive argument from a deductive argument by looking looking at the argument. If all the premises can be true without the conclusion being true, it is an inductive argument:

1.) Socrates was Greek
2.) Most Greeks eat fish
3.) Socrates ate fish

This is an inductive argument. And we know it's not a deductive argument because although the premises may be true, the conclusion does not follow necessarily from the premises; the conclusion may not be true.

Isn't that right?
 
Pyrrho
 
Reply Fri 15 Jan, 2010 02:01 pm
@kennethamy,
kennethamy;120214 wrote:
Zetherin;120208 wrote:
But can't we distinguish between inductive and deductive arguments without considering the intent of the arguer at all?

I don't see how, although, as I said, there are pretty clear cases of both kind when it would be implausible for the arguer's intention not to be the one or the other. In those cases we have what, in legal jargon, we might call, "constructive intent". That it was the arguer's intent whether or not it actually was (or the arguer was confused).


I would rather say, we do not know what the argument is without knowing the intentions of the arguer. But once we know what the argument is, we then may be able to determine whether it is deductively valid or not, and whether it is inductively valid or not.

Perhaps, though, this is a mere verbal distinction, without any importance at all.
 
kennethamy
 
Reply Fri 15 Jan, 2010 02:06 pm
@Zetherin,
Zetherin;120217 wrote:
But we can distinguish an inductive argument from a deductive argument by looking looking at the argument. If all the premises can be true without the conclusion being true, it is an inductive argument:

1.) Socrates was Greek
2.) Most Greeks eat fish
3.) Socrates ate fish

This is an inductive argument. And we know it's not a deductive argument because although the premises may be true, the conclusion does not follow necessarily from the premises; the conclusion may not be true.

Isn't that right?


Why can't it be an argument with true premises and a false conclusion be an invalid deductive argument? In fact, why can't an argument with true premises and a true conclusion be an invalid deductive argument?

All fish can swim
All sharks can swim

All sharks are fish

Is invalid. (Fallacy of the undistributed middle term).
 
fast
 
Reply Fri 15 Jan, 2010 02:15 pm
@Emil,
Emil,

I thought what you were meaning to ask for is an analysis of deductive arguments and/or an analysis of inductive arguments. You already know the difference between the two, so you do not need an explanation of what each is. Instead, what you want is an analysis, for merely knowing the difference between the two doesn't therefore imply that you can always be given an argument and definitively determine whether or not the logical argument is a deductive argument or inductive argument, for sometimes, being privy to the argument is insufficient information to determine whether or not an argument is deductive or inductive.

That of course has no bearing on whether or the argument is deductive or inductive, just as truth doesn't depend on knowledge of the truth.

[QUOTE]2. What is an inductive argument and what is an inductively valid argument?[/QUOTE]I don't think you should ever regard inductive arguments as valid or invalid.
 
Zetherin
 
Reply Fri 15 Jan, 2010 02:17 pm
@Emil,
I got soundness and validity confused. Validity speaks nothing of truth, only form. To be valid means that the conclusion follows from the premises. An argument being valid does not mean that it is true. Validity is a necessary but not sufficient condition for soundness. It is not a sufficient condition because an argument not only needs to be valid to be sound, but it also needs to be true.

Is this right?
 
 

 
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