Deductive and inductive arguments

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Emil
 
Reply Tue 19 Jan, 2010 11:22 am
@Emil,
As per various people's misunderstandings in this thread I have added the following section to the intro.

[INDENT]Avoiding misunderstandings

I am not discussing how to best judge what kind of argument an argument is, that is, whether it is deductive or inductive. That is a matter of methodology. Some people have confused the intention theory of deductive and inductive arguments (which I write of in this essay) with the intention theory/approach of how to best discover what kind of argument it is. They are not the same. They do not logically imply each other either. That the intention theory of arguments is true, does not imply that using the arguer's intentions is the best way to discover what kind an argument is. Conversely, that the best way to discover what kind an argument is is to 'look' at the arguer's intentions, does not imply that the intention theory of arguments is true.
[/INDENT]
 
Pyrrho
 
Reply Tue 19 Jan, 2010 01:23 pm
@Emil,
Emil;120593 wrote:
...


I agree that the argument above is valid (= "deductively valid"), but that does not imply that it is deductive. So, you beg the question when you write "Modus Ponens is a deductive form of argument, regardless of how anyone intends it to be taken.".

This is what is at issue. I'm not endorsing any specific theory. Maybe you have a third theory on the matter? That's good. But it would be better if you told us about it.



That is like saying, to someone who says that all bachelors are unmarried, that that person is begging the question about what the term "bachelor" means.


Emil;120599 wrote:
Because according to the intention theory iff the arguer intended an argument to be inductive, then it is inductive. And some arguers intend that a valid argument is inductive. Thus, there is a valid inductive argument.

So by saying that you are merely begging the question against the intention theory.

I don't think the deductive induction distinction is analogous to the addition subtraction distinction. That remains to be argued.

---------- Post added 01-17-2010 at 04:53 AM ----------



Where can I read about that theory? It was not mentioned in the IEP article. The IEP article clearly presumes the intention theory.

...


Emil;120768 wrote:
Let me add, that the names of these two theories are, AFIAK, my invention and no one, AFAIK, besides us here talks about them. The IEP article, the only academic resource I could find on this, does not mention two theories but it endorses the intention theory of deductive and inductive arguments. At least it does not seem to me that the article is simply 'advocating' using arguer intentions as a method of discover what kind of argument it is.



I think you have misunderstood the IEP article. I do not think that the author seriously endorses what you are calling the "intention theory". I believe that he or she is attempting to give a practical way of figuring out what argument it is that is being discussed. When someone presents an argument, you first need to understand what they are talking about so that you can know what argument it is that is to be evaluated. It is only after you know what the argument is that you will be in a position to know whether it is valid or invalid, sound or unsound, etc.

As you already know, many people jump to wild conclusions about what argument someone is talking or writing about, and so they end up with useless discussions that are totally beside the point that the person is trying to make. So, from a practical standpoint, it is a good idea to emphasize the attempt at understanding intentions when dealing with arguments in the real world.

If you wish to say that the person's remarks literally entail your "intention theory", then I will only say, if that is so, then the article is improperly written.

I do not believe you will find any credible source that explicitly endorses your "intention theory".

To go back to your article in post 68, your "Validity theory", in which you state, "An argument is deductive iff it is valid.
An argument is inductive iff it is invalid."

That is also unsatisfactory, for the reasons you state. So, with both of the theories you have presented, you have given reasons to reject them. But neither theory is one that I have ever even heard of anyone endorsing.

You seem to be wanting a definition of a deductive argument and an inductive argument, of the form, "an argument is ... if and only if....", such that everything is rigidly and absolutely determined. You do not always get what you want, and I will not give you any such definition now. A deductive argument is one which is valid or one which resembles a valid argument. Thus, the fallacy of affirming the consequent is a deductive argument, because it resembles the valid argument modus ponens. The fallacy of affirming the consequent is a deductive argument because it looks like such a thing. It appears as though the conclusion is supposed to necessarily follow from the premises, and so it is a deductive argument. An inductive argument is any argument that is not deductive. Or we could say, an inductive argument is one in which the premises appear to offer some sort of support for the conclusion that is less than conclusive. (Anything that does not offer or appear to offer any kind of support is not an argument.)

Wikipedia expresses it this way:

[INDENT][INDENT]In logic, an argument is a set of one or more meaningful declarative sentences (or "propositions") known as the premises along with another meaningful declarative sentence (or "proposition") known as the conclusion. A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises; an inductive argument asserts that the truth of the conclusion is supported by the premises.[/INDENT][/INDENT]
Argument - Wikipedia, the free encyclopedia

Now, I fully expect you to be dissatisfied with this, but I don't think you are always going to get platonic essences for meanings of terms, and instead end up with something that fits a Wittgensteinian concept of a family resemblance instead. (After that introduction, you can read more at: Ludwig Wittgenstein (Stanford Encyclopedia of Philosophy).)
 
Emil
 
Reply Tue 19 Jan, 2010 04:09 pm
@Pyrrho,
Emil wrote:
...


I agree that the argument above is valid (= "deductively valid"), but that does not imply that it is deductive. So, you beg the question when you write "Modus Ponens is a deductive form of argument, regardless of how anyone intends it to be taken.".

This is what is at issue. I'm not endorsing any specific theory. Maybe you have a third theory on the matter? That's good. But it would be better if you told us about it.


Pyrrho;121075 wrote:
That is like saying, to someone who says that all bachelors are unmarried, that that person is begging the question about what the term "bachelor" means.


If two people were discussing what "bachelor" means and one of them said that, then yes, he would be begging the question.


Emil wrote:
Because according to the intention theory iff the arguer intended an argument to be inductive, then it is inductive. And some arguers intend that a valid argument is inductive. Thus, there is a valid inductive argument.

So by saying that you are merely begging the question against the intention theory.

I don't think the deductive induction distinction is analogous to the addition subtraction distinction. That remains to be argued.

---------- Post added 01-17-2010 at 04:53 AM ----------



Where can I read about that theory? It was not mentioned in the IEP article. The IEP article clearly presumes the intention theory.

...


Emil wrote:
Let me add, that the names of these two theories are, AFIAK, my invention and no one, AFAIK, besides us here talks about them. The IEP article, the only academic resource I could find on this, does not mention two theories but it endorses the intention theory of deductive and inductive arguments. At least it does not seem to me that the article is simply 'advocating' using arguer intentions as a method of discover what kind of argument it is.


Pyrrho;121075 wrote:
I think you have misunderstood the IEP article. I do not think that the author seriously endorses what you are calling the "intention theory". I believe that he or she is attempting to give a practical way of figuring out what argument it is that is being discussed. When someone presents an argument, you first need to understand what they are talking about so that you can know what argument it is that is to be evaluated. It is only after you know what the argument is that you will be in a position to know whether it is valid or invalid, sound or unsound, etc.


I think that is possible, but consider this quote from the IEP article:
[INDENT]"A deductive argument is an argument in which it is thought that the premises provide a guarantee of the truth of the conclusion. In a deductive argument, the premises are intended to provide support for the conclusion that is so strong that, if the premises are true, it would be impossible for the conclusion to be false.


An inductive argument is an argument in which it is thought that the premises provide reasons supporting the probable truth of the conclusion. In an inductive argument, the premises are intended only to be so strong that, if they are true, then it is unlikely that the conclusion is false.


The difference between the two comes from the sort of relation the author or expositor of the argument takes there to be between the premises and the conclusion. If the author of the argument believes that the truth of the premisesdefinitely establishes the truth of the conclusion due to definition, logical entailment or mathematical necessity, then the argument is deductive. If the author of the argument does not think that the truth of the premises definitely establishes the truth of the conclusion, but nonetheless believes that their truth provides good reason to believe the conclusion true, then the argument is inductive."


[/INDENT]Any straightforward reading of that results in one thinking that it endorses the intention theory. It uses almost the exact same phrases as does the intention theory (more specifically, my formulation of it). Compare:[INDENT]"A deductive argument is an argument in which it is thought that the premises provide a guarantee of the truth of the conclusion. In a deductive argument, the premises are intended to provide support for the conclusion that is so strong that, if the premises are true, it would be impossible for the conclusion to be false." (first three paragraphs in IEP article) [my bolds]



"An argument is deductive iff it is intended by the arguer to be deductive.
An argument is inductive iff it is intended by the arguer to be inductive." (from my essay draft above) [my bolds here, not in original formulation]
[/INDENT]Though it is not of vital importance to the points that I make in my essay that the IEP article supports the intention theory.


Pyrrho;121075 wrote:
As you already know, many people jump to wild conclusions about what argument someone is talking or writing about, and so they end up with useless discussions that are totally beside the point that the person is trying to make. So, from a practical standpoint, it is a good idea to emphasize the attempt at understanding intentions when dealing with arguments in the real world.



I agree with this. But that does not imply either of the two theories above and it is consistent with both.


Pyrrho;121075 wrote:
If you wish to say that the person's remarks literally entail your "intention theory", then I will only say, if that is so, then the article is improperly written.



Why? Because it endorses a theory among many?


Pyrrho;121075 wrote:
I do not believe you will find any credible source that explicitly endorses your "intention theory".



Maybe, maybe not. I haven't found any credible source dedicated to this issue.


Pyrrho;121075 wrote:
To go back to your article in post 68, your "Validity theory", in which you state, "An argument is deductive iff it is valid.
An argument is inductive iff it is invalid."

That is also unsatisfactory, for the reasons you state. So, with both of the theories you have presented, you have given reasons to reject them. But neither theory is one that I have ever even heard of anyone endorsing.



Then you have not read the threads to which I linked in the beginning of this thread. There is a person on FRDB who seems to be a high quality poster that supports the validity theory. Though the name is my invention. I could have called it the formalist theory, but validity theory seems to capture the important point better, so I will stick with that. Also "formalist" has other connotations that I would like to avoid.


Pyrrho;121075 wrote:
You seem to be wanting a definition of a deductive argument and an inductive argument, of the form, "an argument is ... if and only if....", such that everything is rigidly and absolutely determined. You do not always get what you want, and I will not give you any such definition now.



I would not call it a definition, but rather an analysis, akin to an analysis of the concept of knowledge.


Pyrrho;121075 wrote:
A deductive argument is one which is valid or one which resembles a valid argument. Thus, the fallacy of affirming the consequent is a deductive argument, because it resembles the valid argument modus ponens. The fallacy of affirming the consequent is a deductive argument because it looks like such a thing. It appears as though the conclusion is supposed to necessarily follow from the premises, and so it is a deductive argument. An inductive argument is any argument that is not deductive. Or we could say, an inductive argument is one in which the premises appear to offer some sort of support for the conclusion that is less than conclusive. (Anything that does not offer or appear to offer any kind of support is not an argument.)



I find it odd that you go on to state what looks like an analysis of the concept of deductive argument.


Also, your first analysis of inductive argument is a negative one, that is, it characterizes an inductive argument by a lack of certain properties. That is perhaps a good idea.


I like all your proposed analyses.


Pyrrho;121075 wrote:
Wikipedia expresses it this way:[INDENT][INDENT]In logic, an argument is a set of one or more meaningful declarative sentences (or "propositions") known as the premises along with another meaningful declarative sentence (or "proposition") known as the conclusion. A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises; an inductive argument asserts that the truth of the conclusion is supported by the premises.[/INDENT][/INDENT]


In this case it 'talks' about arguments asserting things, but arguments, I think, do no such thing. That is an anthropomorphism. Some humans use arguments to support their assertions.

But supposing that it is not an anthropomorphism. Then there is some property of arguments about how they assert their conclusion. That is odd but I wouldn't be totally dismissive of it, at least to begin with. If there is such a property then all definitions of "argument" that I have read are wrong since none of them mentioned that property but only something like "(philosophy, logic) A series of statements organized so that the final statement is a conclusion which is intended to follow logically from the preceding statements, which function as premises." (Source).

Pyrrho;121075 wrote:
Now, I fully expect you to be dissatisfied with this, but I don't think you are always going to get platonic essences for meanings of terms, and instead end up with something that fits a Wittgensteinian concept of a family resemblance instead. (After that introduction, you can read more at: Ludwig Wittgenstein (Stanford Encyclopedia of Philosophy).)


But I am not particularly unsatisfied with it. Smile In fact you gave some useful proposals for a correct analysis of deductive argument and of inductive argument. I will have to think more about them.

What are platonic essences, anyway?
 
Pyrrho
 
Reply Tue 19 Jan, 2010 05:15 pm
@Emil,
Emil;121110 wrote:
...
Pyrrho;121075 wrote:

As you already know, many people jump to wild conclusions about what argument someone is talking or writing about, and so they end up with useless discussions that are totally beside the point that the person is trying to make. So, from a practical standpoint, it is a good idea to emphasize the attempt at understanding intentions when dealing with arguments in the real world.



I agree with this. But that does not imply either of the two theories above and it is consistent with both.



The point is that there is a strong motivation to push an interest in intentions, which may explain why someone might get carried away and say something that appears to suggest that that someone believes your "intention theory" when the person does not.


Emil;121110 wrote:
Pyrrho;121075 wrote:

If you wish to say that the person's remarks literally entail your "intention theory", then I will only say, if that is so, then the article is improperly written.



Why? Because it endorses a theory among many?



No, because it is a silly theory, for the reasons you have already given.


Emil;121110 wrote:
...
Pyrrho;121075 wrote:

To go back to your article in post 68, your "Validity theory", in which you state, "An argument is deductive iff it is valid.
An argument is inductive iff it is invalid."

That is also unsatisfactory, for the reasons you state. So, with both of the theories you have presented, you have given reasons to reject them. But neither theory is one that I have ever even heard of anyone endorsing.


Then you have not read the threads to which I linked in the beginning of this thread. There is a person on FRDB who seems to be a high quality poster that supports the validity theory. Though the name is my invention. I could have called it the formalist theory, but validity theory seems to capture the important point better, so I will stick with that. Also "formalist" has other connotations that I would like to avoid.



You may recall that in the opening post, you did not request that people actually read the threads, only "skim" them. And if it is as you say, I am glad that I did not waste my time reading them thoroughly. But it may be that the person was simply misstating their position, akin to what I think may be going on with the IEP article.


Emil;121110 wrote:
...
Pyrrho;121075 wrote:
A deductive argument is one which is valid or one which resembles a valid argument. Thus, the fallacy of affirming the consequent is a deductive argument, because it resembles the valid argument modus ponens. The fallacy of affirming the consequent is a deductive argument because it looks like such a thing. It appears as though the conclusion is supposed to necessarily follow from the premises, and so it is a deductive argument. An inductive argument is any argument that is not deductive. Or we could say, an inductive argument is one in which the premises appear to offer some sort of support for the conclusion that is less than conclusive. (Anything that does not offer or appear to offer any kind of support is not an argument.)



I find it odd that you go on to state what looks like an analysis of the concept of deductive argument.


Also, your first analysis of inductive argument is a negative one, that is, it characterizes an inductive argument by a lack of certain properties. That is perhaps a good idea.


I like all your proposed analyses.



I do not know why you find my comments odd. But then I have found this whole thread odd, so this is not really too surprising.

As for an inductive argument, one of its defining qualities is that it does not provide conclusive support for its conclusion, even at the best of times (not to mention when the argument is totally dreadful).

In any case, I am glad you like my proposed analyses.



Emil;121110 wrote:
...
Pyrrho;121075 wrote:

Now, I fully expect you to be dissatisfied with this, but I don't think you are always going to get platonic essences for meanings of terms, and instead end up with something that fits a Wittgensteinian concept of a family resemblance instead. (After that introduction, you can read more at: Ludwig Wittgenstein (Stanford Encyclopedia of Philosophy).)



But I am not particularly unsatisfied with it. Smile In fact you gave some useful proposals for a correct analysis of deductive argument and of inductive argument. I will have to think more about them.

What are platonic essences, anyway?



Essentialism - Wikipedia, the free encyclopedia
 
Emil
 
Reply Tue 19 Jan, 2010 05:59 pm
@Pyrrho,
Emil wrote:
I agree with this. But that does not imply either of the two theories above and it is consistent with both.


Pyrrho wrote:
The point is that there is a strong motivation to push an interest in intentions, which may explain why someone might get carried away and say something that appears to suggest that that someone believes your "intention theory" when the person does not.


I cannot read minds. I read what they write and if they write something else than they mean, what can I do? It is useful to think that in general people mean what they write.

Emil wrote:
Why? Because it endorses a theory among many?


Pyrrho wrote:
No, because it is a silly theory, for the reasons you have already given.


I don't think it is a silly theory, however. But I don't accept it.

Emil wrote:
Then you have not read the threads to which I linked in the beginning of this thread. There is a person on FRDB who seems to be a high quality poster that supports the validity theory. Though the name is my invention. I could have called it the formalist theory, but validity theory seems to capture the important point better, so I will stick with that. Also "formalist" has other connotations that I would like to avoid.


Pyrrho wrote:
You may recall that in the opening post, you did not request that people actually read the threads, only "skim" them. And if it is as you say, I am glad that I did not waste my time reading them thoroughly. But it may be that the person was simply misstating their position, akin to what I think may be going on with the IEP article.


I consider it very unlikely, but I could not find the post wherein I remember him to state his position. It is possible that I am misremembering it.

Also with the IEP article. The evidence that I have offered heavily supports my belief that it endorses the intention theory. One needs a radical re-interpretation of its words to get it to 'talk' about merely a technique for identifying arguments.

Emil wrote:
I find it odd that you go on to state what looks like an analysis of the concept of deductive argument.

Also, your first analysis of inductive argument is a negative one, that is, it characterizes an inductive argument by a lack of certain properties. That is perhaps a good idea.

I like all your proposed analyses.


Pyrrho wrote:
I do not know why you find my comments odd. But then I have found this whole thread odd, so this is not really too surprising.


It is odd that you write what you write because you wrote just before that that you would not offer an X is an Y iff ... type analysis, and then you procede to do exactly that. Here this is what you wrote "I will not give you any such definition now." and "A deductive argument is one which is valid or one which resembles a valid argument.", this latter sentence is best interpreted as expressing a bi-conditional probably something close to "An argument is deductive iff it resembles a valid argument or is valid".

Pyrrho wrote:
As for an inductive argument, one of its defining qualities is that it does not provide conclusive support for its conclusion, even at the best of times (not to mention when the argument is totally dreadful).


This is almost exactly what a supporter of the validity theory would say. (I think he would drop the "one of ..." and simply write "The defining ...".) A supporter of intention theory thinks that some inductive arguments are valid so you beg the question against him.
 
Pyrrho
 
Reply Tue 19 Jan, 2010 06:40 pm
@Emil,
Emil;121125 wrote:
I cannot read minds. I read what they write and if they write something else than they mean, what can I do? It is useful to think that in general people mean what they write.



It is useful to realize that people often misstate things, and even when they don't, they often do not mean for their remarks to be taken literally.


Emil;121125 wrote:

It is odd that you write what you write because you wrote just before that that you would not offer an X is an Y iff ... type analysis, and then you procede to do exactly that. Here this is what you wrote "I will not give you any such definition now." and "A deductive argument is one which is valid or one which resembles a valid argument.", this latter sentence is best interpreted as expressing a bi-conditional probably something close to "An argument is deductive iff it resembles a valid argument or is valid".


I wrote:

"You seem to be wanting a definition of a deductive argument and an inductive argument, of the form, "an argument is ... if and only if....", such that everything is rigidly and absolutely determined. [emphasis added] You do not always get what you want, and I will not give you any such definition now."

Saying "A deductive argument is one which is valid or one which resembles a valid argument" does not really give precision, as the concept of "resembles" gives it some ambiguity. I attempted to add some clarity (as well as defining an inductive argument) by continuing: "Thus, the fallacy of affirming the consequent is a deductive argument, because it resembles the valid argument modus ponens. The fallacy of affirming the consequent is a deductive argument because it looks like such a thing. It appears as though the conclusion is supposed to necessarily follow from the premises, and so it is a deductive argument. An inductive argument is any argument that is not deductive. Or we could say, an inductive argument is one in which the premises appear to offer some sort of support for the conclusion that is less than conclusive. (Anything that does not offer or appear to offer any kind of support is not an argument.)" But that does not give one an exact method of determining, in all cases, whether an argument is deductive or inductive. And although it may seem like a vice that it lacks absolute precision (and in some respects, it is a vice), it is a virtue that it matches up well with common usage among logicians, which was the goal.

I hope it is clear that I am not pretending to be the first to have the ideas that I am expressing in this thread; before you started the thread, I had thought it was common knowledge among those who have studied logic.


Emil;121125 wrote:
Pyrrho wrote:

As for an inductive argument, one of its defining qualities is that it does not provide conclusive support for its conclusion, even at the best of times (not to mention when the argument is totally dreadful).


This is almost exactly what a supporter of the validity theory would say. (I think he would drop the "one of ..." and simply write "The defining ...".) A supporter of intention theory thinks that some inductive arguments are valid so you beg the question against him.



"Almost exactly" means that it is different. But I don't think this is even very close to the same. Your "validity" theory states:

An argument is deductive iff it is valid.
An argument is inductive iff it is invalid.


But with what I have stated, the fallacy of affirming the consequent is not an inductive argument, nor are many other invalid arguments.

I suppose, though, you could say that I am endorsing half of each of those ideas:

[INDENT]An argument is deductive if it is valid.

An argument is inductive only if it is not valid.[/INDENT]


But the other half of both are not things with which I agree.
 
Fil Albuquerque
 
Reply Tue 19 Jan, 2010 10:41 pm
@Pyrrho,
ACTION must be NECESSARY)

Now, play with that if you can...Laughing
 
Emil
 
Reply Wed 20 Jan, 2010 08:14 am
@Fil Albuquerque,
Emil wrote:
It is odd that you write what you write because you wrote just before that that you would not offer an X is an Y iff ... type analysis, and then you procede to do exactly that. Here this is what you wrote "I will not give you any such definition now." and "A deductive argument is one which is valid or one which resembles a valid argument.", this latter sentence is best interpreted as expressing a bi-conditional probably something close to "An argument is deductive iff it resembles a valid argument or is valid".



Pyrrho;121132 wrote:
I wrote:

"You seem to be wanting a definition of a deductive argument and an inductive argument, of the form, "an argument is ... if and only if....", such that everything is rigidly and absolutely determined. [emphasis added] You do not always get what you want, and I will not give you any such definition now."


Yes, I recall what you wrote. I did not put much into that phrase that you are highlighting. I don't even know what it means and thought it was just some outrage against, what is sometimes called, formalist thinking.

Pyrrho;121132 wrote:
Saying "A deductive argument is one which is valid or one which resembles a valid argument" does not really give precision, as the concept of "resembles" gives it some ambiguity. I attempted to add some clarity (as well as defining an inductive argument) by continuing: "Thus, the fallacy of affirming the consequent is a deductive argument, because it resembles the valid argument modus ponens. The fallacy of affirming the consequent is a deductive argument because it looks like such a thing. It appears as though the conclusion is supposed to necessarily follow from the premises, and so it is a deductive argument. An inductive argument is any argument that is not deductive. Or we could say, an inductive argument is one in which the premises appear to offer some sort of support for the conclusion that is less than conclusive. (Anything that does not offer or appear to offer any kind of support is not an argument.)" But that does not give one an exact method of determining, in all cases, whether an argument is deductive or inductive. And although it may seem like a vice that it lacks absolute precision (and in some respects, it is a vice), it is a virtue that it matches up well with common usage among logicians, which was the goal.


It seems to me that it does give a method (what's an exact method in this context?) in all cases. For any argument, if it resembles a valid argument or is a valid argument, then it is deductive, otherwise it is inductive. That covers all arguments.

So even though your theory uses vague terms ("resembles"), then I have not so far found a counter-example to it or a questionable consequence.

Let me restate the theory in clearer language:
[INDENT]Resemblance theory
An argument is deductive iff it is valid or resembles a valid argument.
An argument is inductive iff it is not deductive.
[/INDENT]Though of course some work needs to be done to explain how "resembles" is supposed to be understood. One must be careful not to simply use it as a cover for the intention theory. Also, this theory may need to deny (DIS) as resembling is a continuum term, not an either/or term. There may be some arguments that are in the grey area and it is not clear whether they resemble a valid argument or not.

Pyrrho;121132 wrote:
I hope it is clear that I am not pretending to be the first to have the ideas that I am expressing in this thread; before you started the thread, I had thought it was common knowledge among those who have studied logic.


Well, apparently not! For I and Kennethamy have studied logic and we knew no such thing as what you just wrote. (At least, Kennethamy if he knew it did not write it.)
 
 

 
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