# Deductive and inductive arguments

Emil

Sat 16 Jan, 2010 12:12 am
@kennethamy,
kennethamy;120403 wrote:
Why does the opposite and analogous exception clause not hold too then?: An argument is deductive iff the arguer intended for it to be deductive, except when it is invalid, then it is inductive.

Because that rule would suppose that all inductive arguments are really just failed deductive arguments, and that is not only unintuitive, but it is wrong.

Care to offer an argument for this?

Likewise, your exception clause would suppose that "that all deductive arguments are really just failed inductive arguments".

kennethamy;120403 wrote:
I remember one person teaching his class that although the affirming the consequent is fallacious deductively, it is fine inductively, which is an example of this sort of nonsense.

Ok. I do not see the connection.

kennethamy;120403 wrote:
I don't see why, in the interests of neatness and charity, an exception clause cannot be added. As I said before, following the lawyers, we can talk about the argument being "constructively deductive".

We're talking about how to explain what a deductive and an inductive argument is, respectively. Not what is pragmatically to consider deductive/inductive.

Kielicious

Sat 16 Jan, 2010 03:10 am
@kennethamy,
kennethamy;120371 wrote:
Deductive arguments need not have true premises, and need not have a conclusion that necessarily follows. You can have a deductive argument with false premises, and an invalid deductive argument does not have a conclusion that necessarily follows. Invalid deductive arguments have counterexamples. In fact, that is one way of showing that they are invalid.

I would have thought that an argument can be false is more along the lines of, welll, a given. And your reply that invalid deductive arguments have counterexamples is also, again, a given. Thats like saying a wrong answer is wrong. Seems a bit too obvious for me. So back to my question, if valid deductive arguments imply necessity then there cannot be a logically possible situation in which it is wrong, right?

Emil

Sat 16 Jan, 2010 03:18 am
@Kielicious,
Kielicious;120413 wrote:
I would have thought that an argument can be false is more along the lines of, welll, a given. And your reply that invalid deductive arguments have counterexamples is also, again, a given. Thats like saying a wrong answer is wrong. Seems a bit too obvious for me. So back to my question, if valid deductive arguments imply necessity then there cannot be a logically possible situation in which it is wrong, right?

It makes no sense to say that an argument is false.

What does it even mean for an argument to imply necessity? That's another category error, it's actually a double category error because first it makes no sense to speak of arguments implying things and it does not make sense to "imply necessity".

Please, do not derail the thread. If you don't know logic, this is not the place to learn it. If you PM me I will send you a logic textbook.

Kielicious

Sat 16 Jan, 2010 03:39 am
@Emil,
Emil;120414 wrote:
It makes no sense to say that an argument is false.

What does it even mean for an argument to imply necessity? That's another category error, it's actually a double category error because first it makes no sense to speak of arguments implying things and it does not make sense to "imply necessity".

Please, do not derail the thread. If you don't know logic, this is not the place to learn it. If you PM me I will send you a logic textbook.

Do you prefer the term 'invalid' then?

Geez sometimes I wonder about you guys. Ive taken reasoning classes so I dont know where Im wrong. Care to show me? Hell even your first link says the same thing.

kennethamy

Sat 16 Jan, 2010 07:37 am
@Kielicious,
Kielicious;120413 wrote:
I would have thought that an argument can be false is more along the lines of, welll, a given. And your reply that invalid deductive arguments have counterexamples is also, again, a given. Thats like saying a wrong answer is wrong. Seems a bit too obvious for me. So back to my question, if valid deductive arguments imply necessity then there cannot be a logically possible situation in which it is wrong, right?

Arguments cannot be false, so it certainly is not a "given" that an argument can be false.

I don't have any idea what you mean when you say that valid deductive arguments imply necessity. And, it makes no sense to say that an argument is wrong. Perhaps what you have in mind is something like this:

All valid deductive arguments have conclusions that follow necessarily from their premises. Therefore, it is not logically possible for a conclusion of a valid deductive argument not to follow from the premises. But, of course, that is what you would call, "a given".

Emil

Sat 16 Jan, 2010 08:23 am
@kennethamy,
kennethamy;120437 wrote:
Arguments cannot be false, so it certainly is not a "given" that an argument can be false.

I don't have any idea what you mean when you say that valid deductive arguments imply necessity. And, it makes no sense to say that an argument is wrong. Perhaps what you have in mind is something like this:

All valid deductive arguments have conclusions that follow necessarily from their premises. Therefore, it is not logically possible for a conclusion of a valid deductive argument not to follow from the premises. But, of course, that is what you would call, "a given".

Please, do not derail the thread further with this. It is irrelevant for the thread. If he wants to learn logic, he should read a textbook.

kennethamy

Sat 16 Jan, 2010 08:29 am
@Emil,
Emil;120443 wrote:
Please, do not derail the thread further with this. It is irrelevant for the thread. If he wants to learn logic, he should read a textbook.

As you know, I think this forum has a dual purpose: discussion, and also, teaching. I think that participants should learn things, and that includes why they are wrong.

Emil

Sat 16 Jan, 2010 09:13 am
@kennethamy,
kennethamy;120447 wrote:
As you know, I think this forum has a dual purpose: discussion, and also, teaching. I think that participants should learn things, and that includes why they are wrong.

Yes, but could they use another thread for 101 logic questions to the professor? This thread is about something else. I am getting tired repeating this.

On topic. I've written about four pages on my essay on deductive and inductive arguments. I'll post it here, the current draft.The formatting is slightly off due to incompatibilities between forum software and Open Office.

---------- Post added 01-16-2010 at 04:14 PM ----------

Deductive and inductive arguments

Intro
In this essay I will discuss theories that attempt to explain/give an analysis of what a deductive argument is and what an inductive argument is.

Relevant theses
Relevant to this discussion are some other thesis which may or may not be true.
[INDENT] DIS. An argument is either deductive or inductive and not both.
[/INDENT] (DIS) is commonly assumed to be true in logic textbooks.

Intention theory
A first simple formulation of the central theses is:
[INDENT] 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.
[/INDENT]
Questions/objections

Lack of knowledge of the distinction
What about arguers that do not know about the deductive and inductive distinction? Think of arguers in the 5 century BC and people not training in logic.
The arguer need not know about the distinction. It is enough if the arguer intended the conclusion to follow necessarily from the premises or some similar vague idea which people often have, even when not training in logic.1 Similarly for inductive arguments. Refined explanations are then:
An argument is deductive iff it is intended by the arguer to be deductive (in a broad sense).
An argument is inductive iff it is intended by the arguer to be inductive (in a broad sense).

Validity is not a fact about psychology
An objection is that it seems that any correct theory of deductive and inductive arguments do not depend on facts about human psychology such as what the arguer intends the argument to be. The justification for this is an analogy like the following:
Similarly to validity and soundness, whether an argument is deductive or inductive is not dependent on facts about human psychology.
Whether this analogy is apt I don't know. Perhaps the deductive and inductive distinction is different from the other terms.
There may be some confusion between tokens and types, so let's distinguish between them clearly:
An argument type is a number of propositions where one, the conclusion, follows from the other, the premises, in some sense.
An argument token is what is literally in this essay. Argument tokens is a number of sentences that express an argument type. Tokens have a location and a time of writing.2
All argument types are sound/unsound and valid/invalid. Are (all/some?) argument tokens sound/unsound and valid/invalid? It seems to me that a proper evaluation of the issue of deductive and inductive arguments depend on this.3

Two different argument tokens may express the same argument type. Let's imagine that there are three identical tokens and that a single person has written them. In the first two cases the person intends the arguments tokens to be deductive and in the third case he intends it to be inductive.
The question is now: Do all the three argument tokens express the same argument type? It seems to me that the answer according to intention theory is "no". The first two express the same argument type, but the last expresses a different argument type. These tokens, recall, are identical and so all the premises expressed by them are identical. The only difference between the two first and the third is the arguer's intention.
Thus, someone accepting this and accepting intention theory and (DIS) has to (for consistency) agree that there are two different argument types too, one deductive and one inductive. So the intention theory is ontologically more complex. This seems unnecessary and Occam's Razor advises us not to multiply entities beyond necessity. Are there really two different argument types? What is this property "being deductive" and "being inductive"? They seem very mysterious.
One could also accept both intention theory and that there is only one argument type but then that type would be both inductive and deductive and so the distinction between them would be false, that is, (DIS) would be false.

One could also accept both intention theory and that there is only one type but believe that the deductive and inductive distinction is only about argument tokens and not types. To clarify:[INDENT] DIS. An argument (token or type) is either deductive or inductive and not both.
DIS-token. An argument token is either deductive or inductive and not both.
DIS-type. An argument type is either deductive or inductive and not both.4
[/INDENT]So that person would reject (DIS) and (DIS-type) but accept (DIS-token). In that case the deductive and inductive distinction between argument tokens is dependent on facts of human psychology, but facts about argument types such as validity and soundness are not dependent on facts about human psychology.

Validity theory

A first simple formulation of the central theses is:
[INDENT] An argument is deductive iff it is valid.
An argument is inductive iff it is invalid.
[/INDENT]
Questions/objections

All deductive arguments are valid
It implies that all deductive arguments are valid. But that implies that one cannot fail at making a deductive valid argument (though one could fail at making a deductive argument), for there are no invalid deductive arguments. Consider an analogy with addition (mathematics):[INDENT] "Not distinguishing between deductive arguments, and valid deductive arguments, is just like not distinguishing between addition, and correct addition." (Kennethamy, source)
"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. [Both] 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." (Kennethamy, source.)
[/INDENT]The question is if this analogy is apt. I think it has at least a lot of initial plausibility.

First, lacking a 'formal machinery' to evaluate analogies in, the conclusions reached about such matters are lacking a great deal of certainty.
Second, I note that the analogy goes on the level of the act of adding and the act of deducing and not at the level of additive arguments and deductive arguments. The analogy uses the word "correct". What is that to be understood as? I suppose it refers to validity in both cases. But let's assume that it refers to just validity in the case of deductive arguments. Then, what is the analogous part of validity in deductive arguments, in additive arguments if not validity itself? It seems to me that the analogous part of validity in deductive arguments, in additive arguments is validity. The analogy is circular. For this reason I think that it is not convincing.

Notes
1These vague ideas of "following necessarily" and "not following necessarily but giving reason to believe" may be products of evolution.

2There are also verbal argument tokens, but they do not strictly speaking consist of sentences but consist of sound waves that express sentences, I suppose.

3This case is very familiar to the case of whether sentences are true/false by proxy. See my previous discussions of pluralistic theories of truth bearers, here.

4(DIS) is thus logically equivalent with the conjunction of (DIS-token) and (DIS-type).

Zetherin

Sat 16 Jan, 2010 11:39 am
@Emil,

Where do you get this

Quote:
Similarly to validity and soundness, whether an argument is deductive or inductive is not dependent on facts about human psychology.

from?

I understand you acknowledge deductive and inductive may be different types of terms, but how did you reach this possible conclusion in the first place?

Emil

Sat 16 Jan, 2010 11:56 am
@Zetherin,
Zetherin;120479 wrote:

Where do you get this

from?

I understand you acknowledge deductive and inductive may be different types of terms, but how did you reach this possible conclusion in the first place?

I did not get it from anywhere and that is why it is not in quotation marks. I don't understand the question.

kennethamy

Sat 16 Jan, 2010 11:59 am
@Zetherin,
Zetherin;120479 wrote:

Where do you get this

from?

I understand you acknowledge deductive and inductive may be different types of terms, but how did you reach this possible conclusion in the first place?

But the intention theory does not make the distinction between deduction and induction depend on psychology. The distinction is still logical between whether the argument is conclusive or not. Where intention comes in is in trying to decide whether the argument is deductive or inductive. That is an epistemological issue, not a logical issue. Intention theory does not psychologize logic (Frege's bid bugaboo). It may psychologize the epistemology of logic, though. But is that so bad?

Pyrrho

Sat 16 Jan, 2010 12:00 pm
@Emil,
Emil;120375 wrote:
...

Pyrrho;120220 wrote:
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.

Not at all! This is the crucial point. In this post you are endorsing the intention theory. That's fine, but the theory has its problems some of which I have mentioned already.
...

I think you need to articulate precisely what you mean by "the intention theory", as I do not believe that is what I stated at all.

When speaking with others, one is trying to understand what they mean (well, hopefully!). So that when a person is presenting an argument, one is interested in figuring out what the person means, so that one does not waste time on an argument that is irrelevant to what the person intends. This, however, does not make the argument, in itself, dependent upon intentions, as when trying to understand a mathematical problem someone is telling one about, one needs to understand the person in order to understand what math problem it is, but once one knows this, the persons intentions become irrelevant. 2 + 2 = 4, regardless of anyone's intentions, and arguments of the form

[INDENT][INDENT][INDENT][INDENT]If P then Q
P
________
Therefore Q[/INDENT][/INDENT][/INDENT][/INDENT]

are deductively valid regardless of anyone's intentions.

http://www.philosophyforum.com/philosophy-forums/branches-philosophy/logic/7330-deductive-inductive-arguments-2.html#post120455

it becomes clear that I am not advocating your "intention theory" at all ("An argument is deductive iff it is intended by the arguer to be deductive."), for the deductive validity of Modus Ponens (the argument form above, for those who don't know) is not in any way dependent upon what someone intends. Modus Ponens is a deductive form of argument, regardless of how anyone intends it to be taken.

Kielicious

Sat 16 Jan, 2010 12:23 pm
@kennethamy,
kennethamy;120437 wrote:
Arguments cannot be false, so it certainly is not a "given" that an argument can be false.

Me wrote:
Do you prefer the term 'invalid' instead of 'false'?

You and emil seem to have a hard time with implied statements.

Youre absolutely right, arguments cannot be 'false'. But Its also not that hard to figure out I meant 'invalid'. Learn what people mean and not necessarily what they write. I dont understand how one can get caught up over such trivial matters.

ken wrote:
I don't have any idea what you mean when you say that valid deductive arguments imply necessity. And, it makes no sense to say that an argument is wrong. Perhaps what you have in mind is something like this:

All valid deductive arguments have conclusions that follow necessarily from their premises. Therefore, it is not logically possible for a conclusion of a valid deductive argument not to follow from the premises. But, of course, that is what you would call, "a given".

Again thats pretty much sums up what I said. Granted you can be anal about precise terms but I know what my terms mean and it shouldnt be that hard to figure it out, but again, it would require one to be good at implied statements. That doesnt seem to be working so well...

Pyrrho

Sat 16 Jan, 2010 12:26 pm
@kennethamy,
kennethamy;120389 wrote:
I think fast means that to call inductive arguments invalid is a category mistake. I think that is right.

At the risk of Emil regarding this as a derail, I do not agree. I do not think that it is a category mistake to say that all inductive arguments are deductively invalid. Do you really think there is a problem with saying that?

I would, however, regard it as a category mistake to say that a tree is invalid.

kennethamy

Sat 16 Jan, 2010 12:29 pm
@Kielicious,
Kielicious;120489 wrote:
You and emil seem to have a hard time with implied statements.

Youre absolutely right, arguments cannot be 'false'. But Its also not that hard to figure out I meant 'invalid'. Learn what people mean and not necessarily what they write. I dont understand how one can get caught up over such trivial matters.

Again thats pretty much sums up what I said. Granted you can be anal about precise terms but I know what my terms mean and it shouldnt be that hard to figure it out, but again, it would require one to be good at implied statements. That doesnt seem to be working so thought...

How should I know that by "false" you mean, "invalid"? I am not a mind-reader. If you meant "invalid", why didn't you say so? (And I really still don't know that you meant, "invalid" since I doubt you know what "invalid" means). Anyway, if you know the correct word, then what is the point of using the incorrect word, and leaving it to the reader to try to figure out what you were talking about?

Pyrrho

Sat 16 Jan, 2010 12:33 pm
@Kielicious,
Kielicious;120489 wrote:
You and emil seem to have a hard time with implied statements.

Youre absolutely right, arguments cannot be 'false'. But Its also not that hard to figure out I meant 'invalid'. Learn what people mean and not necessarily what they write. I dont understand how one can get caught up over such trivial matters.

Again thats pretty much sums up what I said. Granted you can be anal about precise terms but I know what my terms mean and it shouldnt be that hard to figure it out, but again, it would require one to be good at implied statements. That doesnt seem to be working so thought...

I looked back at your post and I do not think it was obvious at all that you meant "invalid" when you said "false". Many times, when people speak of arguments being "false", they mean that the conclusion is false, which has nothing to do with whether the argument is valid or not (as a valid argument may have a false conclusion if at least one of its premises is false). And so you see, it is important when speaking about logic to use correct terminology, so that others will know what you are talking about. And if one is not using standard terminology, it is good to explain what one means.

Kielicious

Sat 16 Jan, 2010 12:51 pm
@kennethamy,
kennethamy;120494 wrote:
How should I know that by "false" you mean, "invalid"? I am not a mind-reader. If you meant "invalid", why didn't you say so? (And I really still don't know that you meant, "invalid" since I doubt you know what "invalid" means). Anyway, if you know the correct word, then what is the point of using the incorrect word, and leaving it to the reader to try to figure out what you were talking about?

Its called jargon and the evolution of words.

Again, I bet you and emil have a hard time with implied statements huh?

It doesnt really matter though if you trivialize over such matters, I dont hold it against you. It can be confusing and I shouldve used the correct terminology. I just thought you guys would want more of a deep conversation instead of just keeping it at the surface. Uh oh, I used a metaphor! What ever do I mean?....

kennethamy

Sat 16 Jan, 2010 12:55 pm
@Kielicious,
Kielicious;120498 wrote:
Its called jargon and the evolution of words.

Again, I bet you and emil have a hard time with implied statements huh?

It doesnt really matter though if you trivialize over such matters, I dont hold it against you. I just thought you guys would want more of a deep conversation instead of just keeping it at the surface. Uh oh, I used a metaphor! What ever do I mean?....

Why don't you just say what you mean, if you know what you mean, and if you know how to say what you mean? And stop making excuses. You are just wasting time.

Kielicious

Sat 16 Jan, 2010 12:57 pm
@kennethamy,
kennethamy;120500 wrote:
Why don't you just say what you mean, if you know what you mean, and if you know how to say what you mean? And stop making excuses. You are just wasting time.

Wasting time?

Whos time Mr. 5000 posts?

Do you read poetry? If not I understand why...

kennethamy

Sat 16 Jan, 2010 01:02 pm
@Kielicious,
Kielicious;120501 wrote:
Wasting time?

Whos time Mr. 5000 posts?

Do you read poetry? If not I understand why...

But you are wasting time when you make people guess at what you are saying. And, philosophy is not poetry. Poetry is enriched by ambiguity (sometimes). Philosophy is confused by ambiguity (all the time).