# Non-deductive VERSUS Inductive

Extrain

Sat 10 Apr, 2010 03:04 am
@Extrain,
See:

Venn Diagrams for Categorical Syllogisms

INDUCTIVE ARGUMENTS:

(1) No inductive argument is valid means:
The class of all inductive arguments nowhere overlaps with the class of all valid arguments.

(2) No inductive argument is invalid means:
The class of all inductive arguments nowhere overlaps with the class of all invalid arguments.

Therefore, no inductive argument is either valid or invalid.
Period.

Here are further consequences of this. For any single existent inductive argument x...

X is non-valid
means,
X does not lie within the class of valid arguments.
but this does NOT entail that,
X therefore lies within the class of all invalid arguments since this contradicts (2).

X is non-invalid
means,
X does not lie within the class of invalid arguments.
but this does NOT entail that,
X therefore lies within the class of all valid arguments since this contradicts (1)

DEDUCTIVE ARGUMENTS:

All deductive arguments are either valid or invalid, and not both means:

(1) The class of all deductive arguments partly or fully ovelaps with the class of all valid arguments.
OR
(2) The class of all deductive arguments partly or fully overlaps with the class of all invalid arguments.
AND
(3) For all deductive arguments, NO deductive argument is both within the class of all valid arguments while being in the class of all invalid arguments.

Here are the further consequences of this:

For any particular existent deductive argument X...

X is non-valid
means,
X does not lie within the class of valid arguments.
But since X must be either valid or invalid, it logically follows that,
X lies within the class of invalid arguments.

X is non-invalid
means,
X does not lie within the class of invalid arguments.
But since X must be either valid or invalid, it logically follows that,
X lies within the class of valid arguments.

Extrain

Sat 10 Apr, 2010 04:24 pm
@Emil,
Emil;150165 wrote:

[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]

Emil;150165 wrote:
The question is if this analogy is apt. I think it has at least a lot of initial plausibility....[but] The analogy is circular. This analogy is very plausible initially but not plausible when one thinks about it carefully....But wait, what kind of arguments are additive arguments? They are deductive arguments! Additive arguments are a proper subset of deductive arguments.

Argument by analogies don't fail to be good analogies on account of their "being circular." They fail on account of their being disanalogous--which his argument is not. Do you even know what an argument by analogy is? Kennethamy is not trying to prove to you that some deductive arguments are really invalid. He is only showing that when we say someone has made a mistake, that this alleged mistake is not evidence for thinking that all deductive arguments have to be valid in order to be deductive arguments, just as making a mistake in addition is not evidence for thinking that the sum has to be correct in order for the sum to be a statement of equality, however incorrect that equality is.

You think that whether or not someone made a mistake at all is left undecided until someone shows you that a deductive argument can really be invalid, or that an equality can really be incorrect, before you countenance that there are such things as invalid deductive arguments, or that there are such things as incorrect equalities.

I hate to break the news to you: but there are invalid deductive arguments just as there are incorrect equalities. If there were no such things, then none of us would even be able to distinguish error from truth.

If deductive arguments are really deductive arguments, then all deductive arguments are valid. Some deductive arguments are not valid. So, not all deductive arguments are deductive arguments. But since all deductive arguments are deductive arguments, therefore, all deductive arguments have to be valid.

Your material conditional is false as it is, because you have just groundlessly assumed from the start that all deductive arguments have to be valid in order to be deductive arguments. But then you use this assumption to prove that all deductive arguments are valid. This is a form of BEGGING THE QUESTION. So you haven't demonstrated anything at all, and the problem is yours, not anyone else's.

What is the problem that is in such desperate need of a solution, here?

Is there even a well-defined problem at all?

Emil;150165 wrote:
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.

So? That's what mistakes are: Acts that make a mistake. No one needs to prove that deductive arguments are both valid and invalid in order to prove to you that a mistake has been made. Rather, the burden of proof is on you, my friend, to show that a mistake has, in fact, been made if there are no invalid deductive arguments whatsoever. If p then q, q, therefore p was not an invalid deductive argument, then we wouldn't even know what the correct modus ponens style of argument was.

There is nothing wrong with deductive arguments being valid or invalid unless you can show otherwise, logically.

Emil;150165 wrote:
Still that all deductive arguments are valid is something that is denied in pretty much all logic textbooks, but again, textbooks have been wrong in the past.

sheesh...so not only are all textbooks wrong, but all logicians in the world are wrong too?:rolleyes:

So all deductive arguments are valid? nonsense.

If p then q
q
therefore p.

This is both deductive and invalid.

It's not even a strong or weak inductive argument either.

It's simply deductively invalid.

fast

Mon 12 Apr, 2010 07:38 am
@Extrain,
Extrain;150050 wrote:

Fast,

I misspoke in the quote you *quoted* from me. I edited it. Can you do me a favor and delete it or something? Lol! I just don't want to get misinterpreted for making a claim I am not actually claiming--which seems to be the trend adopted by some others in this thread...:a-ok:

Thanks, buddy.

Or something? No problem! :devilish:

Extrain

Mon 12 Apr, 2010 08:39 am
@fast,
fast;150814 wrote:
Or something? No problem! :devilish:

fast

Mon 12 Apr, 2010 08:47 am
@Emil,
[QUOTE=Emil;150165]

Relevant theses and concepts

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

[/QUOTE]

This goes to the very heart of what this thread is about. If there's anything that you and Extrain agree on, it seems to be that if an argument is not deductive, then an argument is inductive; moreover, if an argument is not inductive, then an argument is deductive--or so you and he (and I suppose many others) believe.

However, it's that very assumption that I'm questioning. I'm trying to apply what I know about the differences between "invalid" and "not valid" to this issue. It's my understanding that "deductive" and "not deductive" is collectively exhaustive (not to mention "inductive" and "not inductive"), and even though "deductive" and "inductive" may be contrary (and that it's merely contrary is the real confusion), I don't see that "deductive" and "inductive" exhaust all possibilities.

Hence, it's possible to have an argument that is both 1) not deductive and 2) not inductive. An example would be a non-deductive argument that isn't enumerative.

Of course, some people may indeed mean what "not deductive" means when they say, "inductive", but unless the term means what they, themselves mean, it's unimportant. At any rate, I believe it's a legitimate distinction to be made (the distinction between "non-deductive" and "inductive") just as it's legitimate to distinguish between "not valid" and "invalid" (and just as it's legitimate to distinguish between "not true" and "false").

PS: What does DIS mean?

Extrain

Mon 12 Apr, 2010 09:19 am
@fast,
No, fast. I am not saying that.

I make the distinction between what logicians call "formal" and "informal" arguments. And most non-deductive arguments are not "numerative" (or inductive) arguments anyway.

For instance, these are all non-deductive informal kinds of arguments:

(1) Argument by Analogy
(2) Inference to the Best Explanation.
(3) Those arguments using the principle of sufficient reason.
(4) Evidential
(5) Appeal to proper authority
(6) Appeal to Self-Evident First Principles
(7) Pragmatic-style arguments
(8) Appeal to Testimony
(9) Appeal to Empirical and Logical probabilities
etc. etc.,...

the list goes on and on.

The term "inductive" is just sometimes (though probably incorrectly) used to characterize all those arguments that are not deductive (or formal) arguments. But I don't think that should be a problem...whatever distinction you want to make, it only requires that we be able to recognize the difference between validity and strength. That's the difference defining the two classes of arguments.

fast

Mon 12 Apr, 2010 09:44 am
@Extrain,
[QUOTE=Extrain;150837]But I don't think that should be a problem...whatever distinction you want to make, it only requires that we be able to recognize the difference between validity and strength. That's the difference defining the two classes of arguments.[/QUOTE]

Just to expound, deductive arguments have to do with validity (i.e. Is this argument valid/invalid?), and inductive arguments have to do with strength (i.e is this argument weak/strong?)

Notice that with deductive arguments, it's either valid, or it's invalid. There are no matters of degree as is with the strength of inductive arguments.

No valid/invalid argument is weak/strong.
No weak/strong argument is valid/invalid.

All deductive arguments are valid/invalid.
All inductive arguments are weak/strong.

Extrain

Mon 12 Apr, 2010 09:52 am
@fast,
fast;150849 wrote:

Just to expound, deductive arguments have to do with validity (i.e. Is this argument valid/invalid?), and inductive arguments have to do with strength (i.e is this argument weak/strong?)

Notice that with deductive arguments, it's either valid, or it's invalid. There are no matters of degree as is with the strength of inductive arguments.

No valid/invalid argument is weak/strong.
No weak/strong argument is valid/invalid.

All deductive arguments are valid/invalid.
All inductive arguments are weak/strong.

Right. That's correct.

kennethamy

Mon 12 Apr, 2010 10:49 am
@Extrain,
Extrain;150837 wrote:
No, fast. I am not saying that.

I make the distinction between what logicians call "formal" and "informal" arguments. And most non-deductive arguments are not "numerative" (or inductive) arguments anyway.

For instance, these are all non-deductive informal kinds of arguments:

(1) Argument by Analogy
(2) Inference to the Best Explanation.
(3) Those arguments using the principle of sufficient reason.
(4) Evidential
(5) Appeal to proper authority
(6) Appeal to Self-Evident First Principles
(7) Pragmatic-style arguments
(8) Appeal to Testimony
(9) Appeal to Empirical and Logical probabilities
etc. etc.,...

the list goes on and on.

The term "inductive" is just sometimes (though probably incorrectly) used to characterize all those arguments that are not deductive (or formal) arguments. But I don't think that should be a problem...whatever distinction you want to make, it only requires that we be able to recognize the difference between validity and strength. That's the difference defining the two classes of arguments.

The term, I think, is "enumerative induction", not "numerative". It is also known as, "inductive generalization". Hume discussed enumerative induction exclusively during his discussions of the justification of induction, and his influence was so great that enumerative induction that enumerative induction became identified with induction in general. Thus, we needed a term like "non-deductive argument" to cover the rest of what should have been called. "inductive arguments".

fast

Mon 12 Apr, 2010 11:34 am
@kennethamy,
[QUOTE=kennethamy;150897]The term, I think, is "enumerative induction", not "numerative". It is also known as, "inductive generalization". Hume discussed enumerative induction exclusively during his discussions of the justification of induction, and his influence was so great that enumerative induction that enumerative induction became identified with induction in general. Thus, we needed a term like "non-deductive argument" to cover the rest of what should have been called. "inductive arguments".[/QUOTE]

This is not the same outline as I had envisioned before. With this outline, "inductive" is the superset while the two subsets are 1) enumerative induction (aka inductive generalization) and 2) remaining inductive arguments. If this is the case, then both 1 and 2 are both inductive and non-deductive-even though there are still differences between them.

What I understood before (or thought I understood) was actually more complex. I had thought we were dealing with two different outlines with overlap such that some non-deductive arguments were not inductive, but if you are in fact saying that 1 and 2 above are subsets of induction, then maybe things are simpler than I thought.

kennethamy

Mon 12 Apr, 2010 11:40 am
@fast,
fast;150922 wrote:

This is not the same outline as I had envisioned before. With this outline, "inductive" is the superset while the two subsets are 1) enumerative induction (aka inductive generalization) and 2) remaining inductive arguments. If this is the case, then both 1 and 2 are both inductive and non-deductive-even though there are still differences between them.

What I understood before (or thought I understood) was actually more complex. I had thought we were dealing with two different outlines with overlap such that some non-deductive arguments were not inductive, but if you are in fact saying that 1 and 2 above are subsets of induction, then maybe things are simpler than I thought.

Yes, that is what I am saying. Ceteris paribus, the simpler the better, so that's good.

Extrain

Mon 12 Apr, 2010 11:47 am
@kennethamy,
kennethamy;150897 wrote:
The term, I think, is "enumerative induction", not "numerative". It is also known as, "inductive generalization". Hume discussed enumerative induction exclusively during his discussions of the justification of induction, and his influence was so great that enumerative induction that enumerative induction became identified with induction in general. Thus, we needed a term like "non-deductive argument" to cover the rest of what should have been called. "inductive arguments".

Of course. Call it whatever you want. I am perfectly aware of all this, which is why I listed other non-deductive non-enumerative style of arguments.

The Problem of Induction (Stanford Encyclopedia of Philosophy)

Emil

Mon 12 Apr, 2010 11:51 am
@fast,
fast;150828 wrote:

This goes to the very heart of what this thread is about. If there's anything that you and Extrain agree on, it seems to be that if an argument is not deductive, then an argument is inductive; moreover, if an argument is not inductive, then an argument is deductive--or so you and he (and I suppose many others) believe.

However, it's that very assumption that I'm questioning. I'm trying to apply what I know about the differences between "invalid" and "not valid" to this issue. It's my understanding that "deductive" and "not deductive" is collectively exhaustive (not to mention "inductive" and "not inductive"), and even though "deductive" and "inductive" may be contrary (and that it's merely contrary is the real confusion), I don't see that "deductive" and "inductive" exhaust all possibilities.

Hence, it's possible to have an argument that is both 1) not deductive and 2) not inductive. An example would be a non-deductive argument that isn't enumerative.

Of course, some people may indeed mean what "not deductive" means when they say, "inductive", but unless the term means what they, themselves mean, it's unimportant. At any rate, I believe it's a legitimate distinction to be made (the distinction between "non-deductive" and "inductive") just as it's legitimate to distinguish between "not valid" and "invalid" (and just as it's legitimate to distinguish between "not true" and "false").

PS: What does DIS mean?

You may be one of those that mean enumeration by
"induction".
I don't. "Enumeration" seems to be a good word for that, why use "induction"?

Of course, if we stipulate that "induction" means
enumeration, then deductive arguments and inductive arguments do not exhaust all possibilities; there exists an argument that is neither deductive or inductive.

What "DIS" means is irrelevant. The reason I chose it was that "distinction" was too long and it had to be with an important distinction. It's not important.

In any case, I'll write a section explaining my usage of "induction".

PS. You still have not answered what you mean when you write "invalid". For me it is quite simple. I just mean non-valid, an argument that is not valid.

kennethamy

Mon 12 Apr, 2010 11:55 am
@Emil,
Emil;150931 wrote:
You may be one of those that mean enumeration by
"induction".
I don't. "Enumeration" seems to be a good word for that, why use "induction"?

Of course, if we stipulate that "induction" means
enumeration, then deductive arguments and inductive arguments do not exhaust all possibilities; there exists an argument that is neither deductive or inductive.

What "DIS" means is irrelevant. The reason I chose it was that "distinction" was too long and it had to be with an important distinction. It's not important.

In any case, I'll write a section explaining my usage of "induction".

PS. You still have not answered what you mean when you write "invalid". For me it is quite simple. I just mean non-valid, an argument that is not valid.

"Non-valid" no more means "not valid", than does, "non-intelligent" mean "not-intelligent" (or "unintelligent").

Extrain

Mon 12 Apr, 2010 11:57 am
@Emil,
Emil;150931 wrote:
You may be one of those that mean enumeration by
"induction". I don't. "Enumeration" seems to be a good word for that, why use "induction"?

Of course, if we stipulate that "induction" means enumeration, then deductive arguments and inductive arguments do not exhaust all possibilities; there exists an argument that is neither deductive or inductive.

What "DIS" means is irrelevant. The reason I chose it was that "distinction" was too long and it had to be with an important distinction. It's not important.

In any case, I'll write a section explaining my usage of "induction".

PS. You still have not answered what you mean when you write "invalid". For me it is quite simple. I just mean non-valid, an argument that is not valid.

It's like listening to a broken record.

I despair seeing people insist on abandoning logic in philosophy like this.

I'm out, guys. Good luck dealing with this.

Emil

Mon 12 Apr, 2010 12:04 pm
@fast,
fast;150922 wrote:

This is not the same outline as I had envisioned before. With this outline, "inductive" is the superset while the two subsets are 1) enumerative induction (aka inductive generalization) and 2) remaining inductive arguments. If this is the case, then both 1 and 2 are both inductive and non-deductive-even though there are still differences between them.

What I understood before (or thought I understood) was actually more complex. I had thought we were dealing with two different outlines with overlap such that some non-deductive arguments were not inductive, but if you are in fact saying that 1 and 2 above are subsets of induction, then maybe things are simpler than I thought.

These things are easier visually.

http://img442.imageshack.us/img442/651/argumentsdeductiveinduc.jpg

---------- Post added 04-12-2010 at 08:14 PM ----------

kennethamy;150932 wrote:
"Non-valid" no more means "not valid", than does, "non-intelligent" mean "not-intelligent" (or "unintelligent").

"The argument is non-valid." "The argument is not valid." These two mean the same. And I mean the same by the sentence "The argument is invalid." as I mean by the other two. You may not do that. If you don't then your language usage differs my mine in this aspect. I still haven't got an answer for what "invalid" would then mean. I have asked many times.

That may not be analogous with a different word like "intelligent". Words differ in many aspects.

"The person is non-intelligent." I don't take to mean anything.

"The person is not intelligent." I take to be an euphemism for that the person is of lower than average intelligence. Similarly, the sentence "The person is intelligent." means that the person is of above average intelligence. Contrast with "The species is intelligent." which means that members of the species generally posses intelligence.

"The person is unintelligent." (a bit disanalogous because it uses a different negation prefix; -UN instead of -IN) I take to mean that the person is of low intelligence.

kennethamy

Mon 12 Apr, 2010 12:31 pm
@Emil,
Emil;150938 wrote:
These things are easier visually.

http://img442.imageshack.us/img442/651/argumentsdeductiveinduc.jpg

---------- Post added 04-12-2010 at 08:14 PM ----------

"The argument is non-valid." "The argument is not valid." These two mean the same. And I mean the same by the sentence "The argument is invalid." as I mean by the other two. You may not do that. If you don't then your language usage differs my mine in this aspect. I still haven't got an answer for what "invalid" would then mean. I have asked many times.

That may not be analogous with a different word like "intelligent". Words differ in many aspects.

"The person is non-intelligent." I don't take to mean anything.

"The person is not intelligent." I take to be an euphemism for that the person is of lower than average intelligence. Similarly, the sentence "The person is intelligent." means that the person is of above average intelligence. Contrast with "The species is intelligent." which means that members of the species generally posses intelligence.

"The person is unintelligent." (a bit disanalogous because it uses a different negation prefix; -UN instead of -IN) I take to mean that the person is of low intelligence.

But it doesn't follow from the fact that you do not choose to recognize a distinction that the distinction does not exist. There is a distinction in English between "disinterested" and "uninterested", but some people, either because they don't know the distinction, or because they refuse to recognize the distinction, use "disinterested" and not "uninterested". But why does that matter? It is the distinction that counts, not the words. I may call all cats "dogs", but cats and dogs are different anyway.

fast

Mon 12 Apr, 2010 12:39 pm
@Emil,
Emil;150931 wrote:
PS. You still have not answered what you mean when you write "invalid". For me it is quite simple. I just mean non-valid, an argument that is not valid.

An argument that can't possibly be valid can't possibly be invalid.

A deductive argument can possibly be valid, so it can possibly be invalid.
An inductive argument cannot possibly be valid, so it cannot possibly be invalid.

---------- Post added 04-12-2010 at 02:46 PM ----------

Emil;150938 wrote:

Awesome!

I would say to be very careful with the term, "non-enumerative." You wouldn't want to inadvertently include deductive arguments.

jack phil

Mon 12 Apr, 2010 12:46 pm
@fast,
I think it was Charles Pierce that wrote greatly on deduction, induction, and also abduction(?).

Emil

Mon 12 Apr, 2010 03:12 pm
@kennethamy,
kennethamy;150953 wrote:
But it doesn't follow from the fact that you do not choose to recognize a distinction that the distinction does not exist. There is a distinction in English between "disinterested" and "uninterested", but some people, either because they don't know the distinction, or because they refuse to recognize the distinction, use "disinterested" and not "uninterested". But why does that matter? It is the distinction that counts, not the words. I may call all cats "dogs", but cats and dogs are different anyway.

Right. I agree with this.

---------- Post added 04-12-2010 at 11:14 PM ----------

jack;150969 wrote:
I think it was Charles Pierce that wrote greatly on deduction, induction, and also abduction(?).

Yes, abduction. Although that word is a bit problematic to use as people sometimes think one means:

3. (law) The wrongful, and usually the forcible, carrying off of a human being.

abduction - Wiktionary

It is also called inference to best explanation.

---------- Post added 04-12-2010 at 11:16 PM ----------

fast;150961 wrote:
An argument that can't possibly be valid can't possibly be invalid.

A deductive argument can possibly be valid, so it can possibly be invalid.
An inductive argument cannot possibly be valid, so it cannot possibly be invalid.

This begs the question against me, but from your post of view, yes. Though I wonder what you mean by "can't possibly". What kind of possibility is it that you are denying? Logical? Doesn't seem plausible, but what else could it be?

Also, you did not answer the question. Again!

---------- Post added 04-12-2010 at 02:46 PM ----------

Quote:
Awesome!

I would say to be very careful with the term, "non-enumerative." You wouldn't want to inadvertently include deductive arguments.
Oh, yes, you are right about that. I should choose another word if I redraw the figure. Still it is very useful to draw things when talking about sets, subsets and supsets.