# Non-deductive VERSUS Inductive

Extrain

Wed 7 Apr, 2010 08:42 pm
@Emil,
Emil;149460 wrote:
Whatever. (Symbols...)

I am not valid. Does it therefore follow that I am invalid?:rolleyes:

To say so is your own logical fallacy, just as you conclude that because no inductive argument is valid, any inductive argument is therefore invalid.--This argument is invalid in itself, and the conclusion itself is false.

Emil;149460 wrote:
All arguments are valid or invalid.

This is false. All arguments are either valid, invalid, strong, or weak--and/or: sound/unsound or cogent/uncogent.

Emil;149460 wrote:
Invalid = not valid.

This is false. "X is invalid" actually means "X is non-valid."

Emil;149460 wrote:
Is this another case of your reluctance to accept the common usage of negation prefixes? (IN-, UN-, NON-, ANTI-, etc.) like with the previous "unjustified = non justified" confusion?

These prefixes only negate the predicate. They don't negate propositions. Confusing the two is precisely why your view is a category mistake. All category mistakes are logical fallacies.

Emil;149460 wrote:
By "invalid" I mean "not valid" and nothing else.

Then you would be wrong.

Emil;149460 wrote:
Questions:
[INDENT]1. Are there valid inductive arguments? No
2. Are there non-valid inductive arguments? No
3. Are there valid deductive arguments? Yes
4. Are there non-valid deductive arguments? Yes
[/INDENT]

For all Inductive arguments Px, for all valid arguments Qx, and for all invalid arguments non-Qx...

~(Ex) (Px and Qx)

is true since no inductive argument is a valid argument.

But this is not logically equivalent to,

(Ex) (Px and non-Qx)

which says there is at least one invalid inductive argument. They don't say the same thing. The first says there are no valid inductive arguments at all; the latter says there is at least one invalid inductive argument. The first does not entail the second.

Rather, the situation looks like this:

(1) ~(Ex) (Px and [Qx or non-Qx])

says that no inductive argument is either valid or invalid, and it is NOT logically equivalent to

(2) (Ax) (Px --> [Qx or non-Qx])

which says that all inductive arguments are either valid or invalid.

The former is true. The latter is false.

But (1) IS logically equivalent to,

(3) (Ax) (Px --> ~ [Qx or non-Qx])

which says that all inductive arguments are neither valid nor invalid. And (3) is true if and only if (1) is true.

Your view is an equivocation on negation "it is not the case that" and the predicate "invalid."

In other words, "X is not valid" does not mean the same thing as "X is invalid" or "X is non-valid."

I am not valid, but I am not thereby "invalid" or "non-valid."

Again, category mistake.

Further, "validity" just means

For all deductive arguments, if the premises are true, then the conclusion must be true.

But the definition of validity, here, does not tell you that the feature of validity applies to anything beyond the domain of deductive arguments.

"Strength" (analogous to validity) just means,

For all inductive arguments, if the premises are true, then the conclusion is probably (more likely than not) true.

But just because validity is not a feature of strong inductive arguments, it does not logically follow that invalidity is a feature of strong inductive arguments.

This, in itself, is your logical fallacy here:

No inductive argument is valid.
Therefore, all (or at least one) inductive arguments are invalid.

*This argument is invalid, and the conclusion is even false.

(a) No P are Q

does not entail,

(b) All P are non-Q

nor does it entail,

(c) Some P are non-Q

at most, it entails

(d) It is not the case that some P are Q

Emil

Thu 8 Apr, 2010 01:01 am
@Extrain,
Extrain;149467 wrote:
I am not valid. Does it therefore follow that I am invalid?:rolleyes:

To say so is your own logical fallacy, just as you conclude that because no inductive argument is valid, any inductive argument is therefore invalid.--This argument is invalid in itself, and the conclusion itself is false.

This is false. All arguments are either valid, invalid, strong, or weak--and/or: sound/unsound or cogent/uncogent.

This is false. "X is invalid" actually means "X is non-valid."

These prefixes only negate the predicate. They don't negate propositions. Confusing the two is precisely why your view is a category mistake. All category mistakes are logical fallacies.

Then you would be wrong.

For all Inductive arguments Px, for all valid arguments Qx, and for all invalid arguments non-Qx...

~(Ex) (Px and Qx)

is true.

And it is not logically equivalent to,

(Ex) (Px and non-Qx)

They are not the same thing. The first say there are no valid inductive arguments; the latter says there are some invalid inductive arguments. The first does not entail the second.

Rather, the situation looks like this:

(1) ~(Ex) (Px and [Qx or non-Qx])

which says that no inductive argument is either valid or invalid, is NOT logically equivalent to

(2) (Ax) (Px --> [Qx or non-Qx])

which says that all inductive arguments are either valid or invalid.

The former is true. The latter is false.

But (1) IS logically equivalent to,

(3) (Ax) (Px --> ~ [Qx or non-Qx])

which says that all inductive arguments are neither valid nor invalid. And (3) is true just as (1) is true.

Your view is an equivocation on negation "it is not the case that" and the predicate "invalid."

In other words, "X is not valid" does not mean the same thing as "X is invalid" or "X is non-valid."

I am not valid, but I am not thereby "invalid" or "non-valid."

Again, category mistake.

Further, "validity" just means

For all deductive arguments, if the premises are true, then the conclusion must be true.

But the definition of validity, here, does not tell you that the feature of validity applies to anything beyond the domain of deductive arguments.

"Strength" (analogous to validity) just means,

For all inductive arguments, if the premises are true, then the conclusion is probably (more likely than not) true.

But just because validity is not a feature of strong inductive arguments, it does not logically follow that invalidity is a feature of strong inductive arguments.

This, in itself, is your logical fallacy here:

No inductive argument is valid.
Therefore, all (or at least one) inductive arguments are invalid.

*This argument is invalid, and the conclusion is even false.

(a) No P are Q

does not entail,

(b) All P are non-Q

nor does it entail,

(c) Some P are non-Q

at most, it entails

(d) It is not the case that some P are Q

Please stop responding to my posts. I can't stand having my fallacies revealed!

kennethamy

Thu 8 Apr, 2010 01:51 am
@Emil,
Emil;149460 wrote:

Invalid = not valid. Is this another case of your reluctance to accept the common usage of negation prefixes? (IN-, UN-, NON-, ANTI-, etc.) like with the previous "unjustified = non justified" confusion?. In any case, whatever it is that you mean by "invalid" over and above not valid. I don't mean that. By "invalid" I mean "not valid" and nothing else.

Well, in that case, fine. I agree. All inductive arguments are not-valid arguments. Or, by obversion, no inductive arguments are valid arguments. (I wish I had thought to say all inductive arguments are non-valid arguments. That would have, perhaps, made it clearer). All arguments are either valid or not valid. But it is not true that all arguments are either valid or invalid. It is analogous to the distinction between LEM, and the law of bi-valence. For all statements S, either S or not-S. But not every statement is either true or false.

(Had I read Extrain's most recent post before this one, I would not have written this post).

Extrain

Thu 8 Apr, 2010 02:13 am
@kennethamy,
kennethamy;149503 wrote:
Well, in that case, fine. I agree. All inductive arguments are not-valid arguments. Or, by obversion, no inductive arguments are valid arguments. (I wish I had thought to say all inductive arguments are non-valid arguments. That would have, perhaps, made it clearer). All arguments are either valid or not valid. But it is not true that all arguments are either valid or invalid. It is analogous to the distinction between LEM, and the law of bi-valence. For all statements S, either S or not-S. But not every statement is either true or false.

Excuse my strict-attention to logical form. But I would think the "not" and the "non" perform different functions. You said that,

"All inductive arguments are non-valid arguments," which means,

All inductive arguments are non-valid (invalid) arguments, which is false,

Though it is true that,

All inductive arguments are "not" valid arguments because it is true (by obversion) that,

No inductive argument is a non-valid argument, it is not true that,

All inductive arguments are non-valid arguments.

kennethamy

Thu 8 Apr, 2010 02:25 am
@Extrain,
Extrain;149507 wrote:
Excuse my strict-attention to logical form. But I would think the "not" and the "non" perform different functions. You said that,

"All inductive arguments are non-valid arguments," which means,

All inductive arguments are non-valid (invalid) arguments, which is false,

But are "invalid" and "non-valid" synonymous?

Extrain

Thu 8 Apr, 2010 02:35 am
@kennethamy,
kennethamy;149510 wrote:
But are "invalid" and "non-valid" synonymous?

For strict logical purposes concerning quantification, I would say "definitely yes" because they represent classes--and the statement

"All inductive arguments are non-valid"

is ambiguous. You can't tell if it means to say that,

No inductive argument is valid (or invalid)--which is true,

or if it is saying,

All inductive arguments are invalid--which is false.

Similarly, the alleged quantifier "Anybody" is ambiguous in ordinary discourse, too, and needs to be translated with some kind of precision.

Colloquial talk, might dictate otherwise, however.

I'm just being a "stickler"....so no worries.

Extrain

Thu 8 Apr, 2010 04:49 am
@Emil,
Emil;149495 wrote:
Please stop responding to my posts. I can't stand having my fallacies revealed!

lol. But it's not as if "validity is optional" for you--especially when the topic is Logic!:devilish:

fast

Thu 8 Apr, 2010 07:31 am
@Extrain,
[QUOTE=Extrain;149467]This is false. All arguments are either valid, invalid, strong, or weak--and/or: sound/unsound or cogent/uncogent. [/QUOTE]

Just to expound on this (and to see how I do),

Terms that apply to deductive arguments are:
1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
5) "Cogent"
6) "Uncogent"

Terms that apply to inductive arguments are:
1) "Strong"
2) "Weak"
3) "Cogent"
4) "Uncogent"

More thoughts,

Just as "Deductive" and "non-deductive" are collectively exhaustive, so too are "Inductive" and "non-inductive".

Terms that apply to non-deductive arguments are the same terms that apply to inductive arguments.

Terms that apply to non-inductive arguments, however, can include:
1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
5) "Cogent"
6) "Uncogent"
7) "Weak"
8) "Strong"

because an argument that is a non-inductive argument may either be a deductive argument or a non-deductive argument, but if it is a non-deductive argument, that's not to say it's necessarily an inductive argument.

kennethamy

Thu 8 Apr, 2010 07:38 am
@fast,
fast;149571 wrote:

Just to expound on this (and to see how I do),

Terms that apply to deductive arguments are:
1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
5) "Cogent"
6) "Uncogent"

Terms that apply to inductive arguments are:
1) "Strong"
2) "Weak"
3) "Cogent"
4) "Uncogent"

More thoughts,

Just as "Deductive" and "non-deductive" are collectively exhaustive, so too are "Inductive" and "non-inductive".

Terms that apply to non-deductive arguments are the same terms that apply to inductive arguments.

Terms that apply to non-inductive arguments, however, can include:
1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
5) "Cogent"
6) "Uncogent"
7) "Weak"
8) "Strong"

because an argument that is a non-inductive argument may either be a deductive argument or a non-deductive argument, but if it is a non-deductive argument, that's not to say it's necessarily an inductive argument.

Tipity-top!..............

Emil

Thu 8 Apr, 2010 12:14 pm
@kennethamy,
kennethamy;149503 wrote:
Well, in that case, fine. I agree. All inductive arguments are not-valid arguments. Or, by obversion, no inductive arguments are valid arguments. (I wish I had thought to say all inductive arguments are non-valid arguments. That would have, perhaps, made it clearer). All arguments are either valid or not valid. But it is not true that all arguments are either valid or invalid. It is analogous to the distinction between LEM, and the law of bi-valence. For all statements S, either S or not-S. But not every statement is either true or false.

(Had I read Extrain's most recent post before this one, I would not have written this post).

I don't get it. What is it that you agree with, if not that all arguments are valid or invalid?

I don't agree that the analogy is apt. Did by "statement" what did you mean? Propositions? I think (excluding problems with various paradoxes notably liar paradoxes) that all propositions are either true or false. Did you mean sentences? Given a pluralistic proposition theory of truth carriers, some sentences are not true or false (because they do not express propositions). Given a monistic proposition theory of truth carriers (I guess you might accept a such, I'm more inclined to accept a pluralistic theory of truth carriers), then no sentence is true or false.

---------- Post added 04-08-2010 at 08:17 PM ----------

Extrain;149534 wrote:
lol. But it's not as if "validity is optional" for you--especially when the topic is Logic!:devilish:

I meant to make a rude remark. The general idea is that you now respond with a rude remark and we continue exchanging such remarks until the mods get here.

---------- Post added 04-08-2010 at 08:20 PM ----------

fast;149571 wrote:

Just to expound on this (and to see how I do),

Terms that apply to deductive arguments are:
1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
5) "Cogent"
6) "Uncogent"

Terms that apply to inductive arguments are:
1) "Strong"
2) "Weak"
3) "Cogent"
4) "Uncogent"

More thoughts,

Just as "Deductive" and "non-deductive" are collectively exhaustive, so too are "Inductive" and "non-inductive".

Terms that apply to non-deductive arguments are the same terms that apply to inductive arguments.

Terms that apply to non-inductive arguments, however, can include:
1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
5) "Cogent"
6) "Uncogent"
7) "Weak"
8) "Strong"

because an argument that is a non-inductive argument may either be a deductive argument or a non-deductive argument, but if it is a non-deductive argument, that's not to say it's necessarily an inductive argument.

Give an example of a non-deductive non-inductive argument.

You summed up what seems to be the standard opinion around here. Now, will you argue it? It is not surprisingly much easier to sum it up and claim it to be the case/true without arguing it. I think I have done well questioning all positions on this and I don't hold a position on what deductive arguments and inductive arguments are, but Pyrrho offered some good theories last I tried talking to him about it. The underlying quandary is what deductive arguments and inductive arguments are. Then there is the usual reluctance for some reason to apply valid/invalid to inductive/non-deductive arguments.

At least, Pyrrho offered something else than an implicit intention theory like the one Ken seems to accept. Hard to tell from his writing it is.

fast

Thu 8 Apr, 2010 12:50 pm
@Emil,
Emil;149651 wrote:
I don't get it. What is it that you agree with, if not that all arguments are valid or invalid?
You think that not a single inductive argument is a valid argument, and he agrees with you, and so do I.

Extrain

Thu 8 Apr, 2010 01:11 pm
@fast,
EDIT:

fast;149571 wrote:

Just to expound on this (and to see how I do),

Terms that apply to deductive arguments are:
1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
(5) "Cogent"
6) "Uncogent"

No. "Cogent" and "uncogent" do not apply to deductive arguments--only to (non-deductive) inductive arguments.

[QUOTE=fast;149571]Terms that apply to inductive arguments are:[/QUOTE]
fast;149571 wrote:

1) "Strong"
2) "Weak"
3) "Cogent"
4) "Uncogent"

Bingo.

fast;149571 wrote:

More thoughts,
Just as "Deductive" and "non-deductive" are collectively exhaustive, so too are "Inductive" and "non-inductive".

yes.

[QUOTE] Terms that apply to non-deductive arguments are the same terms that apply to inductive arguments.[/QUOTE]

yes.

[QUOTE] Terms that apply to non-inductive arguments, however, can include:[/QUOTE]
Quote:

1) "Valid"
2) "Invalid"
3) "Sound"
4) "Unsound"
5) "Cogent"
6) "Uncogent"
7) "Weak"
8) "Strong"

No. "Strong, weak, cogent, uncogent" do not apply to deductive arguments.

I suggest just using the old distinction "deductive argument" and "inductive argument" as mutually exculsive terms. You don't need to be using "non-deductive" or "non-inductive." If an argmunt is not deductive, then it is inductive. If an argument is not inductive, then it is deductive.

[QUOTE] because an argument that is a non-inductive argument may either be a deductive argument or a non-deductive argument, but if it is a non-deductive argument, that's not to say it's necessarily an inductive argument.[/QUOTE]

No, I think you may be making it more confusing that it is. All arguments are either deductive or inductive, but never both. Period. That's exactly why that distinction is there in the first place.

All inductive and deductive arguments come in wide varieties too. But their spheres never overlap. Part of a person's larger argument (or philosophical thesis) can be inductive, and the other part deductive. But an inductive argument alone is never deductive, or vice versa.

fast

Thu 8 Apr, 2010 01:27 pm
@Extrain,
Extrain;149664 wrote:
No. "Cogent" and "uncogent" do not apply to deductive arguments--only to (non-deductive) inductive arguments.
I thought a cogent argument was an argument where the premises are known to be true.

Extrain

Thu 8 Apr, 2010 01:29 pm
@Emil,
Emil;149651 wrote:
I don't get it. What is it that you agree with, if not that all arguments are valid or invalid?

I don't agree that the analogy is apt. Did by "statement" what did you mean? Propositions? I think (excluding problems with various paradoxes notably liar paradoxes) that all propositions are either true or false. Did you mean sentences? Given a pluralistic proposition theory of truth carriers, some sentences are not true or false (because they do not express propositions).

Given a monistic proposition theory of truth carriers (I guess you might accept a such, I'm more inclined to accept a pluralistic theory of truth carriers), then no sentence is true or false.

What is "a monistic proposition theory of truth carriers"?
What is "a pluralistic theory of truth carriers"? Is that what has been called "Fuzzy Logic" which rejects LEM? "Either P or not-P"?

---------- Post added 04-08-2010 at 08:17 PM ----------

Emil;149651 wrote:
I meant to make a rude remark. The general idea is that you now respond with a rude remark and we continue exchanging such remarks until the mods get here.

I am not swayed by anyone's "rude" remarks. You can call me names for all I care. I just thought it was funny you got upset at my logical critiques. And there is nothing wrong with saying that your argument is "invalid" and your premises are "false." That's part of philosophy. This isn't a politically correct forum.

---------- Post added 04-08-2010 at 08:20 PM ----------

Emil;149651 wrote:
Give an example of a non-deductive non-inductive argument.

They don't exist. All arguments are either inductive or deductive, but not both. But part of a larger argument can be deductive and the other part inductive.

Emil;149651 wrote:
You summed up what seems to be the standard opinion around here. Now, will you argue it? It is not surprisingly much easier to sum it up and claim it to be the case/true without arguing it. I think I have done well questioning all positions on this and I don't hold a position on what deductive arguments and inductive arguments are, but Pyrrho offered some good theories last I tried talking to him about it. The underlying quandary is what deductive arguments and inductive arguments are. Then there is the usual reluctance for some reason to apply valid/invalid to inductive/non-deductive arguments.

At least, Pyrrho offered something else than an implicit intention theory like the one Ken seems to accept. Hard to tell from his writing it is.

huh? Pyrrho according to whom? Sextus Empiricus? According to which skeptic philosophy?

We are not even sure what the guy actually wrote because of so many secondary sources on him.

"Pyrrhonian Skepticism" (primarily advanced by Sextus) is not necessarily the same thing as "what Pyrrho wrote."

kennethamy

Thu 8 Apr, 2010 01:32 pm
@Emil,
Emil;149651 wrote:

At least, Pyrrho offered something else than an implicit intention theory like the one Ken seems to accept. Hard to tell from his writing it is.

But what is supposed to be wrong with such a theory? Why think that whether an argument is deductive or non-deductive is intrinsic to the argument itself? We cam infer intentions from the argument most of the time. And, in the case of a deductive argument, if the argument is valid, then don't we infer the intention of the arguer from the argument (with the help of charity)? After all, we reconstruct arguments by trying to divine the intentions of the arguer too. So, why should we not let the intentions of the arguer be what decides what kind of argument it is?

fast

Thu 8 Apr, 2010 01:36 pm
@Extrain,
Extrain;149667 wrote:
And there is nothing wrong with saying that your argument is "invalid" or "false." That's part of philosophy. This isn't a politically correct forum.
I don't think we should say that arguments are false.

By the way, I think he might have been referring to a poster with the screen name Pyrrho.

Extrain

Thu 8 Apr, 2010 01:37 pm
@fast,
fast;149666 wrote:
I thought a cogent argument was an argument where the premises are known to be true.

Correct. But I wouldn't say "known to be true." I would just say "true." Even if someone doesn't know that P, even if P is true--P is still true, even if they don't know that it is.

Deductive arguments are valid or invalid and sound or unsound.
Inductive arguments are strong or weak and cogent or uncogent.

Valid deductive arguments which are sound also have true premises, but not all valid arguments have true premises.

Example:

All wines are whiskeys
Ginger ale is a wine.
Therefore, ginger ale is a whiskey.

This argument is valid, but unsound--because it has false premises.

Strong inductive arguments which are cogent also have true premises, but not all strong arguments have true premises.

Example:

All Presidents of the United States so far have been women.
Therefore, the next president of the united states will probably be a woman.

The argument is strong, but is also uncogent because it has a false premise.

---------- Post added 04-08-2010 at 01:40 PM ----------

fast;149670 wrote:
I don't think we should say that arguments are false.

Yes, yes. thanks. Only premises and conclusions are true or false.

fast

Thu 8 Apr, 2010 01:44 pm
@Extrain,
[QUOTE=Extrain;149671]Correct. But I wouldn't say "known to be true." I would just say "true." Even if someone doesn't know that P, even if P is true--P is still true, even if they don't know that it is. [/QUOTE]Knowledge implies truth, but truth doesn't imply knowledge. I agree.

But, I don't know why you wouldn't say, "known to be true," and that wasn't the issue anyhow. I thought you said the term "cogent" doesn't apply to deductive arguments, but the problem I have with that is that the premises of some deductive arguments are known to be true, and even if whether it's known is a contention, you still said, "I would just say 'true,'" and since some premises of deductive arguments are true, it seems to me that you would agree that the term, "cogent" can be applied to deductive arguments.

kennethamy

Thu 8 Apr, 2010 01:52 pm
@fast,
fast;149674 wrote:
Knowledge implies truth, but truth doesn't imply knowledge. I agree.

But, I don't know why you wouldn't say, "known to be true," and that wasn't the issue anyhow. I thought you said the term "cogent" doesn't apply to deductive arguments, but the problem I have with that is that the premises of some deductive arguments are known to be true, and even if whether it's known is a contention, you still said, "I would just say 'true,'" and since some premises of deductive arguments are true, it seems to me that you would agree that the term, "cogent" can be applied to deductive arguments.

Yes, that is the difference between a cogent and a sound argument. The premises of a cogent argument are known true, those of a sound argument are true. So, cogent implies sound, but not conversely.

Extrain

Thu 8 Apr, 2010 01:57 pm
@fast,
fast;149674 wrote:
Knowledge implies truth, but truth doesn't imply knowledge. I agree.

But, I don't know why you wouldn't say, "known to be true," and that wasn't the issue anyhow. I thought you said the term "cogent" doesn't apply to deductive arguments,

Right. "Cogent" and "uncogent" do not apply to deductive arguments.

[QUOTE=fast;149674]but the problem I have with that is that the premises of some deductive arguments are known to be true, and even if whether it's known is a contention, you still said, "I would just say 'true,'" and since some premises of deductive arguments are true, it seems to me that you would agree that the term, "cogent" can be applied to deductive arguments.[/QUOTE]

But this isn't a problem for Logic. This is a problem for epistemology and philosophers.

For an argument to be cogent or uncogent, the premises don't have to be known to be true by persons X and Y. Truth and knowledge are not the same.

---------- Post added 04-08-2010 at 01:59 PM ----------

kennethamy;149677 wrote:
Yes, that is the difference between a cogent and a sound argument. The premises of a cogent argument are known true, those of a sound argument are true. So, cogent implies sound, but not conversely.

I don't think that's right, Ken. One person may know a premise to be true of a cogent argument, the other person may not.

So knowing that P is not a necessary condition for an argument to be cogent or uncogent. Further, "cogent" never implies sound, and "sound" never implies cogent.