Non-deductive VERSUS Inductive

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Extrain
 
Reply Fri 9 Apr, 2010 01:16 pm
@Emil,
Emil;149984 wrote:
Extrain, I don't read your posts.


And for what other reason than that you can't (or don't want to) answer any of my questions?
:rolleyes:

---------- Post added 04-09-2010 at 01:41 PM ----------

Emil;150007 wrote:
Sure.

In less words:
[INDENT]1. For all propositions, if it is true, then it is not false.
2. For all propositions, if it is false, then it is not true.
3. For all propositions, if it is not true, then it is false.
4. For all propositions, if it is not false, then it is true.
[/INDENT]I tentatively believe in all of them (due to certain semantic paradoxes especially the liar paradox). You do not believe all of them, but you believe in 1-2. These four propositions above (1-4) are part of classical logic and they give rise to certain paradoxes the most famous being liar type paradoxes, e.g.:
[INDENT]Liar 1. The proposition expressed by this sentence is false.
[/INDENT]Some people think that if we deny 3-4 we don't have any problems with liar 1. However there are other versions of it that go through without 3-4 being true, e.g.
[INDENT]Liar 2. The proposition expressed by this sentence is not true.
[/INDENT]Baring the technical details. This is just for your consideration. I might have expressed the liars a bit wrong too etc, but it is not important for present purposes.

Another relevant proposition is proposition bivalence:
[INDENT]Proposition bivalence. For all propositions, it is true or false and not true and false.

[/INDENT]I'm glad you mention it. In any case, I could try to appeal to my own authority but it wouldn't do very well for I am not that much of an authority. I did read a couple of textbooks, yes, and I did study advanced logic, formal logic, non-classical logic, modal logic, epistemic logic etc., but I'm not a professor or have a similar authority giving profession or credential (yet!). Also Ken is the best authority around here even if his main area is not logic (I don't know what it is, maybe epistemology or history of philosophy). But then again, in general, authorities are not worth much in philosophy.



I know. I don't know what theory you accept about truth carriers but it does involve sentences. Do you believe that propositions exist too? You may want to read up on the nomenclature that I have developed for this discussion and I think it is a very interesting discussion. Here is some of it.



That is incorrect. I do not believe in any theory at the moment, but I disbelieve in monistic sentence theories. What you think I am holding is a monistic proposition theory (= a theory where only propositions are true/false). I used to hold that so you are probably excused.



I like to use this one:
[INDENT]Chomsky. Colorless green ideas sleep furiously.
[/INDENT]We agree about Chomsky not expressing any proposition, and that the sentence is neither true or false.



About sentences, yes. Analogous to 1-4 above, there is a set for sentences too:
[INDENT]1. For all sentences, if it is true, then it is not false.
2. For all sentences, if it is false, then it is not true.
3. For all sentences, if it is not true, then it is false.
4. For all sentences, if it is not false, then it is true.
[/INDENT]Which ones do you believe in? I believe in 1-2 and disbelieve in 3-4. I think you do likewise. Is that correct?

There is also the sentence version of bivalence:
[INDENT]Sentence bivalence. For all sentences, it is true or false and not true and false.

[/INDENT]I think sentence bivalence is false and not true. I suppose you do the same. Is that so?


Why would anyone believe in "sentence bivalence"? There are numerous sentences neither true nor false.

"Colorless green Ideas sleep furiously" is one.

I will ask again, in what respects does general semantics, Gricean implicature, propositions and sentences in a given language, the liar paradox, etc., etc., bear on propositional argumentative validity/invalidity in deductive logic? Again, propositional first-order logic does not encounter any of the difficulties you enumerated above since it is purely a formal language, not a natural language.
 
Emil
 
Reply Fri 9 Apr, 2010 02:29 pm
@fast,
Emil wrote:
1. For all propositions, if it is true, then it is not false.
2. For all propositions, if it is false, then it is not true.
3. For all propositions, if it is not true, then it is false.
4. For all propositions, if it is not false, then it is true.

I tentatively believe in all of them (due to certain semantic paradoxes especially the liar paradox). You do not believe all of them, but you believe in 1-2.


Fast wrote:
Actually, I do believe all four propositions are true.

"Not true" can imply "false," but that it can isn't to say it always does. In other words, X not being true doesn't entail that X is false. It depends on what X is. If X is a proposition, then yes. If X is a sentence, then maybe. If X is a sentence that expresses a proposition, then yes. If X is a sentence that doesn't express a proposition, then no. See, it depends on why X is not true. If something is false, then we know immediately that something is not true, but such is not the case conversely.


If you do, then explain what you meant by this:

Fast, before wrote:
At this point, not only do we believe and agree that "false" implies "not true," but it's also true that "false" implies "not true," and that is, of course, the important point. However, I (and apparently unlike you) do not believe that the converse is true. What I mean by that is that although the former implies the latter, the latter does not imply the former; hence, I do not believe that "not true" implies "false," but based on your quote, you seem to believe just that, that "not true" does imply false, but you shouldn't believe that, nor should I agree with that, for it's not true.


I don't get it. You said here that you don't believe that not true implies false. But now you say that you do believe it because you believe in 3. So which is it? Unless you really believe both and are thus affirming a contradiction (as e.g. Priest does).

Besides, what does "Not true" can imply "false," even mean? The only thing that I can come up with is a true material implication for some sentence, but I don't know what you meant. Why do you talk about sentences and propositions? Maybe you should re-read 1-4, for they are clearly only about propositions cf. "for all propositions". 1'-4' deal with sentences.

Fast wrote:
I believe that propositions exist, yes. Of course, with this being a philosophy forum, there's no telling how that might be interpretted. Let me say that I think there are propositions. After all, they are what is expressed by sentences, and I believe sentences are used to express X--whatever that might be. What is meant, (I think) is one contender for what that might be.


So, since you also believe that some sentences are true/false and some propositions are true/false, then you believe in some pluralistic theory. That seems plausible to me, I currently find a pluralistic proposition theory the most plausible. Whether you believe a pluralistic sentence theory or a pluralistic proposition theory (belief theory etc.) depends on which truth carrier you think is the basic one. Which do you think it is? I'm inclined to believe it is a proposition, not a sentence. But some people (e.g. Quine) thinks that sentences are the basic truth carrier, and indeed that there are no propositions. (Mystical entities.)

Fast wrote:
Exactly!

The sentence is not true. But, because it doesn't express a proposition, it's not false. So, the sentence is both 1) not true and 2) not false.


Right.

Fast wrote:
I think a sentence is true if 1) the sentence expresses a proposition and 2) the proposition expressed by the sentence is true.

I think a sentence is false if 1) the sentence expresses a proposition and 2) the proposition expressed by the sentence is false. Any such sentence is not only false but not true as well.


So basically what I wrote in an earlier essay about pluralistic proposition theories.

Fast wrote:
So, let's talk about your four propositions:

1. For all sentences, if it is true, then it is not false.
2. For all sentences, if it is false, then it is not true.
3. For all sentences, if it is not true, then it is false.
4. For all sentences, if it is not false, then it is true.

I agree with number 1, and I agree with number 2. I can tell you that technically, I don't agree with 3 and 4 (but only because you said, "for all sentences.") If a sentence is not true, then it may be false--if the sentence expresses a false proposition. If a sentence is not false, then it may be true--if it expresses a true proposition. Again, if a sentence doesn't express a proposition, then it's neither true nor false (hence, it's not true, and it's not false).


Right.

Fast wrote:
I'm sorry, but I'm just not comprehending that. If there is a sentence, then it's either not true or not false. But, that's not to say, "if there is a sentence, then it's either true or false." Why? Because some sentences are neither true nor false, as not all sentences express propositions.


What do you mean that you don't "comprehend that"? Do you mean that you do not understand it, or that you do not understand why someone would believe it, or something else? I cannot tell what you mean. Though I get that you disbelieve in sentence bivalence, and so do I. Because of sentences like Chomsky.
 
fast
 
Reply Fri 9 Apr, 2010 03:19 pm
@Emil,
[QUOTE=Emil;150021]If you do, then explain what you meant by this:[/QUOTE]
Emil;150021 wrote:


I don't get it. You said here that you don't believe that not true implies false. But now you say that you do believe it because you believe in 3. So which is it? Unless you really believe both and are thus affirming a contradiction (as e.g. Priest does).


I'm not really talking about sentences or propositions (per se) when I say that "false" implies "not true." But, I can talk about sentences and propositions, and I have been.

I will say that if a sentence is false, then a false sentence is not true, for all false sentences are sentences that are not true.

However, I will not say that all sentences that are not true are false sentences, for some sentences are neither true nor false.

I now move on to propositions:

All false propositions are propositions that are not true, and all propositions that are not true are false propositions. Does that mean "false" implies "not true." I don't think so. But, all false propositions are propositions that are not true.

If a sentence is not true, then it may be false; for example, a sentence that expresses a proposition that is false is a sentence that is both not true and false. However, I said that it may be false. That doesn't mean it is false, nor does it mean that it's true either; for example, if a sentence fails to express a proposition, then the sentence is neither true nor false, so just because a sentence is not true, that doesn't mean it's also false.

That is why I say that "false" doesn't imply "not true." A sentence that is not true may either be 1) a sentence that expresses a false proposition (and thus the sentence is not true) or it may be 2) a sentence that doesn't express a proposition at all (and is thus a sentence that is not true).

[QUOTE]Besides, what does "Not true" can imply "false," even mean?[/QUOTE]I probably shouldn't have said, "can."

I still don't want to say that "not true" implies "false." If a sentence is not true, we can't take that information and rightly conclude that whatever we're talking about is therefore false, and the reason for that is that it might be a sentence that doesn't express a proposition at all. Any sentence that fails to express a proposition is a sentence that is not true, but there's no way I'm going to say that a sentence that fails to express a proposition is false, for I do not believe we ought to say of sentences that they are false when they fail to express propositions.

[QUOTE]So, since you also believe that some sentences are true/false and some propositions are true/false, then you believe in some pluralistic theory. [/QUOTE]You got part of it right. I believe that some sentences are true, I believe that some sentences are false, and I believe that some sentences are neither true nor false. However, when it comes to propositions, they are all either true or false. I will never say that a proposition is neither true nor false.

"True" and "false" are not collectively exhaustive, but "true" and "not true" are collectively exhaustive.

[QUOTE]That seems plausible to me, I currently find a pluralistic proposition theory the most plausible. Whether you believe a pluralistic sentence theory or a pluralistic proposition theory (belief theory etc.) depends on which truth carrier you think is the basic one. Which do you think it is? I'm inclined to believe it is a proposition, not a sentence. [/QUOTE]I'm not exactly sure what a truth carrier is.

[QUOTE]But some people (e.g. Quine) thinks that sentences are the basic truth carrier, and indeed that there are no propositions. (Mystical entities.)[/QUOTE]I don't think that there are no propositions. I think that there are propositions.

[QUOTE]What do you mean that you don't "comprehend that"? Do you mean that you do not understand it, or that you do not understand why someone would believe it, or something else? [/QUOTE]I mean that I don't understand it. That happens a lot, btw.

This is what you said:
[QUOTE]There is also the sentence version of bivalence: [/QUOTE]
Quote:

Sentence bivalence. For all sentences, it is true or false and not true and false.
I think sentence bivalence is false and not true. I suppose you do the same. Is that so?
I got mixed up with all those operators in the definition.

I will say that all sentences are either true or not true, but I won't say that all sentences are true or false. I will say that some sentences are true, and I will say that some sentences are false. Remember, "true" and "false" is not collectively exhaustive. A sentence can be neither true nor false. When? When they fail to express propositions.

I will say that all propositions are either true or false. But, I'm saying no such thing about sentences.

Does this mean "not true" implies "false"? No, I don't think it does, as when it's said, it's not clear whether or not we're talking about sentences or propositions or something else entirely.
 
kennethamy
 
Reply Fri 9 Apr, 2010 03:32 pm
@fast,
fast;150030 wrote:


I'm not really talking about sentences or propositions (per se) when I say that "false" implies "not true." But, I can talk about sentences and propositions, and I have been.

I will say that if a sentence is false, then a false sentence is not true, for all false sentences are sentences that are not true.

However, I will not say that all sentences that are not true are false sentences, for some sentences are neither true nor false.

I now move on to propositions:

All false propositions are propositions that are not true, and all propositions that are not true are false propositions. Does that mean "false" implies "not true." I don't think so. But, all false propositions are propositions that are not true.

If a sentence is not true, then it may be false; for example, a sentence that expresses a proposition that is false is a sentence that is both not true and false. However, I said that it may be false. That doesn't mean it is false, nor does it mean that it's true either; for example, if a sentence fails to express a proposition, then the sentence is neither true nor false, so just because a sentence is not true, that doesn't mean it's also false.

That is why I say that "false" doesn't imply "not true." A sentence that is not true may either be 1) a sentence that expresses a false proposition (and thus the sentence is not true) or it may be 2) a sentence that doesn't express a proposition at all (and is thus a sentence that is not true).

I probably shouldn't have said, "can."

I still don't want to say that "not true" implies "false." If a sentence is not true, we can't take that information and rightly conclude that the sentence is therefore false, and the reason for that is that it might be a sentence that doesn't express a proposition at all. Any sentence that fails to express a proposition is a sentence that is not true, but there's no way I'm going to say that a sentence that fails to express a proposition is false, for I do not believe we ought to say of sentences that they are false when they fail to express propositions.

You got part of it right. I believe some that sentence are true, and I believe that some sentences are false, and I believe that some sentences are neither true nor false. However, when it comes to propositions, they are all either true or false. I will never say that a proposition is neither true nor false.

"True" and "false" are not collectively exhaustive, but "true" and "not true" are collectively exhaustive.

I'm not exactly sure what a truth carrier is.

I don't think that there are no propositions. I think that there are propositions.

I mean that I don't understand it. That happens a lot, btw.

This is what you said:
I got mixed up with all those operators in the definition.

I will say that all sentences are either true or not true, but I won't say that all sentences are true or false. I will say that some sentences are true, and I will say that some sentences are false. Remember, "true" and "false" is not collectively exhaustive. A sentence can be neither true nor false. When? When they fail to express propositions.

I will say that all propositions are either true or false. But, I'm saying no such thing about sentences.

Does this mean "not true" implies "false"? No, I don't think it does, as when it's said, it's not clear whether or not we're talking about sentences or propositions or something else entirely.


I do not understand all this twisting and turning. The sentence (statement, proposition) "Colorless green ideas dream quietly" is not true, but it is not false. Therefore, false implies not true. (By contraposition). But there is no reason to think that not true implies false. And, therefore, there is no reason to believe that the sentence, "Colorless green ideas dream quietly" is false. unless Emil, or someone has some other reason to believe it.
 
Extrain
 
Reply Fri 9 Apr, 2010 03:51 pm
@Emil,
Premise (1) is false in the following argument right from the get-go; so it doesn't even matter which theory countenances that (1) is true:

Quote:
1. For all things, that it is a truth carrier logically implies that it is a sentence.
2. There exists a thing such that it is a truth carrier and that it is logically necessarily the case.
Thus, 3. There exists a thing such that it is a sentence and that it is logically necessarily the case. [from 1, 2]............


The following problems hold only if the person assumes that sentences just are propositions. But there is more reason to think this is false than true.

Quote:

Sentences as Secondary Truth Bearers in a Pluralistic Proposition Theory

It seems to me that monist sentence theories are too implausible, but might it not nonetheless be the case that some sentences are true/false? In this essay I will discuss sentences as secondary truth bearers.


The common phenomenon of mere sentence ambiguity is not a sufficient reason for thinking there is more than one proposition that is expressed by all sentences, anyway, since that there is even two propositions being expressed by a single ambiguous sentence is questionable as it is. Which proposition the sentence expresses is just indeterminable by the reader or listener. So there is nothing problematic about ambiguous sentences.

Quote:

Pragmatic value
I can see that it has some pragmatic value to say that sentences are also sometimes true/false in addition to propositions. The pragmatic value is that it makes it easier to talk about certain things without having to use complex phrases like "the proposition expressed by (the sentence) is true (or false)". Perhaps this is a good enough reason to posit that sentences also in some cases have the properties true/false.


Right! This is why it is so commonly called an "INDISPENSIBILITY ARGUMENT" in philosophy which is totally consistent with Ockham's PRINCIPLE OF PARSIMONY.

The violation of this rule only comes about when we multiply entities needlessly.

But if entities are, in fact, needed to make sense of what is going on, then there is very good reason for thinking these entities exist.

Quote:
An alternative solution is to invent some shorthands for talking about propositions expressed. See (N. Swartz, R. Bradley, 1979).


These kinds of reductive approaches typically fail time and again to capture what is really going on. Thinking that a thorough reductive short-hand paraphrase is needed in order not to violate Ockham's Razor is only presupposed by the prior assumption Reduction Theorists make which is that there does, in fact, exist a violation of Ockham's Razor from the start. But there is no reasons at all for thinking this is true. They first have to show that their proposed short-hand reductions are successful (which they are typically not--not for the more important sentences, anyway) before they can claim that Ockham's Razor has been violated. If they are not successful in a given matter, then Ockham's Razor has not been violated.

Quote:

Parsimony

The problem I see with it is that of parsimony. "Entities must not be multiplied beyond necessity" (Wiki). Is that not exactly what we are doing? At least if properties are entities. I think they are since entity is the most inclusive set (similar to "thing")1. But perhaps it is not as problematic to multiply properties as it is to multiply other kinds of entities in an explanation. I don't know.


No, we are not doing this.

"Schnee ist Weiss"
"Snow is white."

These are two different token utterances of the same sentence-type in two different languages. And it is reasonable to think these two different sentence-types can express the same proposition, namely,

[White[snow]]

or, given that W=the semantic value of "white and Weiss" in both languages, and S=the semantic value of "snow and Schnee" in both languages, the proposition expressed by both languages is,

[W[S]]

Therefore, sentences are distinct from propositions.

Quote:

What are the conditions for a sentence being true/false?

This is how I see understand the position:

A sentence is true iff it expresses exactly one proposition and that proposition is true.
A sentence is false iff it expresses exactly one proposition and that proposition is false.

The phrase " expresses exactly one proposition" seems to avoid the ambiguity problem that I wrote about earlier.


Though the necessary and sufficient conditions are correct, I don't see how this would lead to any problems. The problem only arises if you think all sentences are truth-valuable, which they clearly are not. Only some sentences are truth-valuable. All propositions expressed by sentences are truth-bearers, and only some sentences are truth-bearers because not all sentences express propositions.
 
fast
 
Reply Fri 9 Apr, 2010 04:04 pm
@Extrain,
Extrain,

Got a question for ya. This may (or may not) have anything to do with what you just said. But still:

P1: Some propositions are true.
P2: Some sentences are true.
P3: Some statements are true.

I believe all three propositions are true. Do you believe that too? I asked this a while back on another thread, and I believe I was asked what I meant by each of those three words, and I'll tell you that I mean exactly what they mean; nothing more, nothing less.
 
Extrain
 
Reply Fri 9 Apr, 2010 04:11 pm
@fast,
fast;150048 wrote:

Got a question for ya. This may (or may not) have anything to do with what you just said. But still:

P1: Some propositions are true.
P2: Some sentences are true.
P3: Some statements are true.

I believe all three propositions are true. Do you believe that too? I asked this a while back on another thread, and I believe I was asked what I meant by each of those three words, and I'll tell you that I mean exactly what they mean; nothing more, nothing less.


I am inclined to agree with exactly how you put it here. So, yes. But this is precisely what Emil seems not to understand.

The only difference between some sentences/statements and all propositions is that some sentences and some statements fail to be truth-valuable at all because we can't determine which propositions get expressed by those sentences and statements. But this is rather obvious, right? Should that be problematic for any reason? It happens all the time when we ask eachother, "what do you mean by saying_____?"

I don't see how this means we should be adopting what Emil calls a "pluralistic proposition theory" for each and every sentence. Why would anybody think that? What's the motivation? The motivation only comes in if somebody thought propositions just are sentences. But this is false.
---------- Post added 04-09-2010 at 05:04 PM ----------

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.
 
Emil
 
Reply Fri 9 Apr, 2010 05:38 pm
@kennethamy,
kennethamy;150036 wrote:
I do not understand all this twisting and turning. The sentence (statement, proposition) "Colorless green ideas dream quietly" is not true, but it is not false. Therefore, false implies not true. (By contraposition). But there is no reason to think that not true implies false. And, therefore, there is no reason to believe that the sentence, "Colorless green ideas dream quietly" is false. unless Emil, or someone has some other reason to believe it.


There is no proposition expressed by the Chomsky sentence. You give the impression that there is by mentioning statements (what is that? I dislike the term seems like some term that is just ambiguous between sentence and proposition) and propositions. But I don't think you think that there is a proposition expressed by Chomsky, just that you misspoke.

I don't have any reason to believe that Chomsky-sentence is false. I don't believe it is. I think it is neither false nor true.
 
Extrain
 
Reply Fri 9 Apr, 2010 05:47 pm
@Emil,
Emil;150085 wrote:
There is no proposition expressed by the Chomsky sentence. You give the impression that there is by mentioning statements (what is that? I dislike the term seems like some term that is just ambiguous between sentence and proposition) and propositions. But I don't think you think that there is a proposition expressed by Chomsky, just that you misspoke.

I don't have any reason to believe that Chomsky-sentence is false. I don't believe it is. I think it is neither false nor true.


Though this is correct, I think the point is that not all sentences are governed by the supposed principle of "sentence-bivalence."

The reason is that sentences are distinct from propositions (which are governed by the prinicple of bivalence).

"[You] Go get me a beer" is a sentence, but it doesn't assert anything truth-valuable because it is a command, not an assertion.

Therefore, not all sentences are truth-bearers.

But none of this should be a motivation for adopting what you call a "pluralistic proposition theory" for sentences. Why would you think this? What is the motivation here? What problem are you trying to solve?

Adopting such a theory would only be a motivation for someone who thought propositions were numerically identical to sentence-types in a given language. But propositions are not identical to sentence-types. You seem to think they are, in fact, identical because you assume the Principle of Parsimony is somehow being violated if we suppose propositions are distinct from sentence-types. But no such violation of this Principle is taking place by concluding that sentence-types are distinct from propositions. This is obvious on so many linguistic fronts. It is precisely because sentence-types are distinct from propositions that it becomes possible for two different language speakers to communicate at all.

Quine had problems explaining exactly this phenomenon. He couldn't because of his own theory of The Indeterminacy of Translation between different language users.
 
kennethamy
 
Reply Fri 9 Apr, 2010 06:01 pm
@Emil,
Emil;150085 wrote:
There is no proposition expressed by the Chomsky sentence. You give the impression that there is by mentioning statements (what is that? I dislike the term seems like some term that is just ambiguous between sentence and proposition) and propositions. But I don't think you think that there is a proposition expressed by Chomsky, just that you misspoke.

I don't have any reason to believe that Chomsky-sentence is false. I don't believe it is. I think it is neither false nor true.


I don't think there is a proposition expressed by the Chomsky sentence, and therefore, that sentence is not true. But certainly, it is not false either. Equally, an inductive argument is not valid, but it is certainly not invalid either.
 
Emil
 
Reply Fri 9 Apr, 2010 07:05 pm
@kennethamy,
kennethamy;150098 wrote:
I don't think there is a proposition expressed by the Chomsky sentence, and therefore, that sentence is not true. But certainly, it is not false either. Equally, an inductive argument is not valid, but it is certainly not invalid either.


I don't see any analogy between them. What do you think "invalid" means if not "not valid" or "non-valid"? What is the extra meaning that you think is there? I don't get it. And no logic textbook that I've read mentions some kind of distinction between "invalid" and "not valid", "non-valid".
 
Extrain
 
Reply Fri 9 Apr, 2010 07:17 pm
@Emil,
Emil;150118 wrote:
I don't see any analogy between them. What do you think "invalid" means if not "not valid" or "non-valid"? What is the extra meaning that you think is there? I don't get it. And no logic textbook that I've read mentions some kind of distinction between "invalid" and "not valid", "non-valid".


Nor does any logic textbook say that because inductive arguments are not valid that they are therefore invalid. Again, to think otherwise is your logical fallacy.

I've already told you this, but you directly said you don't read my posts because you don't like your logical fallacies being corrected:

"It is not the case that X is valid"

does not mean,

"X is invalid" BECAUSE

the first is a proposition itself which negates the truth of another affirmative proposition "that x is valid."

The latter is an affirmative proposition which simply ascribes a positive predicate to an entity X, but it is not negating another proposition at all.

If you don't understand this distinction, then we will all have to go back to Logic 101, because this concept is incredibly basic.
 
Emil
 
Reply Fri 9 Apr, 2010 07:33 pm
@Emil,
Quote:
I'm not really talking about sentences or propositions (per se) when I say that "false" implies "not true." But, I can talk about sentences and propositions, and I have been.


Oh! How could I know. I thought you were talking about propositions or sentences, not whatever things it is that you are talking about. But please then be more explicit about your quantifiers in the future. I could not know what you quantified over. Quantifiers are, in case you don't know (due to lack of reading of textbooks), the thing (idea or whatever) expressed by phrases such as "for all" "for any", "some" etc. ("for alle" in danish). Saying that not false does not imply true is really talking in a short-hand language. This is why I was very explicit about what my quantifiers ranged over.

Quote:
I will say that if a sentence is false, then a false sentence is not true, for all false sentences are sentences that are not true.


In order words: You believe in 2'. Recall the now 8 principles (by which I just mean propositions of special interest):

[INDENT]1. For all propositions, if it is true, then it is not false.
2. For all propositions, if it is false, then it is not true.
3. For all propositions, if it is not true, then it is false.
4. For all propositions, if it is not false, then it is true.

1'. For all sentences, if it is true, then it is not false.
2'. For all sentences, if it is false, then it is not true.
3'. For all sentences, if it is not true, then it is false.
4'. For all sentences, if it is not false, then it is true.
[/INDENT]
For some reason I forgot to add an apostrophe before when writing these. That was silly of me and allowed confusion to be between 1 and 1'. One is about propositions and one is about sentences.

I believe in 1-4 and 1'-2'. Which do you believe in?

Quote:
However, I will not say that all sentences that are not true are false sentences, for some sentences are neither true nor false.


Right, so you don't believe in 3'.

Quote:
All false propositions are propositions that are not true, and all propositions that are not true are false propositions. Does that mean "false" implies "not true." I don't think so. But, all false propositions are propositions that are not true.


Your writing is too unclear for me to answer. What does your quantifier range over here? Is it every thing, every sentence, every proposition or something else? In case you mean "for every proposition", then yes it does imply that the material implication holds. If you did mean propositions then you state that you believe in 2 and 3.

Quote:
If a sentence is not true, then it may be false; for example, a sentence that expresses a proposition that is false is a sentence that is both not true and false. However, I said that it may be false. That doesn't mean it is false, nor does it mean that it's true either; for example, if a sentence fails to express a proposition, then the sentence is neither true nor false, so just because a sentence is not true, that doesn't mean it's also false.


Right. You deny 1'.

Quote:
That is why I say that "false" doesn't imply "not true." A sentence that is not true may either be 1) a sentence that expresses a false proposition (and thus the sentence is not true) or it may be 2) a sentence that doesn't express a proposition at all (and is thus a sentence that is not true).


So you are quantifying over sentences? Or something else and sentences? I cannot tell, you are not being clear enough.

Quote:
I still don't want to say that "not true" implies "false." If a sentence is not true, we can't take that information and rightly conclude that whatever we're talking about is therefore false, and the reason for that is that it might be a sentence that doesn't express a proposition at all. Any sentence that fails to express a proposition is a sentence that is not true, but there's no way I'm going to say that a sentence that fails to express a proposition is false, for I do not believe we ought to say of sentences that they are false when they fail to express propositions.


Right, now you are talking about sentences again and I agree with what you said. In other words: I agree that 3' is false.

Quote:
You got part of it right. I believe that some sentences are true, I believe that some sentences are false, and I believe that some sentences are neither true nor false. However, when it comes to propositions, they are all either true or false. I will never say that a proposition is neither true nor false.

"True" and "false" are not collectively exhaustive, but "true" and "not true" are collectively exhaustive.


I didn't get anything wrong. Read what I wrote again. That I wrote "some" does not imply not all. That is to invoke a kind of implicature which is generally not a clever thing to do in philosophy, especially logic.

You think that proposition bivalence is true. I agree.

Quote:
I'm not exactly sure what a truth carrier is.


When I talk about truth carriers I mean a kind of thing that can be (it doesn't have to) true/false. Other people may use the term for other meanings I don't think there is strict agreement to what its meaning is.

Quote:
I don't think that there are no propositions. I think that there are propositions.


Ok, then you do not believe in a monist sentence theory.

Quote:
I mean that I don't understand it. That happens a lot, btw.


[INDENT]Sentence bivalence. For all sentences, it is true or false and not true and false.
[/INDENT]
I see how it could be possible to misunderstand it. Try a rephrasing:

[INDENT]Sentence bivalence. For all sentences, it is true or false, and not true and false.Proposition bivalence.
Quote:
Does this mean "not true" implies "false"? No, I don't think it does, as when it's said, it's not clear whether or not we're talking about sentences or propositions or something else entirely.


Why do you keep saying it then? Why do you say something you, yourself, find unclear? I don't get it.
 
Extrain
 
Reply Fri 9 Apr, 2010 08:07 pm
@Emil,
Emil;150123 wrote:
Oh! How could I know. I thought you were talking about propositions or sentences, not whatever things it is that you are talking about. But please then be more explicit about your quantifiers in the future. I could not know what you quantified over. Quantifiers are, in case you don't know (due to lack of reading of textbooks), the thing (idea or whatever) expressed by phrases such as "for all" "for any", "some" etc. ("for alle" in danish). Saying that not false does not imply true is really talking in a short-hand language. This is why I was very explicit about what my quantifiers ranged over.

In order words: You believe in 2'. Recall the now 8 principles (by which I just mean propositions of special interest):
[INDENT]1. For all propositions, if it is true, then it is not false.
2. For all propositions, if it is false, then it is not true.
3. For all propositions, if it is not true, then it is false.
4. For all propositions, if it is not false, then it is true.

1'. For all sentences, if it is true, then it is not false.
2'. For all sentences, if it is false, then it is not true.
3'. For all sentences, if it is not true, then it is false.
4'. For all sentences, if it is not false, then it is true.
[/INDENT]

[INDENT]No, these are not "principles." The latter set about sentences, in particular, are purely philosophical universal generalizations that spring from your own private view which no one agrees with. Further, you haven't even told anyone why you think the latter formulations ought to hold for all sentences anyway. No grammarian thinks the latter set have to be true, and certainly most philosophers of language don't either. So why you think bivalence ought to hold for all sentences remains a complete mystery....
[/INDENT]
Quote:
Sentence bivalence. For all sentences, it is true or false and not true and false.

I see how it could be possible to misunderstand it. Try a rephrasing:
[INDENT]Sentence bivalence. For all sentences, it is true or false, and not true and false.Proposition bivalence.


This won't work. You are trying to pin everyone into your own private logical formulations using quantification and the principle of bivalence. Based on what Fast has told me, Fast and myself are only committed to our own logical formulations here:

For all propostions Px, for all true propostions Tx, and for all false propositions Fx,

(Ax) (Px --> ([Tx or Fx] and ~[Tx and Fx]))

For all sentences Sx, for all true sentences Tx, and for all false sentences Fx.

(Ex) (Sx and ([Tx or Fx] and ~[Tx and Fx]))

They don't mean the same thing.

For propositions, this says,

For all propositions x, x is either true or false, and not both.

For sentences, this says,

For some sentences x, x is either true or false, and not both.

We are only asserting bivalence holds for some sentences.

What do you not understand?

Ignoring what fast may think about the rest, I am also denying that bivalence holds for all sentences. So I think your own universal generalization for sentences,

(Ax) (Sx --> ([Tx or Fx] and ~[Tx and Fx]))

is false.

So I am actually committed to its denial, namely,

~(Ax) (Sx --> ([Tx or Fx] and ~[Tx and Fx]))

and this is perfectly consistent with the truth of,

(Ex) (Sx and ([Tx or Fx] and ~[Tx and Fx]))

and my denial of your universal generalization also logically entails that,

(Ex) (Sx and ~([Tx or Fx] and ~[Tx and Fx]))

which says there are some sentences which are not (either true or false, and not both).

Truly, I'm deeply curious, do you not know how Aristotle's Traditional Square of Logical Opposition actually works or something? It's been around for over 2 thousand years and forms the backdrop of all current quantificational logic. And you continue to make the same logical fallacy in this thread with respect to it.
 
Extrain
 
Reply Fri 9 Apr, 2010 10:39 pm
@Extrain,
Why does the same categorical fallacy continue to happen here?
 
kennethamy
 
Reply Fri 9 Apr, 2010 10:50 pm
@Emil,
Emil;150118 wrote:
I don't see any analogy between them. What do you think "invalid" means if not "not valid" or "non-valid"? What is the extra meaning that you think is there? I don't get it. And no logic textbook that I've read mentions some kind of distinction between "invalid" and "not valid", "non-valid".


No, that distinction is a semantic issue, not a logical issue. I guess I think that, for instance, to say that an oyster is not intelligent is true, but it is not true to say of an oyster that it is unintelligent. Oysters cannot be unintelligent because they cannot be intelligent. But they are certainly not intelligent. And inductive argument cannot be invalid because they cannot be valid. But they certainly are not valid.
 
Emil
 
Reply Fri 9 Apr, 2010 11:04 pm
@kennethamy,
kennethamy;150156 wrote:
No, that distinction is a semantic issue, not a logical issue. I guess I think that, for instance, to say that an oyster is not intelligent is true, but it is not true to say of an oyster that it is unintelligent. Oysters cannot be unintelligent because they cannot be intelligent. But they are certainly not intelligent. And inductive argument cannot be invalid because they cannot be valid. But they certainly are not valid.


I see what you mean but I disagree still. Yes, in some cases the negation prefixes including "-UN" (etc. the others I mentioned) do mean something else than mere negation, like in your example with unintelligent. "Unintelligent" is ambiguous between (at least) 1. Having a lower intelligence, 2. Not having any intelligence. Though I'd say that in this case the first meaning is far more common. In other cases the simply negation meaning is the most common, think of "uncommon" as an example. I can't readily think of another meaning of "uncommon" besides not common.

But what is the other meaning of "invalid"? I certainly only mean "non-valid" when I use it. You should be able to simply accept my usage for the sake of the discussion and I don't know what else anyone would mean by it. If you cannot do that, I could attempt to convince myself to use a different word/phrase, just for you and Fast's sake but it really shouldn't be necessary.

In case it is, simply replace any mention of "invalid" with "non-valid".

Using that word, an intention theory, at least the ones I have thought of, implies that there exists some inductive arguments that are valid. That is odd, don't you think?

And a validity theory, at least the ones I know, implies that all deductive arguments are valid. That is generally regarded as false by most textbooks but I suppose it could nonetheless be wrong. Some textbooks have been wrong in the past and pretty much every textbook gets something wrong just as pretty much any work of non-fiction gets something wrong. At least, if they make a high number of claims, by probability something is probably wrong. (Think also of the preface paradox.)

You keep writing things that suggest that you believe one and the other of them (I did quote you last time), but they are contrary (not contradictory) and so I'm confused as to what you believe.
 
Extrain
 
Reply Sat 10 Apr, 2010 12:26 am
@Emil,
Emil;150157 wrote:
In other cases the simply negation meaning is the most common, think of "uncommon" as an example. I can't readily think of another meaning of "uncommon" besides not common.
But what is the other meaning of "invalid"? I certainly only mean "non-valid" when I use it. You should be able to simply accept my usage for the sake of the discussion and I don't know what else anyone would mean by it. If you cannot do that, I could attempt to convince myself to use a different word/phrase, just for you and Fast's sake but it really shouldn't be necessary.


That's not the point. The point is not everything falls into one or the other of a binary classes of things.

There are two types of negation in quantificational (categorical) logic:

Affirmative vs. Negative universals. "No, All"
Affirmative vs. Negative copulas. "is, are" "is not, are not"

You confuse the negation of the "not" in the copula with the denial that two classes of things overlap.

The class of all inductive arguments doesn't overlap with the classes of validity and invalidity. Neither does the class of all people overlap with the classes of validity and invalidity.

Emil;150157 wrote:
Using that word, an intention theory, at least the ones I have thought of, implies that there exists some inductive arguments that are valid. That is odd, don't you think? And a validity theory, at least the ones I know, implies that all deductive arguments are valid. That is generally regarded as false by most textbooks but I suppose it could nonetheless be wrong. Some textbooks have been wrong in the past and pretty much every textbook gets something wrong just as pretty much any work of non-fiction gets something wrong. At least, if they make a high number of claims, by probability something is probably wrong.


It would behoove you to show us a demonstration, otherwise none of us are required to take any of this stuff seriously.

Emil;150157 wrote:
You keep writing things that suggest that you believe one and the other of them (I did quote you last time), but they are contrary (not contradictory) and so I'm confused as to what you believe.


This is exactly the mistake you keep making, not kennethamy. You have numerous implicit metaphysical presuppositions at work here.

"Non-valid" and "non-invalid" are just negative predicates that effectively exclude the thing in question from the class of entities negated. But they don't actually denote any really existent properties, nor do they denote any classes either. You obviously have never worked with Venn Diagrams before. But you desperately need to take a look at those things. So...

Denying that something possesses a property from a pair of contrary (or binary properties) is not the same thing as ascribing the contrary property to that thing. Though "Non-valid" might be a word, the alleged property non-valid is certainly not a property something has simply because non-valid is not a property. Likewise, "Non-invalid" might be a word, but non-invalid is not a property anything can possess because non-invalid is not a property.

Again, though negative prefixes might be added to a given predicate in question, these words don't actually designate any really existent negative properties. You seem to think that if we say something is not red, then that implies the thing possesses the property of non-red. But there is no such thing as the property non-red. If Oysters are not intelligent, that does not entail oysters have the property of non-intelligence, nor does it mean I have just said that all oysters are stupid simply because oysters are not sentient kinds of creatures that can possess the property of intelligence or possess the property of stupidity anyway. If you want to say something is intelligent, you have to say exactly that, "X is intelligent." You don't get to say "X is does not possess the property of non-intelligence," because non-intelligence is not a property at all, only stupidity is a property.

So here is the consequence: "Valid" and "invalid" are positive predicates denoting positive properties and to deny that something possesses one or the other property is not to simultaneously ascribe the contrary property to it, unless you already assume the bivalence governing the ascription and denial of these properties necessarily applies to the domain of all things that exist. But this is precisely your repeated categorical fallacy.

Your metaphysical thesis that anything in the world must be either valid or invalid is false--but you assume this must hold for all things because you want to say that the principle of bivalence holds for any ascription or denial of a property to a thing from any given list of contrary opposites.

Boy and Girl are contrary properties, but if a chair is not a boy that doesn't entail the chair is a girl.

Hot and cold are contrary relational properties between myself and an object, but that does not entail that if my idea is not hot, then my idea must therefore be cold.

Plant and animal are the two contrary properties of all living things, but if a building is not an animal, that does not mean the building is a plant.

Likewise, valid and invalid are contrary properties of deductive arguments, but if any ordinary thing is not valid, that does not entail it is therefore invalid, simply because this bivalence of contrary properties valid/invalid holds only for the class of all deductive arguments, just as plant and animal hold only for the class of all living things, and just as intelligence and stupidity hold only for the class of all sentient creatures, and just as boy and girl hold only for the class of all human beings. To assume that validity/invalidity holds for anything else other than deductive arguments is just being stubbornly absent-minded, because it is an incredibly absurd metaphysical thesis that is obviously false.

The list goes on and on....

Continually repeating the same categorical fallacy does not succeed in demonstrating your view is correct. You first have to show there is something quite mistaken about the categorical distinction everyone makes to begin with.

No one has yet seen a demonstration of what on earth you are talking about, so why should anyone take this view seriously?

Fluff.
 
Emil
 
Reply Sat 10 Apr, 2010 12:33 am
@fast,
As for the discussion of what deductive and inductive arguments are, here is an updated version of my essay draft. Some of the formatting is slightly off due to limitations on the forum software or limitations with my mastery of the software.

This is primarily for Fast since Ken doesn't seem to take an interest into the issue and neither does Pyrrho. E. may have some fun pointing out various imagined fallacies. Due to the length (~2,600 words), he may get a lot of pleasure out of it.

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. I have not been able to find any academic writing that discusses the issues that I discuss in this essay.

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. For an analogy consider the similar case between what a dictionary says a word means and how to best discover what a word means. These are logically independent.

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.

Concepts
Relevant to this discussion are some concepts. Read here for clarification and enlightenment.[INDENT]Validity. An argument is valid iff it is impossible that (all the premises are true and the conclusion false).1
[/INDENT]An argument that is not valid is non-valid which means that same as it is invalid. Some people think that "invalid" means something else than "non-valid" does. These people simply have to go on and accept my word usage for the sake of discussion.

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]There are some other very similar ways, consider e.g.:[INDENT] An argument is deductive iff it is intended by the arguer to be deductive.
An argument is inductive iff it is not intended by the arguer to be deductive.
[/INDENT]This theory is endorsed by an article published on the IEP, consider:[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.[/INDENT][INDENT]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.[/INDENT][INDENT]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 premises definitely 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][INDENT]Compare specifically the first paragraph with my formulation of the intention theory above. [/INDENT][INDENT]I cannot think of any another interpretation where it does not. Some people have challenged my interpretation and think that the IEP article only endorses intention as a method to discovering what kind of argument it is. It is not of critical importance to my essay whether the IEP article supports the intention theory.[/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 trained in logic. Similarly for inductive arguments. Refined theses are then:[INDENT] 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).
[/INDENT]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:[INDENT] Similarly to validity and soundness, whether an argument is deductive or inductive is not dependent on facts about human psychology.
[/INDENT]Whether this analogy is apt I don't know. Perhaps the deductive and inductive distinction is different from the other terms. But it does have some plausibility.

Arguments? What arguments?
There may be some confusion between sentence-arguments and proposition arguments2, so let's distinguish between them clearly:[INDENT] A proposition-argument is a number of propositions where one, the conclusion, follows from the other, the premises, in some sense. So it is a collection of premises that stand in some relation.

A sentence-argument is what is literally in this essay. A sentence-argument is a number of sentences that express a proposition-argument. Argument-sentences have a location and a time of writing.3
[/INDENT]Also, for those who know about the token-type distinction, I am talking about tokens of both though I can't see much of a difference between proposition-argument tokens and types.

All proposition-argument are sound/unsound and valid/invalid. Are (all/some?) sentence-arguments sound/unsound and valid/invalid? It seems to me that a proper evaluation of the issue of deductive and inductive arguments depend on this.4

Two different sentence-arguments may express the same proposition-argument. Let's imagine that there are three identical sentence-arguments and that a single person has written them. In the first two cases the person intends the sentence-arguments to be deductive and in the third case he intends it to be inductive.

The question is now: Do all the three sentence-argument express the same proposition-argument? It seems to me that the answer given intention theory is "no". The first two express the same proposition-argument, but the last expresses a different proposition-argument. These sentence-arguments, 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 proposition-arguments 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 proposition-argument? 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 proposition-argument but then that proposition-argument 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 proposition-argument but believe that the deductive and inductive distinction is only about sentence-arguments and proposition-arguments. To clarify, there are three related distinction theses:[INDENT]DIS. An argument (sentence or proposition) is either deductive or inductive and not both.
DIS-sentence. An sentence-argument is either deductive or inductive and not both.
DIS-proposition. An proposition-argument is either deductive or inductive and not both.5
[/INDENT]So that person would deny (DIS) and (DIS-proposition) but believe in (DIS-sentence). In that case the deductive and inductive distinction between sentence-arguments is dependent on facts of human psychology, but facts about proposition-arguments such as validity and soundness are not dependent on facts about human psychology. This may better capture intuitions that some people have and it avoids some contradictions, though there may be other that I have not found.

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]The good thing about this theory is that it does not imply that what kind of argument is depends on the arguer, which is seen as a false implication of an intention theory. I have not seen another consideration in favor of the theory, and I have seen it simply suggested because it is the best theory known as the intention theory is seen as worse.

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 in the sense that one produces instead an invalid deductive argument (though one could fail at making a deductive argument and instead make an inductive one), 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.
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. I don't know whether this is relevant or not.
But wait, what kind of arguments are additive arguments? They are deductive arguments! The analogy is circular. Additive arguments are a proper subset of deductive arguments. This analogy is very plausible initially but not plausible when one thinks about it carefully.
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.

Resemblance theory
A third theory was suggested by Pyrrho (nickname) here. Here is what he wrote:[INDENT] "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."
[/INDENT]Maybe he wasn't the first to have the idea, but I haven't seen it elsewhere and a number of people who have studied logic did not suggest it either. That gives reason to believe that it is common knowledge among people who studied logic.

From Pyrrho's writing above I extracted these two theses that is a simple formulation of the resemblance theory:
An argument is deductive iff it is valid or resembles a valid argument.
An argument is inductive iff it is not deductive.
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.

Objections/Questions
When does an argument resemble a valid argument enough to be a valid argument; what is the threshold for resemblance? If there is none, then is the deductive-inductive distinction a continuum and not as it is commonly thought an either/or case?

These questions need to be answered to some degree for the theory to be plausible. Suppose it is a case of a certain threshold, then what is it? I can't think of any line to draw, but again, it may be a good idea to look at arguments. Can you come up with an argument that would be in the grey area and where we would be in doubt about whether it was deductive or inductive? I cannot. Keep in mind that any argument that has as parts of it both deductive and inductive arguments is inductive. It may be a case of my limited imagination but if a long time passes and no one can come up with a problematic example, that is some evidence for the theory.
It seems to me that thinking that the deductive-inductive distinction is a continuum is very odd and very implausible, and so that version of the theory is implausible.

Notes
1There are a number of logically equivalent definitions. I chose one of the relatively easy ones to understand. It does not matter much for the purposes of this essay which is chosen.

2I will here assume a proposition theory of truth carriers.

3There are also verbal sentence-arguments, but they do not strictly speaking consist of sentences but consist of sound waves that express sentences, I suppose. It is not important for present purposes.

4This 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.

5(DIS) is thus logically equivalent with the conjunction of (DIS-sentence) and (DIS-proposition).
 
Extrain
 
Reply Sat 10 Apr, 2010 12:49 am
@Emil,
Emil;150165 wrote:
I have not been able to find any academic writing that discusses the issues that I discuss in this essay.


you haven't found any academic writing on this supposed "topic" precisely because you mistakenly think first-order propositional logic is purely a linguistic discipline. To assume this is absurd.

Emil;150165 wrote:
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.


whatever. Your entire following alleged "analysis" rests on the premise that if "intention theory" is false, then it is not the case that arguments are either deductive or inductive and not both.

But this material conditional is false as it is. So your argument is a strawman. I agree, Intention Theory is false. But that doesn't demonstrate the truth of your conculsion. So all of the subsequent meanderings are pointless.

Emil;150165 wrote:
Concepts
Relevant to this discussion are some concepts. Read here for clarification and enlightenment.
[INDENT]Validity. An argument is valid iff it is impossible that (all the premises are true and the conclusion false).1
[/INDENT]An argument that is not valid is non-valid which means that same as it is invalid. Some people think that "invalid" means something else than "non-valid" does. These people simply have to go on and accept my word usage for the sake of discussion.


Again, this is a categorical error because you left out to which category of things validity/invalidity applies. Again, you are just stipulating your own definitions without telling anyone why you are doing this. So you completely lack justification for doing this altogether. All we have to do is disagree with you.

Validity: A deductive argument is valid iff it is impossible for the premise(s) to be true and the conclusion false.


Emil;150165 wrote:
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]There are some other very similar ways, consider e.g.:
[INDENT]An argument is deductive iff it is intended by the arguer to be deductive.
An argument is inductive iff it is not intended by the arguer to be deductive.
[/INDENT]This theory is endorsed by an article published on the IEP, consider:
[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.
[/INDENT][INDENT]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.
[/INDENT][INDENT]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 premises definitely 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][INDENT]Compare specifically the first paragraph with my formulation of the intention theory above.
[/INDENT][INDENT]I cannot think of any another interpretation where it does not. Some people have challenged my interpretation and think that the IEP article only endorses intention as a method to discovering what kind of argument it is. It is not of critical importance to my essay whether the IEP article supports the intention theory.
[/INDENT]

"Intention theory" is false. Arguments are not deductive or inductive iff someone intends them to be one way or the other. A person can "intend" to put down a deductive argument, but then have that argument end up looking like both an inductive and deductive argument at once because his use of English words, such as "Anybody," for instance, is ambiguous. But ambiguity doesn't legislate which argument is actually being put forth in fact, nor is natural language ambiguity evidence at all for thinking there exists no distinction between deductive and inductive style of arguments. The semantic ambiguity just show us that which kind of argument actually gets expressed is not always determinable from the natural language sentence meanings the person used to try to construct a logical argument. But why is this problematic for deductive/inductive distinctions? So there may not be any fact of the matter at all about which kind of argument is there in the first place. And if the speaker intends to put down a deductive argument, but then succeeds in putting down an inductive argument, then, necessarily, that argument is actually inductive, not deductive. But if the speaker doesn't know the difference between inductive and deductive arguments, and puts down what looks like both an inductive and deductive argument at once, then there is simply no argument at all that got expressed, in spite of the speaker's intentions. So intention theory is false.

If P then Q
P
Therefore Q

Is deductive regardless of speaker or writer intention.

Most P are Q
Therefore, probably all P are Q

Is Inductive regardless of speaker or writer intention.
Again, just as everyone has been saying, you are confusing intensionalist-based semantics and Gricean Conversational Implicature with propositional logic. Whoever tries to derive a substantive logical thesis from natural language sentence meanings is deeply misguided, and lacks any knowledge of what propositional calculus actually does. So your views are essentially strawmans from the get go.

I will repeat what I said before:

"How is it that "intention theory" logically implies that there are valid (or even invalid) inductive arguments? The problem is purely semantic, not logical. Suppose someone offers the following ambiguous argument in natural language:

Anybody who hunts lions is fearless.
So, all people who hunt lions are fearless.

"Anybody" is vague in the first sentence as a premise. It could mean "all," or it could mean "some" or "at least one." What the conclusion is actually saying, however, is clear.

Construing the first sentence one way, the argument we interpret the above two sentences as expressing is a valid deductive tautology. Construing the first sentence another another way, the argument we interpret the above two sentences as expressing is inductively strong or weak. But the ambiguity found in natural language, here, does not tell us anything about whether inductive propositional arguments themselves are valid or invalid. In merely shows that which kinds of arguments are actually being expressed by natural language sentences--deductive or inductive arguments--can sometimes be very difficult to determine. Any Logic 101 textbook will tell you this."

Emil;150165 wrote:
Arguments? What arguments?
There may be some confusion between sentence-arguments and proposition arguments2, so let's distinguish between them clearly:
[INDENT]A proposition-argument is a number of propositions where one, the conclusion, follows from the other, the premises, in some sense. So it is a collection of premises that stand in some relation.

A sentence-argument is what is literally in this essay. A sentence-argument is a number of sentences that express a proposition-argument. Argument-sentences have a location and a time of writing.3
[/INDENT]


Which is precisely why "proposition-arguments" are not the same as "sentence-arguments" since they too often mismatch like in the example I gave above. Again, this is Semantics vs. First-order propositional logic. They are not the same disciplines.

Emil;150165 wrote:
Also, for those who know about the token-type distinction, I am talking about tokens of both though I can't see much of a difference between proposition-argument tokens and types.


Right. Every philosopher is familiar with this distinction. And you failed to notice that the article doesn't say anything about validity/invalidity with respect to propositional logic. In fact, it directly says the type-token distinction is a metaphysical distinction (as I quoted below). It doesn't say there are any logical distinctions being made. It says right in the beginning that the type-token distinction has applications everywhere throughout philosophy, including linguistics. But there is nothing problematic about this distinction with respect to validity/invalidity, strength/weakness in deductive and inductive logic.

So why you think any of this has implications for logic as a purely formal calculus is beyond all of us. You simply don't know what you are saying.

Quote:
The distinction between a type and its tokens


Emil;150165 wrote:
All proposition-argument are sound/unsound and valid/invalid. Are (all/some?) sentence-arguments sound/unsound and valid/invalid? It seems to me that a proper evaluation of the issue of deductive and inductive arguments depend on this.4


What issue? All deductive sentence arguments are either V or I, and S or U. But which deductive proposition-type argument gets expressed by the sentence-type in question is another matter. For instance, as in,

Anybody who hunts lions is fierce.
So, all people who hunt lions are fierce.

It is not clear if the proposition type is.

All P are Q
So all P are Q

or,

At least one P are Q
So, All P are Q.

or,

Most P are Q
So, All P are Q

So it's not clear whether this is inductive or deductive because "Anybody" is ambiguous. But so what? That entails nothing with regard to the clear distinction between deductive/inductive proposition-type arguments such as in,

P
Q
Therefore, P and Q

Most P are Q
Therefore, probably all P are Q.

Emil;150165 wrote:
Two different sentence-arguments may express the same proposition-argument. Let's imagine that there are three identical sentence-arguments and that a single person has written them. In the first two cases the person intends the sentence-arguments to be deductive and in the third case he intends it to be inductive.


Can you give us examples, please??? It does no good for your thesis to be making these claims without explicitly showing us how this is supposed to work. So far, all this is just hot air.

Besides, who cares what he intended. It makes no difference. The proposition-type argument may be difficult to determine because of natural language sentence ambiguity. And which proposition-type argument gets expressed by which sentence-type argument is irrelevant. So all of these questions are for philosophers of language to explore; these are not questions that need to be addressed by logic because they are not problematic for logic. Everyone keeps telling you this, but you still don't seem to get it. Do all the problems encountered in mathematics necessarily overlap with the problems encountered in physics? No, because they are not the same disciplines.

Emil;150165 wrote:
The question is now: Do all the three sentence-argument express the same proposition-argument? It seems to me that the answer given intention theory is "no". The first two express the same proposition-argument, but the last expresses a different proposition-argument. These sentence-arguments, 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.


"Intention Theory" is false anyway. So who cares.

Again, can you give us examples, please?? Hot air.

Emil;150165 wrote:
Thus, someone accepting this and accepting intention theory and (DIS) has to (for consistency) agree that there are two different proposition-arguments 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 proposition-argument? What is this property "being deductive" and "being inductive"? They seem very mysterious.


Again, "Intention theor" is false. So it doesn't matter.

And of course, a given set of sentences can only express one and only argument at a time, assuming that set of sentences express any argument at all. But if we can't determine what kind of propositional argument those sentences express, then it is likely that those set of sentences express no argument at all. But so what? What does this have to do with Logic?

Emil;150165 wrote:
One could also accept both intention theory and that there is only one proposition-argument but then that proposition-argument would be both inductive and deductive and so the distinction between them would be false, that is, (DIS) would be false.


sheesh....So now there is only one proposition argument expressed by a given set of sentences, but now that proposition argument is both deductive and inductive at once??! But inductive and deductive are mutually exclusive types of arguments. Therefore, you would have two arguments expressed by one and only one set of sentences and also only one proposition argument expressed by that same set of sentences. But this is a contradiction. Therefore, we know this idea is false.:rolleyes:

Emil;150165 wrote:
One could also accept both intention theory and that there is only one proposition-argument but believe that the deductive and inductive distinction is only about sentence-arguments and proposition-arguments.


But what makes you think formal propositional calculus is reducible to the sets of sentences that express them anyway??? You haven't told anyone any reason for thinking this is true. We all think it is false. And so does every other logician in the world. So the rest of your subsequent alleged "analysis" is so far deeply mistaken because it rests on contradictions and deeply implausible and groundless assumptions. Therefore, no rational person is required to believe it, much less even consider it.
 
 

 
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