Non-deductive VERSUS Inductive

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kennethamy
 
Reply Thu 8 Apr, 2010 02:10 pm
@Extrain,
Extrain;149680 wrote:
Right. "Cogent" and "uncogent" do not apply to deductive arguments.



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 ----------



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.


But that is how, "cogent" is defined. An argument whose premises are known to be true. If your objection were a good one, then it would apply to the term, "validity" since one person might know that an argument was valid, and another not know that. But, so what? A proposition which is known need not be known to be known, in order to be known. A person may know that p, and not know he knows that p.
 
fast
 
Reply Thu 8 Apr, 2010 02:23 pm
@kennethamy,
[QUOTE=kennethamy;149677]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.[/QUOTE]I don't therefore-see that cogent implies sound.

If an argument is valid, then an argument is a deductive argument, and if the premises of a valid (and thus deductive) argument are true, then the argument is a sound (and thus valid and thus deductive) argument, and if the premises are not only true, but known to be true as well (which is what I thought a cogent argument was), then the argument is a cogent argument. But, that an argument is a cogent argument is no good reason to think that an argument is a sound argument (unless I'm mistaken about what a cogent argument is), as the premises of both some unsound deductive arguments and some inductive arguments are known to be true.

It's starting to sound like a cogent argument is more than merely an argument with premises that are known to be true.
 
Extrain
 
Reply Thu 8 Apr, 2010 02:24 pm
@kennethamy,
kennethamy;149683 wrote:
But that is how, "cogent" is defined. An argument whose premises are known to be true. If your objection were a good one, then it would apply to the term, "validity" since one person might know that an argument was valid, and another not know that. But, so what?


huh? Ken, I'm pretty sure you're mistaken. The dictionary may define "cogent" that way. But no logic textbook does. And if it did, it would be wrong. Why would you think this anyway?

Example:

(1) All Presidents of the United States so far have been men.
(2) Therefore, the next president of the United States will probably be a man.

The argument is inductively strong and cogent.

But an alien from outer space does not have to know (1) is true for the argument to be cogent. So the argument's cogency is not dependent on whether this or that individual knows that it is, or whether or not an individual knows that (1) is true. Though a person may not be able to determine whether or not the argument is cogent for him or her self, the argument is cogent regardless of whether this or that individual knows that it is.

Further, what do strong and cogent inductive arguments have to do with valid and sound deductive arguments?

kennethamy;149683 wrote:
A proposition which is known need not be known to be known, in order to be known. A person may know that p, and not know he knows that p.


True.

---------- Post added 04-08-2010 at 02:45 PM ----------

fast;149686 wrote:
I don't therefore-see that cogent implies sound.


Because it doesn't. Cogent implies that the argument is strong.

[QUOTE=fast;149686] If an argument is valid, then an argument is a deductive argument, and if the premises of a valid (and thus deductive) argument are true, then the argument is a sound (and thus valid and thus deductive) argument,[/QUOTE]

Correct.

[QUOTE=fast;149686] and if the premises are not only true, but known to be true as well (which is what I thought a cogent argument was), then the argument is a cogent argument.[/QUOTE]

This is false. That is not what a cogent argument is.

[QUOTE=fast;149686] But, that an argument is a cogent argument is no good reason to think that an argument is a sound argument[/QUOTE]

That's correct--because cogent arguments are not "sound" arguments anyway--cogent arguments are only strong arguments.

Validity/invalidity does not come in degrees. Strong/weak, on the other hand, does come in degrees.

[QUOTE=fast;149686] (unless I'm mistaken about what a cogent argument is),[/QUOTE]

Unfortunately, you are mistaken--just as Ken is mistaken.

[QUOTE=fast;149686] It's starting to sound like a cogent argument is more than merely an argument with premises that are known to be true.[/QUOTE]

It's actually less. You guys are making logic say more than it does. A "cogent argument' only means that argument is both inductively strong and the premises are true--nothing more, nothing less. A "cogent argument" doesn't mean "the premises have to be known to be true." This is false.
 
kennethamy
 
Reply Thu 8 Apr, 2010 02:47 pm
@fast,
fast;149686 wrote:
I don't therefore-see that cogent implies sound.

If an argument is valid, then an argument is a deductive argument, and if the premises of a valid (and thus deductive) argument are true, then the argument is a sound (and thus valid and thus deductive) argument, and if the premises are not only true, but known to be true as well (which is what I thought a cogent argument was), then the argument is a cogent argument. But, that an argument is a cogent argument is no good reason to think that an argument is a sound argument (unless I'm mistaken about what a cogent argument is), as the premises of both some unsound deductive arguments and some inductive arguments are known to be true.

It's starting to sound like a cogent argument is more than merely an argument with premises that are known to be true.


Sorry, I was just assuming the argument was valid. But, you are right.

---------- Post added 04-08-2010 at 04:52 PM ----------

Extrain;149687 wrote:
huh? Ken, I'm pretty sure you're mistaken. The dictionary may define "cogent" that way. But no logic textbook does. And if it did, it would be wrong. Why would you think this anyway?

Example:

(1) All Presidents of the United States so far have been men.
(2) Therefore, the next president of the United States will probably be a man.

The argument is inductively strong and cogent.

But an alien from outer space does not have to know (1) is true for the argument to be cogent. So the argument's cogency is not dependent on whether this or that individual knows that it is, or whether or not an individual knows that (1) is true. Though a person may not be able to determine whether or not the argument is cogent for him or her self, the argument is cogent regardless of whether this or that individual knows that it is.

Further, what do strong and cogent inductive arguments have to do with valid and sound deductive arguments?



True.

---------- Post added 04-08-2010 at 02:45 PM ----------

[/COLOR]

Because it doesn't. Cogent implies that the argument is strong.



Correct.



This is false. That is not what a cogent argument is.



That's correct--because cogent arguments are not "sound" arguments anyway--cogent arguments are only strong arguments.



Unfortunately, you are mistaken--just as Ken is mistaken.



It's actually less. You guys are making logic say more than it does.


"Cogent" is a technical term. Some logic books discuss it. Some do not even mention it. Copi does not even mention it. I don't see how it is possible I am mistaken about it. I suppose you are using it differently from me. I use it to mean, "the premises are known to be true". You can disagree. But that does not mean I am mistaken. "Cogent" does not have the standard use that "valid" or that "sound" has.
 
Extrain
 
Reply Thu 8 Apr, 2010 02:57 pm
@kennethamy,
kennethamy;149691 wrote:

"Cogent" is a technical term. Some logic books discuss it. Some do not even mention it. Copi does not even mention it. I don't see how it is possible I am mistaken about it. I suppose you are using it differently from me. I use it to mean, "the premises are known to be true". You can disagree. But that does not mean I am mistaken. "Cogent" does not have the standard use that "valid" or that "sound" has.


That's right. "cogent" IS a technical term. But then you insist on using "cogent" colloquially all you want. But that doesn't mean you are correct. In fact, your view entails a contradiction:

(1) All presidents of the united states so far have been men.
(2) So, the next president of the united states will probably be a man.
(3) (1)-(2) is a cogent argument.
(4) All cogent arguments are arguments whose premises are known to be true.
(5) ET from outer space does not know that (1) is true.
(6) Therefore, (1)-(2) is not a cogent argument.
(7) Contradiction. [(3) and (6)]
 
kennethamy
 
Reply Thu 8 Apr, 2010 03:03 pm
@Extrain,
Extrain;149696 wrote:
That's right. "cogent" IS a technical term. But then you insist on using "cogent" colloquially all you want. But that doesn't mean you are correct. In fact, your view entails a contradiction:

(1) All presidents of the united states so far have been men.
(2) So, the next president of the united states will probably be a man.
(3) (1)-(2) is a cogent argument.
(4) All cogent arguments are arguments whose premises are known to be true.
(5) ET from outer space does not know that (1) is true.
(6) Therefore, (1)-(2) is not a cogent argument.
(7) Contradiction. [(3) and (6)]


When I say, "known to be true" I mean, a matter of general knowledge or personal knowledge. Something does not have to be known by ET in order to be a matter of general knowledge. That the Moon smaller than Earth is a matter of general knowledge, but some people don't know it, and certainly, ET doesn't know it.
 
Extrain
 
Reply Thu 8 Apr, 2010 03:08 pm
@kennethamy,
kennethamy;149698 wrote:
When I say, "known to be true" I mean, a matter of general knowledge or personal knowledge. Something does not have to be known by ET in order to be a matter of general knowledge. That the Moon smaller than Earth is a matter of general knowledge, but some people don't know it, and certainly, ET doesn't know it.


Sure. But none of that is a necessary condition for the argument itself to be cogent or uncogent.

If knowledge was a necessary condition for an argument to be cogent or uncogent, then you would have to specify whose knowledge provides the necessary condition for all cogent arguments to be cogent arguments.

You can't just arbitrarily decide to include person X, Y, and Z's knowledge as necessary conditions, and then exclude ET's knowledge as being a necessary condition.
 
fast
 
Reply Thu 8 Apr, 2010 03:15 pm
@Extrain,
Extrain;149687 wrote:
It's actually less. You guys are making logic say more than it does. A "cogent argument' only means that argument is both inductively strong and the premises are true--nothing more, nothing less. A "cogent argument" doesn't mean "the premises have to be known to be true." This is false.
A cogent argument is an argument with premises that are known to be true. We're not saying that a cogent argument is an argument with premises that must be known.
 
Extrain
 
Reply Thu 8 Apr, 2010 03:47 pm
@fast,
fast;149702 wrote:
A cogent argument is an argument with premises that are known to be true. We're not saying that a cogent argument is an argument with premises that must be known.


huh? What's the difference? You are saying, "All cogent arguments are arguments whose premises are known to be true." "An argument whose premises are known to be true" is therefore a necessary condition for an argument to be cogent.

So whose knowledge is necessary for an argument to be cogent? Bob's, Bill's, or ET's? All of them at once? Only some of them? Bob's and Bill's, but not ET's? Your view entails a contradiction if you don't specify this.

Your view works just like this:

For all cogent arguments Px, and for all arguments whose premises are known to be true Qx,

All Px are Qx.

In other words, (Ax) (Px --> Qx).

Next, suppose an argument c is a cogent argument because you and I both know that argument c has true premise(s). So, we can write:

(Pc and Qc)

which says that argument c is a cogent argument because it has premise(s) known to be true (by us).

From this, by the rule of "and-elimination," it logically follows that,

Pc

which merely says argument c is a cogent argument.

Next, suppose ET does not know that a premise of the SAME argument c is a true premise. So we can write this:

(~Pc and ~Qc)

which says that the argument c is not cogent because ET does not know that c has a true premise.

Again, by the logical rule of "and-elimination" we can infer that.

~Pc

which just says that c is not a cogent argument.

Therefore, argument c both is, and is not, a cogent argument.

Pc and ~Pc

Contradiction.

Therefore,

(Ax) (Px--> Qx)

is false.
 
fast
 
Reply Thu 8 Apr, 2010 04:24 pm
@Extrain,
Extrain;149717 wrote:
So whose knowledge is necessary for an argument to be cogent? Bob's, Bill's, or ET's? All of them at once? Only some of them? Bob's and Bill's, but not ET's? Your view entails a contradiction if you don't specify this.
Consider the proposition, "Earth is the third planet from the sun." That proposition is true, but more importantly, it's known to be true, as it's common knowledge, but that it's common knowledge doesn't mean that Bob, Bill, nor ET must know that it is true, or even believe that it's common knowledge for that matter.

All that's important is that it is common knowledge. Hence, that it's actually common knowledge, not that it must (must, I say) be common knowledge.
 
Extrain
 
Reply Thu 8 Apr, 2010 04:32 pm
@fast,
fast;149730 wrote:
Consider the proposition, "Earth is the third planet from the sun." That proposition is true, but more importantly, it's known to be true, as it's common knowledge, but that it's common knowledge doesn't mean that Bob, Bill, nor ET must know that it is true, or even believe that it's common knowledge for that matter.


I agree. But this is irrelevant. We are talking about cogent arguments, not about people's knowledge (or lack thereof) of whether or not the premises in a cogent argument are true, or even whether or not people know a particular argument is cogent.

"All cogent arguments are arguments whose premises are known to be true" still entails a contradiction. Though people can know that cogent arguments are arguments whose premises are known to be true. Cogent arguments do not have to be arguments whose premises are known to be true to be cogent arguments.

fast;149730 wrote:
All that's important is that it is common knowledge. Hence, that it's actually common knowledge, not that it must (must, I say) be common knowledge.


What do people's knowledge about this or that have anything to do with whether or not arguments are cogent or uncogent?
 
kennethamy
 
Reply Thu 8 Apr, 2010 04:37 pm
@Extrain,
Extrain;149699 wrote:
Sure. But none of that is a necessary condition for the argument itself to be cogent or uncogent.

If knowledge was a necessary condition for an argument to be cogent or uncogent, then you would have to specify whose knowledge provides the necessary condition for all cogent arguments to be cogent arguments.

You can't just arbitrarily decide to include person X, Y, and Z's knowledge as necessary conditions, and then exclude ET's knowledge as being a necessary condition.


Why can't the necessary condition just be that it is a matter of general knowledge that the Moon is smaller than Earth. Why could that not be a premise? I don't see that.

---------- Post added 04-08-2010 at 06:39 PM ----------

Extrain;149733 wrote:



What do people's knowledge about this or that have anything to do with whether or not arguments are cogent or uncogent?


That's what the cogency of an argument is. I don't understand your question. This is just a verbal dispute about what "cogent argument" means. It is trivial. I just stipulate that "cogent argument" means that the premises of the argument are known to be true.
 
Extrain
 
Reply Thu 8 Apr, 2010 04:47 pm
@kennethamy,
kennethamy;149734 wrote:
Why can't the necessary condition just be that it is a matter of general knowledge that the Moon is smaller than Earth. Why could that not be a premise? I don't see that.


"General knowledge"?

"Premise" for which conclusion, exactly?

I would certainly agree it acts as a premise in this kind of sound deductive argument:

(1) Premise: Most people know that the Moon is smaller than the Earth. (true)
(2) Premise: If a person knows that P, then P. (true)
(a) Conclusion: Therefore, the Moon is smaller than the Earth. (true)

But now what does "general knowledge" have to do with anything? This style of argument only requires the truth that one person knows the Moon is smaller than the Earth for the argument to be deductively sound.

I can know a premise of an inductive argument is true, entertain that argument to myself, and then have that argument be cogent. But that the argument is cogent doesn't require most everyone else knows my premises are true. No one may know this. But my argument would still be cogent.

The necessary and jointly sufficient conditions for an inductive argument to be cogent are:

(1) Premises are true.
(2) The conclusion more likely follows than not (greater than 50% chance) from the premises (that is, the inference is strong).

kennethamy;149734 wrote:
That's what the cogency of an argument is. I don't understand your question. This is just a verbal dispute about what "cogent argument" means. It is trivial. I just stipulate that "cogent argument" means that the premises of the argument are known to be true.


If it were just a verbal dispute, that would mean we both agree on something but are just talking past eachother. Can you please help me? I truly don't understand.

It is necessary that P is true for inductive argument Q in which P occurs to be cogent. But it is not necessary that I know that P for inductive argument Q to be cogent. After all, my argument can still be cogent even though I believe, but not know, that P because I fail to meet the necessary justification condition for knowing that P. (assuming you think K=JTB)
 
Emil
 
Reply Thu 8 Apr, 2010 05:20 pm
@kennethamy,
kennethamy;149668 wrote:
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?


I don't claim to have any smack-down arguments for any theoru. I try to see the bigger picture, and to think in a web of belief framework. I am inclined to think that it is necessary to think in such framework to be justified in one's choice of theory.

An intention theory has some odd implications that I don't know if you want to accept. For instance, that there exists valid inductive arguments. We discussed this before. I thought you denied the existence of valid inductive arguments. That would be inconsistent. Otherwise I agree that the theory has some plausibility.

The validity (because it has to do with validity) theory suggested by Kritikos over on FRDB certainly also has odd implications, for instance that all deductive arguments are valid.

So both theories imply something that is considered questionably.

Pyrrho had some third theory. I don't recall it now only that I judged it to be more plausible than the other two above.

I also did some more careful analysis introducing a distinction between arguments as a collection of propositions standing in a relation, and one as a collection of sentences. One idea is to restrict deductive/inductive to sentence-arguments since there are many of them. Proposition-arguments are not deductive or inductive. At least that was one possibility that I considered. I didn't come to any favored conclusion, but then again, it was only a first draft that I posted on the board. I have many such essays lying around waiting for me to get some bright idea that may never come!

But then you keep confusing my with first writing something that a intention theory-ist would write, and then preceding to write something a validity theory-ist would write. I don't know what your position is at all!

[INDENT]"So, why should we not let the intentions of the arguer be what decides what kind of argument it is?"

"But non-deductive [i.e. inductive] arguments are arguments whose premises constitute only support for the conclusion, and do not guarantee the truth of the conclusion."

[/INDENT]There was a very good smiley on FRDB that isn't here. It is called confused.

http://s560.photobucket.com/albums/ss49/aos_images/smilies/confused-smiley-013.gif
 
Extrain
 
Reply Thu 8 Apr, 2010 05:40 pm
@Emil,
Emil;149744 wrote:
An intention theory has some odd implications that I don't know if you want to accept. For instance, that there exists valid inductive arguments.


How is it that "intention theory" (whatever that is) logically implies that there are valid (or even invalid) inductive arguments? Isn't the problem purely semantic, not logical? I don't see how this is supposed to work. 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.

So can you please give me an example of what you are talking about?

---------- Post added 04-08-2010 at 06:13 PM ----------

Emil;149744 wrote:
I thought you denied the existence of valid inductive arguments. That would be inconsistent. Otherwise I agree that the theory has some plausibility.


No valid inductive arguments exist. But this does not entail all inductive arguments are invalid. "For No Px, x is valid" does not mean "For all Px, x is invalid"; it only means "For No Px, x is valid."
No P are Q

does not entail

All P are non-Q

nor does it entail,

Some P are non-Q

It only entails,

It is not the case that some P are Q.

Emil;149744 wrote:
for instance that all deductive arguments are valid.


huh? How is that supposed to work?

Emil;149744 wrote:
I also did some more careful analysis introducing a distinction between arguments as a collection of propositions standing in a relation, and one as a collection of sentences.


Natural language can be ambiguous, so which proposition a sentence expresses can be ambiguous. But that phenomenon does not count as evidence that propositional first-order logic is inductive--or that all deductive arguments are valid--or that there is something deeply peculiar about logic itself. You seem to equivocating on how to go about determining which proposition gets expressed by linguistic meaning, and which purely formal features found in propositional logic actually belong to propositional logic itself.

Emil;149744 wrote:
One idea is to restrict deductive/inductive to sentence-arguments since there are many of them.


What do you mean by "restricting deductive/inductive arguments"? Restricting them to what? To sentences in natural language? Which propositions do you decide that the sentences in natural language express without first knowing that that sentence does, in fact, express that proposition? That may be difficult to determine in some cases. But again, if linguistic utterances are ambigous, that has no bearing on the validity/invalidity, strength/weakness encountered in deductive and inductive propositional logic. You are dealing with purely semantic isssues, not logical ones.

Emil;149744 wrote:
Proposition-arguments are not deductive or inductive. At least that was one possibility that I considered.


This is false, unless you can logically demonstrate otherwise.
 
fast
 
Reply Thu 8 Apr, 2010 09:22 pm
@Emil,
Emil;149744 wrote:
An intention theory has some odd implications that I don't know if you want to accept. For instance, that there exists valid inductive arguments. We discussed this before. I thought you denied the existence of valid inductive arguments. That would be inconsistent. Otherwise I agree that the theory has some plausibility.

When you say that (what I bolded above, that is), I get the feeling that you think that he thinks there are valid inductive arguments. He doesn't think that, and neither do I, and neither does Extrain. Only you and those that confuse "not valid" with "invalid" think that.

"Invalid" implies "not valid" just as "false" implies "not true," but just as "not true" doesn't imply "false," neither does "not valid" imply "invalid."

All inductive arguments are not valid; hence, no inductive argument is valid, but we are not saying (not at all) that all inductive arguments are invalid, for we do not hold that, as we hold that inductive arguments are neither valid nor invalid--only that they're not valid.
 
Emil
 
Reply Fri 9 Apr, 2010 10:41 am
@fast,
fast;149813 wrote:
When you say that (what I bolded above, that is), I get the feeling that you think that he thinks there are valid inductive arguments. He doesn't think that, and neither do I, and neither does Extrain. Only you and those that confuse "not valid" with "invalid" think that.

"Invalid" implies "not valid" just as "false" implies "not true," but just as "not true" doesn't imply "false," neither does "not valid" imply "invalid."

All inductive arguments are not valid; hence, no inductive argument is valid, but we are not saying (not at all) that all inductive arguments are invalid, for we do not hold that, as we hold that inductive arguments are neither valid nor invalid--only that they're not valid.


An intention theory implies that. I didn't say he thinks it. There is a difference between them.

There is no difference between invalid and not valid. And not true implies false too.

But if you are too hard-headed to change your usage of "invalid" to match common usage, ok. The implications still follow, of course. An intention theory implies that there are not valid (or non-valid if you wish which is another synonym for invalid) inductive arguments (or non-deductive which is another synonym). That is odd don't you think?

Extrain, I don't read your posts.
 
fast
 
Reply Fri 9 Apr, 2010 11:47 am
@Emil,
[QUOTE=Emil;149984]There is no difference between invalid and not valid. And not true implies false too.[/QUOTE]
You believe (and I agree) that some propositions are true, and you believe (and I agree) that some propositions are false, and we both believe that if a proposition is false, then we also believe that a proposition is not true, for we both believe (and agree) that "false" implies "not true."

Of course, what we believe, and whether we agree is neither here nor there, as only what matters is if it's all true, but I have taken it upon myself to mention what we believe and whether we agree just so we know exactly where each of us stands.

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.

Now, I suspect that you don't want to take my word for it, and if you didn't take my word for it, I can't say that I would rightly blame you, for I (as you know) have never formally studied any of this and thus do not have the credentials to bring to bare on this, so all I'm left with is the hope that I may be able to muster up an argument to show you that what I say is true, but I am awful at constructing arguments, so I'm left with nothing but what I have that I believe to be good reasons for you to think what I think.

To do that, I turn your attention to a topic you alluded to earlier (in this thread) with Kennethamy. You started talking about sentences and whether they can be (or cannot be) true or false. Incidentally, I do think that some sentences are true and that some sentences are false, but more on that later, if you like.

What I find important is that you think that no sentence is true or false--only that propositions are true or false. But, if it's so that you think no sentence is true, then isn't it also true that you think sentences are not true? And if so, then although you do think sentences are not true, it's still the case that you think no sentence is false, yet you said above, "not true" implies false, but how can that be?

Consider a sentence that fails to express a proposition. Do you have one in mind? You think that the sentence is not true, just as I think the sentence is not true. Additionally, you think that the sentence is not false, just as I think the sentence is not false. Remember, you think that only propositions are true or false. You do not think that sentences are true or false. Yet, isn't it so that we both believe (and agree) that it is not only not true but not false as well?

"Not true" is stronger than "false," so although the former implies the latter, the latter doesn't imply the former.
 
Emil
 
Reply Fri 9 Apr, 2010 12:20 pm
@fast,
fast;150000 wrote:

You believe (and I agree) that some propositions are true, and you believe (and I agree) that some propositions are false, and we both believe that if a proposition is false, then we also believe that a proposition is not true, for we both believe (and agree) that "false" implies "not true."

Of course, what we believe, and whether we agree is neither here nor there, as only what matters is if it's all true, but I have taken it upon myself to mention what we believe and whether we agree just so we know exactly where each of us stands.

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.


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]
Quote:
Now, I suspect that you don't want to take my word for it, and if you didn't take my word for it, I can't say that I would rightly blame you, for I (as you know) have never formally studied any of this and thus do not have the credentials to bring to bare on this, so all I'm left with is the hope that I may be able to muster up an argument to show you that what I say is true, but I am awful at constructing arguments, so I'm left with nothing but what I have that I believe to be good reasons for you to think what I think.


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.

Quote:
To do that, I turn your attention to a topic you alluded to earlier (in this thread) with Kennethamy. You started talking about sentences and whether they can be (or cannot be) true or false. Incidentally, I do think that some sentences are true and that some sentences are false, but more on that later, if you like.


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.

Quote:
What I find important is that you think that no sentence is true or false--only that propositions are true or false. But, if it's so that you think no sentence is true, then isn't it also true that you think sentences are not true? And if so, then although you do think sentences are not true, it's still the case that you think no sentence is false, yet you said above, "not true" implies false, but how can that be?


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.

Quote:
Consider a sentence that fails to express a proposition. Do you have one in mind? You think that the sentence is not true, just as I think the sentence is not true. Additionally, you think that the sentence is not false, just as I think the sentence is not false. Remember, you think that only propositions are true or false. You do not think that sentences are true or false. Yet, isn't it so that we both believe (and agree) that it is not only not true but not false as well?


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.

Quote:
"Not true" is stronger than "false," so although the former implies the latter, the latter doesn't imply the former.


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?
 
fast
 
Reply Fri 9 Apr, 2010 01:05 pm
@Emil,
Emil;150007 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.
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.

Quote:
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?
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.

Quote:
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.

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.

Quote:
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?


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.

I think a sentence that fails to express a proposition is neither true nor false, but I nevertheless hold that it is 1) not true and 2) not false.

So, let's talk about your four propositions:

[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]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).

Quote:

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?
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.
 
 

 
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