Are the laws of logic important to theology?

zippy2006 said:

Propositions exist in minds, hence my point about subjects. Indeed truth is more properly a relation between reality and a (knowing) subject than between reality and a mind-dependent proposition.

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You can't be serious. There are several problems with this:

First, a "knowing subject" is a subject who has knowledge. Knowledge entails much more than simply a proposition existing in the mind of that subject. For example, I may have the proposition "It is raining in Canada" in my mind, but if I've arrived at that belief by flipping a coin, then I do not have knowledge -- regardless of whether it is actually raining in Canada. However, that proposition is either true or false depending on the reality of whether it is raining in Canada. Knowledge requires more than simply a true proposition existing in the mind of a subject. It requires justification, and most likely, some sort of anti-luck component to work around Gettier situations.

Second, there are all sorts of true propositions that no one has knowledge of yet. For example, if I was the first person to think "Mt. Everest is the tallest mountain on earth," that doesn't mean it wasn't already true that Mt. Everest was the tallest mountain on earth. It is silly to think that a human must believe something in order for it to be true. By that logic, if everyone but one person died tomorrow, the only true propositions would be the propositions that person believes, which is absurd.

zippy2006 said:

You're begging the question. The only reason such a thing is said to be "logically impossible" is the LEM itself (or its corollary, the LNC). Or, if you don't think you're begging the question, what principle other than the LEM are you appealing to?

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I'm appealing to the law of non-contradiction, not the LEM. X cannot equal both "y" and "not-y." That is a violation of the law of non-contradiction. So, to say that "The present King of France is bald" and "The present king of France is not bald" are both true is a violation of the law of non-contradiction.

essentialsaltes said:

Well, then in which set does the present King of France appear?

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Neither, but that doesn't imply that both propositions can be true. If anything, it might be argued that "The present King of France is bald" and "The present King of France is not bald" are not propositions. In no case, however, can they both be true.

With regard to "The present King of France is bald," it seems as though there are two options:

1. It is meaningless, meaning that it is not a proposition because "King of France" has no referent. In this case, it is not a proposition and is neither true nor false.

2. It should be interpreted along the lines of "There is some x such that x=king of france, x is bald, and there is only one x." In this case, it is false because there is no such x.

With regard to "The present King of France is not bald," there are also three options:

1. It is meaningless, meaning that it is not a proposition because "King of France" has no referent. In this case, it is not a proposition and is neither true nor false.

2. It should be interpreted as "There is some x such that x=king of france, x is not bald, and there is only one x." In this case, it is false because there is no such x.

3. It should be interpreted as "There is not an x that is bald and is the king of France." In this case, it is true because there is no such x.

Songsmith said:

Firstly, what are they?
Law of identity: A is A
Law of non-contradiction: A can't be A and non A at the same time and in the same way
Law of excluded middle: A is either A or non-A, there is no in between.

So, the questions are these. Are these laws absolute? If they are then how does the relativist deal with the fact that there are absolutes while still holding to the view that there are not? If they are not then can you explain how or why? And finally, if there are absolutes then what would preclude God from declaring that there are such things as sin (for our purposes falling short of an absolute standard of behavior), for example murder, rape, etc.?

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A relativist is dealing with half the deck and that is why they can never come to any truth.
Once they realize that God deals in the supernatural, He exists outside the boundaries of time, and he created Man "by dirt", "by rib", "by virgin", and also normal pregnancy..
When they realize that there is a Spiritual world, and not only just a physical realm.....
When they realize that opinion is not truth... and theory is just a theory...
When they realize that a miracle is God stepping out of eternity where He lives..... and into the "box of time" designed by Him for us... where we reside, and within time he reconstructs a circumstance that was harming and changes it into the prayer request answered...... and this IS the miracle..
When they begin to realize some of these things and more that i could list............the relativist has taken his first baby steps into wisdom and light.
Most never even take a peek., but occasionally a thinker thinks and takes a good long look., and when that happens, God is everywhere they look, and they wonder why they never noticed before.
And they realize, shockingly.... that the answer is that you cant find God where he is being hidden by those who dont want you to know.
Its sort of like studying the color black for 34 years and wondering why you cant find Red or Yellow or Blue.
The question is dumb, but the answer is their reality check.

Architeuthus said:

I think you misread that Wikipedia article: "Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle...

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I did not misread it--at least not on that basis. If you read further into the article you will hear about the founder of the intuitionist school and his reasons for prescinding from the LEM in certain cases. That is what I was referring to.

Conscious Z said:

You can't be serious. There are several problems with this:

First, a "knowing subject" is a subject who has knowledge. Knowledge entails much more than simply a proposition existing in the mind of that subject. For example, I may have the proposition "It is raining in Canada" in my mind, but if I've arrived at that belief by flipping a coin, then I do not have knowledge -- regardless of whether it is actually raining in Canada. However, that proposition is either true or false depending on the reality of whether it is raining in Canada. Knowledge requires more than simply a true proposition existing in the mind of a subject. It requires justification, and most likely, some sort of anti-luck component to work around Gettier situations.

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That has absolutely nothing to do with what I said.

Second, there are all sorts of true propositions that no one has knowledge of yet.

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No, propositions do not exist apart from minds. Else go find me one existing all on its own.

For example, if I was the first person to think "Mt. Everest is the tallest mountain on earth," that doesn't mean it wasn't already true that Mt. Everest was the tallest mountain on earth.

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The content of propositions exist prior to their formulations, but the relation between knower and known does not. Truths do not exist apart from minds... unless you are a Platonist?

Conscious Z said:

zippy2006 said:

You're begging the question. The only reason such a thing is said to be "logically impossible" is the LEM itself (or its corollary, the LNC)...

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I'm appealing to the law of non-contradiction, not the LEM. X cannot equal both "y" and "not-y." That is a violation of the law of non-contradiction. So, to say that "The present King of France is bald" and "The present king of France is not bald" are both true is a violation of the law of non-contradiction.

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Fine, the LNC. You're still begging the question. In concluding that two contradictory statements are both true he is opposing both principles. Like I said, the LNC is just a corollary of the LEM.

zippy2006 said:

That has absolutely nothing to do with what I said.

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It certainly does. You said that truth is a relation between reality and a knowing subject. Thus, without a knowing subject, there is no such thing as truth. However, the requirement that a subject have knowledge is superfluous here. Knowledge entails much more than a proposition merely existing in the mind. Knowledge requires a justified method, anti-luck criteria, etc. Suggesting that there is no truth to the proposition "There are currently 515 mountain gorillas on earth" simply because no one can know whether there are 515 mountain gorillas on earth is silly. It's an arbitrary requirement.

zippy2006 said:

No, propositions do not exist apart from minds. Else go find me one existing all on its own. The content of propositions exist prior to their formulations, but the relation between knower and known does not. Truths do not exist apart from minds... unless you are a Platonist?

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Propositions are relations of ideas. Imagine no person has ever actually thought "3416 times 2184 equals 7,460,544." Does that mean that it was not previously true that 3416 x 2184=7,460,544? Much like math, propositions are discovered.

Again, you are imposing an arbitrary requirement of knowledge here. "Knowledge" and a proposition existing in a mind are not the same thing.

Even if we were to grant that a proposition must exist in the mind of a person in order for it to be true, the truthfulness of that proposition would still depend on the relationship between the proposition and reality, not the person and reality.

zippy2006 said:

Fine, the LNC. You're still begging the question. In concluding that two contradictory statements are both true he is opposing both principles. Like I said, the LNC is just a corollary of the LEM.

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He did not say that he was opposing both principles. He simply said that both statements were true, and held that up as proof that the LEM is false. Me pointing out that such reasoning is illogical because it violates the LNC is not begging the question. Rejecting the idea that a proposition must be either true or false does not imply that one is rejecting the idea that a proposition cannot be both true and false, even if you believe that the LEM implies the LNC.

Had he said he was rejecting the LNC, I wouldn't have said, "That's wrong because it violates the LNC." But rejecting the LEM does not imply that one is rejecting the LNC.

Conscious Z said:

It certainly does. You said that truth is a relation between reality and a knowing subject. Thus, without a knowing subject, there is no such thing as truth. However, the requirement that a subject have knowledge is superfluous here.

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Okay...

Knowledge entails much more than a proposition merely existing in the mind. Knowledge requires a justified method, anti-luck criteria, etc.

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What does this have to do with anything?

Suggesting that there is no truth to the proposition "There are currently 515 mountain gorillas on earth" simply because no one can know whether there are 515 mountain gorillas on earth is silly. It's an arbitrary requirement.

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Propositions are either true or false, but they require minds to articulate them. There is truth (or falsity) to the proposition... because there is a proposition... because you proposed it. No minds -> no propositions -> no truth.

Propositions are relations of ideas. Imagine no person has ever actually thought "3416 times 2184 equals 7,460,544." Does that mean that it was not previously true that 3416 x 2184=7,460,544? Much like math, propositions are discovered.

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Go read about theories of truth, particularly the correspondence theory. Not so many hold to Platonic universals any more, but you are free to if you like. (I am ending this part of the conversation)

He did not say that he was opposing both principles. He simply said that both statements were true, and held that up as proof that the LEM is false. Me pointing out that such reasoning is illogical because it violates the LNC is not begging the question. Rejecting the idea that a proposition must be either true or false does not imply that one is rejecting the idea that a proposition cannot be both true and false, even if you believe that the LEM implies the LNC.

Had he said he was rejecting the LNC, I wouldn't have said, "That's wrong because it violates the LNC." But rejecting the LEM does not imply that one is rejecting the LNC.

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I think you're just failing to understand how closely conjoined they are. Provide an example of something which violates the LNC but not the LEM. His assumption directly entails an instantiation of the LNC. Indeed if you don't rely on Wikipedia to mediate the LNC, it could be seen as a direct instantiation rather than an entailment.

zippy2006 said:

Okay...

What does this have to do with anything?

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I do not understand the confusion. You are claiming that a knowing subject is required for truth. Thus, the requirements of knowledge are requirements for truth. However, as I've demonstrated, the requirements for knowledge are entirely superfluous to the requirements for truth.

There is no good reason why Smith must have arrived at the conclusion that "It is raining in Canada" with proper justification in order for "It is raining in Canada" to be true.

zippy2006 said:

Propositions are either true or false, but they require minds to articulate them. There is truth (or falsity) to the proposition... because there is a proposition... because you proposed it. No minds -> no propositions -> no truth.

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Let's get to the heart of our disagreement here: You claimed that truth is a relation between knower and reality. Even if a mind is required for a proposition to exist, truth is still a relation between the proposition and reality.

zippy2006 said:

I think you're just failing to understand how closely conjoined they are. Provide an example of something which violates the LNC but not the LEM. His assumption directly entails an instantiation of the LNC. Indeed if you don't rely on Wikipedia to mediate the LNC, it could be seen as a direct instantiation rather than an entailment.

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I agree that the LEM entails the LNC. If X must be either true or false, then it is true that X cannot be both true and false. However, that does not imply that rejecting the LEM entails that one is also rejecting the LNC (that is the relevant question, not whether one can violate the LNC but not the LEM). An example of rejecting the LEM but not the LNC would be "X is neither true nor false." That statement clearly violates the LEM, but it does not violate the LNC.

Edit to clarify: He said "The King of France is bald" and "The King of France is not bald." I agree that that is a violation of both the LNC and the LEM. However, in the context of the discussion -- a discussion about the LEM -- I did not realize that he was also claiming the LNC was false. In fact, he didn't mention anything about the LNC, and rejecting the LEM does not imply a rejection of the LNC (look at my example above). Of course, if both of his propositions are true, then the LNC is out. I get that. But I do not see how it is improper of me to assume that he still thinks the LNC holds and is simply not understanding all of the implications of what he has said.

I'm not sure we have any disagreement here other than a disagreement about how to interpret a post.

What does your Wikipedia line mean?

zippy2006 said:

I did not misread it--at least not on that basis. If you read further into the article you will hear about the founder of the intuitionist school and his reasons for prescinding from the LEM in certain cases. That is what I was referring to.

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Like I said, Brouwer's personal ideas are not terribly relevant to constructive mathematics as it exists today, which is a branch of mathematics with the LNC but without the LEM.

See http://en.wikipedia.org/wiki/Intuitionistic_logic#Axiomatization for an axiomatisation of the underlying logic. There is no LEM (adding the LEM as an extra axiom will give classical logic) but there is the LNC (formally, A /\ ~A -> false is derivable from the rules there) and ex contradictione sequitur quodlibet (false -> B).

Conscious Z said:

However, that does not imply that rejecting the LEM entails that one is also rejecting the LNC (that is the relevant question, not whether one can violate the LNC but not the LEM).

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Hence my reference to constructive mathematics, which rejects the LEM but not the LNC.

Firstly, what are they?
Law of identity: A is A
Law of non-contradiction: A can't be A and non A at the same time and in the same way
Law of excluded middle: A is either A or non-A, there is no in between.

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Its maybe just my preference of expression rather than in your understanding of the logical principles themselves.

excluded middle

may be better expressed simply "either A or non-A" - Either there is a fridge in my kitchen or there is not.



non-contradiction likewise for clarity could be expressed:

"A cannot be non-A in the same way and in the same respect at the same time."

So, the questions are these. Are these laws absolute? If they are then how does the relativist deal with the fact that there are absolutes while still holding to the view that there are not? If they are not then can you explain how or why? And finally, if there are absolutes then what would preclude God from declaring that there are such things as sin (for our purposes falling short of an absolute standard of behavior), for example murder, rape, etc.?

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This is a great question. As to the importance of logic to theology, my answer would be that the foundational prerequisites are grace and faith. But mystery and paradox in addition to logic then are important in the articulation. Mystery puts bounds on how far one attempts to logically explain a doctrine. Its not in my view meant to be removed by logic, but to remind us of the need for revelation and faith, and that we only know in part. It therefore differs from 'a mystery' popularly understood as something to be solved. In both it would indicate that our understanding is incomplete. But in theology it indicates that knowledge will not be complete in this scene of time.

In regard to human thought these principles are necessary, but not in isolation. I have the following quote in a notebook but can't say for sure the source but it makes a valid point about logic not standing alone.

"If there is one thing more than any other that the development of modern philosophy impresses on our mind, it is the unsatisfactory character of the results obtained, where Logic alone is employed as the organ for the agnition of truth, as that by which, instead of that according to which we are to proceed. We may indeed feel ourselves held in the meshes of our own thinking, the mode of which Logic embodies, but we do not feel carried along or convinced, in the way in which the intuitional agnition of actuality convinces us."

If moral relativism were true, it would have to be false because it claims there is no absolute truth - it would therefore be self-contradictory. That which is false cannot be true. That there are people who subscribe to relativism or at least entertain the notion is no doubt the case. That doesn't make it true. They usually are not consistent...

Both christians and non-christians may reason at times in a flawed manner.

Conscious Z said:

It certainly does. You said that truth is a relation between reality and a knowing subject. Thus, without a knowing subject, there is no such thing as truth. However, the requirement that a subject have knowledge is superfluous here. Knowledge entails much more than a proposition merely existing in the mind. Knowledge requires a justified method, anti-luck criteria, etc. Suggesting that there is no truth to the proposition "There are currently 515 mountain gorillas on earth" simply because no one can know whether there are 515 mountain gorillas on earth is silly. It's an arbitrary requirement.

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Here's why it doesn't matter: if truth is a relation between intellect and reality, then truth will not exist without intellects regardless of our specific epistemologies (since all such epistemologies presuppose subjects). The specification of a knowing subject is just part and parcel of the proper adequation of the intellect to reality. If no subjects exist, then truth cannot exist even in principle. If subjects exist, it is still possible that truth does not exist (if those subjects do not have knowledge).

Propositions are relations of ideas. Imagine no person has ever actually thought "3416 times 2184 equals 7,460,544." Does that mean that it was not previously true that 3416 x 2184=7,460,544? Much like math, propositions are discovered.

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The reality exists, the truth doesn't. You're just repeating yourself here.

Again, you are imposing an arbitrary requirement of knowledge here. "Knowledge" and a proposition existing in a mind are not the same thing.

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I never said they were: again, this has nothing to do with what I said.

Even if we were to grant that a proposition must exist in the mind of a person in order for it to be true, the truthfulness of that proposition would still depend on the relationship between the proposition and reality, not the person and reality.

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I've already covered this: are you a Platonist or not?

He did not say that he was opposing both principles.

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It is logically impossible to conclude that two contradictory propositions are true without presupposing the falsity of both principles. Like I said, they go hand in hand. Regardless of the syntax he used, your counter begs the question and will have no effect on his point. I think you begged the question in a strict way, because we could have asked him at the beginning if he was opposing one principle and not the other and he would have answered negatively. Yet you could plausibly argue that you only begged the question loosely. Either way it fails to critique the heart of his challenge.

Conscious Z said:

I agree that the LEM entails the LNC... However, that does not imply that rejecting the LEM entails that one is also rejecting the LNC (that is the relevant question, not whether one can violate the LNC but not the LEM). An example of rejecting the LEM but not the LNC would be "X is neither true nor false." That statement clearly violates the LEM, but it does not violate the LNC.

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We agree that the LEM entails the LNC.

According to Wikipedia the LEM states that "for any proposition, either that proposition is true, or its negation is true." The "or" is obviously being used exclusively.

The negation of the LEM would therefore say that both a proposition and its negation could be true (or false). Yet this clearly violates the LNC as well, for a proposition and its negation are "antithetical propositions" (to quote Wikipedia). So the falsity of the LEM entails the falsity of the LNC. I think this fact makes it clear enough to say that the rejection of the LEM entails the rejection of the LNC. I don't think the fellow who wrote that proof would have taken it back had he seen the implication (indeed, presumably he did see it).

Architeuthus said:

Hence my reference to constructive mathematics, which rejects the LEM but not the LNC.

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Again, it doesn't reject it, it prescinds from it. It doesn't not explicitly take the LEM as an axiom. That is far different from rejecting it as false. My other earlier points have more to say about the legitimacy of that prescinding.

...this is the common answer and it derives from David Hume's distinction between "is" and "ought." He famously stated that you can't get an "ought" from an "is." While his statement is controversial, it certainly isn't clearly false.

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Have you seen Josef Pieper's diagram of the structure of moral acts?

True Scotsman said:

Yes they are because the law of identity is absolute. The relativist uses rationalization, which is the opposite of reason. Your last question is moot since the law of identity and the other axioms of philosophy make a god metaphysically impossible.

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Not hardly! In fact, in philosophy, by logic, there have been discerned over 15 different arguments that indicate there must be a god (some from non-religious people - like Aristotle's uncreated first cause) and not one that indicates there must not be a god. Now that does not PROVE there is a god but clearly shows how a god is both logical and reasonable to assume for those who have no materialistic evidence of a god.

Paul

pshun2404 said:

Not hardly! In fact, in philosophy, by logic, there have been discerned over 15 different arguments that indicate there must be a god (some from non-religious people - like Aristotle's uncreated first cause) and not one that indicates there must not be a god. Now that does not PROVE there is a god but clearly shows how a god is both logical and reasonable to assume for those who have no materialistic evidence of a god.

Paul

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And all of those arguments commit the fallacy of the stolen concept. They do this by accepting the concept of logic while denying a concept at its conceptual base, the primacy of existence. The primacy of existence is the most fundamental issue in philosophy. It has to do specifically with the relationship between existence and consciousness. Is consciousness the faculty which perceives and identifies reality or the faculty which creates reality? That existence has primacy in this most fundamental of relationships is perceptually self evident and literally undeniable. It is axiomatic in that in attempting to deny it you would be forced to accept it. If you doubt this then go ahead and deny it without using it.

dms1972 said:

Have you seen Josef Pieper's diagram of the structure of moral acts?

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I have not. Where might I find it?

Conscious Z said:

However, that does not imply that rejecting the LEM entails that one is also rejecting the LNC (that is the relevant question, not whether one can violate the LNC but not the LEM). An example of rejecting the LEM but not the LNC would be "X is neither true nor false." That statement clearly violates the LEM, but it does not violate the LNC.

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Sorry, I was in a rush last time I replied to you. I didn't answer this very well.

What would it mean to say that a proposition is neither true nor false? Without getting too technical, it seems to me that a proposition is an intentional statement about the truth of something and thus is true or false by definition.

This is related to why I don't think the computational theories that prescind from the LEM are legitimate. If you look at the applications, they usually relate to things like linguistic ambiguities or epistemic gaps. But the LEM is an ontological statement, not a linguistic or epistemic statement. It's just misleading to claim that you don't make use of the LEM based on such considerations and applications. Furthermore (and ironically) a computer either makes use of the LEM or it doesn't, and it has nothing to do with the program it runs. It's not clear how computational theory could decide the validity of the LEM even in principle.

I'm not sure we have any disagreement here other than a disagreement about how to interpret a post.

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I agree. Given his assumption, I just don't think he was taking the LNC as a premise. To be quick: even if you didn't strictly beg the question, I don't think you addressed his argument.

dms1972 said: ↑
Have you seen Josef Pieper's diagram of the structure of moral acts?

I have not. Where might I find it?

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Hi, I was searching on the internet to see if I could find it to post a link, its in a double-volume of his called Living the Truth, published by Ignatius. Very interesting. If I find it online I'll let you know. The book itself is very good