Are the laws of logic important to theology?

[Ana the Ist]

Not at you personally but your signature made me consider the idea so it is what caused me to comment on the subject.



I'm not trying to do anything more than give my POV on the subject of circular reasoning. I hope I did not give you the impression that I thought you were close minded on the subject. That was not my intent. I specifically did not quote you as my comment ], though inspired by your signature, was not meant to be about you but more a general comment.

Gotcha...my mistake. You can probably understand why I made the mistake...I thought perhaps you didn't quote me just because our signatures don't get quoted.

I suppose I've always thought that for logic to be sound, the assumptions that one starts with when creating a logical statement must also be sound. If the assumptions are false or baseless, then so is the logical statement...regardless of how carefully they followed the rules of logic after they made the false assumptions.

 

[Songsmith]

They are assumptions, assumed to be true in a particular logical system.



Heraclitus wrote "You cannot step twice into the same river". In a manner of speaking, this is a rejection of the law of identity. The law of identity does not have to be assumed; you can do without it.

Heraclitus was wrong. A river is defined, and I must assume always has been defined, as "a large natural stream of water flowing in a channel to the sea, a lake, or another such stream." The river is made up of all the waters from it's head to it's mouth. What he was trying to do was make the point that change is imperative to life. His statement is simply not true. It is true the you cannot touch the same molecules of h2o that you first touched, but those are only constituent parts of the thing called a river, not the river itself. And those molecules have an identity as well. I forget who it was, but another dude came along and tried to one up Heraclitus by saying that you can't even step into the river once.

Heraclitus in no way invalidated the law of identity.

 

[essentialsaltes]

The river is made up of all the waters from it's head to it's mouth.

If that's true, then the river changes from moment to moment, as it gathers new water at its head, and discharges other water at its mouth.

Heraclitus in no way invalidated the law of identity.

It's not an attempt to invalidate the law of identity. But the law of identity is only an axiom. If you assume it, then it's valid within that system. If you don't, it ain't necessarily so.

Look, things that are identical have the same properties. I have a college degree, but the me of 30 years ago didn't. So I am not identical to my past self. Most things change over time, and if the law of identity cannot be used to connect former and present objects as the same thing, it seems kinda useless. And that's why one wouldn't assume it for such cases.

 

[football5680]

Yes, the laws of logic are important but it is difficult to apply human logic to God. We make certain assumptions that to us seem like absolutes but they may not apply elsewhere.

 

[Architeuthus]

Are the laws of logic important to theology?

Of course. That's why there was so much development of formal logic during the Middle Ages.

 

[zippy2006]

Sure, there are laws of logic and they do appear to be absolute. Luckily for me and my relativistic views, they don't have anything to do with ethics/morality.

...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.

Beyond that, Relativism isn't so much a rejection of laws of logic as much as a specific epistemology. One can admit the laws of logic exist and yet the infant certainly isn't able to deduce mathematical truths. For the Moral Relativist, we are infants with respect to morality. It is too far beyond human powers of knowing, and may derive from preferences rather than laws (thus depriving it of any binding and universal force).

 

[zippy2006]

They are assumptions, assumed to be true in a particular logical system.

They are also true, not to mention presupposed in every logical system.

The law of identity does not have to be assumed; you can do without it.

Except you can't. Aristotle demonstrates this early in his Metaphysics, certainly before book IV.

The words you use, the thoughts you think, and the letters you type would not make any sense without the law of identity (and the law of non-contradiction which follows).

Take a word, such as "green." We suppose green is one thing and not another. It isn't yellow, or orange. It is true that green=green and untrue that green= ~green. If you want to deny the law of identity and not performatively contradict yourself when you say, "My shirt is green," then you would have to admit that each word (and concept) contained in the proposition need not have any finite semantic range, any exclusivity of meaning, any selective application to reality. Thus to say, "My shirt is green," could be the same thing as saying, "Your pants are zebra," given the rejection of such fundamental laws. If you suppose your statements mean something, then you're not doing without the law of identity. Given your contribution, I presume you do so believe.

Dancing around in logical systems is one thing, but when it comes down to it some logical systems (and axioms thereof) are true and some are false. Some are more obviously true than others. It doesn't get any more obvious than the law of identity.

Edit:

Heraclitus wrote "You cannot step twice into the same river". In a manner of speaking, this is a rejection of the law of identity.

I think you are confusing the temporal persistence of material objects with the law of identity. Heraclitus' rejection of the former in no way lessens his accountability to the latter. In fact both Heraclitus' and Parmenides' unintuitive theories build directly on the law of identity. The law of identity says A=A, it does not say A[sub]t1[/sub]=A[sub]t2[/sub]; it has no necessary implication for temporal persistence. The proposition that material objects persist through time is nowhere near as fundamental as the law of identity.

 

[Songsmith]

They are also true, not to mention presupposed in every logical system.



Except you can't. Aristotle demonstrates this early in his Metaphysics, certainly before book IV.

The words you use, the thoughts you think, and the letters you type would not make any sense without the law of identity (and the law of non-contradiction which follows).

Take a word, such as "green." We suppose green is one thing and not another. It isn't yellow, or orange. It is true that green=green and untrue that green= ~green. If you want to deny the law of identity and not performatively contradict yourself when you say, "My shirt is green," then you would have to admit that each word (and concept) contained in the proposition need not have any finite semantic range, any exclusivity of meaning, any selective application to reality. Thus to say, "My shirt is green," could be the same thing as saying, "Your pants are zebra," given the rejection of such fundamental laws. If you suppose your statements mean something, then you're not doing without the law of identity. Given your contribution, I presume you do so believe.

Dancing around in logical systems is one thing, but when it comes down to it some logical systems (and axioms thereof) are true and some are false. Some are more obviously true than others. It doesn't get any more obvious than the law of identity.

Edit:



I think you are confusing the temporal persistence of material objects with the law of identity. Heraclitus' rejection of the former in no way lessens his accountability to the latter. In fact both Heraclitus' and Parmenides' unintuitive theories build directly on the law of identity. The law of identity says A=A, it does not say A[sub]t1[/sub]=A[sub]t2[/sub]; it has no necessary implication for temporal persistence. The proposition that material objects persist through time is nowhere near as fundamental as the law of identity.

I yeild to your superior ability of expression.
Good stuff there.

 

[durangodawood]

Are the laws of logic are important to theology, which is a human endeavor? Of course they are.

Are they consistent across all possible realms, material and divine? Who knows?!!!

 

[essentialsaltes]

They are also true, not to mention presupposed

Right, assumed. That's what I said. Not the same as true.

I think you are confusing the temporal persistence of material objects with the law of identity. Heraclitus' rejection of the former in no way lessens his accountability to the latter. In fact both Heraclitus' and Parmenides' unintuitive theories build directly on the law of identity. The law of identity says A=A, it does not say A[sub]t1[/sub]=A[sub]t2[/sub]

That almost gives everything away. The Socrates of 450 did not die, so Socrates[sub]t1[/sub] is not mortal.

 

[KCfromNC]

They are also true, not to mention presupposed in every logical system.

Not sure if you're specifically talking about the law of identity or more generally about the ideas in the OP. See Non-classical logic - Wikipedia, the free encyclopedia for examples of logical systems which do without the latter. Like classical logic, they work reasonably well for problems in their particular domains. Like any tool, though, they can be misused.

 

[zippy2006]

Right, assumed. That's what I said. Not the same as true.

I guess you could just go back and re-read what I wrote...

You said they are presupposed in particular logical systems, I said they are presupposed in all. I also said they are true (as opposed to merely posited). I never said presupposition is the same as truth, and presupposition in every system is different than presupposition in particular systems. (Apparently you missed the point)

That almost gives everything away.

Why? Again, what I already wrote to you stands. Temporal persistence is not the law of identity. Heraclitus has no bearing on this question. Heraclitus' claims presuppose motion/change; the law of identity does not. (I am not claiming that temporal persistence is false, I am just saying that it isn't entailed by the law of identity.)

Not sure if you're specifically talking about the law of identity or more generally about the ideas in the OP. See Non-classical logic - Wikipedia, the free encyclopedia for examples of logical systems which do without the latter. Like classical logic, they work reasonably well for problems in their particular domains. Like any tool, though, they can be misused.

I don't think those systems do anything of the sort. They are just symptoms of a confused analytical philosophy that misunderstands what is meant by the law of identity, etc. This misunderstanding is apparently also present in essentialsaltes. ...But feel free to actually set out an argument in their favor.

(In general I believe they are cousins of the failed project of logical positivism, positing strange definitions of "truth" such as "constructive provability" rather than accepting the colloquial definitions. Although this divorces them from reality and a standard lexicon, these systems themselves also rely on the fundamental laws for their exposition, as explained earlier. That said, they are useful in certain applications, but they in no way replace something like the law of non-contradiction.)

 

[essentialsaltes]

I guess you could just go back and re-read what I wrote...

You said they are presupposed in particular logical systems, I said they are presupposed in all.

KC showed you that they are not presupposed in all.

They are just symptoms of a confused analytical philosophy that misunderstands what is meant by the law of identity, etc.

You claim they are presupposed in all logical systems, and when you are shown logical systems that do not presuppose them all, you wave your hands about in the air and reject the evidence.

these systems themselves also rely on the fundamental laws for their exposition

No, the systems themselves explicitly or implicitly reject (some of) them. What people who rhapsodize in exposition about these systems do is irrelevant.

 

[Conscious Z]

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.?

Very few people are actually relativists. You are likely referring to the view called "moral subjectivism" that says truth is dependent on someone's mind. You may also be referring to moral anti-realism, which is the view that there is no objective moral truth.

Yes, logic is of course important. Even god cannot do the logically impossible.

 

[Conscious Z]

Any statement you make is provable or unprovable depending upon the assumptions you are willing to make. If my basic assumption is that my opinion is fact then it logically follows that

A My opinion is fact
B In my opinion vanilla ice cream is the best
C therefore vanilla ice cream is the best.

See I have proven through faultless logic that vanilla ice cream is the best. You may disagree with my basic assumption and say that it is ridiculous but the logic used is absolutely spot on. All logical statements start with at least one assumption and usually contain unstated ones as well as stated ones and many people will stick to basic assumptions that are as frivolous as the one in my example.

A true logical syllogism is both valid and sound. The example you gave is valid, but it isn't sound -- therefore, you have not "proven" anything with it.

 

[zippy2006]

KC showed you that they are not presupposed in all.

Actually, he linked to a Wikipedia article.

You claim they are presupposed in all logical systems, and when you are shown logical systems that do not presuppose them all, you wave your hands about in the air and reject the evidence.

I asked him to show me something. I actually know what a number of those systems say, and I have doubts that you do. If you did, you would be able to rationally explicate them and demonstrate how they do not require such laws. The fact that you can do nothing more than point fingers at things you do not understand is telling.

No, the systems themselves explicitly or implicitly reject (some of) them.

Pray, tell us how. Do you have any idea whatsoever?

Formal logical systems derived for theoretical computational purposes have nothing to do with the OP. By "classical logic" they mean binary truth-functional models such as those common in simple computers. Alternative models represent a deviation in formal systems for representational purposes. No one actually holds to such inference rules in real life; they are merely useful in computational theory for modeling uncertainties and ambiguities arising from language use. Beyond that, the question of whether formal Aristotelian logic is even a binary truth-functional model is controversial, and also has nothing to do with the OP. Furthermore, the laws noted in the OP are more properly said to be metaphysical laws than logical laws. They transcend (though influence) questions about formal systems. As argued earlier, formal systems rely upon such principles.

Anyway, a real conversation won't exist until you can actually provide an syllogistic argument rather than arguments from "authority" (Wikipedia).

 

[zippy2006]

A true logical syllogism is both valid and sound. The example you gave is valid, but it isn't sound -- therefore, you have not "proven" anything with it.

To offer a bit more clarity...

• An argument is valid iff the conclusion follows from the premises
• An argument is sound iff it is valid and the premises are true

A syllogism or argument is not true or false, it is valid or invalid and sound or unsound. Saying an argument is "valid and sound" is redundant since soundness implies validity. If you want to say that someone's argument is valid but unsound, then you should point out the premise you believe to be false.

 

[essentialsaltes]

I asked him to show me something. I actually know what a number of those systems say, and I have doubts that you do. If you did, you would be able to rationally explicate them and demonstrate how they do not require such laws. The fact that you can do nothing more than point fingers at things you do not understand is telling.

Is it a fact that I can do nothing more than point fingers at nonclassical logic?

Anyway, "fuzzy logic variables may have a truth value that ranges in degree between 0 and 1". This violates the law of the excluded middle referenced in the OP. Łukasiewicz and Gödel created particular systems of their own with multi- and infinite- valued truth, which likewise reject either/or all-or-nothing 0-or-1 truth values implied by the law of the excluded middle.

Anyway, a real conversation won't exist until you can actually provide an syllogistic argument rather than arguments from "authority" (Wikipedia).

Either the present king of France is bald, or he is not bald (LEM)

Lemma1
If someone is bald, they will appear in the set of bald people.
The present King of France is not in the set of bald people.
Therefore the present King of France is not bald.

Lemma2
If someone is not bald, they will appear in the set of not bald people.
The present King of France is not in the set of not bald people.
Therefore the present King of france is not not bald.

Conclusion:
The LEM is false. It can be used where it's sensible to use it. But there are places where it is unsensible to use it.

 

[Conscious Z]

To offer a bit more clarity...

• An argument is valid iff the conclusion follows from the premises
• An argument is sound iff it is valid and the premises are true

A syllogism or argument is not true or false, it is valid or invalid and sound or unsound. Saying an argument is "valid and sound" is redundant since soundness implies validity. If you want to say that someone's argument is valid but unsound, then you should point out the premise you believe to be false.

I said his argument was valid but not sound. The unsound premise is so obvious it doesn't need to be said: My opinions are facts.

There was nothing that needed clarification in my post. By "true," I obviously meant the conclusion, and conclusions are true or false.

 

[variant]

To the extent that the rules of logic are correctly describing the realities they say they do and to and to the extent that logic is important to theology.