Welcome guest, is this your first visit? Create Account now to join.
  • Login:

Welcome to the Online Debate Network.

If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed.

Page 1 of 4 1 2 3 4 LastLast
Results 1 to 20 of 66
  1. #1
    ODN Community Regular

    Join Date
    May 2005
    Posts
    4,896
    Post Thanks / Like

    The Limitations of Logic

    The topic of logic has really gotten me thinking over the past few weeks. Many debates have arisen in which the usage and application of logic has been questioned. I'm not just referring to the threads debating the infallibility of logic - the threads about God, omnipotence, free will, sin, etc all procure many questions regarding the nature of logic as well.

    In this thread, I postulate that logic is founded upon and constrained by human language and understanding, and since both are fallible, logic by extension shares the same vulnerabilities. I shall demonstrate these assertions using examples, and conclude by saying that logic should not be treated as the be-all and end-all in verifying everything in this universe.

    1) Logic is limited by language

    Example 1:
    "This statement is false."
    In this classic Liar Paradox, the paradox arises because the statement is self-referential. If we claim that this statement is true, then it must be false, because it describes itself to be false. Yet if we claim this statement to be false, then it has to be true.

    Attempts to resolve this paradox have invariably contradicted the law of bivalence or resorted to attacking the language upon which this paradox is based. This example is not to demonstrate that logic is false, but that it is highly dependent on language.

    Example 2:
    The adjectives "autological" and "heterological" are defined as follows:

    1. An adjective is autological if and only if it describes itself. For example "short" is autological, since the word "short" is short. "Pentasyllabic" is also autological.

    2. An adjective is heterological if and only if it does not describe itself. Hence "long" is a heterological word, as is "monosyllabic".
    "Heterological is not heterological."
    The Grelling-Nelson paradox arises when we attempt to find out the nature of the word "heterological". Is the word "heterological" heterological? On the one hand, if the word "heterological" is heterological, then it does not describe itself. Since the fact of it not describing itself does, in fact, describe it, it is autological, which means it isn't heterological. On the other hand, if the word "heterological" is not heterological, then it must be autological, which means it describes itself, and therefore it must be heterological. Either case leads to the contradiction that the word "heterological" is both heterological and not heterological, which is impossible.

    Again, we see a case where logic is constrained by the limitations of language.

    2) Logic is limited by the human framework of understanding

    Example 1:
    Suppose a point P is moving between points A and B (just like in the original Racetrack). And suppose also that we stipulate that P is in the state "even" for the first half of the journey, "odd" for the next 1/4, "even" for the next 1/8, and so on. That is, we simply decide to classify P based on where along the journey it is, such that it alternates between what we call an "even" and an "odd" state. We can in addition stipulate that once it is in one state it remains in that state unless it gets switched according to the above rule.
    Here is a paradox which arises when we attempt to use logic to deal with the concept of infinities. The question is: In what state is P at point B?

    Critics of this paradox normally claim that it is physically impossible to divide distance into infinitely small units. While this may be true, that only demonstrates that logic cannot cope with matters out of our physical realm of understanding.

    Example 2:
    1. All justifications in pursuit of certain knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore there can be no end. We are faced with the hopeless situation of 'infinite regression'.
    2. One can stop at self-evidence or common sense or fundamental principles or speaking 'ex cathedra' or at any other evidence, but in doing so the intention to install certain justification is abandoned.
    3. The third horn of the trilemma is the application of a circular and therefore invalid argument.
    This is not a paradox. It is the Munchhausen Trilemma, which argues that all techniques to used to verify truth are fallible as they ultimately cannot justify themselves.

    Many people have claimed that logic is infallible. But the interesting thing is, no one has ever attempted to justify logic as being an infallible system for the verification of knowledge. Instead, the onus is always shifted to the skeptic: "Prove logic is wrong", "Prove that any of the laws of logic are wrong", the defenders of logic say.

    However, the claimant is usually hard-pressed to prove logic on its own. Most of the time one would appeal to empirical evidence and say that in all known cases of logic being utilised, it has never failed before (which is an unsatisfactory answer on its own). But when presented with paradoxes where logic produces contradictory/indeterminate results, the claimant usually produces a wide variety of reasons to justify why logic cannot deal with the said paradoxes. Hence, we see that the application of logic is in effect tautological, as anything that it cannot adequately deal with is cast to the realm of "illogical".

    This then leads to the obvious question: We can say that whatever logic disagrees with is illogical, but can we say that anything logic doesn't agree with, is false? Could it be that logic is just incapable of dealing with that particular phenomena or concept?

    Conclusions:
    1) Logic is useful in explaining our world and verifying facts within our realm of understanding. However, it is by no means infallible, as it is predicated heavily upon our imperfect language and our often flawed and imcomplete understanding of the world.

    2) Since logic is based heavily on human language and understanding, and in fact, is a component of human understanding, it is a human construct rather than a human discovery. A concept cannot exist independently without a conceiver, and logic, as well, is a concept which does not exist on its own. It is a system of reasoning created by humans to understand our world.

    3) Since logic is only capable of verifying facts within our realm of understanding, the fact that it disagrees with certain concepts that transcend human understanding such as God, omnipotence and omniscience, cannot be used as 100% proof of the latter's non-existence.
    Trendem

  2. #2
    ODN Community Regular

    Join Date
    Sep 2004
    Location
    Palace of Kubla Khan and bovine worshippers
    Posts
    3,011
    Post Thanks / Like

    Re: The Limitations of Logic

    Wow... you've outlined and supported your argument very well, Trendem. I am in basic agreement with pretty much everything you said. We sure needed this post a few weeks ago when the infallible crowd was ranting on. You may have stated your case too well, and in doing so scared away those who might tend to disagree with your premise. That's OK, though. We can measure success in absences too.

    Quote Originally Posted by Trendem
    Again, we see a case where logic is constrained by the limitations of language.
    Good job on explaining that. This almost sounds as if language is being used anthropomorphistically by people who use those linguistic conundrums to put forth their argument -- as if the words themselves had intrinsic properties of their own independent from the concepts they were describing.

    Quote Originally Posted by Trendem
    Hence, we see that the application of logic is in effect tautological, as anything that it cannot adequately deal with is cast to the realm of "illogical".
    Yes, and it's hard to get people who are using a tautology to see that they are doing so, because it's somehow in their nature to accept things a priori that have strong appearances of fact within the scope of their own perspective.

    Quote Originally Posted by Trendem
    This then leads to the obvious question: We can say that whatever logic disagrees with is illogical, but can we say that anything logic doesn't agree with, is false? Could it be that logic is just incapable of dealing with that particular phenomena or concept?
    Perish the thought that logic could be the one at fault in anything! If logic's ever wrong, all we need to do to remedy the situation is say that it wasn't logic. Voila! Very convenient, eh?

    Quote Originally Posted by Trendem
    I shall demonstrate these assertions using examples, and conclude by saying that logic should not be treated as the be-all and end-all in verifying everything in this universe.
    I predict the naysayers will pounce on this one statement as if it had meat in the whole argument, and claim that they never said logic was the only method to verifying things. They'll contend that logic is still, however, complete in its own realm, and infallible. In so doing, they'll be attacking a facet of the argument that is not at the core.
    anything could be an illusion and we wouldn't know the difference... proof schmoof...

  3. #3
    ODN Community Regular

    Join Date
    May 2006
    Posts
    3,795
    Post Thanks / Like

    Re: The Limitations of Logic

    First of all, nice job. Impressive OP. And I must agree with you on most points. There are things that defy logic (darn quantum mechanics). (Classical) logic cannot adequately deal with many things. Where logic can address something, however, it is infallible.

    Quote Originally Posted by Trendem
    Logic is useful in explaining our world and verifying facts within our realm of understanding. However, it is by no means infallible, as it is predicated heavily upon our imperfect language and our often flawed and imcomplete understanding of the world.
    Agreed.

    Quote Originally Posted by Trendem
    Since logic is based heavily on human language and understanding, and in fact, is a component of human understanding, it is a human construct rather than a human discovery.
    Agreed.

    Quote Originally Posted by Trendem
    Since logic is only capable of verifying facts within our realm of understanding, the fact that it disagrees with certain concepts that transcend human understanding such as God, omnipotence and omniscience, cannot be used as 100% proof of the latter's non-existence.
    Certain proof? Perhaps not. Very strong evidence? Yes. Chalk another point up for the atheists

    Quote Originally Posted by Trendem
    This statement is false
    I'm tempted to brush this one off as a self-referential axiom that doesn't contain an actual statement, but that would be boring

    Every statement has an implicit assumption of its own truth. Thus, your paradoxical statement is equivalent to "This statement is false and this statement is true". These are two contradictory elements, so the whole thing is false. Note that that does not imply that the first part is false.

    Quote Originally Posted by Trendem
    Heterological is not heterological.
    Let's break this one down: Heterologic is not not descriptive of itself. Heterological is descriptive of itself. For heterological to be descriptive of itself, then it would have to be not descriptive of itself. So we also have, by substituting the definition of heterological (again): heterological is not descriptive of itself. So heterological is both descriptive of itself and not descriptive of itself. This a logical contradiction. The word "heterological", as presented, doesn't work. This "paradox" is exactly like saying "A both exists and doesn't exist". Does A exist? It's silly, because heterological has contradictory properties.

    Quote Originally Posted by Trendem
    In what state is P at point B?
    None; it never gets there.

    Quote Originally Posted by Trendem
    However, the claimant is usually hard-pressed to prove logic on its own. Most of the time one would appeal to empirical evidence and say that in all known cases of logic being utilised, it has never failed before (which is an unsatisfactory answer on its own). But when presented with paradoxes where logic produces contradictory/indeterminate results, the claimant usually produces a wide variety of reasons to justify why logic cannot deal with the said paradoxes. Hence, we see that the application of logic is in effect tautological, as anything that it cannot adequately deal with is cast to the realm of "illogical".
    Fair enough. Logic is tautological. So's everything else. To get anywhere, you have to assume some things. Logic does that. So far, it's working pretty well.

    Quote Originally Posted by Trendem
    We can say that whatever logic disagrees with is illogical, but can we say that anything logic doesn't agree with, is false? Could it be that logic is just incapable of dealing with that particular phenomena or concept?
    Possibly. However, I would call the thumbs-down of logic significant evidence against a concept.
    Freedom is you choosing for yourself. Law is the government choosing for you. The two are opposites.

    Pray - To ask that the laws of the universe be annulled in behalf of a single petitioner confessedly unworthy - Ambrose Bierce
    Faith - Belief without evidence in what is told by one who speaks without knowledge about things without parallel - Ambrose Bierce

  4. #4
    Registered User

    Join Date
    Mar 2005
    Location
    In the moment
    Posts
    2,347
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Rook
    Every statement has an implicit assumption of its own truth. Thus, your paradoxical statement is equivalent to "This statement is false and this statement is true". These are two contradictory elements, so the whole thing is false. Note that that does not imply that the first part is false.
    Where do you get this from? I see no logical reason to assume that every statement assumes itself true. I do not know of any statement that has any ability to think whatever. Please explain.

    The statement says it is false. It does not in any way imply that it is true. You are pulling this out of thin air, with no reason, logic, or argument given for doing so. Your explanation of this statement is entirely imaginary and has no connection to reality.
    I've been meek for a whole day now...

    The world is mine!!


    The power of oui.

    impssible

  5. #5
    ODN Community Regular

    Join Date
    May 2006
    Posts
    3,795
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by PerVirtuous
    I see no logical reason to assume that every statement assumes itself true.
    Look harder Language is communication. That is the point of language. And it makes sense for communication to implicity assume truth, rather than falsehood. In English, a negative implies falsehood, and the default (i.e. without a negative) implication is truth. Saying "This apple is not red" implies the falsehood of the propositions "This apple is red", just as saying "This apple is red" implies the truth of that proposition. That's how English works. It, by default, assumes the truth of a proposition put forth in a sentence.
    Freedom is you choosing for yourself. Law is the government choosing for you. The two are opposites.

    Pray - To ask that the laws of the universe be annulled in behalf of a single petitioner confessedly unworthy - Ambrose Bierce
    Faith - Belief without evidence in what is told by one who speaks without knowledge about things without parallel - Ambrose Bierce

  6. #6
    Registered User

    Join Date
    Mar 2005
    Location
    In the moment
    Posts
    2,347
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Castle
    Look harder Language is communication. That is the point of language. And it makes sense for communication to implicity assume truth, rather than falsehood. In English, a negative implies falsehood, and the default (i.e. without a negative) implication is truth. Saying "This apple is not red" implies the falsehood of the propositions "This apple is red", just as saying "This apple is red" implies the truth of that proposition. That's how English works. It, by default, assumes the truth of a proposition put forth in a sentence.
    You are full of brownstuff!

    Now, this previous sentence has its purpose, yet it has no intent to be "true" in the sense of accuracy, as you have outlined above. Often language is used more subtly to make points that are not actually what the statement says. I do not actually think that if we lopped your head off that you would bleed brown.

    You have continually made the same mistake over and over with your arguments by mistaking CAN mean as you say to MUST mean as you say. Your argument makes sense for some statements. You have made no case whatever that all statements necessarily are intended to be true, or should be assumed to be intended as true.

    That's what happens when I look harder.
    I've been meek for a whole day now...

    The world is mine!!


    The power of oui.

    impssible

  7. #7
    ODN Community Regular

    Join Date
    May 2006
    Posts
    3,795
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by PerVirtuous
    it has no intent to be "true" in the sense of accuracy, as you have outlined above.
    I never said it was literally true. I said that it was true in some sense. If we construct a sentence without a negative, we mean the proposition it outlines to be taken as true. If we construct a sentence with a negative, we mean for the proposition it outlines to be taken as false. That's simply how English works. Every statement is meant to be true, in some sense. It would be redundant, of course, to say so, because it is an implicit assumption that pervades all of the English language, but it is important to recognize that that assumption exists.

    Think about it this way, PerVirtuous. Either a statement is true or it is false. So either all of the statements in English are assumed to be truth, all of them are assumed to be false, or some are assumed to be false and some are assumed to be true. Clearly, not all of them are assumed to be false. Assuming that some are true and some are false is meaningless and destroys the whole point of communication, because you can't seperate what is intended as truth from what is intended as falsehood. It's absurd, and it destroys a language's ability to communicate. Therefore, we are left with every statement being assumed to be true.
    Freedom is you choosing for yourself. Law is the government choosing for you. The two are opposites.

    Pray - To ask that the laws of the universe be annulled in behalf of a single petitioner confessedly unworthy - Ambrose Bierce
    Faith - Belief without evidence in what is told by one who speaks without knowledge about things without parallel - Ambrose Bierce

  8. #8
    ODN Community Regular

    Join Date
    Dec 2005
    Posts
    1,547
    Post Thanks / Like

    Re: The Limitations of Logic

    My only question is:

    How did you manage to prove that logic is limited by language? Did you use logic to do so?
    "If you wish to know how libertarians regard the State and any of its acts, simply think of the State as a criminal band, and all of the libertarian attitudes will logically fall into place." -Murray Rothbard

    "There are a thousand hacking at the branches of evil to one who is striking at the root." -Henry David Thoreau

  9. #9
    Registered User

    Join Date
    Mar 2005
    Location
    In the moment
    Posts
    2,347
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Castle
    I never said it was literally true. I said that it was true in some sense. If we construct a sentence without a negative, we mean the proposition it outlines to be taken as true. If we construct a sentence with a negative, we mean for the proposition it outlines to be taken as false. That's simply how English works. Every statement is meant to be true, in some sense. It would be redundant, of course, to say so, because it is an implicit assumption that pervades all of the English language, but it is important to recognize that that assumption exists.
    No, it is not. English is far more complex than that. What you are describing is only generally true in the scientific and mathematical uses of the language. Outside of those, what you say is not true.

    Think about it this way, PerVirtuous. Either a statement is true or it is false.
    The universe will never end. Tell me, is it true or false and supply proof.



    So either all of the statements in English are assumed to be truth, all of them are assumed to be false, or some are assumed to be false and some are assumed to be true.
    Or some cannot be determined to be true or false and, therefore, are neither.


    Clearly, not all of them are assumed to be false. Assuming that some are true and some are false is meaningless and destroys the whole point of communication, because you can't seperate what is intended as truth from what is intended as falsehood.
    As if you can do that with your method. You are quite conceited if you believe you can.


    It's absurd, and it destroys a language's ability to communicate. Therefore, we are left with every statement being assumed to be true.
    You only think it is absurd. I do not. I think it is ultimately more accurate to admit that I do not know what I do not know. I do not make assumptions so I can live in a cozy little world where I make believe I know things I do not know.
    I've been meek for a whole day now...

    The world is mine!!


    The power of oui.

    impssible

  10. #10
    ODN Community Regular

    Join Date
    May 2006
    Posts
    3,795
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by PerVirtuous
    The universe will never end. Tell me, is it true or false and supply proof.
    It is true or false; law of the excluded middle. I just can't tell you which one

    Quote Originally Posted by PerVirtuous
    Or some cannot be determined to be true or false and, therefore, are neither.
    We're not talking about whether or not they are true or false; we're talking about whether the default assumption is true or false.

    Quote Originally Posted by PerVirtuous
    As if you can do that with your method.
    Of course I can. By definition, all statements are assumed to be true.

    Quote Originally Posted by PerVirtuous
    I think it is ultimately more accurate to admit that I do not know what I do not know.
    We're not talking about whether or not the statement is true or false, just what a sentence conveys about a proposition. Please read the following very closely.

    "This apple is red." That conveys the assumption that the proposition "This apple is red"=T. It does not convey the assumption that the proposition "This apple is red"=F. That applies to every sentence in the English language. That's all I'm saying.
    Freedom is you choosing for yourself. Law is the government choosing for you. The two are opposites.

    Pray - To ask that the laws of the universe be annulled in behalf of a single petitioner confessedly unworthy - Ambrose Bierce
    Faith - Belief without evidence in what is told by one who speaks without knowledge about things without parallel - Ambrose Bierce

  11. #11
    Super Moderator

    Join Date
    Feb 2006
    Location
    Louisiana
    Posts
    9,145
    Post Thanks / Like

    Re: The Limitations of Logic

    Puts on Devils advocate hat.

    The one thing I found missing from your OP is a definition of what Logic "is". As I understand it "Logic" is nothing more than ordered thought.

    Is Logic limited by language?
    If logic is ordered thought, then language is supposed to be a reflection of that thought. For what word ever proceded from a mouth, without first being conceived by a thought? So it seems to me that logic it's self is not limited by language, but language is limited in it's ability to convey logic.

    So what does logic tell us of the statement
    "This statement is false."
    It tells us this a meaningless statement. It is the language equivalent to 1-1 it = 0.

    Is Logic limited by the Human framework of understanding.
    If it is possible to know all things, then logic is not limited. If it is not possible to know all things, then logic can be limited.
    Our ability to us logic may be said to be limited.The Vehicle of thought, that is logic, can not be said to be lacking because we are ignorant.
    It would be like saying, I can not throw a ball more than 40 yards. A ball is therefore limited to being thrown 40 yards.

    So when it is said, ' Logic is limited by the human framework of understanding' you deny that logic is used to stretch the framework of our understanding.
    If Logic enlarges our framework of understanding, in what way can we say logic it's self is limited by that understanding?

    Quote Originally Posted by Trendem
    Many people have claimed that logic is infallible. But the interesting thing is, no one has ever attempted to justify logic as being an infallible system for the verification of knowledge.
    Is it safe to say that nothing has ever been verified as "False" without using logic? What is one thing that has been "verified" "true" without the use of logic?
    It seems to me that when you argue against logic, you are arguing against thought it's self.
    Look at it like this, if Logic is ordered thought. then it should be able to render a conclusion on anything the mind can conceive. So when one says that something is "Knowable" it must fall into the realm of Logic. If something is unknowable then we would not be aware of it to discuss it, so it really becomes a None issue.

    Quote Originally Posted by TRENDEM
    This then leads to the obvious question: We can say that whatever logic disagrees with is illogical, but can we say that anything logic doesn't agree with, is false? Could it be that logic is just incapable of dealing with that particular phenomena or concept?
    When you say something is "illogical". isn't that the same as saying something doesn't make sense, or maybe that it has no real meaning. If then something is determined to have no meaning then hasn't "logic" done it's work, and rendered an accurate reflection of reality?

    Quote Originally Posted by TRENDEM
    Conclusions:
    1) Logic is useful in explaining our world and verifying facts within our realm of understanding. However, it is by no means infallible, as it is predicated heavily upon our imperfect language and our often flawed and incomplete understanding of the world.
    Our language does not limit logic, but is only a limit in our use of logic.
    Our current knowledge is limited, and often times flawed, however it is through logic that our knowledge is increased, and corrected, or even known to be flawed.

    Quote Originally Posted by TRENDEM
    2) Since logic is based heavily on human language and understanding, and in fact, is a component of human understanding, it is a human construct rather than a human discovery. A concept cannot exist independently without a conceiver, and logic, as well, is a concept which does not exist on its own. It is a system of reasoning created by humans to understand our world.
    First I would argue that Language is not of Man to begin with. However, for the atheist I would say that as soon as thought existed so did logic, You can not have language without also having the possibility for ordered thought. Logic is more a recognition of order, which is reflected in all that is known. Because man did not create the first thought, man is not responsible for the existence of logic.

    Quote Originally Posted by TRENDEM
    3) Since logic is only capable of verifying facts within our realm of understanding, the fact that it disagrees with certain concepts that transcend human understanding such as God, omnipotence and omniscience, cannot be used as 100% proof of the latter's non-existence
    I disagree that logic disagrees with the concept of God, omnipotence and omniscience. If one first claims that we know these things exist, logic says that we don't currently have the knowledge to understand it, not that it doesn't exist. If one first claims that we know these things do not exist, logic then has a similar response.
    There are as it seems four answers that logic tells us.
    1) Statement is true
    2) Statement is false
    3) We don't understand statement because it doesn't make any sense, or has no real meaning.
    4) We don't understand statement as it deals in thing we are lacking information on.
    To serve man.

  12. #12
    ODN Community Regular

    Join Date
    May 2005
    Posts
    4,896
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Xanadu Moo
    We sure needed this post a few weeks ago when the infallible crowd was ranting on.
    Actually, that was when I started thinking about logic in depth... before that I was guilty of thinking that logic was an infallible, independent "discovered" entity too. Shows how we tend to take logic for granted rather than really think carefully through our assumptions when using it.

    In a certain sense, logic is the "uncaused cause" of the skeptical world.

    Quote Originally Posted by Castle
    Let's break this one down: Heterologic is not not descriptive of itself. Heterological is descriptive of itself.For heterological to be descriptive of itself, then it would have to be not descriptive of itself. So we also have, by substituting the definition of heterological (again): heterological is not descriptive of itself. So heterological is both descriptive of itself and not descriptive of itself. This a logical contradiction. The word "heterological", as presented, doesn't work. This "paradox" is exactly like saying "A both exists and doesn't exist". Does A exist? It's silly, because heterological has contradictory properties.
    Nice attempt at defending logic, but actually, the bolded parts represent where you tried to use logic (law of noncontradiction, law of the excluded middle) to "solve" the paradox, and the resulting contradiction was actually the consequence of attempting to use logic to solve the paradox.

    So in fact, your argument actually proves my assertion that logic, when applied to paradoxes, produces contradictory results. The reason for this is because our language is such that words and sentences possess different layers of meanings, and logic tends to get tripped up by these complications. The same holds true for the first paradox of the false statement.

    Hence, we can conclude that not only is logic limited by language, but since it is expressed using language, logic cannot be said to be infallible unless the medium used to express it is infallible.

    Quote Originally Posted by Castle
    None; it never gets there.
    If I substituted point A for my school, point B for my house and P for myself, does that mean that I have never reached home?

    Your answer is absurd because you tried to apply logic to solve the problem. As I've said, this paradox trips logic up because it remains out of the sphere of (current) human understanding. I expect that when we learn more about infinites, we will revise our understanding of logic accordingly.

    Quote Originally Posted by PerV
    You are full of brownstuff!


    Quote Originally Posted by Dr. Gonzo
    My only question is:

    How did you manage to prove that logic is limited by language? Did you use logic to do so?
    In a way, yes.

    If logic is not limited by language, then it will be able to coherently interpret any linguistical expression which follows correct linguistic rules.
    Logic cannot coherently interpret any linguistical expression which follows correct linguistic rules.
    Therefore, logic is limited by language.

    I can also go about proving it in another way (though this was not the argument I used in the op):

    If logic is not limited by language, then it can survive independently of language.
    Logic cannot survive indepently of language.
    Hence logic is limited by language.

    However, note that I never argued that logic is wrong in every circumstance. I merely claimed that sometimes, due to limitations in language, logic can fail. Hence, in circumstances where language is not a barrier to effective logical application, logic is useful.

    I'll reply to MT's arguments in a while.

    The below text has been automerged with this post.

    Quote Originally Posted by MindTrap028
    Puts on Devils advocate hat.

    The one thing I found missing from your OP is a definition of what Logic "is". As I understand it "Logic" is nothing more than ordered thought.
    I didn't define logic because I didn't know how to. There are too many different definitions and systems of logic to properly define what logic is. Defining it as "ordered thought" runs the risk of being too vague, as many kinds of thought can be called "ordered thought" without being commonly-perceived as "logic".

    If I had to define it, I would say that logic is a pre-defined system of reasoning.

    Quote Originally Posted by MindTrap028
    Is Logic limited by language?
    If logic is ordered thought, then language is supposed to be a reflection of that thought. For what word ever proceded from a mouth, without first being conceived by a thought? So it seems to me that logic it's self is not limited by language, but language is limited in it's ability to convey logic.
    Since logic and language are inextricably intertwined, I would say that limitations in language would effectively translate into limitations in logic.

    Thinking about it, even when logic is not verbally expressed, when you conduct "ordered thinking", you are still using language to talk to yourself in your head. Hence logic cannot exist independently of language.

    Quote Originally Posted by MindTrap028
    So what does logic tell us of the statement
    "This statement is false."
    It tells us this a meaningless statement. It is the language equivalent to 1-1 it = 0.
    Actually, what you have just done is to consign the statement to the realm of the "meaningless" or "illogical", which, as I have said in my op, is a tautological argument.

    Of course, since humans have no other means to assess the meaning of something other than through the use of logic, we are unable to conclude whether or not this statement actually has meaning. All we know is that when seen through logical lens, it is meaningless. But then what justification do we have for logic being the be-all and end-all means of determining truth?

    Quote Originally Posted by MindTrap028
    Is Logic limited by the Human framework of understanding.
    If it is possible to know all things, then logic is not limited. If it is not possible to know all things, then logic can be limited.
    Our ability to us logic may be said to be limited.The Vehicle of thought, that is logic, can not be said to be lacking because we are ignorant.
    It would be like saying, I can not throw a ball more than 40 yards. A ball is therefore limited to being thrown 40 yards.

    So when it is said, ' Logic is limited by the human framework of understanding' you deny that logic is used to stretch the framework of our understanding.
    If Logic enlarges our framework of understanding, in what way can we say logic it's self is limited by that understanding?
    Hmm, you have a point there. Maybe I should have said, "The application of logic is limited to the human framework of understanding". Though the meanings of both versions don't seem too different after all.

    Quote Originally Posted by MindTrap028
    Is it safe to say that nothing has ever been verified as "False" without using logic? What is one thing that has been "verified" "true" without the use of logic?
    Well, this really depends on your definition of logic, but I would say many, many things, MT. For example, it is true that I am typing out this argument. It is true that I am pressing buttons on the keyboard. Did I use logic to come to that conclusion? No, I used observation and language to come to that conclusion.

    The same would apply to every single event or phenomenon which we perceive as "true" due mainly to empirical evidence (observation).

    Quote Originally Posted by MindTrap028
    It seems to me that when you argue against logic, you are arguing against thought it's self.
    Look at it like this, if Logic is ordered thought. then it should be able to render a conclusion on anything the mind can conceive. So when one says that something is "Knowable" it must fall into the realm of Logic. If something is unknowable then we would not be aware of it to discuss it, so it really becomes a None issue.
    Logic can be said to be ordered thought, but I would dispute calling it "thought" itself. Many of our thoughts can be illogical. When I am day-dreaming about sex, am I in conducting a process of ratiocination? I doubt so.

    As explained above, we can know many things through observation without having to use logic (at least, not my definition of logic).

    Quote Originally Posted by MindTrap028
    When you say something is "illogical". isn't that the same as saying something doesn't make sense, or maybe that it has no real meaning. If then something is determined to have no meaning then hasn't "logic" done it's work, and rendered an accurate reflection of reality?
    Yes, perhaps you could say that by telling us something is "illogical", logic has performed its task. But the hitch comes when we translate this "illogical" into "false" or "meaningless" or "non-existent". When something is illogical, it only means that logic was incapable of deriving meaning from it. But that does not mean that it really does not have any meaning, or has false meaning.

    Quote Originally Posted by MindTrap028
    Our language does not limit logic, but is only a limit in our use of logic.
    Our current knowledge is limited, and often times flawed, however it is through logic that our knowledge is increased, and corrected, or even known to be flawed.
    Yes, I totally agree, I have never disputed the usefulness of logic. What I am disputing is the mentality that whatever disagrees with logic is definitely, objectively false.

    Quote Originally Posted by MindTrap028
    First I would argue that Language is not of Man to begin with. However, for the atheist I would say that as soon as thought existed so did logic, You can not have language without also having the possibility for ordered thought. Logic is more a recognition of order, which is reflected in all that is known. Because man did not create the first thought, man is not responsible for the existence of logic.
    When you claim that man did not create the first thought, is that from a secular viewpoint or a religious viewpoint? Because from the secular viewpoint I cannot see any truth in that statement.

    Quote Originally Posted by MindTrap028
    I disagree that logic disagrees with the concept of God, omnipotence and omniscience. If one first claims that we know these things exist, logic says that we don't currently have the knowledge to understand it, not that it doesn't exist. If one first claims that we know these things do not exist, logic then has a similar response.
    There are as it seems four answers that logic tells us.
    1) Statement is true
    2) Statement is false
    3) We don't understand statement because it doesn't make any sense, or has no real meaning.
    4) We don't understand statement as it deals in thing we are lacking information on.
    Very lucid summation. I would dispute using the term "real meaning" in 3), for just because logic cannot derive meaning from a statement, doesn't mean it has no "real" meaning. To claim that something has no "real" meaning is to claim that it is objectively meaningless, but if we acknowledge that logic is limited, then the statement could merely be subjectively meaningless, i.e. meaningless to humans who use logic to derive meaning.

    As for the rest, I actually agree with you, but for many people they only recognise 1) and 2) as being the only possible options.
    Last edited by Trendem; June 25th, 2006 at 04:36 AM. Reason: Automerged Doublepost
    Trendem

  13. #13
    ODN Community Regular

    Join Date
    Dec 2005
    Posts
    1,547
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Trendem

    In a way, yes.

    If logic is not limited by language, then it will be able to coherently interpret any linguistical expression which follows correct linguistic rules.
    Logic cannot coherently interpret any linguistical expression which follows correct linguistic rules.
    Therefore, logic is limited by language.
    No I think it is just more than language is often illogical in many places. Does the fact that some jerk writes 2+2=34 mean that math is limited by logic...or rather that that statement is simply a flawed one.

    In other words if I say that y=6 and x=2 and then I say x+y=horse, then my logic isn't faulty, but rather I have made a flaw in reasoning.
    If logic is not limited by language, then it can survive independently of language.
    Logic cannot survive indepently of language.
    Hence logic is limited by language.
    How is language limited by logic? Like is there a logical statement that you can use to determine the limits of logic, because if so then it is not limited by language.

    In other words...if you can say "when X word is used in Y way...you should be careful because there is going to be a problem", then you have essentially used logic to show that while language may appear to be the end all...you can fall back on previous logical assessments.

    However, note that I never argued that logic is wrong in every circumstance. I merely claimed that sometimes, due to limitations in language, logic can fail. Hence, in circumstances where language is not a barrier to effective logical application, logic is useful.
    I don't think that it is logic failing, but rather language failing. I really am going to need to read up on my linguistic philosophy again.
    I'll reply to MT's arguments in a while.
    "If you wish to know how libertarians regard the State and any of its acts, simply think of the State as a criminal band, and all of the libertarian attitudes will logically fall into place." -Murray Rothbard

    "There are a thousand hacking at the branches of evil to one who is striking at the root." -Henry David Thoreau

  14. #14
    ODN Community Regular

    Join Date
    May 2006
    Posts
    3,795
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Trendem
    the bolded parts represent where you tried to use logic (law of noncontradiction, law of the excluded middle) to "solve" the paradox, and the resulting contradiction was actually the consequence of attempting to use logic to solve the paradox.
    Actually, the contradiction was the result of applying logic to your original statement. If a paradox results in a contradiction, that's the paradox's fault, not logic's. It shows something was wrong with the question, not with logic.

    Quote Originally Posted by Trendem
    So in fact, your argument actually proves my assertion that logic, when applied to paradoxes, produces contradictory results.
    When applied to contradictions, logic produces contradictory results? Obviously.

    Quote Originally Posted by Trendem
    If I substituted point A for my school, point B for my house and P for myself, does that mean that I have never reached home?
    Ah, sorry, I read the question wrong. Ummm....I'll get back to you on that one (You win).

    Edit: Ah, nevermind, the wisdom of Neverending has revealed the resolution to this "paradox". You don't win

    Quote Originally Posted by Trendem
    Logic cannot survive indepently of language.
    I present to you: mathematics
    Last edited by Castle; June 25th, 2006 at 02:33 PM.
    Freedom is you choosing for yourself. Law is the government choosing for you. The two are opposites.

    Pray - To ask that the laws of the universe be annulled in behalf of a single petitioner confessedly unworthy - Ambrose Bierce
    Faith - Belief without evidence in what is told by one who speaks without knowledge about things without parallel - Ambrose Bierce

  15. #15
    Super Moderator

    Join Date
    Feb 2006
    Location
    Louisiana
    Posts
    9,145
    Post Thanks / Like

    Re: The Limitations of Logic

    Trendem apparently I must spread some rep around before I can hit you with it again.

    Quote Originally Posted by TRENDEM
    If I had to define it, I would say that logic is a pre-defined system of reasoning.
    Speaking of logic here and it's origins. First Who pre-defined this system of reasoning.
    It is either God or Reality, It is for this reason we are able to "discover" what actually works and what does not work. We do not decide what works and what doesn't.
    Quote Originally Posted by TRENDEM
    Thinking about it, even when logic is not verbally expressed, when you conduct "ordered thinking", you are still using language to talk to yourself in your head. Hence logic cannot exist independently of language.
    Language is only our ability to communicate. Because we are often able to conceive of something, but not put it into "words", thought is not limited by language. You must realize that thought is a language all it's own, to deny such is to say that those who don't know a language, do not think.

    Quote Originally Posted by TRENDEM
    Actually, what you have just done is to consign the statement to the realm of the "meaningless" or "illogical", which, as I have said in my op, is a tautological argument.
    Logic recognizes the statement, as Gibberish. Is there a reason to think that it isn't? Or you could say that logic, recognizes it as a sum of 0, which means whatever we can know of the statement, it has no effect on anything.
    Quote Originally Posted by TRENDEM
    Logic can be said to be ordered thought, but I would dispute calling it "thought" itself. Many of our thoughts can be illogical. When I am day-dreaming about sex, am I in conducting a process of ratiocination? I doubt so.
    I would rather call such thoughts, hopefull hypothetical. In which case they may be unlikely, but logical.

    Quote Originally Posted by TRENDEM
    Yes, perhaps you could say that by telling us something is "illogical", logic has performed its task. But the hitch comes when we translate this "illogical" into "false" or "meaningless" or "non-existent". When something is illogical, it only means that logic was incapable of deriving meaning from it. But that does not mean that it really does not have any meaning, or has false meaning.
    There are things which at the moment don't seem to make sense, it doesn't make it illogical in and of it's self, that is only logic telling us that we need more information, or logic telling us there is a variable we are not currently aware of. In this case logic is working to expand our knowledge.
    Is it possible there is a difference between illogical, and logically false?
    If something is logically false, then it is disproven, if however it is only illogical, it could be a case where logic is saying that we don't have enough info, or that it is just Gibberish.
    Quote Originally Posted by TRENDEM
    What I am disputing is the mentality that whatever disagrees with logic is definitely, objectively false.
    I kinda agree with that, only I think logic has more results than only true/false. It would be easier IMO to show something is not logically false, rather not totally understood, or nonsensical. Which really tends to be the claims I see, when dealing with God, and his abilities.

    Quote Originally Posted by TRENDEM
    Very lucid summation. I would dispute using the term "real meaning" in 3), for just because logic cannot derive meaning from a statement, doesn't mean it has no "real" meaning. To claim that something has no "real" meaning is to claim that it is objectively meaningless, but if we acknowledge that logic is limited, then the statement could merely be subjectively meaningless, i.e. meaningless to humans who use logic to derive meaning.

    As for the rest, I actually agree with you, but for many people they only recognize 1) and 2) as being the only possible options.
    If meaning can not be derived from a statement, through logic. Then the meaning of the statement can not be understood by man. Which could be a limit to logic, but is not proof of that, because you assume the existence of something we can not prove, nor comprehend. That would be a very weak challenge to logic.
    To serve man.

  16. #16
    ODN Community Regular

    Join Date
    Mar 2004
    Location
    Grinnell, IA
    Posts
    4,460
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Trendem
    1) Logic is limited by language
    Very true. Logic does not cope well with heterological premises that contradict their own conclusions. Such statements cannot be declared true or false. Of course, in terms of practicality, these statements have no use. They do not apply to anything outside of themselves, so they do not endanger the conclusions of logic in practical matters.
    Quote Originally Posted by Trendem
    Example 1:
    Suppose a point P is moving between points A and B (just like in the original Racetrack). And suppose also that we stipulate that P is in the state "even" for the first half of the journey, "odd" for the next 1/4, "even" for the next 1/8, and so on. That is, we simply decide to classify P based on where along the journey it is, such that it alternates between what we call an "even" and an "odd" state. We can in addition stipulate that once it is in one state it remains in that state unless it gets switched according to the above rule.
    Here is a paradox which arises when we attempt to use logic to deal with the concept of infinities. The question is: In what state is P at point B?

    Critics of this paradox normally claim that it is physically impossible to divide distance into infinitely small units. While this may be true, that only demonstrates that logic cannot cope with matters out of our physical realm of understanding.
    The problem with this paradox is that "infinity" by nature, isn't finite a number. The rule put in place by your example can be portrayed as P is even when given distance d from the finishline, where d = 1-1/2^(n+1), when n is even and odd when n is odd. The problem comes because close to B, n approaches infinite size. Since being "even" and "odd" is a property of finite numbers and no finite number exists such that d = 0 = 1-1/2^(n+1), the problem simply comes in that some concepts are incompatable with each other.
    Quote Originally Posted by Trendem
    Example 2:
    1. All justifications in pursuit of certain knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore there can be no end. We are faced with the hopeless situation of 'infinite regression'.
    2. One can stop at self-evidence or common sense or fundamental principles or speaking 'ex cathedra' or at any other evidence, but in doing so the intention to install certain justification is abandoned.
    3. The third horn of the trilemma is the application of a circular and therefore invalid argument.
    This is not a paradox. It is the Munchhausen Trilemma, which argues that all techniques to used to verify truth are fallible as they ultimately cannot justify themselves.
    Indeed, truths are not fully verifiable, since we must rely on at least some a priori assumptions for logic to work.
    Quote Originally Posted by Trendem
    This then leads to the obvious question: We can say that whatever logic disagrees with is illogical, but can we say that anything logic doesn't agree with, is false? Could it be that logic is just incapable of dealing with that particular phenomena or concept?
    Logic is dependent upon premises. If all the premises given are true, a conclusion derived using proper logic from these premises will be true. In your first example, the statement was self-descriptive and was thus an exception to the rules of logic, specifically the law of the unexcluded middle. However, this one exception comes in an area that doesn't relate to anything outside itself and is thus, for the most part, useless.
    Quote Originally Posted by Trendem
    1) Logic is useful in explaining our world and verifying facts within our realm of understanding. However, it is by no means infallible, as it is predicated heavily upon our imperfect language and our often flawed and imcomplete understanding of the world.
    True. Problems in language and false premises can lead to confusing and/or false conclusions.
    Quote Originally Posted by Trendem
    2) Since logic is based heavily on human language and understanding, and in fact, is a component of human understanding, it is a human construct rather than a human discovery. A concept cannot exist independently without a conceiver, and logic, as well, is a concept which does not exist on its own. It is a system of reasoning created by humans to understand our world.
    I don't think that's true. Humans use logic and portray it to others based upon human language, but logic itself is not based upon human language. Remember, language is a mechanism for portraying concepts from one human to another. Logic itself is a process which weighs concepts. It is possible for a human to make a logical mistake by misusing language and being inconsistant with the concepts it represents, but logic itself is not based on human language. That said, you are right that logic requires one who is able to process information...an intelligent entity. However, we are probably not the only animals on this planet capable of at least basic logic and there may be more intelligent entities on other planets or on the ethereal plane (if it exists).
    Quote Originally Posted by Trendem
    3) Since logic is only capable of verifying facts within our realm of understanding, the fact that it disagrees with certain concepts that transcend human understanding such as God, omnipotence and omniscience, cannot be used as 100% proof of the latter's non-existence.
    No, but if logic finds God to be self-contradictory based upon actual concepts, it is pretty damning evidence. True, it is possible that you were delusional or made a logical error, but if a hypothetical God's properties are indeed self-contradictory, then it is good evidence that either God does not exist or you misinterpretted his characteristics.

    In the case of omnipotence and omniscience, we are presented with an interesting situation. Omniscience most literally means that God knows all things about the universe and about himself, which is an interesting situation because such a situation is impossible in a materialist universe. When it is put in conjuction with omnipotentence...the ability to do anything, we see an apparent contradiction. God knows what he will do and thus, he is forced to do that or else his knowledge will be wrong. This apparent contradiction arises from a misapplication of the terms. I have the ability to kill my family, but it would be completely out of character. So, what is the root of our problem?

    The root of our problem is that we had at least one false premise. The word "ability" is a human construct for a concept that best applies when there is limited knowledge. If we assume that the universe is determinisitic, then we know that things will go a certain way. However, to a limited observer, there is still a potential for me to kill my family. That is because the idea of potential is based upon lack of knowledge, which allows mulitple courses of action to appear to be possible. From the omniscient viewpoint, that is not the case. So, I think that the meaning behind omnipotent originally used was incorrect. What really should be said instead is that God will do anything he wants to do. Once that is set up, there is no logical contradiction. Of course, the concept of God I ended with is different from the one I started with, because one concept is impossible while the other one is possible.
    孟柏民
    Formerly Neverending (for all you old-timers)

  17. #17
    ODN Community Regular

    Join Date
    Sep 2004
    Location
    Palace of Kubla Khan and bovine worshippers
    Posts
    3,011
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by MindTrap
    There are things which at the moment don't seem to make sense, it doesn't make it illogical in and of it's self, that is only logic telling us that we need more information, or logic telling us there is a variable we are not currently aware of. In this case logic is working to expand our knowledge.
    MindTrap, isn't that a tautology? It smacks of a continual re-definining of what logic is. Also, if we don't know all of what logic is, then how could we possibly verify its validity? That's like my saying "I'm thinking of the set of all numbers you have ever spoken." Then, when you say "14?" I say, "Yes, that is also one of them." And then you say "337?" I say, "Yes, that one is included too." (Notice that you can never be wrong) And then I ask "Do you know any numbers from the set that you have never spoken?" and you say "8,206?" And then I say, "No, that one does not qualify for the set you have never spoken. Try again." (Notice that you can never be right) In other words, that one is incorrect, so it's illogical.

    I would submit that logic is an application of thought, rather than an entity unto itself. Much like love is an application and not a thing. The concept of love needs living beings to have affection for other living beings in order to exist -- but even then it still only exists in the abstract. There is no such "thing" as love. It is an application of thought.

    If logic exists apart from human (or other intelligent) understanding, then what are its manifestations apart from what humans have applied to it? We have no examples. Therefore, it becomes a exercise in pure conjecture to assert that there's some objective logic which exists apart from the human (or related) mind.

    Essentially, what is being said here is:

    Logic = whatever is correct
    Absence of logic = whatever is incorrect

    That is way too loose of a definition for logic. How could one ever go wrong with such a presumptuous definition as that?
    anything could be an illusion and we wouldn't know the difference... proof schmoof...

  18. #18
    Owner / Senior Admin

    Join Date
    Nov 2003
    Location
    San Diego, CA
    Posts
    19,394
    Post Thanks / Like

    Re: The Limitations of Logic

    First of all, good post Trend. Should be a fun discussion.

    However, some issues with your conclusions, I don't see how you could have reached them given the propositional arguments beforehand...that is, I see no link...

    Quote Originally Posted by Trendem
    Conclusions:
    1) Logic is useful in explaining our world and verifying facts within our realm of understanding. However, it is by no means infallible, as it is predicated heavily upon our imperfect language and our often flawed and imcomplete understanding of the world.
    How is it predicated heavily upon our imperfect language? I don't see where this has been demonstrated in the op. Is this just an assumption that we are to make?

    Logic has never been claimed here that it can address all things. It doesn't, and I think that those of us who side with logic being discovered, have made it a point to clarify this issue. Logic is merely correct reasoning, it's ordered reasoning, that's all.

    When we use logic to explain and verify our world, all we are doing is using correct thought, correct reasoning, ordered reasoning to do so. Logic itself doesn't explain it, logic is a tool that we use TO explain it.

    Using impractical paradoxes to support the claim that logic is flawed, fails for the simple reason that as you said, it's used to explain the real world, not "all things". Where in the real world, does the paradox exist?

    It's fun to try to poke holes in logic, but the foundation in which the poker works from, is grounded in logic...else...he couldn't begin the poking.

    2) Since logic is based heavily on human language and understanding, and in fact, is a component of human understanding, it is a human construct rather than a human discovery.
    Where in the op is it demonstrated that logic is based heavily on human language and understanding?

    How is it a "component" of human understanding?

    How do either, result in the conclusion that it is a human construct? This seems like a false cause here Trend, there is no connection between the proposition and conclusion.

    A concept cannot exist independently without a conceiver, and logic, as well, is a concept which does not exist on its own. It is a system of reasoning created by humans to understand our world.
    I agree that a concept cannot exist independently w/o a conceiver. However, from a theistic point of view, "we are not alone". Humans can be wiped out right here and now, and logic as the concept, would still exist for God would still be here. Logic isn't dependent upon the HUMAN mind. Logic is a tool discovered and used by the human mind. It has long been in existence before any creation of man.

    3) Since logic is only capable of verifying facts within our realm of understanding, the fact that it disagrees with certain concepts that transcend human understanding such as God, omnipotence and omniscience, cannot be used as 100% proof of the latter's non-existence.
    I don't think this statement makes sense. "Latter" refers to "omniscience".

    Also, you claim that logic disagrees with certain concepts that we don't fully understand. How so?

    You cursory examination of logic just doesn't support the conclusions made Trend. You'll have to draw the connections.

    The below text has been automerged with this post.

    Quick summary:

    You have argued that logic is limited...which is what every logician, philosopher, theist, etc... believe as well...nothing new there.

    But somehow, have made the conclusion that because it is limited, it must be man made and not man disovered. There is no argumentation that supports the latter, only the former...which is already agreed upon by everyone.
    Last edited by Apokalupsis; June 26th, 2006 at 01:07 PM. Reason: Automerged Doublepost
    -=]Apokalupsis[=-
    Senior Administrator
    -------------------------

    I never considered a difference of opinion in politics, in religion, in philosophy, as cause for withdrawing from a friend. - Thomas Jefferson




  19. #19
    Super Moderator

    Join Date
    Feb 2006
    Location
    Louisiana
    Posts
    9,145
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by XM
    MindTrap, isn't that a tautology? It smacks of a continual re-definining of what logic is. Also, if we don't know all of what logic is, then how could we possibly verify its validity? That's like my saying "I'm thinking of the set of all numbers you have ever spoken." Then, when you say "14?" I say, "Yes, that is also one of them." And then you say "337?" I say, "Yes, that one is included too." (Notice that you can never be wrong) And then I ask "Do you know any numbers from the set that you have never spoken?" and you say "8,206?" And then I say, "No, that one does not qualify for the set you have never spoken. Try again." (Notice that you can never be right) In other words, that one is incorrect, so it's illogical.
    Logic is ordered thought. What is unknown about logic? Process?


    Quote Originally Posted by XM
    I would submit that logic is an application of thought, rather than an entity unto itself. Much like love is an application and not a thing. The concept of love needs living beings to have affection for other living beings in order to exist -- but even then it still only exists in the abstract. There is no such "thing" as love. It is an application of thought.
    If logic is only ordered thought, then I would have to agree with you, logic is only applied thought.

    Quote Originally Posted by XM
    If logic exists apart from human (or other intelligent) understanding, then what are its manifestations apart from what humans have applied to it? We have no examples. Therefore, it becomes a exercise in pure conjecture to assert that there's some objective logic which exists apart from the human (or related) mind.
    Is cause & effect part of logic? Does that part of logic exist without the existence of humans?
    Do things occur in order? Which is what ordered thought is supposed to reflect.
    To serve man.

  20. #20
    ODN Community Regular

    Join Date
    May 2005
    Posts
    4,896
    Post Thanks / Like

    Re: The Limitations of Logic

    Quote Originally Posted by Castle
    Actually, the contradiction was the result of applying logic to your original statement. If a paradox results in a contradiction, that's the paradox's fault, not logic's. It shows something was wrong with the question, not with logic.
    Well, isn't that exactly what I predicted in my op - you assume that whenever something disagrees with logic, that means something is wrong with it. However, other than logic, do you have anything to demonstrate that this is wrong? If not, then how are you so sure logic is correct all the time?

    Quote Originally Posted by Neverending
    The problem with this paradox is that "infinity" by nature, isn't finite a number. The rule put in place by your example can be portrayed as P is even when given distance d from the finishline, where d = 1-1/2^(n+1), when n is even and odd when n is odd. The problem comes because close to B, n approaches infinite size. Since being "even" and "odd" is a property of finite numbers and no finite number exists such that d = 0 = 1-1/2^(n+1), the problem simply comes in that some concepts are incompatable with each other.
    Good point, but that is just nit-picking IMO. What if I substituted the terms "even and "odd" with "red" and "blue"? Or even "happy" and "sad"? The paradox still exists.

    So, since logic does not agree with the concept of infinities, does that mean infinities are impossible and do not exist?

    Quote Originally Posted by Neverending
    No, but if logic finds God to be self-contradictory based upon actual concepts, it is pretty damning evidence.
    Why should the fact that something is self-contradictory mean that it doesn't exist? For example, if I say Bob is cruel yet kind, does that mean that either Bob doesn't exist or that Bob cannot be cruel and kind at the same time? Or does it just reveal a limitation in our language and understanding?

    Quote Originally Posted by Neverending
    In the case of omnipotence and omniscience, we are presented with an interesting situation. Omniscience most literally means that God knows all things about the universe and about himself, which is an interesting situation because such a situation is impossible in a materialist universe. When it is put in conjuction with omnipotentence...the ability to do anything, we see an apparent contradiction.
    Precisely, I am saying that logic cannot adequately cope with concepts out of our realm of understanding. Insisting on applying logic to these concepts which trascend human understanding may not result in correct conclusions.

    Quote Originally Posted by Apok
    However, some issues with your conclusions, I don't see how you could have reached them given the propositional arguments beforehand...that is, I see no link...
    Yeah, I admit that I was using the term "conclusions" rather loosely, in that some of my conclusions weren't directly reached using solely my prior arguments. However, my arguments do substantiate such a conclusion, and I will explain further here.

    Quote Originally Posted by Apok
    How is it predicated heavily upon our imperfect language? I don't see where this has been demonstrated in the op. Is this just an assumption that we are to make?
    Haven't I shown two examples of how logic is tied up in knots due to the linguistic property of self-reference?

    If that's not enough, let me further elaborate: Logic is predicated on language because logic deals in language. For example, take the law of excluded middle, A is B or A is not B. How can this law apply if we did not define A and B properly?

    Quote Originally Posted by Apok
    Logic is merely correct reasoning, it's ordered reasoning, that's all.
    I agree that logic is ordered reasoning, but what do you have to prove that logic is correct reasoning? Or is this just an assumption of yours?

    Quote Originally Posted by Apok
    Using impractical paradoxes to support the claim that logic is flawed, fails for the simple reason that as you said, it's used to explain the real world, not "all things". Where in the real world, does the paradox exist?
    Tell me Apok, where in the real world, does God exist? Where in the real world do infinities exist?

    Quote Originally Posted by Apok
    Where in the op is it demonstrated that logic is based heavily on human language and understanding?

    How is it a "component" of human understanding?
    Logic, as you said, is a tool we use to explain and verify our world. Hence, it is a component of our human understanding. For without logic, what can we understand?

    As for why I say logic is based upon human language and understanding, I think that is pretty obvious. For example, from a human POV it is impossible for a set of items to reach an infinite amount, because it is always possible to add one more to that set. Hence, logic can only deal with finite amounts of items (as demonstrated in my op). However, Christians claim that God's power and knowledge are infinite. So does that mean God doesn't exist, because his properties disagree with logic? Or could it just be a limit in our human understanding? Or is it just a problem in the way "infinite" has been defined?

    Another example is that of contradictions. The law of non-contradiction says that A cannot be both B and non-B. However, the only reason this law has any meaning is because of the way we have defined A and B, and the way we understand our world. We assume that an item cannot possess two contradictory characteristics in the same respect at the same time. But why do we think this way? Is non-contradiction a property of A or a property of our language? Is it possible that on another planet, there exists a language which allows an object to have contradictory properties and yet still be meaningful?

    Quote Originally Posted by Apok
    How do either, result in the conclusion that it is a human construct? This seems like a false cause here Trend, there is no connection between the proposition and conclusion.
    Is logic a material object or a concept, Apok? If it is the latter, then how can a concept exist without an conceiver? How can a material object exist without material space for it to occupy?

    And if logic cannot exist indepedently of a conceiver, then how can we say that logic was discovered? That implies that it existed before any conceiver came by to "discover" it.

    Quote Originally Posted by Apok
    However, from a theistic point of view, "we are not alone". Humans can be wiped out right here and now, and logic as the concept, would still exist for God would still be here. Logic isn't dependent upon the HUMAN mind. Logic is a tool discovered and used by the human mind. It has long been in existence before any creation of man.
    Why should God use logic? You said earlier that logic is a tool used by humans to explain and verify our world. Since God is supposedly omniscient and knows everything, why would He need logic to "explain" and "verify" anything at all?

    Touche, Apok.

    But somehow, have made the conclusion that because it is limited, it must be man made and not man disovered. There is no argumentation that supports the latter, only the former...which is already agreed upon by everyone.
    Sorry if my op was lacking in elaboration, I hope this post satisfies you.
    Last edited by Trendem; June 26th, 2006 at 11:51 PM.
    Trendem

 

 
Page 1 of 4 1 2 3 4 LastLast

Similar Threads

  1. Yes, God exists!
    By Josh.24:15 in forum Religion
    Replies: 177
    Last Post: February 25th, 2012, 03:14 PM
  2. Why I'm an Atheist
    By Castle in forum Religion
    Replies: 259
    Last Post: August 21st, 2006, 09:48 PM
  3. 7 Habits of Highly Effective Logicians
    By Xanadu Moo in forum Philosophical Debates
    Replies: 25
    Last Post: June 19th, 2006, 08:07 AM
  4. Uses and Misuse of Logic
    By disinterested in forum Philosophical Debates
    Replies: 2
    Last Post: May 15th, 2006, 10:55 PM
  5. God's Omnipotence: Limited by logic?
    By Apokalupsis in forum Religion
    Replies: 115
    Last Post: February 3rd, 2005, 10:18 AM

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •