Monday, April 1, 2019

Responding to Ron Garret’s Challenges to My Basic Axioms

In response to my first entry in this open conversation, Ron Garrett offered many kind words, along with his respectful criticism concerning my representation of the basic axioms which I believe comprise the pre-requisites for the intelligibility of the universe.  On this point, I do believe we have sufficient common ground to understand one another.

In my original post, I stated three basic axioms which need to be accepted in order for us to have confidence in our ability to know things.  For clarification, those three points are (1) the laws of logic are true, (2) our minds and senses are generally reliable, and (3) the laws of nature are uniform.  I said I believed we were agreed on all of these points but one.  I knew that Ron disagreed with me concerning the axiomatic status of uniformity, but the way I made that statement caused some confusion.  First, Ron actually has material reservations concerning more than just the uniformity of nature.  I did not intend to misrepresent Ron: we had not discussed the laws of logic in any detail as of yet, and only briefly touched on some common ground related specifically to the law of non-contradiction.  Secondly, since I listed the laws of logic as subpoints of my point #1 shortly after my statement that “Ron and I  are agreed on all but one of these preconditions…”, it seemed like I was saying that Ron disagreed with one of the laws of logic, rather than one of the more general preconditions for intelligibility.

To clarify, Ron and I have previously discussed uniformity in nature.  While we both accept that uniformity is true, I believe uniformity is properly held as an axiom, upon which the practice of science depends, while Ron believes that uniformity is a conclusion of science, which depends only on the assumption that “experiment is the ultimate arbiter of truth.”

In point of fact, Ron expresses certain reservations regarding the laws of logic in his response to my first post.  However, his objections appear to concern the application of the laws, rather than the laws themselves.

The first law of logic, which Ron criticizes, is the law of identity, which states that something is what it is, and whatever exists must have a specific nature.  Ron’s objection is in the difficulty of properly and consistently defining the identity of anything.  He proposes composition and arrangement as a common sense way of identifying things.  By this scheme of identification, “my lamp” is identified by its present arrangement of these particular parts, right down to the molecules, atoms, and sub-atomic “particles”.  And then he points out that the particles of every material thing are constantly changing places, and thus “my lamp” today is really a totally different lamp than “my lamp” yesterday.  Thus arises the problem of “continuity of identity”.

My response to this is simply that composition is a poor way to “identify” things.  At one point in our prolonged discussion, I made passing mention to “teleologically discreet bodies”.  I originally formulated this phrase in response to the problem of continuity of identity, as it was presented in Dr. William Lane Craig’s “Time and the Metaphysics of Relativity”.  The phrase refers to the identification of things by their purpose.  Thus, “my lamp” is the thing which I can use to control the lighting in my room.  “My lamp” is thus defined by its purpose, which remains constant throughout its existence.  Even when “my lamp” breaks and no longer gives light, its identity remains intact.  Just because something has been ruined for its original purpose, does not change the fact that its purpose is what it is.

Now, the use of teleology to identify things may create problems that I am not aware of.  It is open to criticism.  However, this shows how the law of identity is not suspended when we fail to be consistent in the way we identify things.  When we are inconsistent, the problem lies in our use of language, not in the law of logic.

On a more fundamental level, Ron’s affirmation of the problem of continuity of identity actually reveals Ron’s basic acceptance of the law of identity itself: for to say that a change in composition must change the identity of a thing, is to say that the thing really did have a specific identity, and that is what has changed.  It was comprised of this set of particles (each of which, we should note, are assumed to be themselves and not the others), and now is comprised of that set of particles – but we can only suppose that those particles are not these particles if each particle is itself and not the other.  It was what it was, and now it is what it is.  Let’s not over-complicate that.

Ron’s objection to my formulation of the law of non-contradiction may be related to his objection to the law of identity.  There are, in fact, other ways express this law.  One could say that “two mutually exclusive statements cannot both be true, in the same way and at the same time.”  This removes any problems associated with a thing having its distinct identity.  At any rate, Ron accepts non-contradiction in some form or another, which is good enough for me.

The third law of logic is the law of excluded middle, and states that a statement is either true or false, with no third option.  Ron appeals to subjectivity (statements of opinion) and tense as cases which contradict the law of excluded middle.  These objections, again, simply entail a burden on our use of language, rather than being problems with the law itself.

The burden entails a responsibility to use words in a way that they have meaning.  President Donald Trump either is, or he is not, a scoundrel.  One or the other must be true, if anything particular is meant by the word “scoundrel”.  If Ron is using the word to mean nothing in particular, then that is Ron’s failure, and not the failure of the law of excluded middle.

Subjectivity does not violate the law of excluded middle, because to the extent any statement is subjective, then the truth or falsehood of the statement must be taken to be relative to the speaker’s subjective experience.

The same can be said of tense.  A statement which is true at one time and false at another time does not violate the law of excluded middle.  The truth or falsehood of a statement is judged relative to the intended temporal framework within which the statement was made.

Can misunderstandings arise on these terms?  Sure.  That is all part of the fun of language.  Effort is often required to ensure that all mean the same thing, even when all are using the same words.

In the conclusion of my original post, I summed up the importance of these basic axioms as “We can know things.”  Despite Ron’s criticism of the way that I formulate basic axioms, we seem to be in agreement on this important point.  Such seems to the virtue of what Ron dubs as “Ron’s Law of Reality”, or RLR:

“The most reliable information you can possibly have about reality is your own subjective experiences.”

Frankly, I agree with Ron’s assertion that this is indeed self-evident.  As he makes clear, this statement is reducible to a tautology.  And, as C.S. Lewis once said in Miracles, calling something a tautology is “another way of saying that they are completely and certainly known.”

Now, RLR is very similar to what I said in my original post, that our minds and senses are generally reliable.  The difference may be purely semantic, but it is still notable.  Subjective experience may be, according to RLR, the “most reliable information you can possibly have”, but that falls short of saying that it is actually reliable.  If we are to have any confidence in our ability to know things, we must be willing to take that affirmative position, “Yes, our minds and senses are reliable.”

Hopefully, this clears up some of the confusion between us.  At the end of this point, I believe we are still standing on common ground.  It may seem insignificant, but in today’s contentious and adversarial culture, there is something very important about recognizing common ground wherever we find it.  In the case of Ron and I, we have found a good deal of common ground at a much higher level.  And yet, if the only thing we can agree on is the fact that “we can know things”, even that is worth celebrating.

20 comments:

  1. > Ron expresses certain reservations regarding the laws of logic in his response to my first post

    No, I'm expressing reservations about your formulations of the "laws of logic". I'm totally down with logic.

    > “my lamp” today is really a totally different lamp than “my lamp” yesterday

    Not "is", merely "could be".

    > ... the identification of things by their purpose. Thus, “my lamp” is the thing which I can use to control the lighting in my room.

    I don't think that's going to work. What if you sell your lamp to me? What if you throw your lamp away and replace it with a new one? What if you sell your lamp to me, but I let you keep it for a while so that now it belongs to me but it's still illuminating your room?

    > Subjectivity does not violate the law of excluded middle

    OK, here are some more examples:

    "Darth Vader is (was?) Luke Skywalker's father." (Or, along a similar vein, "Unicorns have horns.")

    "Our solar system has nine planets."

    "An electron is a particle."

    And even...

    > “We can know things.”

    Even that depends on what you mean by "know". Did Ptolemy "know" that the earth is the center of the universe? Do flat-earthers "know" that the earth is flat?

    > Subjective experience may be, according to RLR, the “most reliable information you can possibly have”, but that falls short of saying that it is actually reliable.

    Yes, exactly right.

    > If we are to have any confidence in our ability to know things, we must be willing to take that affirmative position, “Yes, our minds and senses are reliable.”

    No, I disagree with that. In fact, we know that our minds and senses are *not* reliable under many circumstances, e.g. when we are dreaming.

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    1. >No, I'm expressing reservations about your formulations of the "laws of logic". I'm totally down with logic.

      Erm, yes. My statement was poorly worded. Apologies. I did attempt to make that distinction in the opening line of the blog, "his respectful criticism concerning *my representation* of the basic axioms..."

      >I don't think that's going to work. What if you sell your lamp to me? What if you throw your lamp away and replace it with a new one? What if you sell your lamp to me, but I let you keep it for a while so that now it belongs to me but it's still illuminating your room?

      I'm not sure I see the issue here. If I sell you my lamp, it becomes your lamp. The transaction effects a real change in identity.

      Maybe I'm missing something here. Are you saying that identity is not a real thing unless that identity remains the same at all times and all places? The Law of Identity simply states that a thing is what it is; it does not imply that a thing will always be what it is now.

      >> Subjectivity does not violate the law of excluded middle

      >OK, here are some more examples:

      I'm not sure I perceive any issues with those examples. It's true that the statements you use as an example can be interpreted in ways that are true or false. But in each case, the statement is *either true or false* depending on the assumptions by which the statement is interpreted.

      It is TRUE that Darth Vader stands in the father relationship to Luke Skywalker, *within the fictional universe of Star Wars.* But it is FALSE that Darth Vader stands in the father relationship to Luke Skywalker *outside of the fictional universe of Star Wars*, because Darth Vader and Luke Skywalker only exist within that fictional universe.

      Just because the same statement can be interpreted in different ways, and that one interpretation would be true while the other is false, does not mean that a violation of the law of excluded middle has occurred.

      So again, the problem which is supposed actually relates to the use of language, and not a problem with the law of logic itself. The knowledge being communicated by a "statement" is frequently far greater than that which comes through in the words themselves. This is one of the challenges of communication: being clear about what you do mean, and complete, in order to rule out what you don't mean.

      >No, I disagree with that. In fact, we know that our minds and senses are *not* reliable under many circumstances, e.g. when we are dreaming.

      Forgive my use of overly simplistic language here. My original statement was that our minds and senses are *generally* reliable, which is sufficient for us to know things.

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  2. Jimmy, can you explain whether the statement "This statement is false", is "true" or "false"? This example doesn't seem to have any confusion about what the individual words actually refer to, there is no temporal complexity, and no subjectivity. How does this example relate to your proposed "law of excluded middle"?

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    1. Hi,

      Yes, I had fun spinning this one around in my brain :)

      It seems to me that the statement "This statement is false" is nonsensical, and therefore false. That doesn't make the statement true, because the the statement itself is still nonsense.

      I say it is nonsense because the quality of "falseness" is being applied to a statement that doesn't actually exist. In order to be false, the statement must exist.

      The statement, I say, doesn't exist because it refers to itself, thus creating an infinite regression of reference. It is more clear if you re-order the statement like so:

      "It is false to say this statement". Then, you can substitute the referent into the original, so that you get, "It is false to say 'it is false to say this statement.'" And then it goes on an on.

      "It is false to say, 'It is false to say, "It is false to say, 'It is false to say, "It is false to say..."'"'" ad infinitum.

      Now, you can still do that without re-ordering the phrase:

      "'This statement is false' is false."

      Then...

      This statement is false is false.

      Then...

      This statement is false is false is false.

      Again, ad infinitum.

      Try it in excel. In cell A1, type in "This statement is false".

      Then, in cell A2, type in the formula

      =SUBSTITUTE(A1,"This statement","This statement is false")

      Then copy that down the line. This is what I get in cell A20:

      This statement is false is false is false is false is false is false is false is false is false is false is false is false is false is false is false is false is false is false is false is false.

      Delete
    2. "It seems to me that the statement "This statement is false" is nonsensical, and therefore false. That doesn't make the statement true"

      So if I look at claim X: "Statement Y is false", and you tell me "claim X is false", that doesn't make statement Y true? Is statement Y true, or false? I thought your "law of the excluded middle" means that statement Y must be one of the two. Which is it?

      "because the the statement itself is still nonsense. I say it is nonsense because the quality of "falseness" is being applied to a statement that doesn't actually exist. In order to be false, the statement must exist."

      What does it mean for a statement to be "nonsense"? Each of the individual words has a clear, unambiguous and well-understood definition. The grammar is very simple. On what basis do you label the statement "nonsense"?

      Of course I know that it is challenging to assign "true" or "false" to the statement, and on that basis it "doesn't make sense", aka "nonsense". But isn't that the whole point we're debating? We're asking WHETHER OR NOT it is possible for there to be statements that are neither true nor false. When I give you such a candidate statement, you can't use the RESULT that it is challenging to assign true/false, as the REASON that you're going to claim it is "nonsense" or "doesn't exist".

      The whole point was that we don't agree on whether every statement can be assigned either "true" or "false". You don't get to "win" this argument by retroactively re-defining the term "statement" to only apply to things that actually can be assigned true or false. That just makes your claim an uninteresting tautology. If you want to exclude my example, you're going to have to come up with a justification OTHER than the fact that you can't reasonably assign true/false to it.

      "The statement, I say, doesn't exist because it refers to itself"

      Why does self-reference mean that a statement "doesn't exist"? What does "existence" even mean, for a statement? Surely the individual words "exist", in some sense. And the arrangement of words into a sentence "exists". What is your actual claim, that the statement "doesn't exist"? I don't know what that claim means.

      "it refers to itself, thus creating an infinite regression of reference"

      Self-reference doesn't (necessarily) imply infinite regression. For example, there is nothing particularly troubling about this (false) statement: "This sentence contains one hundred characters."

      My example, "this sentence is false", does have self-reference; but only a single level, not an infinite level. The infinite regression comes as YOU try to THINK about assigning truth values to the sentence. But the meaning of the sentence is very clear, and only has a single level of self-reference. It means much the same thing as this sentence: "This sentence is true." You don't have much problem with this new sentence, do you?

      Or maybe you do! Is the new sentence true, or false? Both assignments "work"! Perhaps the first example is "neither true nor false", while this new example is "both true and false"!

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  3. >What does it mean for a statement to be "nonsense"?

    If a statement violates the laws of logic, it is nonsense. One might say that if you really could produce a statement that was neither true nor false, then it would be in violation of the law of excluded middle, and therefore it would be nonsense.

    If that feels like begging the question, then consider this. "This statement is false" also violates the law of non-contradiction.

    "This statement" refers to the statement "This statement is false." Thus, "This statement is false" is equivalent to the statement "'This statement is false' is false". And if "'This statement is false' is false", then that would mean "This statement is true." Thus, "This statement is false" is equivalent to the statement "This statement is both true and false". This is a self-contradiction. It is nonsense. Thus, it is false, because nonsense is always false.

    >So if I look at claim X: "Statement Y is false", and you tell me "claim X is false", that doesn't make statement Y true? Is statement Y true, or false? I thought your "law of the excluded middle" means that statement Y must be one of the two. Which is it?

    This is not the same as saying "This statement is false." In the example you provided:

    Claim X = "Statement Y is false"
    Claim X = False
    Thus
    "Statement Y is false" is false.
    So Statement Y is true.
    No problem exists here. No violation of the law of excluded middle.

    But "This statement is false" is actually like this:

    Claim X = "Claim X is False"
    Claim X is flase
    Thus
    "Claim X is false" is false
    So Claim X is true.
    So Claim X is both false and true.
    This is contradictory, and therefore nonsense, and therefore false.

    >My example, "this sentence is false", does have self-reference; but only a single level, not an infinite level.

    I don't understand this. How are you limiting it to a single level? Even at one level, you get "'This statement is false' is false." But this statement also has "this statement" in it, which is defined as "This statement is false". How do you suppose the chain is broken? Why, after the first level of substitution, does "this statement" stop meaning "this statement is false"?

    People certainly can speak nonsense. But thanks to the laws of logic, at least we can spot them when they do.

    By the way, the Miriam Webster definition of nonsense is "words or language having no meaning or conveying no intelligible ideas". So even the statement "This statement is true" is nonsense, since its self reference means that it is devoid of any meaning; it conveys no intelligible ideas. Think of the conversation that would ensue:

    "Hey Don, this statement is true."

    "Wait, what statement are you referring to?"

    "The statement, 'This statement is true'."

    "So you're telling me that 'This statement is true', is true?"

    "Yeah."

    "You haven't told me anything."

    "I told you that 'This statement is true'."

    "Yes, but the statement refers to itself, so no actual statement is being made. No facts about the world, no relationships between ideas or anything. There is no substance. Nothing at all that has any meaning in and of itself. Just a self referential definition that goes round and round in a circle."

    Non = no

    Sense = meaning

    No meaning. No Sense. Nonsense. That's all this is.

    People often mistake the ineffability of nonsense for another kind of ineffability. I wonder if that is what you are doing. This is not a case of something transcending the capacity of human intelligence, or anything like that. There is no mystery of the universe here. It's just nonsense. Nothing more.

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    1. "If a statement violates the laws of logic, it is nonsense."

      I thought we had a disagreement on just what the "laws of logic" actually are. You claimed that the "law of the excluded middle" is a "law of logic". I dispute that, and I provided a counterexample (a statement which is neither true, nor false).

      You don't get to claim that my statement is "nonsense" BECAUSE it violates the "laws of logic". I dispute that it violates any laws of logic. I dispute that your "law of the excluded middle" is actually a "law of logic".

      I think you're arguing in circles.

      ""This statement is false" also violates the law of non-contradiction. ... And if "'This statement is false' is false", then that would mean "This statement is true.""

      No. You've left out the alternative that my example is neither true nor false. If you throw out your "law of the excluded middle", then you have no violation of "non-contradiction".

      "Thus, it is false, because nonsense is always false."

      No, the other alternative is that "true" and "false" don't apply to all statements. Your "law of the excluded middle" is NOT actually an axiom of logic.

      "This is not a case of something transcending the capacity of human intelligence, or anything like that. There is no mystery of the universe here."

      Yes, I agree. I was never claiming any great mystery. I was only providing a counterexample to one of your proposed "laws of logic". I don't think you got the "laws of logic" right, because one of your axioms is actually false.

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    2. >No. You've left out the alternative that my example is neither true nor false.

      But your example fails this claim. Your example claims to be both true and false. It is therefore contradictory. It is therefore nonsense. It is therefore false.

      I'm not sure how else to say that. It literally claims to be false. But the way it is formulated, it is also claiming to be true. Those claims are clearly contradictory.

      So how do you suppose that this claim is "neither true nor false"? Even you see that it claims to be false. Do you see how it also claims to be true? So where do you get this idea that it is neither true nor false? It seems like you are just making an assertion without any reasoning.

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    3. Here's another way to demonstrate that what you are saying is nonsense. Go to www.miriam-webster.com. Type in the word "false". Look at definition #3: "not true".

      So false literally just means "not true". So when you say that any statement is "neither true nor false", you make are making 2 claims: #1 the statement is not true. #2 the statement is not false. But statement #1 literally means that the statement is false: because the definition of false is "not true". If the statement is not true, then it's false. So when you say that a statement is "neither true nor false", you are actually saying that the statement is "both false and not false".

      It is contradictory. It is nonsense. It is incoherent, devoid of meaning or any intelligible idea.

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    4. Perhaps we've reached the end of this discussion. Your arguments seem to keep relying on your assumption of your "law of the excluded middle". I'm telling you that your law is not actually a law of logic. And I've given you a counterexample. But you keep dismissing my counterexample ... mostly based on this very same law that we're arguing about in the first place!

      "Your example claims to be both true and false."

      It doesn't matter what the example itself "claims". It's just a statement. Like "The sky is blue" or "Pi has a value of 4". It's a later process, to try to look at the statement an assign a truth value of "true" or "false" to each statement.

      Your "law of the excluded middle" axiom claims that EVERY statement can be assigned either "true" or "false". I've given you a statement that is a counterexample. If you assign my example "true", you run into problems; if you assign it "false", you also run into problems. Neither assignment of truth value is appropriate for my statement.

      What the statement itself "claims" isn't especially important.

      "It literally claims to be false. But the way it is formulated, it is also claiming to be true. Those claims are clearly contradictory."

      Exactly. Which is why neither "true" nor "false" is an appropriate label for my example. Which is why it is a counterexample to your claimed "law of the excluded middle".

      "So where do you get this idea that it is neither true nor false?"

      Because if you attempt to label it "true", you run into a contradiction. And if you attempt to label it "false", you also run into a contradiction. So neither of those labels can be correct.

      "Type in the word "false". Look at definition #3: "not true"."

      Dictionaries can only relate the common usage of terms among the public. They can't resolve complex questions of mathematical logic.

      "If the statement is not true, then it's false."

      No, "false" doesn't work either. Because if a statement is false, then logic requires that its opposite be true. It is certainly the case that my example is not true. But it is also not false.

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    5. >It doesn't matter what the example itself "claims".

      Sure it does. How can you assign a truth value to the statement without analyzing the claims of the statement?

      >Your arguments seem to keep relying on your assumption of your "law of the excluded middle".

      Not even a little bit. I only need the law of non-contradiction to be true, in order to show that the statement is nonsensical.

      >Because if you attempt to label it "true", you run into a contradiction. And if you attempt to label it "false", you also run into a contradiction. So neither of those labels can be correct.

      All that means is that the statement is self-contradictory. That should tell you, proof positive, that this statement is nonsense.

      The falseness of the statement does not arise from the claims of the statements themselves. The statement claims to be both true and false - not neither. The falseness comes from the fact that it is nonsense. And the opposite of nonsense is still nonsense. Nonsense cannot have an opposite because there is nothing for it to be opposed to.

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    6. >Because if a statement is false, then logic requires that its opposite be true.

      Where do you get this law of logic?

      Take this statement: "The police are aware that you frequently beat your wife." Hopefully this statement is false.

      By your own invented law of logic, the opposite of that statement must be true, so "The police are not aware that you frequently beat your wife."

      By this counterexample, we see that the opposite of a false statement is not always true. Your proposed law of logic fails.

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    7. "The police are not aware that you frequently beat your wife."

      That statement would be true (just as expected).

      You clearly have in mind an additional connotation to the statement, and the additional connotation is not true. In that case, your rewording is simply NOT the "opposite" of the original statement. If you care about the connotation, then you failed to generate the correct opposite.

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  4. >"The police are not aware that you frequently beat your wife."

    >That statement would be true

    Stay out of politics, my friend.

    The statement: "The police are not aware that you frequently beat your wife" contains the claim that "you frequently beat your wife". If that claim is not true, then the whole statement is false.

    Regardless, generating the opposite "The police are are aware that you do not frequently beat your wife" is not necessarily true either. It may be the case that the police are not aware of any of the circumstances concerning your domestic situation.

    This all just goes to show that the logical law that you made up is clearly false. These are both valid opposites to the original claim. And the falseness of the original claim does not in any way necessitate the truth of these opposites.

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    1. "Stay out of politics, my friend."

      Did I not already mention "connotation" in my reply? I already addressed this point. I obviously know what common inferences people will naturally derive from those statements. That's different than a question of logical truth.

      "The police are are aware that you do not frequently beat your wife"

      That is not the opposite of the original sentence either.

      "These are both valid opposites to the original claim."

      No, they aren't.

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    2. It's not a connotation, though. It's a claim. You can't be "aware" of a false fact. The statement "I am aware that Don is the number three", is false, regardless of my perception or belief. The supposed truth of the claim is entailed by the use of the word "aware".

      It may be true that "I perceive that Don is the number three," or that "I believe that Don is the number three." But to say that "I am aware that Don is the number three" entails a claim that Don is, in fact, the number three. Since Don is not, in fact, the number three, then it is false to say that I was "aware" of such a fact.

      But honestly, that's enough nonsense for me today. I do appreciate you bringing this riddle to my attention. I enjoyed thinking about it. However, I remain satisfied with my solution: the statement "This statement is false" is nonsensical, because it violates the law of non-contradiction, and is therefore false. It is not false simply because it claims to be false; rather, the statement is false because the claim is nonsensical.

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    3. "You can't be "aware" of a false fact."

      And now you're getting into theories of "belief" and "knowledge", which is a very complex area of philosophy. Let me just say that this new claim of yours is far from self-evident.

      "The supposed truth of the claim is entailed by the use of the word "aware"."

      Sorry, no, that is not what the word "aware" actually means. Requiring "truth" of the underlying belief is quite a heavy requirement, and much more than the common usage of the word. You've chosen a non-standard definition.

      But that's fine. Let's do it your way. (continued...)

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    4. I feel like you probably haven't studied basic logic (https://en.wikipedia.org/wiki/Boolean_algebra). So we can look at your supposed example: "The police are aware that you frequently beat your wife."

      To formalize what you mean by "aware", this is actually two claims:
      P = "you frequently beat your wife"
      Q = "The police believe P"

      Your original statement is "P and Q". You do beat your wife frequently, and also the police know this. You say the original statement is false.

      This means the negation of the original statement is true. That is: "not(P and Q)".

      Following boolean logic, this converts to "(not P) or (not Q)". If you don't know logic, it's important to note that in ordinary English, "or" sometimes means "exclusive or", i.e. either one or the other but not both. But in logic, "or" means the generic "or": either one, or the other, or possibly both.

      So since the original statement is false, the negation of the original statement is true. Namely, EITHER "you don't beat your wife", OR "you do beat your wife but the police don't know it", OR possibly "you don't beat your wife and also the police don't know that either".

      That is what your original example "means", and that is why the original statement being false means that its negation must be true. You just weren't very good at coming up with the negation, which I suspect is because you haven't actually studied logic.

      "the statement is false because the claim is nonsensical"

      No. "False", in logic, is not the same as "nonsensical". Those are different categories of things.

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    5. >I feel like you probably haven't studied basic logic

      I have, but it has been a while, and my study was mostly independent. Apparently mechanical engineers and accountants don't need to know logic...

      I think I see you point here. I think if you had said "negation" instead of "opposite" in the beginning, it might have jogged my memory.

      Memory jogged, and you are right. The proper negation of "The police are aware that you frequently beat your wife," is:

      "The police are not aware that you frequently beat your wife, *or* you do not frequently beat your wife." And such a statement can be assigned a value of true. Well and good.

      Now, taking this back to your original statement, "This statement is false."

      Remember, that since "this statement" refers to the statement "this statement is false", then really this also amounts to two claims:

      P="This statement is false"
      Q="This statement is true" (reduced from "'This statement is false' is false")
      P and Q

      Now, I still don't know why you don't see this as a clear violation of non-contradiction. P and Q cannot both be true, because they are contradictory. However, when I do as you do, I come up with the negation "(not P) or (not Q)", or...

      "This statement is true or false."

      This amounts to a restatement of the law of excluded middle. Which returns us to the question at hand. Now, since I have already accepted the law of excluded middle, I am able to coherently say that yes, it is true that "this statement is true or false." And at the very least this should show how your statement fails as a counterexample to the law of excluded middle. I still have no affirmative reason to believe that the law of excluded middle might be false. We are back at square 1: I accept the law of excluded middle as an axiom and without any indication that it might be false; while you reject the law of excluded middle because...?

      >No. "False", in logic, is not the same as "nonsensical". Those are different categories of things.

      That was not my claim. I said false, because nonsense. If the law of excluded middle is true, then nonsense is within the category of falseness. Not the same thing, just like a square and a rectangle are not the same thing. All squares are rectangles, but not all rectangles are squares. Even so, all nonsense is false, but not all falsehoods are nonsense.

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  5. P.S. If you actually want to get into theories of knowledge and belief (as well as other minds), you might want to start studying some epistemology ( https://plato.stanford.edu/entries/epistemology/ ). Philosophers have been exploring this subject for thousands of years. Saying "You can't be "aware" of a false fact." seems a bit overconfident to me. I suspect you're not familiar with the complexities of this claim you just made.

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