For those who don't know what TAG is, it's the Transcendental Argument for the existence of God. I only know of it being proposed by the apologist Matt Slick on his site, CARM.org, but it might've originated elsewhere. Regardless of if he authored it or not, he definitely loves the argument and at every opportunity he will funnel a debate in that direction.
The full argument can be found here:
https://carm.org/transcendental-argument
I will encapsulate the argument as follows:
1. Logical absolutes exist. Moreover, they exist even if the universe does not.
2. Logic is conceptual by nature.
3. Concepts require thought.
4. Thought requires a mind.
5. The existence of logical absolutes requires the existence of a mind that is transcendent of the universe.
Many have come up with refutations of TAG, so I will present my own observations which, as far as I know, haven't been put forth yet. First, it is amateur. This is not a refutation, but it really needs to be known that Matt is in over his head when it comes to logic and yet he dabbles in it excessively. Would you listen to a geologist who doesn't know about tectonic plates? Second, the premises are false. Third, granting the argument necessarily revokes God's omniscience.
1. The argument is amateur.
The argument cites three logical laws: the law of non-contradiction, the law of excluded middle, and the law of identity. This is a redundancy. The law of non-contradiction and the law of excluded middle are actually the same thing, and they follow from one another. If we take "~" to be "not", "v" to be "or", and "·" to be "and" we will see it more clearly below. Keep in mind that "~v" = "·" and "~·" = "v".
The law of excluded middle looks like this:
X or not X
Xv~X
The law of non-contradiction looks like this:
not (X and not X)
~(X·~X)
Notice what happens when we take the law of non-contradiction and distribute the "not" operator that is on the outside:
We get not X not and not not X, which collapses to not X or X, which is the same thing as X or not X. In other words, we get ~X~·~~X, which is ~XvX, which is Xv~X, which is the law of excluded middle.
So we see that you don't need to cite them both as laws. It's sort of like saying "Thou shalt not commit adultery; also, thou shalt not have sexual relations outside of thy marriage." Only someone who doesn't know what they're talking about would assert the law of excluded middle after already asserting the law of non-contradiction. The whole point of logic is to limit the assumptions and use them to derive other things. If you can derive something, yet assert it instead, then you are literally discarding the one and only use of logic.
2. False premises.
The very claim that logical absolutes exist, or that logic is absolute, could and should be categorized under the "amateur" umbrella. The reason I don't include it there is because I'm leaving the "amateur" category for things which are technically correct but yet show ignorance of the topic, whereas this "false premises" category is for all things false (amateur or otherwise).
His claim about logical absolutes is absolutely incorrect. Humans invented logic. It is not true in any absolute sense. Let me make this perfectly clear:
Logic and mathematics are nothing but assumptions, definitions, and the conclusions that follow. No absolute truth about reality can be proven from assumptions and definitions. Principles of mathematics can be applied in reality because our initial assumptions are designed to describe reality at the human scope.
If you disagree, let me ask you this: Can parallel lines cross? No? Then you are dismissing non-Euclidean geometry, so we cannot do geometry on a sphere. Yes? Then you are dismissing Euclidean geometry, so we cannot do geometry on a plane. The correct approach is to be noncommittal to axioms. We hold them to be tentatively true. Logic only gives us "If ..., then ..." statements, and it is absurd to assert the "if" as absolute.
Perhaps there's a third option: some axioms are made up (such as an axiom about parallel lines), but other axioms are absolute. This is still going to be wrong, but it would be an interesting course of discussion. If this characterizes your views on logic, please list the set of axioms which you find to be absolute and which axioms are assumptions of necessity. Be advised that if you use nothing but Matt'sthree two axioms, you cannot really prove much of anything at all. You can't even prove 2+2=4 with those two axioms or even discuss what 2 is. You will at the very least be conceding that mathematics is made up to suit our observations of reality at the human scope. You need many more starting assumptions to generate mathematics. Which of those assumptions are absolutely true and which are tentative assumptions?
It's also worth noting that quantum superposition violates the law of excluded middle, since an electron is in multiple locations at the same time. If we were to take an arbitrary coordinate in space, it should be the case (given the assumption that Matt's laws of logic are absolute) that a given electron either is there or is not there for a given snapshot of time. We can call this proposition "X or not X", which of course is the law of excluded middle. The double slit experiment has shown with no room for doubt that an electron is at multiple locations at the same time in every literal, physical sense that you could derive from this. The law of excluded middle is violated in our own universe, and the law of excluded middle was shown to be equivalent to the law of non-contradiction. So how is the law of non-contradiction true in all possible realities if it is not even true in this one?
This is why I say that the laws of mathematics, as we've designed them, are true at the human scope. If we lived on the quantum scope of reality, or if somehow we experienced reality the same way an electron does, we would've drawn logic up differently and anyone concocting the law of non-contradiction would be patently insane.
3. Granting the argument revokes God's omniscience.
This topic came about over my discourse with the user @Oncedeceived in another thread. She has heard of TAG and thinks it's a good argument, so clearly the argument needs to be outed as invalid and false.
If logic is "that which is consistent with God's nature" or whatever Matt says (he certainly credits God as being responsible for logic), then why is logic "incomplete"? Here's my digestible version of Gödel's Incompleteness Theorem:
Saying that God cannot violate logic because he cannot violate his own nature necessarily means that he is not omniscient because in order to know everything he must be able to violate logic.
QED
The full argument can be found here:
https://carm.org/transcendental-argument
I will encapsulate the argument as follows:
1. Logical absolutes exist. Moreover, they exist even if the universe does not.
2. Logic is conceptual by nature.
3. Concepts require thought.
4. Thought requires a mind.
5. The existence of logical absolutes requires the existence of a mind that is transcendent of the universe.
Many have come up with refutations of TAG, so I will present my own observations which, as far as I know, haven't been put forth yet. First, it is amateur. This is not a refutation, but it really needs to be known that Matt is in over his head when it comes to logic and yet he dabbles in it excessively. Would you listen to a geologist who doesn't know about tectonic plates? Second, the premises are false. Third, granting the argument necessarily revokes God's omniscience.
1. The argument is amateur.
The argument cites three logical laws: the law of non-contradiction, the law of excluded middle, and the law of identity. This is a redundancy. The law of non-contradiction and the law of excluded middle are actually the same thing, and they follow from one another. If we take "~" to be "not", "v" to be "or", and "·" to be "and" we will see it more clearly below. Keep in mind that "~v" = "·" and "~·" = "v".
The law of excluded middle looks like this:
X or not X
Xv~X
The law of non-contradiction looks like this:
not (X and not X)
~(X·~X)
Notice what happens when we take the law of non-contradiction and distribute the "not" operator that is on the outside:
We get not X not and not not X, which collapses to not X or X, which is the same thing as X or not X. In other words, we get ~X~·~~X, which is ~XvX, which is Xv~X, which is the law of excluded middle.
So we see that you don't need to cite them both as laws. It's sort of like saying "Thou shalt not commit adultery; also, thou shalt not have sexual relations outside of thy marriage." Only someone who doesn't know what they're talking about would assert the law of excluded middle after already asserting the law of non-contradiction. The whole point of logic is to limit the assumptions and use them to derive other things. If you can derive something, yet assert it instead, then you are literally discarding the one and only use of logic.
2. False premises.
The very claim that logical absolutes exist, or that logic is absolute, could and should be categorized under the "amateur" umbrella. The reason I don't include it there is because I'm leaving the "amateur" category for things which are technically correct but yet show ignorance of the topic, whereas this "false premises" category is for all things false (amateur or otherwise).
His claim about logical absolutes is absolutely incorrect. Humans invented logic. It is not true in any absolute sense. Let me make this perfectly clear:
Logic and mathematics are nothing but assumptions, definitions, and the conclusions that follow. No absolute truth about reality can be proven from assumptions and definitions. Principles of mathematics can be applied in reality because our initial assumptions are designed to describe reality at the human scope.
If you disagree, let me ask you this: Can parallel lines cross? No? Then you are dismissing non-Euclidean geometry, so we cannot do geometry on a sphere. Yes? Then you are dismissing Euclidean geometry, so we cannot do geometry on a plane. The correct approach is to be noncommittal to axioms. We hold them to be tentatively true. Logic only gives us "If ..., then ..." statements, and it is absurd to assert the "if" as absolute.
Perhaps there's a third option: some axioms are made up (such as an axiom about parallel lines), but other axioms are absolute. This is still going to be wrong, but it would be an interesting course of discussion. If this characterizes your views on logic, please list the set of axioms which you find to be absolute and which axioms are assumptions of necessity. Be advised that if you use nothing but Matt's
It's also worth noting that quantum superposition violates the law of excluded middle, since an electron is in multiple locations at the same time. If we were to take an arbitrary coordinate in space, it should be the case (given the assumption that Matt's laws of logic are absolute) that a given electron either is there or is not there for a given snapshot of time. We can call this proposition "X or not X", which of course is the law of excluded middle. The double slit experiment has shown with no room for doubt that an electron is at multiple locations at the same time in every literal, physical sense that you could derive from this. The law of excluded middle is violated in our own universe, and the law of excluded middle was shown to be equivalent to the law of non-contradiction. So how is the law of non-contradiction true in all possible realities if it is not even true in this one?
This is why I say that the laws of mathematics, as we've designed them, are true at the human scope. If we lived on the quantum scope of reality, or if somehow we experienced reality the same way an electron does, we would've drawn logic up differently and anyone concocting the law of non-contradiction would be patently insane.
3. Granting the argument revokes God's omniscience.
This topic came about over my discourse with the user @Oncedeceived in another thread. She has heard of TAG and thinks it's a good argument, so clearly the argument needs to be outed as invalid and false.
If logic is "that which is consistent with God's nature" or whatever Matt says (he certainly credits God as being responsible for logic), then why is logic "incomplete"? Here's my digestible version of Gödel's Incompleteness Theorem:
Saying that God cannot violate logic because he cannot violate his own nature necessarily means that he is not omniscient because in order to know everything he must be able to violate logic.
QED
