My Response to Someone who is Woefully Confused about Basic Logic
I recently issued a debate challenge in a creationist group to someone—let’s call him Riaan (as that is his name)—who apparently just received a ‘long-term suspension’ according to one of the admins. Riaan declined my debate challenge, but on my personal Facebook page, he wrote me the following and asked me to ‘respond to the numbered arguments or fuck off.’ While either is equally fine with me, I felt that I should at least use this person’s unbelievably poor understanding of sentential logic as a teaching moment for others, so they do not make the same basic mistakes that he has made numerous times in the creationist group.
Although I am staunchly against Young Earth Creationism, I do have many YEC friends, many of whom I respect, such as Dr. Jonathan Sarfati from creation.com. I believe that Dr. Sarfati and most other creationists would agree that logic is objective, regardless of whether someone is a believer or non-believer. If logic is indeed objective, then anyone can evaluate my arguments and Riaan’s arguments to determine for themselves who is correct in explaining basic concepts in classical logic.
Note: It seems I may have made a simple error in one of my comments where I didn’t type the correct semantic content, which I have already corrected. Riaan keeps repeating that error, even though I’ve acknowledged it and fixed it, so I will not be addressing it here. However, my correction is visible on my page for everyone to see. I made a mistake in the propositional content, but the logical equivalent I provided was correct.
Let’s examine Riaan’s ‘specific arguments’ in detail, and I invite everyone to evaluate both his arguments and mine objectively to determine who is correct. If you find any errors or conceptual misunderstandings in my reasoning, please feel free to message me about them. I will address them promptly, and if any errors do exist, I will happily correct them.
Parts from his post are italicized, my response is not.
“Steve McRae
This is the fucking last time.
I will number my specific arguments, and you will respond to the numbered arguments or fuck off.”
It seems that Riaan has been spreading misinformation in various Facebook groups for years. I doubt this will be the ‘fucking last time,’ but we’ll see.
“1.The logically sound and valid argument is as follows…
If common ancestry,(If P)
Then common genetics.(then Q)”
This is neither a valid nor a sound argument because it doesn’t conform to the structure of an argument. In logic, an argument consists of a set of statements called ‘premises’ that lead to a conclusion. ‘If P then Q’ is not an argument; it is a statement and can be used as a premise in an argument. ‘If P then Q’ is called a ‘conditional implication,’ which, in basic logic, is sometimes ostensibly referred to as a ‘material implication’ (P -> Q), but may have subtle differences in more nuanced discussions relating to logic.
This shows a major conceptual error that Riaan has regarding what constitutes an argument. This is not an isolated case, and he has made this fundamental mistake before. Thus, I am not taking him out of context or failing to apply the principle of charity.
In addtion to that conceptual error, these are not truth-apt statements. Given P as ‘common ancestry’ the semantic content of the proposition is ‘common ancestry’ which is not a truth-apt statement, meaning it cannot hold a truth value (it cannot be true or false). The same applies to Q, as ‘common genetics’ is also not truth-apt.
This reveals another major conceptual error that Riaan has regarding what constitutes a truth-apt proposition. We can identify two conceptual errors in this very first enumeration.
“2.The correct contraposition would be…
If not common genetics(if not Q)
Then not common ancestry(not P)”
Given P →Q then the contrapositive is ¬Q → ¬P which is a logically equivalent statement:
P→Q ⟺ ¬Q → ¬P
Logically this is correct. However, “not common genetics” and “not common ancestry” are not truth-apt statements as noted prior. It also should be noted that “contraposition” is not exactly the same as a contrapositive, which is more a method used to derive a contraposition. I do not believe Riaan knows the difference between “contraposition” and “contrapositive”.
“3The invalid and fallacious contraposition would be…
If not common ancestry(if not P)
Then not common genetics.(not Q)”
I will accept any possible criticism of pettifogging here, but I am not a fan of phrases like ‘invalid contrapositive’ as valid/invalid generally refers to the structure of an argument. Technically, a premise or statement cannot be valid nor invalid. However, I recognize that some publications use this phrase and employ ‘valid’ in a different sense, but I think it leads to confusion, just like the type Riaan has displayed. Assuming ‘invalid contraposition’ is understood as a statement that is not logically equivalent to P → Q, then ¬P → ¬Q is an ‘invalid contraposition’, but is not an invalid statement. ¬P → ¬Q is called an ‘inverse’ of P → Q and cannot be ‘valid’ or ‘invalid’ as it is merely the inverse of the material implication.
I could posit an argument such as:
Premise #1: P → Q
Premise #2: ¬P → ¬Q
Conclusion: Q
One can say that this argument is invalid since the conclusion does not follow from the premises using any rules of inference. The argument is called a ‘non sequitur’ and is, therefore, invalid. However, Premise #2 is perfectly fine to posit, as a premise is neither ‘valid’ nor ‘invalid.’
“4. Note carefully that the invalid contraposition is the argument you have repeatedly presented. It’s unsound because the conclusion you present is not a logical consequence of the premise you present.”
Riaan seems to be confusing two different points I made and treating them as if they were the same argument. I have two separate points he claims are incorrect, but one of them isn’t an argument at all; it was a question. A question that he failed to answer.
I asked:
What is the proper contrapositive if given:
Assume:
P = “All life is not related”
Q = “Life would not share a genetic code”
P → Q
I claimed that the proper contrapositive was:
¬Q → ¬P “If life shares a genetic code, then all life is related”
Riaan couldn’t provide me with what he believed to be the correct contrapositive of P → Q if it’s not “¬Q → ¬P: If life shares a genetic code, then all life is related.” I doubt I’ll ever know what he considers to be the correct contrapositive.
The other point he is referring to is an argument I made in response to a dishonest claim that science commits the “affirming the consequent” fallacy. I explained that one can rephrase an argument in the valid form of Modus Tollens when discussing scientific methodology.
Riaan argued that:
If all life were related, then all life would share a common genetic code.
All life shares a common genetic code.
Therefore, all life is related.
This is indeed an example of the “affirming the consequent” fallacy (P → Q, Q, ∴ P). However, if we rewrite it as:
P → Q: If all life is not related, then life would not share a genetic code.
¬Q: Life does share a genetic code.
∴ ¬P: All life is related.
Then, this becomes a perfectly valid argument.
However, Riaan argued that this was still “affirming the consequent,” which is absolutely incorrect. This argument follows the form P → Q, ¬Q, ∴ ¬P, which is a rule of inference called “Modus Tollens” and is always valid. It cannot fail to be valid, regardless of the semantic content.
Although it is challenging to decipher most of Riaan’s statements, as he seems unable to answer simple and direct questions to clarify his claims, but he apparently believes that this is still “affirming the consequent” due to a fundamental misunderstanding of classical logic. Riaan seems to believe that since “sharing a genetic code” does not necessarily metaphysically entail “all life is related” (his main argument is that life can share a common genetic code due to the design of some “intelligent agent” rather than evolutionary common ancestry or descent), the Modus Tollens argument is still fallacious. This is profoundly wrong. The non sequitur of “affirming the consequent” only means that the logical structure of the argument follows the form P → Q, Q, ∴ P. It has nothing to do with the relevance of Q to P, as classical logic is not a form of relevance logic.
An argument cannot be both “Modus Tollens” and “affirming the consequent” simultaneously.
My argument is clearly Modus Tollens, as demonstrated by the form: P → Q, ¬Q, ∴ ¬P. Consequently, it is logically impossible for it to also be “affirming the consequent,” as Riaan claims. This again demonstrates a significant misunderstanding of logical fallacies and rules of inference.
Riaan states that my argument is “unsound” because “the conclusion presented is not a logical consequence of the premise presented.” This implies that Riaan believes it is unsound due to invalidity. While it’s true that an invalid argument cannot be sound, my argument is Modus Tollens, which is always valid. It is evident that the conclusion follows by logical necessity within the argument’s scope. Therefore, my argument cannot fail to be valid.
Soundness also relates to the truth of the propositions. As someone who accepts that all life is related and shares a genetic code, I would argue that the premises are true, making the argument sound. Riaan, however, is not even arguing that the premises are untrue—an argument he could make as a creationist—but rather, he’s expressly claiming that it’s unsound because the conclusion doesn’t follow. However, as previously mentioned, the conclusion does indeed follow, as Modus Tollens is always valid. Always. Riaan’s confusion may stem from a misconception that Q must have a necessary causal relationship to P, but this is not how classical logic works.
Example:
Premise #1: P → Q: If a cat is a mammal, then the sun is a star
Premise #2: P: A cat is a mammal
Conclusion: Q: The sun is a star
This is a VALID and SOUND argument. It is valid because it uses a rule of inference called Modus Ponens: P → Q, P, ∴ Q. It is sound because Premise #1 (P → Q: If a cat is a mammal, then the sun is a star) is true, since if both P and Q are true, the material implication (P → Q) is also true. (You can verify this by finding a truth table for material implication). Premise #2 (P: A cat is a mammal) is also true, as cats are indeed mammals. Since both Premise #1 and Premise #2 are true, the argument is sound. (It is important to note here that soundness has to do with the premises of the argument being True, not necessarly the atomic propostions of P and Q. If both P and Q are false in a material implication (P → Q) the premise P → Q is “vacuuous” True.)
The relationship between “a cat is a mammal” and “the sun is a star” has absolutely no relevance to whether an argument is valid or sound. This is where I think Riaan has a significant conceptual misunderstanding.
“5.If your argument was not fallacious and unsound….
If not common ancestry then not common genetics.
Then the contraposition would be…
If common genetics then common ancestry.”
Let’s put that in logical notation:
P → Q: If not common ancestry, then not common genetics.
¬Q → ¬P: If common genetics, then common ancestry.
This is correct and similar to what I mentioned earlier: if P → Q, then ¬Q → ¬P. Here, P = “all life is not related,” and Q = “life would not share a genetic code.”
P → Q: If all life is not related, life would not share a genetic code.
Contrapositive: ¬Q → ¬P: If life shares a genetic code, then all life is related.
However, Riaan calls this “affirming the consequent,” which is completely incorrect. It is understatement to say that it is challenging to understand how one could consider a correct contrapositive as “affirming the consequent,” which refers to the structure of an argument rather than merely having a proper contrapositive or not.
P → Q is logically equivalent to ¬Q → ¬P, and to think that a tautological relationship (P → Q ⟺ ¬Q → ¬P) can even be fallacious is profoundly incorrect and, in my opinion, rather bizarre.
You can objectively verify this using truth tables.
“6. And this is still affirming the consequent of common ancestry. Because common genetics doesn’t logically lead to common ancestry.”
I believe Riaan may be misunderstanding these concepts. He refuses to acknowledge that while common genetics does not metaphysically imply common ancestry (i.e., it’s possible that God made it appear that way), the contrapositive, “¬Q → ¬P: If life shares a genetic code, then all life is related,” cannot be incorrect if “P → Q: If all life is not related, life would not share a genetic code.” A contrapositive simply cannot be “affirming the consequent,” nor can a valid argument using Modus Tollens ever be “affirming the consequent.”
Remember, Modus Tollens and “affirming the consequent” are determined solely by the local structure of an argument and nothing else.
Modus Tollens: P → Q, ¬Q, ∴ ¬P (ALWAYS VALID)
“Affirming the consequent”: P → Q, Q ∴ P (ALWAYS INVALID)
You cannot determine if an argument is valid or invalid by examining its semantic content. Validity can only be assessed through the logical form of the argument, which is entirely independent of the semantic content.
“I realize you don’t grasp these facts, but they are still true, and still facts.”
I am quite confident I grasp facts here which are accurate. Riaan’s misunderstandings of logic are profound, and I will most graciously let the reader decide who ‘grasps’ these facts better.
“You will now address the specific arguments I MADE, instead of pretending I made arguments I did not”
Done as per request.
I have attempted to clarify Riaan’s positions to the best of my ability and asked him direct questions to avoid any potential strawman arguments. I believe I have accurately represented his positions in this blog entry. Should he respond and point out any instances where I may have improperly attributed an argument to him, I will happily correct it. However, this is why I preferred to ask questions in real time about his arguments, such as how my Modus Tollens could ever be “affirming the consequent” when they are clearly two very different logical inferences, with one being valid and the other invalid.
“This is your last fucking chance to demonstrate a semblance of intellect, integrity and comprehension.”
I am openly sharing this on my philosophy blog for anyone to objectively evaluate, which, in my view, fairly demonstrates my ‘integrity’ in submitting my arguments for public criticism. I welcome others to assess my comprehension of classical logic at a very introductory level.
“If you fail, you will be blocked on the basis that you’re just too fucking dumb for me to waste my time on.”
Task completed successfully.
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Riaan’s post on my Facebook: https://www.facebook.com/riaan.visser.3998/posts/pfbid09CvHFowKfoDmgrM475cUkn5D7HjTZffpwvZpYzV7aKdNBvwcfZ1PVhrW32mFpaegl
