Average Reading Time: 25 Minutes
Guest post by Derezzed83:
In his latest blog post, written in his usual bellicose, condescending style, AntictizenX attacked InspiringPhilosophy for his video Logic Defended. It’s clear that even though ACX makes a few valid points, his critique is motivated by a deep personal vendetta against IP. Take for instance ACX’s previous post where he said he wouldn’t be surprised if ‘IP abuses his family’, which seems over the top even for someone known for being excessively antagonistic and condescending! Seemingly half of his 1000 word blog post was dedicated to personally attacking IP. Ironically, despite accusing IP of being biased and philosophically ignorant, the blog post highlights a pernicious pattern of bias on the part of ACX. Reading his blog post one can’t help but notice that his position is based on a mishmash of contradictory and often inconsistent metaphysical ideas.
It’s also important to emphasize that there’s no fundamental disagreement between AnticitizenX and InspiringPhilosophy when it comes to the main thesis of the video. Both agree that the logic that is used by the majority of people every day to reason about the world is valid. So one begins to feel like it was really personal animosity for IP which motivated ACX to write such a long blog post, in which he obsessively scrutinizes every line and comes to often wildly inaccurate conclusions about what IP said. Let’s go through his blog post step by step:
IP: “Can we trust the laws of logic?
ACX: “The next question that needs to be asked at this point is, Exactly which “laws of logic” is IP referring to? As I said earlier, there is no such thing as a singular, unifying school of logic… I assume from the context that IP is defending classical propositional logic…”
Who cares if IP says “I’m defending logic” instead of saying “I am defending classic propositional logic” or “I am defending three-valued logic”. Why should IP include philosophical jargon early in his presentation when he is speaking to a general lay audience? It was clear to me and probably to the majority of his audience that he is defending the type of logic that the vast majority of ordinary people use every day to reason about the world or the type of logic used in scientific discourse. The same type of logic that is used by competent everyday speakers of the English language.
IP: “[Is logic] just another man-made construct built on sand?”
ACX: “I realize that IP is being somewhat rhetorical here, but the very nature of his questions reveal a profound bias. Namely, what exactly does IP have against man-made constructs?”
If ACX realizes that IP could be speaking rhetorically, then why is he taking the most uncharitable interpretation possible? This is also a complete strawman. IP did not say logic is worthless just because it’s a man-made construct. For all we know, IP believes that many man-made constructs are worthwhile pursuits and valuable in and of themselves, except logic could be an example of a man-made construct that isn’t. Not because it’s man-made per se, but because it lacks a connection to external reality. What IP said is ambiguous but why be so pedantic and interpret it in the most uncharitable way possible?
IP: “Many argue the laws of logic are not true and use a form of Russell’s paradox to show this.”
ACX: “Notice that we’re not even 30 seconds into the video, and IP is either being inexcusably lazy or just outright dishonest. The phrase many argue is a textbook example of Weasel Wordsña deliberate manipulation tactic designed to make an argument appear more relevant than it actually is. It is also intentionally vague enough so that we are unable to check out the source for ourselves. For instance, who exactly are these many people supposed to be? How influential are they? Where can I read their arguments for myself? Are these people serious academics with PhDs?”
What is ACX talking about here? One of the main motivations why a whole BRANCH of logic other than classical logic (i.e. paraconsistent logic) was developed is because of Russel’s paradox. The philosopher Graham Priest has written extensively on this and itís even listed in his Stanford Encyclopedia entry on dialetheism (a type of non-classical logic). These were not “weasel words” on the part of IP, he is not as ACX alleges, trying to make the argument seem more relevant than it already is. So what if IP didn’t mention these philosophers individually? IP has to juggle between presenting engagingly and concisely or bombarding his audience with too much information, and sometimes information gets left out. Isn’t ACX just trying to hold IP to an excessively high standard?
IP: “Logic simply is a description of everything that is and everything that is possible.”
ACX: “This is very clearly an embarrassing misconception. How on Earth does IP expect to defend the laws of logic when he cannot even define that word correctly? It reminds me of the old adage about playing checkers against an opponent who is playing chess. Only in IP’s case, it’s more like he’s playing Go Fish with a sack of marbles while all the chess players are in a different building down the street.”
Later in the blog:
ACX: “Remember that logic is not a force to be trusted; it is a tool to be exercised. The reason why logic works so well at describing the universe is because we specifically invented logic to do exactly that.”
ACX claims IP can’t even define logic, but he gives the exact same definition of logic as IP later in his blog post! IP said that logic is a description of everything that is and everything that is possible. ACX says that we invented logic to describe the Universe. I don’t understand how ACX thinks his position is different from IP’s? They both think logic is a description of the world, the only difference is that IP thinks logic is also a description of the way things could be. ACX also wastes no time to take a personal jab at IP and his grandiose condescension is nauseating given the fact that he LITERALLY says almost the same thing as IP just using different words!
ACX: “The thing that makes this even more infuriating is the way in which IP specifically frames it all as a direct accusation against atheists”
Sorry, but I must have missed the part where IP treated atheists as a singular homogenous group who deny logic. ACX is attributing a position to IP that he probably doesn’t even hold. IP is specifically addressing a group of people who deny the type of logic people use every day, who may or may not be atheists.
“Here is a simple argument of how they try to show the laws of logic are not true or objective.
Premise 1: Assume that the laws of logic are true.
Premise 2: All propositions are either true or false.
Premise 3: The proposition “This proposition is false is neither true nor false.
Premise 4: There exists at least one proposition that is neither true nor false.
Premise 5: It is not the case that all propositions are either true or false.
Premise 6: It both is and is not the case that all propositions are either true or false.”
ACX: “notice again that IP gives zero citations as to where exactly this mysterious argument is coming from. I even tried to Google it myself, but I could not find a single example of anything remotely similar. It therefore seems to me that, for all practical purposes, IP might as well be inventing it out of nothing. I donít know what to say, other than congratulations on your amazing straw man, dude.”
If ACX thinks IP is inventing this argument from nothing then he is simply ignorant of a whole branch of philosophy which attempted to reconcile the Liar’s paradox with classical logic. This philosophical tradition stretched from Bertrand Russel to Alfred Tarski to Quine and Saul Kripke. The fact that the Liar’s paradox allegedly shows that some propositions may be both true and false (or neither true or false) at the same time is why whole new logical systems (paraconsistent logic or three-valued logic) were invented! AnticitizenX is just showcasing his ignorance here.
IP: “So if this argument works, it would show we cannot trust the laws of logic. However, there are several problems with this argument and line of reasoning that need to be addressed. First, the argument breaks down in premise 2. Not all propositions are either true or false.”
ACX: “The premise that all propositions are either true or false is called bivalence, and it is a core presumption in classical propositional logic. That means when IP rejects this principle, he is effectively rejecting a fundamental law of logic in order to defend the laws of logic. That’s not a very good start.”
I’ve spoken to InspiringPhilosophy and he is defending a three-valued logical system, not classical logic. He is rejecting bivalence because bivalence (i.e. all propositions are either true or false) doesn’t apply to propositions such as “this sentence is false”. There’s absolutely no contradiction on the part of IP here. IP never claimed he was defending classical logic. The fact that he is defending a three-valued logical system is apparent from his video (even if he doesn’t mention the term “three-valued logic” outright) because he says not all propositions are either true or false, rather that’s a false dichotomy, which must mean there’s a third option.
ACX says, “In principle, IP could easily avoid this little trap by simply admitting to the existence of different systems of logic. But you have to remember that IP views logic as an objectively potent force unto itself, independent of human intervention. He is therefore not allowed to accept logic as a human invention because that would immediately render it unreliable (i.e., “built on sand”).”
This is a complete fabrication and a lie on the part of AnticitizenX. IP has never denied the existence of different systems of logic. Although IP has never mentioned three-valued systems or paraconsistent logic in this video, there’s no evidence whatsoever that he has denied they exist. AnticitizenX is attributing words and positions to IP that he has no evidence that IP has ever held.
IP: “A proposition can be defined as a statement or assertion that expresses a judgement or opinion.”
ACX: “Sentences like this are hilarious to me because they perfectly demonstrate how little IP has studied logic. When I Googled the word ‘proposition,’ this was the verbatim definition that came up in my search. However, when I actually looked up the definition from an academic source, the result was something very different. According to Richard E. Hodel’s textbook, An Introduction to Mathematical Logic, a simple proposition is a declarative sentence that is either true or false and has no connectives. Likewise, a proposition is a declarative sentence that either is a simple proposition or is built up from simple propositions using one or more of the connectives not, or, and, if-then, and if-and-only-if.
To be fair, the distinction between these two definitions is a bit subtle, but it does illustrate the extent of IPís ‘research’ for these videos. He completely avoids any contact with authentic, scholarly references, but instead relies entirely on 10-second Google searches to get his information. It also shows that, again, classical logic requires all propositions must be either true or false. IP is flat-out denying a fundamental law of logic in his defense of the laws of logic.”
IP may not have used the academic definition of “proposition” (“a proposition is a declarative sentence that is either true or false”) because as we can see from his video he is defending a three-valued logical system, where not all propositions are either true or false! Also on what evidence does ACX base his assertion that IP is not interacting with scholarly literature? Just because he uses a layman’s definition of a proposition? Are not his videos attempts to simplify complex ideas for a more general audience? The academic and layman’s definition of a proposition are effectively synonymous on the logical system that IP is defending!
IP: “Consider the statement ‘Easter is the best holiday.’ This cannot be proven true or false. It is just an expression of opinion.”
ACX: “I find it truly baffling that IP thinks this is supposed to be compelling. All we have to do is ask ourselves what exactly we mean by that statement. For example, if we take this proposition to mean ‘It is my opinion that Easter is the best holiday,’ then we absolutely have a statement of truth. Sure, it may just be my opinion that Easter is the best holiday, but it is verifiably true that I hold to this opinion (or, if I do not hold such an opinion, then it would be false).
Alternatively, we could take this proposition to mean something more like ‘It is an objective fact that Easter is the best holiday.’ However, that proposition has a truth value as well. By definition, opinions are subjective facts that only apply to individuals and their preferences. It is therefore a contradiction in terms to speak of an objectively correct opinion, and the proposition simply becomes false. So no matter how we interpret his proposition, there exists a definite assignment of truth.”
IP’s argument is very compelling since, contra AnticitizenX, the closest interpretation of the statement that “Easter is the best holiday!” is neither (A) “My subjective opinion is Easter is the best holiday” or (B) “it is an objective fact that Easter is the best holiday”. The closest interpretation to “Easter is the best holiday!” is captured by the statement “Hurrah for Easter!”, which is an expression of one’s subjective emotional state. It has no definite truth value because it is not describing a property of the external world.
ACX: “The Liars paradox is a textbook example of the kind of proposition that binary logic struggles to deal with. ThatÌs why we have, for example, systems of tri-state logic. Unfortunately, that would again require IP to acknowledge the existence of multiple logics, which he has specifically refused to do from the outset. It would also force him to completely overhaul his entire conception of truth itself.”
If I was as hypercritical as AnticitizenX, I would accuse him of not having any clue of what he was talking about, because the expression “tri-state logic” relates to digital electronics and has nothing to do with three-valued logical systems. Also, AnticitizenX keeps repeating the lie that IP has denied the existence of alternative logical systems, which IP has never done.
ACX: “Remember that IP thinks logic is an objective force of nature unto itself and thus independent of human design. By the same token, IP also tends to think of truth itself as something very similar. If we take the more modern approach, however, then truth is just a label that we assign to propositions.”
First, IP has never said logic is a force of nature unto itself. AnticitizenX is openly lying. His exact words are, “logic is a description of everything that is [external reality] and everything that could be”. Ironically, it is AnticitizenX who is contradicting himself here. Previously he wrote that logic was invented by humans to describe the universe and works very well at that task. Now he is saying truth is just a label that we assign to propositions? These two statements reveal a deep confusion about the nature of truth and logic. On one hand, AnticitizenX takes a deflationary account of truth, where a truth is merely assigned according to the axioms of a system. On the other hand, he thinks true propositions are the ones that accurately describe the external world, which is a non-deflationary account of truth. Obviously, these two positions can’t both be true.
ACX: “If we take the more modern approach, however, then truth is just a label that we assign to propositions. This immediately solves the liar’s paradox by rendering it undecidable because there is no procedure you can apply through axioms and rules of inference to arrive at a final truth value (at least, not if you want to preserve consistency). The only problem with this approach is that it forces us to give up on any platonic ideal of truth. Truth, in effect, is reduced in meaning to the bare procedure that was constructed to assign it (at least, for analytic propositions it is). For us pragmatists, that’s perfectly acceptable because we’re not interested in some nonsensical platonic ideal of truthiness. We just want a system of communication that allows us to talk at each other effectively. For IP, unfortunately, that’s not allowed. He has to believe in his magical world of metaphysical mystery.”
I spoke with IP, he is not a Platonist. Furthermore, having a three-valued logical system doesn’t force you to “reduce the meaning of truth to the bare procedure that was constructed to assign it”. Propositions under the three-valued logical system can still be true and false, and we are not given any reason by AnticitizenX as to why a proposition that is true under a three-valued logical system could not correspond or reflect external reality. In other words, adopting a three-valued logical system doesn’t force us to take a deflationary view of truth.
IP: “Carloman was murdered by his brother Charlemagne so he could have the throne for himself.
This statement is either true or false. However, we cannot be sure if it is true due to lack of information. We do not have enough records or evidence to confirm whether or not Carloman was murdered or died naturally. It is simply beyond the scope of our knowledge today. Which brings us to the next problem with this argument. This argument itself is based on Gödel’s theorems, which many think shows logic doesn’t work. But in a nutshell, they actually only show that no consistent system of axioms, whose theorems can be listed by an ‘effective procedure’ is capable of proving all truth. In other words, Gödel’s theorems show we cannot fully prove something is true, just because it seems like it is or is consistent. All Gödel did was show we are limited in having total proof of something. But even without Gödel that is intuitively obvious. Many things will always just be 99% probably true, but absolute certainty will always be beyond our reach.”
ACX: “This paragraph is so hopelessly muddled that I literally stared at it in confusion for two minutes before thinking of something to say. For starters, the uncertainty surrounding Carloman’s death has absolutely nothing to do with Gödel’s incompleteness theorems. That’s because Carloman’s death is a matter of synthetic propositions where truth is assigned in accordance with a preponderance of empirical data. In contrast, Gödel’s theorems are a statement about the nature of language itself.”
Notice that blatant lie by AnticitizenX?
Let’s call the statement “Carloman was murdered by his brother Charlemagne so he could have the throne for himself” (statement (A)).
And let’s called the following argument the dialetheist argument.
Premise 1: Assume that the laws of logic are true.
Premise 2: All propositions are either true or false.
Premise 3: The proposition “This proposition is false” is neither true nor false.
Premise 4: There exists at least one proposition that is neither true nor false.
Premise 5: It is not the case that all propositions are either true or false.
Premise 6: It both is and is not the case that all propositions are either true or false.
IP argued that we can’t know whether statement (A) is true or false on the current evidence we possess. He argues that this shows that one of the premises (premise 2) of the dialetheist argument is unsound. I think it’s pretty clear to me that IP did not claim, as AnticitizenX alleges, that statement (A) has something to do with Gödel’s incompleteness theorem.
When he says, “which brings us to the next problem with this argument”, IP clearly outlines that he is bringing up Gödel s incompleteness theorem in relation to the dialetheist argument and not in relation to statement (A). I think that at this point it’s clear that AnticitizenX has so much hostility towards IP that he can’t even read properly what IP is saying.
ACX: “Secondly, notice the repeated use of weasel words: Many think that Gödel’s theorems show logic doesn’t work. Seriously, who exactly are these people? I have never once encountered a single human being in the entire universe who claims this. IP is again arguing against total phantoms, all with the same unspoken subtext that, no really, it’s atheists.”
Just because AnticitizenX has not encountered a single human being in the entire universe who has claimed this, that doesn’t make Gödel’s incompleteness theorem any less relevant to the discussion. I don’t know why AnticitizenX thinks the entire universe revolves around him. As the philosopher, S. Choi outlines: “one of the Priest’s main motivations for Dialetheism is Gödel’s theorem. He applies Gödel sentence to a naive notion of proof in natural language and attempts to make an argument for Dialetheism”
“one of the main proponents of dialetheism, Graham Priest, has argued that Gödel’s first incompleteness theorem implies the existence of dialetheias” (On the Gˆdelian argument for dialetheism, K. Zahidi)
IP: “This argument itself is based on Gödel’s theorems, which many think shows logic doesn’t work. But in a nutshell, they actually only show that no consistent system of axioms, whose theorems can be listed by an ‘effective procedure’ is capable of proving all truth.”
ACX: “Notice that IP specifically removed any mention of arithmetic and natural numbers. This is important because it limits the context in a way that contradicts IP’s interpretation. He must have done this on purpose, too, because I see no possible way to accidentally remove such a key piece of information. The guy just flat-out lied to his audience, all so he could invent some obtuse interpretation about logic that doesnít even apply to its original context.”
IP has removed mentions of arithmetic and numbers because he is referencing Gödel’s incompleteness theorem not in reference to arithmetic but in reference to logic in natural languages. This is in response to people who make similar arguments to Graham Priest, people who take Gödel’s first incompleteness theorem and argue for dialetheism.
IP: “So because of that, we can also deny premise 3 and say that it is a false dichotomy.”
ACX: “This sentence is especially confusing, in that IP is now outright contradicting himself. He just spent the last two paragraphs explaining in great detail that not all propositions have to be true or false, and now he is denying a premise claiming that not all propositions have to be true or false! Seriously. Read that premise again: Premise 3: The proposition ‘This proposition is false; is neither true nor false. You just categorically denied the very thing you set out to prove, you imbecile!”
Ad hominem attacks aside, AnticitizenX actually has a valid point here. I’ve spoken to IP and he says he misspoke during the video and meant to say that he is denying Premise 2, (“All propositions are either true and false”) and not premise 3. I think there’s a fair bit of evidence to support IP’s claim that he made a simple mistake and meant to say “premise 2” not “premise 3”. For instance, when he says that the premise is a false dichotomy that only makes sense if we apply to premise 2 (“All propositions are either true and false”). Such a simple mistake is entirely forgivable during a 15-minute video and there’s zero need to lambast IP for it, given the fact that AnticitizenX has made similar mistakes such as confusing the terms “tri-state logic” with “three-valued logic”.
IP: “I can explain how and why if we reduce the problem to mathematics, which can show the statement this statement is false can actually be solved. Allow me to explain using the work of G. Spencer Brown.
The proposition can be represented as X = -1/X. Now like the statement in our argument, if you try to solve with x = 1, the equation will yield negative 1. If you try X = -1, then positive 1 comes back. The solution oscillates between one and negative one, like true or false. One being true, and negative one being false, just like our proposition. If you say it is true, then it canÌt be because it claims it is false. If you say it is false, then it cannot be true in claiming it is false. Same problem, just represented mathematically. So how do we escape this vicious cycle? The solution is to use i, which is also the same as the square root of negative one. If you substitute x for i, you get i = -1/i, and negative one over i is also i. Thus, mathematically, the problem can be solved, because i transcends the paradox.”
ACX: “This is the part where IP really flies off the rails, and it is truly baffling where he got the idea to present this information. For starters, G. Spencer Brown is essentially no one. The guy has almost no historical significance or philosophical influence to speak of. Secondly, I attempted briefly to read through G. Spencer Brownís book, and all I found was a meaningless word salad of incoherent gibberish. To illustrate, these are the first words Brown writes in the forward to the text:
“The theme of this book is that a universe comes into being when a space is severed or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can begin to reconstruct the basic forms underlying linguistic, mathematical physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance.”
The book pretty much rambles endlessly in this style of prose, and it only gets worse the deeper you dig into it.”
Who cares who formulated the argument? I think arguments should be judged based on their merit not on who originated them. This is a genetic fallacy.
Academic credentials aside, I still did my best to charitably interpret the underlying train of thought. Basically, Brown is saying that the equation x^2 = -1 has no solution within the set of natural numbers. Thus, something other than a natural number is required in order to solve it. By analogy, classical binary logic cannot assign a truth value to the Liar’s paradox. Thus, a new system of logical truth values must be invented that does.
ACX: “This stuff is important because it completely undermines IP’s central thesisñthe idea that the laws of logic can be ‘trusted.’ Clearly the laws of classical binary logic are not trustworthy because they completely break down when exposed to self-referential negations (remember, this is IP’s own argument!)”
ACX is again attributing an argument to IP that he has not made. IP is not defending classic binary logic, and he has said so in the comment section of his video multiple times. When taken as a whole, it’s clear that IP is defending a three-valued logical system, he thinks not all propositions are either true or false, and some propositions are neither, i.e. the statement Easter is the best holiday.
IP: “The only problem is that we cannot epistemically understand the mathematical usage of i.”
ACX: “This claim is just laughable. Mathematicians are very well-acquainted with the ‘mathematical usage of i.’ The imaginary unit is, by definition, the number that produces -1 when squared.”
There are two interpretations of what IP said, and again ACX is assuming the worst. The first interpretation is that we can’t understand “i” epistemically, and the other is that we can’t understand the mathematical use of “i”. Could IP have written this sentence a bit more clearly? Sure, he is fine admitting that. But I think it’s clear to most people what he meant. It’s clear that IP meant that we can conceptualize what the natural numbers like 1,2,3,etc. are supposed to be, since, for instance, we have a concept of what 1 apple is compared to 2 apples or what having 1 coin as opposed to 2 coins, but it’s impossible to conceptualize ‘i’ in the same way, because we cannot tie it to something that exists in reality. What is an i apple supposed to be? In the same way, statements which are undecidable, such as “this statement is false” is undecidable because it has no connection to external reality, it just references itself.
“IP: “Thus, Gödel was proven right, and not the absolute skeptic who doubts logic is true.”
ACX: “I’m just going to recap IPís argument over the last few sentences and see if you can make sense out of it.
Imaginary numbers “transcend” integers.
By analogy, the liar’s paradox transcends true and false.
Therefore, Gödel was right.
Therefore, logic is true.
Seriously, dude. How do you have patrons?”
That’s clearly not a valid recap of the argument IP was making. To me it’s clear that the argument IP was making can be summarized as:
Gödel has shown that no consistent set of axioms is capable of proving all truths.
The formula x=-1/x is a putative example of a mathematical formula whose truth is not provable since the solution oscillates between 1 and -1 in the same way that the truth of the proposition, “this sentence is false,” oscillates between true and false.
A solution to the Liar’s paradox is that the proposition, “this sentence is false” is undecidable, in the same way, that the solution to the equation x=-1/x is substitution i for x.
There are several analogies between mathematical unprovable formulas such as x=-1/x and undecidable statements. First, both are self-referential. Second, we have trouble conceptualizing what an undecidable proposition like, “This sentence is false!” is supposed to represent, in the same way we have trouble conceptualizing i.
If I understood all of this in 3 minutes, why is it so hard for AnticitizenX to understand it?
In summary, ACX scrutinizes every single word spoken by IP, but it’s clear that he himself is deeply confused about the nature of truth. He offers various contradictory accounts; on one hand, he seems to think logic describes the universe. While on the other hand, he thinks a true proposition is only true by virtue of truth assignments and axioms.
He is seemingly unaware of the vast philosophical literature on the Liar’s paradox and Gödel’s incompleteness theorem in relation to dialetheism. And while he makes a few valid points, there’s an undercurrent of outright hostility towards IP and this antagonism biases whatever valid critiques he has to offer.