If there is one thing you can always count on from an Inspiring Philosophy (IP) video, it is a philosophical train wreck of muddled confusion. So when IP finally came out with a video called The Laws of Logic Defended, you would think this should have been the first presentation I could actually get behind. After all, I like to consider myself a pretty logical guy, and I even have some formal training in mathematical logic and proof theory. Unfortunately, IP is not your ordinary, everyday apologist. Even when it comes to something as simple as a defense of basic logic, he still cannot help but get his entire presentation wrong. Not just erroneous, mind you, but often deliberately manipulative and transparently unethical.
To give a crude analogy, suppose someone is about to argue against the recreational use of heroine. In principle, this is something we should all be able to agree upon because heroin is highly addictive and mentally disabling. But what if the principle argument was that too much heroin literally causes your skin to turn inside out? Or that heroin is a mechanism for injecting demons into your body and getting possessed by Satan? That’s what it’s like to listen to IP defend logic.
Speaking broadly, the single, foundational blunder that permeates this entire presentation is the simple fact that IP does not understand logic. He does not know what logic is, he does not know how logic works, and he has no clue that logic is an ever-changing human construction. In IP’s world, logic is like an ethereal force interwoven into the fabric of space and time. At one point, he even draws a picture of the universe resting inside a bubble of logic, as if the laws of logic somehow encompass the physical behavior of nature itself. It’s a dead giveaway that the guy has never even touched an actual textbook on the subject. He has no authority whatsoever, yet he still felt the overwhelming compulsion to put together an entire video anyway.
I personally find this sort of behavior highly irritating. To me, it is inherently dishonest to pretend to be an expert in things you obviously do not understand. In IP’s case, however, I have to wonder if it might just be a classic example of Dunning-Kruger effect. The guy is so woefully uneducated about logic that he literally cannot fathom how uneducated he is. He thus self-evaluates as being rather competent and then plows right ahead with full confidence.
I personally find this sort of behavior highly irritating. To me, it is inherently dishonest to pretend to be an expert in things you obviously do not understand. In IP’s case, however, I have to wonder if it might just be a classic example of Dunning-Kruger effect. The guy is so woefully uneducated about logic that he literally cannot fathom how uneducated he is. He thus self-evaluates as being rather competent and then plows right ahead with full confidence.
For what it’s worth, the word logic does tend to mean different things under different circumstances, which makes it somewhat forgivable that most people do not really understand it. If, however, you actually open a formal textbook on the subject, then there is a consistent theme on which experts do tend to agree: Logic is essentially a bunch of highly formalized rules built into human language. For example, the Stanford Encyclopedia of Philosophy says that:
A logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics.
The immediate implication is that there is no such thing as a singularly “correct” logic, but rather a varied assortment of competing and complementary logics, each with their own distinct areas of focus. At best, you can really only speak of “good” logics that are meaningful and descriptive for certain applications, and “bad” logics that fail to help us communicate effectively. When you follow the rules of logic in your speech, then we would simply say that you are being logical. Conversely, when you fail to express an argument through the rules of logic, then you are simply not being logical.
This is an important point to emphasize, because it immediately undermines IP’s entire argument before he even opens his mouth. To quote his own definition,
Logic simply is a description of everything that is and everything that is possible.
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.
Another thing that really jumps out at me from this presentation is the way in which IP deliberately lies and manipulates for no reason. His use of weasel words is particularly blatant, but he also has a bad habit of cherry-picking, quote-mining, and oddly-ambiguous phrasing. There is even a thinly-veiled attack against atheists, as if atheists have to literally deny logic in order to deny the existence of God. It’s all so clumsy, too, and it really makes me wonder how this guy could possibly gather such a loyal fan base. But loyal they are, and IP no doubt earns quite the generous income from his many donations. That’s why I feel compelled to publicly analyze his arguments in detail so that maybe a few of his potential sponsors find something better to do with their money.
To begin, IP opens as he always does by saying something really weird.
Can we trust the laws of logic? Is logic safe from criticism? Or is it just another man-made construct built on sand?
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?” The conversation has barely even begun, and he is already imposing a rather bizarre presupposition. Either logic is a transcendent, singular force unto itself, or it is nothing but a worthless creation from a bunch of bumbling morons. He speaks as if human beings are utterly incapable of creating a formal system of logic that has any significant value.
Another funny thing about this opener is IP’s use of the word “trust.” Pray tell, what does it even mean to trust the laws of logic? IP is speaking as if we cannot directly justify the use of logic, but must instead take it on a kind of faith. It’s a constant theme that permeates the entire discussion, and it shows how little IP understands about the nature of logic.
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. There are actually many distinct systems of logic, all with competing interpretations within them. Not all of these logics are even compatible with each other, either, which means sooner or later you have to pick and choose which logics you intend to apply. I assume from the context that IP is defending classical propositional logic, but he also seems to reject several tenets of that system as this video progresses.
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. There are actually many distinct systems of logic, all with competing interpretations within them. Not all of these logics are even compatible with each other, either, which means sooner or later you have to pick and choose which logics you intend to apply. I assume from the context that IP is defending classical propositional logic, but he also seems to reject several tenets of that system as this video progresses.
Remember that logic is not a force to be trusted; it is a tool to be exercised. The reason why logic seems to work so well at "describing the universe" is because we specifically invented logic to help us do exactly that. If logic were not useful at formulating meaningful arguments, then we would simply discard it and invent something else that does (and then call that thing “logic” instead). Thus, for all practical purposes, people who fail to exercise logic are essentially using words incorrectly. The consequence is nothing more than ambiguity and miscommunication.
Many argue the laws of logic are not true, and use a form of Russel’s paradox to show this.
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 Words---a 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? Or is IP getting this from Billy, the angry basement-dweller with an internet connection? He simply does not say. We are therefore left wondering whether such people even exist at all, or if they are just a figment of IP’s imagination.
It turns out that I’m not the only person to ask these questions, and there are plenty of comments on his video wondering the same thing. On at least one occasion, IP actually gave an answer, which you can see here:
There's our answer, folks. This entire video is a response to some random anonymous doofus on the internet. Thank you, Inspiring Philosophy, for saving us from this terrible menace.
The thing that makes this even more infuriating is the way in which IP specifically frames it all as a direct accusation against atheists. He does not come out and say it in so many words, but that is exactly how his fans have interpreted it. A simple perusal of his video comment section quickly reveals dozens of fanboys railing against the silly atheists, and IP makes zero effort to publicly correct this perception. Just look:
So it’s not that atheists are all out there denying logic; it's just that a bunch of atheists are out there denying logic. At least, that's the interpretation IP is more than happy to encourage.
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 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.
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.
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 don’t know what to say, other than congratulations on your amazing straw man, dude.
But hey, if that’s how IP wants to play it, then fine. I can play that game too. According to some, reason and logic are enemies of God. In fact, here are some direct quotes to that effect:
Reason is a whore, the greatest enemy that faith has; it never comes to the aid of spiritual things, but more frequently than not struggles against the divine Word, treating with contempt all that emanates from God.
Or it that wasn’t convincing, here’s another doozy:
If, somewhere within the Bible, I were to find a passage that said 2+2=5, I wouldn’t question what I’m reading in the Bible. I would believe it, accept it as true, and then do my best to work it out and to understand it.
Still not satisfied? How about this one?
It is entirely right, rational, reasonable, and proper to believe in God without any evidence or argument at all.
The irony here is that I don’t have to hide behind weasel words to make my point. The first quote is from Martin Luther, the second quote is from Pastor Peter LaRuffa, and the third is from Alvin Plantinga---all Christians of significant influence and notoriety. So if IP wants to pick on atheists for denying logic, then perhaps he should take a cold, hard look at his own camp, first. People in glass houses shouldn’t throw stones.
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.
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.
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”). So no matter how IP proceeds, he has no choice but to trip over his own ignorance and bias. The result, as we shall see, is a clumsy mess of awkward nonsense.
A proposition can be defined as a statement or assertion that expresses a judgement or opinion.
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 IP’s “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.
Consider the statement “Easter is the best holiday.” This cannot be proven true or false. It is just an expression of opinion.
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 very best example of an unprovable proposition is almost trivially easy to prove (depending on how you interpret it).
So you can have propositions that are neither true nor false. Nothing in logic or language denies this.
Again, classical bivalent logic absolutely denies the existence of any “alternative” truth values beyond true and false. I don’t know what else I can say to this, other than IP is just categorically wrong.
The sad thing about all this is that IP is actually headed in a very worthwhile direction with his discussion. The Liar’s paradox is a textbook example of the kind of proposition that binary logic struggles to deal with. That’s 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.
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. 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.
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”). So no matter how IP proceeds, he has no choice but to trip over his own ignorance and bias. The result, as we shall see, is a clumsy mess of awkward nonsense.
A proposition can be defined as a statement or assertion that expresses a judgement or opinion.
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 IP’s “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.
Consider the statement “Easter is the best holiday.” This cannot be proven true or false. It is just an expression of opinion.
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 very best example of an unprovable proposition is almost trivially easy to prove (depending on how you interpret it).
So you can have propositions that are neither true nor false. Nothing in logic or language denies this.
Again, classical bivalent logic absolutely denies the existence of any “alternative” truth values beyond true and false. I don’t know what else I can say to this, other than IP is just categorically wrong.
The sad thing about all this is that IP is actually headed in a very worthwhile direction with his discussion. The Liar’s paradox is a textbook example of the kind of proposition that binary logic struggles to deal with. That’s 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.
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. 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.
So the rest of the argument breaks down if premise 2 doesn’t even work. So building on that, let’s consider this statement:
“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.
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 Carlomon’s death has absolutely nothing to do with Gödel’s incompleteness theorems. That’s because Carlomon'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. More specifically, they have to do with the ability to derive theorems out of axioms through the formal exercise of rules of inference. IP's attempt to somehow conflate the two is just clumsy. It’s as he's just mish-mashing a bunch of fancy words together in the hopes that it will make him sound all smart and sophisticated to his fans. For those of us who are actually trained in the material, however, it is almost painfully obvious that IP has no clue what he’s even talking about.
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.
Thirdly, IP has deliberately misrepresented Gödel’s theorems. The quote he gave here was copied verbatim from Wikipedia, but with a few key words removed. For reference, this is the actual quote in its entirety, but with the missing bits underlined:
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers.
“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.
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 Carlomon’s death has absolutely nothing to do with Gödel’s incompleteness theorems. That’s because Carlomon'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. More specifically, they have to do with the ability to derive theorems out of axioms through the formal exercise of rules of inference. IP's attempt to somehow conflate the two is just clumsy. It’s as he's just mish-mashing a bunch of fancy words together in the hopes that it will make him sound all smart and sophisticated to his fans. For those of us who are actually trained in the material, however, it is almost painfully obvious that IP has no clue what he’s even talking about.
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.
Thirdly, IP has deliberately misrepresented Gödel’s theorems. The quote he gave here was copied verbatim from Wikipedia, but with a few key words removed. For reference, this is the actual quote in its entirety, but with the missing bits underlined:
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers.
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 doesn’t even apply to its original context.
So because of that, we can also deny premise 3 and say that it is a false dichotomy.
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!
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 can’t 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.
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 Brown’s 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.
So because of that, we can also deny premise 3 and say that it is a false dichotomy.
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!
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 can’t 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.
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 Brown’s 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. The idea that IP actually read through this thing in any rigorous detail is therefore just laughable to me. It’s like the guy randomly found this book in his attic one day and decided to shoe-horn it into his presentation.
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.
This stuff is important, because it completely undermines IP’s central thesis---the 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!). In practice, the usual way to solve the problem is to simply invent a new system of logic that rejects bivalence. In a sense, that’s exactly what IP even suggests, too, but he seems to be utterly incapable of realizing it. Instead, he seems to think that some universal, capital-L “Logic” must have existed the entire time, and really we humans were just applying the wrong logic from the beginning.
To make matters even more awkward, IP seems to treat imaginary numbers as a mysterious mathematical entity with properties totally beyond our comprehension.
The only problem is that we cannot epistemically understand the mathematical usage of i.
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 (Seriously, that’s all it is). It is no more transcendent or mysterious than the idea that -1 is, by definition, the number that produces zero when incremented. IP quite obviously does not understand any of this, and he is apparently just projecting that ignorance onto all mathematicians and philosophers across the globe.
Thus, Godel was proven right, and not the absolute skeptic who doubts logic is true.
I’m just going to recap IP’s argument over the last few sentences and see if you can make sense out of it.
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.
This stuff is important, because it completely undermines IP’s central thesis---the 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!). In practice, the usual way to solve the problem is to simply invent a new system of logic that rejects bivalence. In a sense, that’s exactly what IP even suggests, too, but he seems to be utterly incapable of realizing it. Instead, he seems to think that some universal, capital-L “Logic” must have existed the entire time, and really we humans were just applying the wrong logic from the beginning.
To make matters even more awkward, IP seems to treat imaginary numbers as a mysterious mathematical entity with properties totally beyond our comprehension.
The only problem is that we cannot epistemically understand the mathematical usage of i.
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 (Seriously, that’s all it is). It is no more transcendent or mysterious than the idea that -1 is, by definition, the number that produces zero when incremented. IP quite obviously does not understand any of this, and he is apparently just projecting that ignorance onto all mathematicians and philosophers across the globe.
Thus, Godel was proven right, and not the absolute skeptic who doubts logic is true.
I’m just going to recap IP’s 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?
There is no contradiction in logic. We just cannot know or prove all truth or fully understand everything. Just like with our proposition, we cannot know the answer due to our epistemic limits. But the fact that we are limited and unable to totally prove logic does not mean the laws of logic are not true.
Now it almost sounds as if IP thinks we cannot even prove logic. That is to say, we cannot prove how Carlomon was killed because of “epistemic limits,” even if we are perhaps very confident of a particular answer. By the same token, we cannot exactly prove logic per se, but just have to take it on a kind of faith.
This is again a classic example of how little IP understands logic. Starting with a few definitions of some basic terms (e.g., true-value, axiom, connective, etc.), plus a few basic rules of inference, it is actually very easy to derive every so-called “law of logic” you can think of. It’s all right there in every standard textbook on mathematical logic, and it does not require any faith or trust. All it requires is your willingness to abide by some simple definitions and rules.
The other thing to remember is that you just cannot deny the laws of logic. Any attack on the laws of logic is self-refuting.
As the philosopher Thomas Nagel says,
“We cannot criticize some of our own claims of reason without employing reason at some point to formulate and support those criticisms.”
In other words, to attack the laws of logic, you have to assume your attack on logic is logically formulated. If you actually didn’t think the laws of logic we true, you would not be relying on logical reasoning to show the laws of logic are not true. It completely undermines your very argument, because showing your conclusion, the laws of logic are not true, means your logical reasoning used to acquire that conclusion didn’t work.
It’s called a proof by contradiction, you jackass. I've seen you use it a hundred times in your own videos. The argument you gave us assumed a very specific law of logic, only to derive a conclusion that violated the laws of logic. You cannot complain about “self-refuting arguments” when the very logic you speak of is also apparently self-refuting. Either bivalence is a law of logic, or it is not. If it is, then we have a contradiction, and logic is screwed. It not, then everything is fine and dandy.
This is of course because it is also impossible to think or imagine something where logic doesn’t apply. You can’t simply escape logic and step outside of it like a set of boundaries. It is not something changeable. If something is outside of logic, then it is nothing. Logic simply is a description of everything that is and everything that is possible. Nothing can be outside of logic, so to speak. Any thought you have will be logical and definable in some sense.
Here, let me show you something:
It is true that I am married and it is true that I am not married.
There. I just violated logic. What are you going to do about it?
Notice that the universe did not implode on itself, nor did any philosophical logic police come rushing to arrest me. All I did was put words together wrongly, and so your brain failed to cohere them into a meaningful idea. That’s what happens when you violate logic.
The reason why it is so difficult to describe something where logic doesn’t apply is because logic itself is the basis by which we describe things in the first place. Logic is a formal set of rules built into language. If, however, you start viewing the world through the eyes of a creature without language skills (say, for example, a dog or cat), then all of a sudden it becomes very easy to navigate the world without logic. Just act entirely on stimulus and instinct, making no use of formal propositions in your behavior. That is a world entirely outside of any formal logic.
As Nagel says, “in skepticism about logic, we can never reach a point at which we have two possibilities with which all the evidence is compatible and between which it is therefore impossible to choose. The forms of thought that must be used in any attempt to set up such an alternative force themselves to the top of the heap. I cannot think, for example, that I would be in an epistemically identical situation if 2+2 equaled five, but my brains were being scrambled—because I cannot conceive of 2+2 being equal to five. The epistemological skeptic relies on reason to get us to a neutral point above the level of thoughts that are the object of skepticism. The logical skeptic can offer no such external platform.”
Basically, Nagel thinks you have to assume logic to deny logic. At least, that’s what I think he’s trying to say, because it’s nigh-impossible to confidently interpret this incoherent word salad. He also commits a blatant fallacy of arguing from ignorance, too. For example, in the world of modular arithmetic, it is actually perfectly consistent and meaningful to let 12+1 = 1. We even do it all the time in real life. It’s called a clock. This entire paragraph does nothing except show to the world that Thomas Nagel apparently doesn’t understand logic any better than IP does.
If you’re dealing with an epistemic skeptic, a good position to remember is particularism. Particularism is a formal response to the skeptic who doubts logic and knowledge.
We do not doubt or are skeptical of something unless we are given good reason to think so.
For example, we do not doubt all the mathematical knowledge which shows us 2+2=4. Unless the skeptic can give us reason to think so. We do not doubt we are conscious and our cognitive faculties work, unless the skeptic can give us reason to think so. The skeptic of course disagrees, and thinks we need to prove knowledge claims are 100 percent true, or else we should doubt them. The particularist turns this on the skeptic, and reminds him/her we do not doubt knowledge or intuition unless the skeptic can give us good reason to think we should. For example, perhaps we doubt our intuitive perspective “the sun is small than the earth,” because we have good evidence in astronomy and physics to think so. However, we do not doubt things like the laws of logic because we don’t have good reasons, like with the size of the sun, to doubt them. And the skeptic has not provided any, other than the mere possibility they might be false and that we cannot be 100% sure. But those are not good enough reasons to throw out knowledge and intuition.
So because not all propositions need to be true, we have already accepted we cannot be 100% certain in truth of all things. Attacks on the laws of logic are self-defeating. Through particularism, we have no reason to doubt our knowledge. We can see the attack on logic is an utter failure. The epistemic skeptic does nothing more than a clever trick, and fearmongering from a mere possibility. The laws of logic are objectively true, and there is no reason to doubt them.
Yeah, whatever. I don’t even care anymore. Virtually everything IP has said up to this point was categorically wrong, and even occasionally outright deceptive. This entire discussion could have been completely avoided with a single sentence:
There is no contradiction in logic. We just cannot know or prove all truth or fully understand everything. Just like with our proposition, we cannot know the answer due to our epistemic limits. But the fact that we are limited and unable to totally prove logic does not mean the laws of logic are not true.
Now it almost sounds as if IP thinks we cannot even prove logic. That is to say, we cannot prove how Carlomon was killed because of “epistemic limits,” even if we are perhaps very confident of a particular answer. By the same token, we cannot exactly prove logic per se, but just have to take it on a kind of faith.
This is again a classic example of how little IP understands logic. Starting with a few definitions of some basic terms (e.g., true-value, axiom, connective, etc.), plus a few basic rules of inference, it is actually very easy to derive every so-called “law of logic” you can think of. It’s all right there in every standard textbook on mathematical logic, and it does not require any faith or trust. All it requires is your willingness to abide by some simple definitions and rules.
The other thing to remember is that you just cannot deny the laws of logic. Any attack on the laws of logic is self-refuting.
As the philosopher Thomas Nagel says,
“We cannot criticize some of our own claims of reason without employing reason at some point to formulate and support those criticisms.”
In other words, to attack the laws of logic, you have to assume your attack on logic is logically formulated. If you actually didn’t think the laws of logic we true, you would not be relying on logical reasoning to show the laws of logic are not true. It completely undermines your very argument, because showing your conclusion, the laws of logic are not true, means your logical reasoning used to acquire that conclusion didn’t work.
It’s called a proof by contradiction, you jackass. I've seen you use it a hundred times in your own videos. The argument you gave us assumed a very specific law of logic, only to derive a conclusion that violated the laws of logic. You cannot complain about “self-refuting arguments” when the very logic you speak of is also apparently self-refuting. Either bivalence is a law of logic, or it is not. If it is, then we have a contradiction, and logic is screwed. It not, then everything is fine and dandy.
This is of course because it is also impossible to think or imagine something where logic doesn’t apply. You can’t simply escape logic and step outside of it like a set of boundaries. It is not something changeable. If something is outside of logic, then it is nothing. Logic simply is a description of everything that is and everything that is possible. Nothing can be outside of logic, so to speak. Any thought you have will be logical and definable in some sense.
Here, let me show you something:
It is true that I am married and it is true that I am not married.
There. I just violated logic. What are you going to do about it?
Notice that the universe did not implode on itself, nor did any philosophical logic police come rushing to arrest me. All I did was put words together wrongly, and so your brain failed to cohere them into a meaningful idea. That’s what happens when you violate logic.
The reason why it is so difficult to describe something where logic doesn’t apply is because logic itself is the basis by which we describe things in the first place. Logic is a formal set of rules built into language. If, however, you start viewing the world through the eyes of a creature without language skills (say, for example, a dog or cat), then all of a sudden it becomes very easy to navigate the world without logic. Just act entirely on stimulus and instinct, making no use of formal propositions in your behavior. That is a world entirely outside of any formal logic.
As Nagel says, “in skepticism about logic, we can never reach a point at which we have two possibilities with which all the evidence is compatible and between which it is therefore impossible to choose. The forms of thought that must be used in any attempt to set up such an alternative force themselves to the top of the heap. I cannot think, for example, that I would be in an epistemically identical situation if 2+2 equaled five, but my brains were being scrambled—because I cannot conceive of 2+2 being equal to five. The epistemological skeptic relies on reason to get us to a neutral point above the level of thoughts that are the object of skepticism. The logical skeptic can offer no such external platform.”
Basically, Nagel thinks you have to assume logic to deny logic. At least, that’s what I think he’s trying to say, because it’s nigh-impossible to confidently interpret this incoherent word salad. He also commits a blatant fallacy of arguing from ignorance, too. For example, in the world of modular arithmetic, it is actually perfectly consistent and meaningful to let 12+1 = 1. We even do it all the time in real life. It’s called a clock. This entire paragraph does nothing except show to the world that Thomas Nagel apparently doesn’t understand logic any better than IP does.
If you’re dealing with an epistemic skeptic, a good position to remember is particularism. Particularism is a formal response to the skeptic who doubts logic and knowledge.
We do not doubt or are skeptical of something unless we are given good reason to think so.
For example, we do not doubt all the mathematical knowledge which shows us 2+2=4. Unless the skeptic can give us reason to think so. We do not doubt we are conscious and our cognitive faculties work, unless the skeptic can give us reason to think so. The skeptic of course disagrees, and thinks we need to prove knowledge claims are 100 percent true, or else we should doubt them. The particularist turns this on the skeptic, and reminds him/her we do not doubt knowledge or intuition unless the skeptic can give us good reason to think we should. For example, perhaps we doubt our intuitive perspective “the sun is small than the earth,” because we have good evidence in astronomy and physics to think so. However, we do not doubt things like the laws of logic because we don’t have good reasons, like with the size of the sun, to doubt them. And the skeptic has not provided any, other than the mere possibility they might be false and that we cannot be 100% sure. But those are not good enough reasons to throw out knowledge and intuition.
So because not all propositions need to be true, we have already accepted we cannot be 100% certain in truth of all things. Attacks on the laws of logic are self-defeating. Through particularism, we have no reason to doubt our knowledge. We can see the attack on logic is an utter failure. The epistemic skeptic does nothing more than a clever trick, and fearmongering from a mere possibility. The laws of logic are objectively true, and there is no reason to doubt them.
Yeah, whatever. I don’t even care anymore. Virtually everything IP has said up to this point was categorically wrong, and even occasionally outright deceptive. This entire discussion could have been completely avoided with a single sentence:
It is not necessary to impose such a strict interpretation of bivalence onto logic.
BAM. Problem solved. Instead, we have to wade through this endless quagmire because IP doesn't know what a "textbook" is.
The sad thing about all of this is that IP works very hard to assemble these arguments in defense of Christianity. Yet, as this essay clearly shows, IP does not even have a grasp on the basic fundamentals of logic itself. At the same time, however, he seems to think very highly of his ability to do logic. He is thus cursed with a high degree of confidence that only leads to a series of embarrassing failures with each and every presentation. That sadness is only amplified even further by the deliberate malice and manipulation he brings to the discussion. How does this guy ever expect to make a compelling case for Christ when he cannot even educate himself on the very rules of reason itself?
Thanks for reading.
Thanks for reading.
