The Impossibility of Illogical Thought
Thought can never be of anything illogical, since, if it were, we should have to think illogically.
It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an 'illogical' world would look like.
It is as impossible to represent in language anything that 'contradicts logic' as it is in geometry to represent by its a coordinates a figure that contradicts the laws of space, or to give the coordinates of a point that does not exist....
In a certain sense, we cannot make mistakes in logic....
Self-evidence, which [Bertrand] Russell talked about so much, can be dispensable in logic, only because language itself prevents every logical mistake.--What makes logic a priori is the impossibility of illogical thought.
--Ludwig Wittgenstein, Tractatus Logico-Philosophicus
3.03, 3.031, 3.032, 5.473, 5.4731
(H/T: Roderick T. Long)
Sorry, Sheldon, but that is *very* unconvincing. Any human language is noticeably inconsistent and I would say illogic in its construction, which is why programming languages were invented. Try to parse the sentence "Time flies like a banana": are we talking about something akin to houseflies liking a fruit, or about time passing in a peculiar way?
ReplyDeleteI'm not sure that's responsive, Joe. You can say "square circles" too, but you can't talk or think about them. Word salad is certainly possible, but what that have to do with Wittgenstein's point.
ReplyDeleteI see the third paragraph as completely "illogical": it is *quite* possible to represent in language something (an infinite number of things, actually) that contradicts logic, or in other words, an erroneous statement. The fourth is also very weak (or tautological): people make logic mistakes rather frequently, don't you think? Even if we define terms and agree on their meaning, like what is an odd number, what divisible means, etc., although it's obvious that "the first positive odd number is 2" is incorrect, someone can make an assertion like "9409 is a prime number" that is much harder to prove wrong.
DeleteThe ability to make hard-to-refute erroneous assertions sounds like something other than what Wittgenstein is talking about. He wouldn't deny it. What he's saying is that, strictly speaking, to infer wrongly is not to infer; to add a column of numbers wrongly is not to add them; to think illogically is not to think. Thinking logically is just what we mean by thinking--just as acting praxeologically (i.e. rationally) is just what we mean by acting. (See Long's paper that I link to above.) We may speak otherwise colloquially, but that's fine. Wittgenstein is hardly saying people are infallible. He's saying we cannot imagine an illogical world, so it makes no sense to talk about a boundary between a logical and nonlogically realm.
DeleteBut reality, i.e. actual people, disproves the last sentence: billions of people have imagined and continue to imagine illogical worlds. Leaving aside religion (although in part it influenced this), people believed for a long time that the earth was at the center of the universe and the sun and planets rotated around it, even when some had suggested from the 4th century BCE that the "logical" thing was something else. For many years, to explain the nature of light and electromagnetic waves, people posited the existence of "ether", something through which the waves moved, until an experiment disproved that possibility (even then some questioned or imagined an alternate explanation). There are examples in astronomy, biology, geology, mathematics, climatology and, needless to say, politics. Plus, even logic itself as conceived by Aristotle, wasn't entirely consistent.
DeleteI think you've missed Wittgenstein's point. He's not saying you can't imagine a counterfactual world. Disney imagined a world where mice speak. LW's saying you can't imagine an illogical world--where A is also not-A, where square circles exist, where triangles can have angles that sum up to more than 180 degrees, etc.
DeleteThe problem lies with what the definition of "logical" is. Is a world "logical" where billions of people believe, many of them fervently, in the existence of one of several deities or "spirits" and deny the existence of others? Where millions of people make pilgrimages to various place where some supposed miracle happened? In the physics realm, the Big Bang theory posits that no atoms existed some 14 billions years ago (only some precursor particles) and that the entire universe was in high density state which started expanding and continues to do so (and we can confirm due to the cosmic microwave background that that was must've happened). But physics can't say that space and time existed before this singular event. Plus in relativistic physics and quantum mechanics there are things such as time dilation, length contraction, entaglement of particles that are kilometers apart, that defy logical explanations. Also, in non-Euclidean, non-plane mathematics, triangles do not have angles that add up to 180 degrees. Square circles do not exist because of how a circle is defined. Even when one tries to define mathematics precisely in terms of logic, like Bertrand Russell, along comes Godel with his incompleteness theorem. As far as I'm concerned, LW is in very shaky ground.
DeleteHow can one speak (or think) meaningfully about anything without presupposing identity, noncontradiction, and excluded middle?
DeleteJoe, you are of course free to use the word "logical" however you like. But you cannot legitimately use it with the broad, vague meaning you're giving it, while simultaneously taking issue with Sheldon's and Wittgenstein's claims as though they're using "logical" in the same broad, vague way you are.
ReplyDeleteYes, admittedly I haven't read Wittgenstein's _Tractatus_ so I can't tell from Sheldon's short quotes how precise he was trying to be. Sheldon above appears to have narrowed it down to identity, noncontradiction and the excluded middle. Nevertheless, I still believe that saying that "if one does not think according to those three axioms, one is not thinking" is simply making up a definition of thinking, the practical effect being that, according to that rule, a lot of people most of the time aren't "thinking", but what good is that?
DeleteI still think that some physical and mathematical laws, which are not at all "vague", sometimes lead to contradictions. Say you draw a circle on a sphere like the equator. If you look at it from one of the poles, it is a circle, but from a lower angle it is an eclipse and from the equator it's just a line segment. And sometimes we can only assign probabilities to matter, like in the double-slit experiment. Considering the law of identity, what is an electron or a photon: a particle or a wave? Is a meter stick traveling at half the speed of light really a meter long? And Sheldon has written here before something like "existence exists". OK, so what existed more than 15 billion years ago?
A stick looks disjointed when partially submerged in water. Things, even light, respond differently under different circumstances. I don't see the logical problem here. A thing is what it is, and that presupposition is built into your language. The fact of existence can't specify what exists. That's what scientists try to do. People intuit that illogical "thinking" is just not what we mean by thinking. How many school children, after getting a math problem wrong, were admonished, "Use your head!"
Delete"A thing is what it is": but in many cases, we can't tell what a "thing" is, even after defining terms, doing precise measurements and using mathematical formulas.
DeleteIt is perhaps for this that I still don't see how one can call some process of reasoning as *absolutely not* thinking, because it lapsed into some possibly incorrect deductions or reached a not fully substantiated conclusion. Coming up with a theory would then be classified as "not thinking", or perhaps "illogical thinking"?
"I still don't see how one can call some process of reasoning as *absolutely not* thinking, because it lapsed into some possibly incorrect deductions or reached a not fully substantiated conclusion."
DeleteI've not done that, and I seriously doubt that Wittgenstein ever did.
In the first quote, Wittgenstein says "Thought can never be of anything illogical". Doesn't that say: if we reason about something that is not logical, then we're not thinking. Isn't that essentially what I stated? Isn't following a train of propositions and making a non sequitur (something that does not follow from the given premises), an example of illogical reasoning and thus something that Wittgenstein would say is "impossible" as in "never can be" and thus he'd say you can't call that "thought" or "thinking" because, as he asserts "we should have to think illogically" (IOW, he is ruling out "illogical reasoning" as "thinking").
DeleteThe first quote seems to say we can't think about what's illogical. So demarcating between the logical and illogical makes no sense. And, further, the idea that we impose logic on the world or the world imposes it on us makes no sense because it assumes that without the imposition the world or we could be illogical. He also says that inferring incorrectly is to not infer, just as a incorrectly adding up a column of numbers is not to really add. I think we're going in circles here, Joe.
DeleteYes, you obviously have a very different interpretation of what the quote means and even of your title. In a comment above, you wrote that Wittgenstein was "saying is that, strictly speaking, to infer wrongly is not to infer; to add a column of numbers wrongly is not to add them; to think illogically is not to think." Now you say "we can't think about what's illogical. So demarcating between the logical and illogical makes no sense." I'm sorry Sheldon, but to me that doesn't compute, so I guess we'll have to leave it at that.
DeleteSo we'll agree to disagree. Still, I cannot let stand your claim that I shifted my position. I did not. I'll leave it to readers to judge. I appreciate the dialogue.
DeleteSheldon, I wasn't trying to imply that you shifted your position. By "that doesn't compute", I was only trying to indicate that the statements I quoted didn't make sense to me. It appears that your title and your understanding of what Wittgenstein expressed in those quotes is either quite different than mine or they are something I cannot grasp (maybe it's because I haven't read Wittgenstein).
DeleteSince I was reading the following just now, maybe a concrete example may help: "In itself, money was not productive, and as such, it should not be allowed to 'breed' (obtain an amount in excess of the original amount lent), because, in his mind, this would be getting something for nothing. That which was 'barren' (money) could not bare 'offspring' (interest on a loan). [more context here: https://fee.org/articles/aristotle-understood-the-importance-of-property/ ]. It's basically about Aristotle thinking that collecting interest is not proper (or natural).
So, was Aristotle "thinking" when he reasoned that way? If he was "thinking", was he thinking "logically"? My answers: he was thinking, and he was thinking logically, but he was not taking into account certain "facts". OTOH, on the question of slavery (earlier in the article), I think Aristotle was thinking "illogically" because I doubt that there were any distinguishing characteristics that he could point out to say, "Oh, this guy is obviously born for servitude, but that other is "higher" and deserves a life of leisure".
I think Wittgenstein would say that if Aristotle drew an erroneous conclusion from his premises, then he had not reasoned; his mental activity would not count as thinking.
DeleteYou didn't respond to the concrete examples I gave, but I will not insist further. However, I still fail to see any usefulness in declaring that Aristotle's "mental activity would not count as thinking" if he "drew an erroneous conclusion from his premises". It's like saying that Einstein (or any theoretical physicist) wasn't "doing physics" when he came up with a "thought experiment": stating that does not add any value to discourse IMHO. Another example would be saying that an athlete isn't "exercising" unless he or she moves the muscles in a "proper" way.
DeleteWhile I think we've gone around on this, it may be useful to mention the distinction between a valid and a sound argument.
DeleteI think of the old Woody Allen syllogism: All men are mortal; Socrates was a man; therefore all men are Socrates.
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