Truisms and Tautologies Bug Me
Well, that's all I pretty much have to say. But I found this so-called "axiom" of Objectivism to be one of the most annoying truism ever: "Existence exists."Well, yeah. Here's a fun exercise, though. What is existence? Without telling you anything (existence is kind of a fuzzy concept), I'm going to say existence is the set of all things that exist. And so the above statement reduces to "Things that exist, exist."
Well yeah... Things that fly, fly. Things that swim, swim. Things that do A, do A. It's a truism, and a tautology, and it pisses me off. Why? Because it conveys no useful information. Okay, that's just an annoyance: what pisses me off is when people proudly chant tautologies like they're useful. e.g. calling the statement an "axiom" from which something could be derived. I was going to do a post about "false axioms", but really I don't need to. I just want to point to various math axioms postulated throughout the centuries and say those aren't "false axioms" because they're proper. Even the ones that were later reduced to theorems, were not "false axioms". But the Objectivist "axioms" are indeed "false axioms", and I'm certain I could find more if I went googling.
"Tautologies are like tautologies" is a humorous phrase. I like truisms and tautologies when used for humor, as I like many things when used for humor (like the depiction of someone getting hit in the groin). But truisms and tautologies outside of that scope are just annoying, like getting hit in the groin outside the comedy realm is just painful.
Sometimes that "existence exists" is phrased as "A is A", or "A = A". Funnily enough, while it has been used as an axiom of equality in math, that particular axiom is really a theorem in ZFC set theory. See the proof. Also fun is when A = B. Yay for isomorphic statements as well as math identities! sin^2(x) + cos^2(x) = 1 is an example of A = B.
Unjustified arrogance is probably at the root of my displeasure here... People are actually proud for chanting these meaningless things... Ah well. One of the great criticisms I've read of Atlas Shrugged is that it convinces even the dumbest people that they can be geniuses if they just work hard enough. Whatever. End rant.
Addendum: This page is very enlightening. My annoyance from the tautology above comes from taking it as a tautology when Rand meant it for something more. (And of course that something more is not logically sound, as that link goes through.)
Posted on 2009-12-25 by Jach
Tags: rant
Permalink: https://www.thejach.com/view/id/61
Trackback URL: https://www.thejach.com/view/2009/12/truisms_and_tautologies_bug_me
Jach
December 28, 2009 07:55:11 AM
"The set of all things exists" is even more useless. What things? What does it mean to exist, what does it mean to not exist? It's retarded.
"A rose by any other name would smell just as sweet." It would be nice if I could generalize that you can never be wrong with labels. Instead I have to use the weaker statement that one should be very careful when one uses lazy English to make an argument.
"A rose by any other name would smell just as sweet." It would be nice if I could generalize that you can never be wrong with labels. Instead I have to use the weaker statement that one should be very careful when one uses lazy English to make an argument.
Jach
December 28, 2009 07:59:37 AM
While we're talking about sets, see the axioms of ZFC set theory: http://en.wikipedia.org/wiki/ZFC_set_theory
Those are very non-useless axioms; indeed nearly all of mathematics is derived from them. (And actually derived with step-by-step proofs! Not clever arguing.)
Those are very non-useless axioms; indeed nearly all of mathematics is derived from them. (And actually derived with step-by-step proofs! Not clever arguing.)
Amaroq
December 29, 2009 05:20:18 AM
I'm not really interested in reading it. I skimmed a little bit of it, and it appears to be mathematical in nature, which I expected.
I believe that our disagreement on Objectivism's axioms is at least partially due to a disagreement on the definition of axiom.
Rand defined an axiom as "An irreducible primary." Mathematical axioms, as defined by you/mathematicians, aren't just that, but have other properties that you take as being prerequisite to being an axiom.
Existence, Identity, and Consciousness are considered axioms by Objectivism because they are an individual's three starting points for everything they can know. If any one of them is missing, you can not be aware of anything. (There's your falsifiability right there. If any of Oism's axioms were false, we wouldn't be having this or any other conversation with each other or anyone else.)
If you're so intent on proving that existence isn't axiomatic, let's see you reduce existence into some fundamental parts. The onus for that one should be on you, since you're the one who asserts that it should be reducible, while I assert that it is an axiom and therefore irreducible.
I believe that our disagreement on Objectivism's axioms is at least partially due to a disagreement on the definition of axiom.
Rand defined an axiom as "An irreducible primary." Mathematical axioms, as defined by you/mathematicians, aren't just that, but have other properties that you take as being prerequisite to being an axiom.
Existence, Identity, and Consciousness are considered axioms by Objectivism because they are an individual's three starting points for everything they can know. If any one of them is missing, you can not be aware of anything. (There's your falsifiability right there. If any of Oism's axioms were false, we wouldn't be having this or any other conversation with each other or anyone else.)
If you're so intent on proving that existence isn't axiomatic, let's see you reduce existence into some fundamental parts. The onus for that one should be on you, since you're the one who asserts that it should be reducible, while I assert that it is an axiom and therefore irreducible.
Jach
December 29, 2009 07:27:52 PM
You don't understand falsifiability. Take a science course.
If you want to understand what an axiom (assumption) actually is, see here: linky.
I call your axioms false axioms because they're just truisms and tautologies, whose truth is inherent in the logical structure in which they're phrased, and who convey no additional information. You also have offered no axiomatically derived theorems. I also don't deny that "existence exists" anymore than I could deny "flying things fly". Basically, they don't deserve the title of "axiom". Rand chose that to make them seem special, because "axioms" are generally regarded as special, but these aren't. It's a propaganda move to call them axioms.
I'm very confident that "existence" can be reduced, or at the very least identified as a wrong question and the cognitive algorithms that give rise to the question can be reduced. I'd put weight that the answer is the latter.
If you accept that existence is just another word for reality, then everything is simple: we have atoms (which were supposed to be irreducible: they aren't) which exist in reality, but they aren't what "existence" (reality) is made of. We have a clear and ever clearer idea of what "reality" is, and it's still not ultimately reduced.
To be a little mischievous, take your favorite truism "existence exists", and I respond with the question: why?
If you want to understand what an axiom (assumption) actually is, see here: linky.
I call your axioms false axioms because they're just truisms and tautologies, whose truth is inherent in the logical structure in which they're phrased, and who convey no additional information. You also have offered no axiomatically derived theorems. I also don't deny that "existence exists" anymore than I could deny "flying things fly". Basically, they don't deserve the title of "axiom". Rand chose that to make them seem special, because "axioms" are generally regarded as special, but these aren't. It's a propaganda move to call them axioms.
I'm very confident that "existence" can be reduced, or at the very least identified as a wrong question and the cognitive algorithms that give rise to the question can be reduced. I'd put weight that the answer is the latter.
If you accept that existence is just another word for reality, then everything is simple: we have atoms (which were supposed to be irreducible: they aren't) which exist in reality, but they aren't what "existence" (reality) is made of. We have a clear and ever clearer idea of what "reality" is, and it's still not ultimately reduced.
To be a little mischievous, take your favorite truism "existence exists", and I respond with the question: why?
Amaroq
January 09, 2010 05:41:51 AM
Even if you do find the most fundamental particle in the universe (should quarks be reducible), that particle still exists. You have not reduced existence itself, you have reduced existents.
I read the link about axioms, and even read-skimmed another page he wrote in the same section. The guy appears to dislike Aristotle (the father of logic), and seems to be a pragmatist who thinks you should just choose your own axioms.
Other than that, I'm not quite sure what he was trying to get at. He just seemed to be attacking axioms to render them uncertain. He's probably a philosophical skepticist.
I uphold the very dictionary definition that he rejected. The #1 definition especially. Existence, Identity, and Consciousness are so obvious, that I can't see how any sane, rational person can reject them.
Though rejecting them as axioms and outright rejecting them themselves are two different things. I can see maybe rejecting consciousness as an axiom, since our brains can be reduced. Though all of your knowledge requires that you were conscious in the first place to gain it. That's why it's an axiom. I can't see how you can reject existence and identity as axioms though. I have yet to see you reduce them.
I read the link about axioms, and even read-skimmed another page he wrote in the same section. The guy appears to dislike Aristotle (the father of logic), and seems to be a pragmatist who thinks you should just choose your own axioms.
Other than that, I'm not quite sure what he was trying to get at. He just seemed to be attacking axioms to render them uncertain. He's probably a philosophical skepticist.
I uphold the very dictionary definition that he rejected. The #1 definition especially. Existence, Identity, and Consciousness are so obvious, that I can't see how any sane, rational person can reject them.
Though rejecting them as axioms and outright rejecting them themselves are two different things. I can see maybe rejecting consciousness as an axiom, since our brains can be reduced. Though all of your knowledge requires that you were conscious in the first place to gain it. That's why it's an axiom. I can't see how you can reject existence and identity as axioms though. I have yet to see you reduce them.
Jach
January 09, 2010 07:23:46 AM
This, too, is an exercise in futility.
Also, it's A is A, not A = A. It's an easy mistake to make, and one that I made too until recently. An apple is an apple and not an orange, as opposed to apple equals apple and does not equal orange. Identity as opposed to equality.
If you take Existence as you defined it, the set of all things that exist, the phrase Existence Exists can be said as "The set of all things Exist." As opposed to nothing existing. I think the statement becomes useful once you word it that way.