Ok, according to Leibniz's rule nothing should equal nothing. Therfore there should be nothing. Those other rules do not apply because at one point there was nothing.
Ridiculously flawed logic. If I say "all green unicorns are green" it doesn't follow that there are any green unicorns. And if you say my premise is wrong because there are no unicorns, then you can't use your premise either without assuming what you seek to prove (there is something), making your argument circular.
@asdfaxsdgg In first-order quantificational logic, the Law of Identity is taken as true, the inference rule of Universal elimination allows you to infer from (∀x) x = x, a = a. The inference rule of Existential Instantiation allows you to infer from a = a, (∃x) x = x. Technically speaking, the argument is sound. So, in order to challenge the argument, you must challenge the law of identity, the rule of Universal elimination, or the rule of Existential instantiation (or all of the above).
@JonathanM00r3 I don't have to challenge the logical rules, it's just that they presuppose the existence of something, which is fine since in any case we don't need proof THAT there is something rather than nothing. But it means the argument is circular and does nothing to help explain the real question of WHY there is something rather than nothing.
@asdfaxsdgg The answer is given, (i.e. it would be contradictory for there to be nothing). Short of showing that the logical system is flawed or that there is a better system of logic that doesn't have (∃x) x = x as a theorem, the question is unmotivated. It would be just as silly as asking why (∀x) x v ~x or why 2+2 = 4? Our regimented theory of the world includes first-order QL. We accept the ontological commitments of QL just like we accept the ontological commitments of atomic theory.
@JonathanM00r3 It's only contradictory in a logical system that presupposes existence. This doesn't mean such a logical system is flawed, it just doesn't help in giving a satisfying answer to this particular philosophical question. Of course, a better way of putting the question would be "Why is the universe the way it is and not any other way?" (The other way might be "nothingness" but also any other of an infinite number of possibilities.)
@asdfaxsdgg My point was not that you should show that the logic is flawed, rather my point was that the burden is on you to provide an alternative logic that doesn't include (∃x) x = x as a theorem but is equally powerful. If you can, for purposes of ontological simplicity, we would be obliged to accept that system of logic over classical QL. I view QL in the same light as any other theory in science (i.e. We accept for it's explanatory power as well as other theoretical virtues).
@asdfaxsdgg However, if one cannot provide an alternative logic of equal power, we must accept QL like we would accept any other theory, and accepting it involves accepting it's ontology (Because, of course, that's the only way the theorems could be true). "it just doesn't help in giving a satisfying answer to this particular philosophical question." I find it satisfying. Whether an answer is satisfying is relative to the individual.
@asdfaxsdgg ""Why is the universe the way it is and not any other way?" (The other way might be "nothingness" but also any other of an infinite number of possibilities.)" It COULDN'T be "nothingness" because System K of Modal Logic says that it's impossible that there be nothing. In any case though, this is a different question than the original. On any meaningful interpretation, this question appears to be a question for a cosmologist (since they study the structure of the universe).
@asdfaxsdgg Presumably, the theories of the cosmologist will explain why our universe behaves in the way that it does and not in some other way. This question/problem doesn't appear to be significantly philosophical.
@asdfaxsdgg "It's only contradictory in a logical system that presupposes existence." Similar things could be said like "It's only contradictory to reject electrons within a physical theory that posits electrons." While that statement is true, it only points out the need to provide an alternative theory that does not posit electrons but is equal in its explanatory power.
@JonathanM00r3 Such a system of logic has explanatory power in an obviously existing world, but does not seem applicable to this particular question. There is an obvious difference between the banal "proof" of the video and a physical theory that you can test in practical experiments. As to the cosmologist, he will at best say the world is how it is because of certain physical laws, but he can't answer the more fundamental question as to why those laws are as they are.
@asdfaxsdgg "There is an obvious difference between the banal "proof" of the video and a physical theory that you can test in practical experiments." The abstractness of the question precludes a concrete answer like one we would expect in physical theory. It presumably requires an explanation/answer that is similarly abstract. Asking for a physical explanation is out of place here. Furthermore, while there is a difference, it's not obvious that it's a difference in kind (in degree, perhaps).
@asdfaxsdgg "Such a system of logic has explanatory power in an obviously existing world, but does not seem applicable to this particular question." Atomic theory only has explanatory power in a world with atoms. I fail to see your point. Yes, we live in an "existing world". Our theory is supposed to explain why that is the case. In this instance, our regimented theory tells us that it would be inconsistent for there to be nothing. If we accept that theory, we should accept that answer.
@JonathanM00r3 Obviously the question is profound for many people, yet you are making it into a triviality by essentially saying "Anything exists because it exists." That does not explain why. Incidentally I am not convinced the logic is even technically correct. It seems to be an existential instantiation fallacy, by which you could as well prove the existence of green unicorns. Just by common sense, "all" can be less than one; saying anything about "all x" doesn't mean there exists any x.
@asdfaxsdgg It's actually not an existential instantiation fallacy given the fact that '=' is treated as a predicate in first-order QL. Many universal statements such as "All Unicorns are Green" (∀x) (Ux -> Gx) do not imply the existence of unicorns because the structure of this sentence takes the form of a conditional involving TWO predicates. The truth conditions for the material conditional have it that it's false only when the antecedent is true and the consequent is false, else it's true.
@asdfaxsdgg So trust me. It's technically correct given the rules of first-order quantificational logic. In Natural Deduction, you use the rules "Universal elimination" and "Existential Introduction" to generate the proof. In the tree method for QL, the argument with the premise and the negation of the conclusion closes, showing the original argument to be valid. It's also valid and sound in System K of Quantified Modal Logic, as I've mentioned before.
@asdfaxsdgg "yet you are making it into a triviality by essentially saying "Anything exists because it exists."" I have never said this and this is not my view. My position has always been, "Something exists because it would be logically inconsistent for nothing to exist (~(Something exists)), given first-order quantificational logic." It's true that people believe the question to be profound, but that certainly is not evidence that it actually is.
@asdfaxsdgg Existential instantiation fallacy cont.: So, the reason we can't infer the existence of green unicorns from the sentence "All Unicorns are green" is because that sentence is a conditional and there is an interpretation that makes that sentence true even if there are no unicorns (i.e. The antecedent is false). Statements of identity don't take that form.
@JonathanM00r3 What about "all unicorns are unicorns" then? There you have an identity. Anyway, you may be right or not about the technical correctness of the argument according to any given logic system. But I'm not impressed by that, since it doesn't make sense to me on its face, and any logic system may be flawed if only for this particular case. And your stated position seems to be just a more fancy, but no more convincing, way of saying "Anything exists because it exists."
@asdfaxsdgg "What about "all unicorns are unicorns" then? There you have an identity." It's not an identity. It has this form: (∀x) (Ux -> Ux) (U(1): is a unicorn). It's true even if there are no unicorns because it's in the form of a conditional. "And your stated position seems to be just a more fancy, but no more convincing, way of saying "Anything exists because it exists." But it isn't. Those two sentences have a different semantic interpretation.
@JonathanM00r3 (1) (∀unicorns x) (x = x), (2) so, for any particular unicorn, u = u, (3) therefore there exists a unicorn u for which u = u. How is this different?
@asdfaxsdgg "(∀unicorns x) (x = x)". Improper use of the Universal quantifier. This isn't a well-formed sentence in the language of first-order logic, given the notation for universally quantified expressions.
@asdfaxsdgg The universal quantifier ranges over variables. "Is a Unicorn" is a predicate that attaches to variables or constants. "(∀unicorns x)" just doesn't have an interpretation/meaning in the language of QL.
@asdfaxsdgg First-order logic doesn't include set-membership. You need second-order logic for that. But even in second-order logic, this sentence isn't well-formed (i.e. it doesn't obey the syntax of second-order logic)
If what you're trying to say is "Every member of the set of unicorns is self-identical", then you're just saying something false. Due to the axiom of extensionality, U = ∅. It would be false to say "Every member of the null set is self-identical". There are no members of ∅.
@asdfaxsdgg If you're interested in an alternative logic that doesn't involve the ontological commitments that we've been talking about, then you should check out "free logic". I think you might be interested.
@JonathanM00r3 That makes sense. Indeed the Wikipedia article on free logic shows an example from classical logic that proofs the existence of "Pegasus." That's what I meant. Apparently classical logic allows you to prove the existence not just of something but of anything.
@asdfaxsdgg I actually just read the Wikipedia article on free logic and it goes on to explain exactly why you can't prove the existence of "Pegasus" in standard first-order logic because one cannot substitute nondesignating constants for variables.
@JonathanM00r3 Well, then the article does not really explain well what the problem with classical logic is that free logic is supposed to fix. If the assumption of the existence of "something" is the only problem, then it may make practical sense for everyday purposes to let that go, instead of complicating everything else just to cover this. But for this particular question I would indeed use a logic that is careful about existential presuppositions.
@asdfaxsdgg Go to the Stanford Encyclopedia of Philosophy article on "Free Logic". It's better and it gives an explanation of the motivations for free logic.
@asdfaxsdgg "But I'm not impressed by that, since it doesn't make sense to me on its face, and any logic system may be flawed if only for this particular case." Ok, fair enough. But then we're back to what I said earlier. The burden is on the skeptic to provide an alternative logical system that has equivalent or greater power. The current system is practically indispensable for scientific reasoning and ordinary reasoning. Many philosophers work on alternative logics.
@asdfaxsdgg I myself am interested in alternative logics because there are features of the current system that are counterintuitive to me as well (e.g. the truth conditions for the material conditional. See "Relevance Logic"). But, I don't take that as evidence that the system is not fundamentally correct. And until some philosopher/logician can provide a rival system, I'm compelled to accept this one. I feel the same way about scientific theories.
@asdfaxsdgg "As to the cosmologist, he will at best say the world is how it is because of certain physical laws, but he can't answer the more fundamental question as to why those laws are as they are" That's a bold assertion! You might need to provide support for that claim. In any case, I think it's possible that the physical cosmologist could develop a theory that explains why the physical laws are as they are. Nothing, at this point, seems incoherent about that idea.
@JonathanM00r3 Without prior restraints other than self-consistency, it is easy to imagine all kinds of possible worlds different from the one we live in. The physicist can only describe our world as it is, but he can't say it couldn't logically be any other way. So we have a fundamental philosophical question here.
@asdfaxsdgg It's also not circular in any problematic way. For instance, one can start with the assumption that nothing exists [~(∃x) x = x] and derive a contradiction (Reductio ad Absurdum). One can even do this in System K of Modal Logic with the claim "It's possible that nothing exist" [◊~(∃x) x = x] and also derive a contradiction. If this theorem is problematic, then all theorems of QL or K are equally problematic.
A person asking the question is instantly answering it.
Language is the problem here.
Maybe it is better to put it in terms "Why is there Everything instead of Nothing".
Something (subset of Everything) , implies that there is also Something that doesn't exist. A concept of Selection kicks in, which triggers a concept of Choice and intelligence.
Its not as "begging" as "why is there a creation, but its close.
A person asking the question is instantly answering it.
Language is the problem here.
Maybe it is better to put it in terms "Why is there Everything instead of Nothing".
Something (subset of Everything) , implies that there is also Something that doesn't exist. A concept of Selection kicks in, which triggers a concept of Choice and intelligence.
Its not as "begging" as "why is there a creation, but its close.
One must start from the simple observation that something currently does exist. What exists in fact, must be possible. That means, as we extrapolate into the past, and into past states of being, we have to conclude that ever current and future state of existence must exist as a "potential" or possible state in the past.
Obviously, if the present state of existence had not been possible in the past, it could not exist now.
(cont'd) (2) If one accepts this premise (and I'm not sure on what basis one could dispute it) then one would have to accept that there could never have been a point in the past at which the potential for existence, and for every actual state of existence, did not itself exist.
True nothingness -- absolute nothingness would have to be devoid of such potential (because potential is obviously *something*) -- and absent that potential, there could be no existence at all. Ever.
The best answer to this question I have come across is this:
Nothing exists except logical possibility, which necessarily exists, and our perception of material existence is an epiphenomenon of our being logical subcomponents of a logically possible universe.
I'd link you to the website where I read that but YouTube won't let me, so type into Google: "Nothing exists except logical possibility" in quote marks, & you'll be able to find the answer on the knowinghumans website among others.
Of course there isn't always something rather than nothing.
In fact, there are countless universes where absolutely nothing exists. Unfortunately no one is there to count them or communicate this fact to the outside.
From Answers.com: "The implications of a proposition as to what exists. If a proposition entails the existence of something, then it has existential import. It should be noticed that in the predicate calculus the universal quantification (∀x)(Fx → Gx) has no existential import, since it is true when nothing is F."
@MoonMankkkkkk but the existence claim didn't come from a universally quantified statement. It came from an existentially quantified statement. it came from a statement for which something must exist for it to be true.
It doesn't matter. You still derived an existentially quantified statement from a universally quantified statement, which is considered an invalid inference in predicate logic.
@MoonMankkkkkk Dude, you don't have to take my word for it; see the wiki article on "free logic" or you can look up James's Garson's book "Model logic for Philosophers". This is not my derivation; it is well known and fully accepted as a valid inference given the standard rules governing logical constants. Heck, I spent the first 1/2 of the video explaining why the rules for existential quantification are valid.
In free logic, the proposition "there exists at least one x" cannot be derived solely from "far all x, x is equal to x." (The Wikipedia article shows that your method of proof is invalid in first-order logic). A logic where the former proposition can be derived from the latter must already have existential presuppositions. If that is the logic you are employing, your argument is therefore circular. If your argument is not circular, it is invalid. Which is it?
"Consider the following classically valid theorems. 1. ∀xA -> ∃xA"
This was the argument that you used; if there exists some predicate that is true of all entities, (you used identity), you presumed it could be inferred that there exists at least one thing that is equal to itself. Of course, this is only a valid argument in a logic that has "existential presuppositions."
"Classically, ∃x(x=y) is deducible from the open equality axiom y=y by particularization."
This was the logic that you used. In free logic, however:
"In free logic, (1) is replaced with 1b. ∀xA ∧ E!t -> ∃xA, where E! is an existence predicate (in some but not all formulations of free logic, E!t can be defined as ∃y(y=t))."
Again, you didn't say whether you were using free logic, but you are wrong if you are. I am quoting directly from the article you referred to.
It's quite clear that the second premise had no meaning in predicate logic terms, (it wasn't in predicate logic notation and thus wasn't in well-formed formula). That is, unless you meant for "A" to be an entity, (which of course would make it improperly capitalized as capitalized letters stand for predicates). This would the inference rule of universal generalization. You then (implicitly) derived (3) from (2) using the rule of existential generalization.
The problem here is that it is a specific restriction of the rule of Existential Generalization that in deriving a quantified statement from a singular statement, (as you did), the singular statement must not have been derived through universal generalization. But this is that you did. You derived "A=A" from "(x)(x=x)."
To restate, the rule of Existential Generalization does not allow you to derive "(∃x)(x=x)" from the singular statement "A=A" because "A=A" was derived from "(x)(x=x)", a universal statement.
You have derived this proposition by misusing the rules of inference for predicate logic. Thus, the inference is invalid.
Of course, now that I have proved the invalidity of your argument, I, (consequently), expect you to either remove the video or make it clear you aware of the fact that the reasoning exhibited in the video is fallacious.
While you and Lewis Carroll might (have) disagree(d) with this, he recognized that any author may take whatever policy they wish when it pertains to the creations of their own system. (As far as I am aware), the modern square of opposition affirms that universal statements lack existential import. Ergo, the proposition, "something exists", cannot be derived from the law of identity and is an axiom.
It has been a well-settled doctrine that in modern logic, all universal propositions necessarily lack existential import. For instance, by the rules of symbolic logic, the proposition, "All men are mortal," does not prove that there exists something which is a man, much less does it prove that there exists something that is both a man and a mortal thing.
@lindarajalin1 Think about it this way: suppose I want to answer the question "why is there a solution to the equation 2+2=X"? A way to answer that question is "because this is a deductive proof which shows the solution is X=4". By the same token, then, why isn't a good answer to the question "why is there something rather than nothing" the same kind of answer: "because I have a deductive proof which shows it exists".
You never answered the title of the video lol. WHY is there something rather than nothing. You answered, prove something exists. Which I don't really understand why this needs to be proven at all.
@JesusEclipse hink about it this way: suppose I want to answer the question "why is there a solution to the equation 2+2=X"? A way to answer that question is "because this is a deductive proof which shows the solution is X=4". By the same token, then, why isn't a good answer to the question "why is there something rather than nothing" the same kind of answer: "because I have a deductive proof which shows it exists".
Good video, but why does logic exist? haha. Well basically for any proof of this you must assume the existence of something (logic) to determine the existence of everything. Oh well, I enjoyed the video!
If you define the quantifiers in more formal terms I think you will find that only the existential quantifier has an ontological commitment. And this is, as you sort of mentioned, only an assumption (a quite safe one, though).
I just think it's a bit weird to imply that logic can prove the existence of anything, since it's, strictly speaking, wrong.
That being said, it shouldn't be a problem to accept that there exists something. Logic isn't alpha and omega.
The title of this video seems to imply that the default natural state is 'nothing'. This is indeed the stance adopted by most people, particularly religionists, and an anthropormorophic stance that is assumed due to our everyday observations of 'cause and effect'. But an equally valid question is 'why is there nothing rather than something?'
Didn't watch the video, sorry. I've seen more than enough creationist (shit-for-brains) arguments here.
BWAHAHAHAHAHAHA dude I'm an atheist and this is not a creationist video.... if you are going to be a troll at least be a halfway competant one. You fail.
@randyhelzerman I didn't say I thought this was a creationist video, I just didn't watch it because the title seems to imply 'nothing' is default over 'something'. My comment is sound, and I'm an atheist too. If I were a troll I'd be ripping the video content to pieces and then telling you to calm down when you respond.
you are so full of fail....the video is directed against people who think that is a useful question. Just as well you didn't watch the video, you probably couldn't understand it anyways.
@randyhelzerman ok. I'll watch the video later when I have time and then I'll let you know what I think. It is an interesting question, but I can't see much use in it (yet?). I still believe that 'something' is no more important than 'nothing', and that the only reason we're not asking the question the other way round is simply because there is 'something'. In short: that we exist is no big deal, we just 'are' and the 'reason' for this is meaningless.
@randyhelzerman Ok, I've now watched your video. I found it interesting even though it doesn't answer the title question or even prove that at least one thing exists. I'm glad you mentioned this at the end though. (4 stars.)
Is it possible to prove that at least one thing exists, without first making the assumption that something exists? You might want to solve this problem and present your solution in a similar video. Please let me know when it's ready.
Why don't you think I answered the title question? Suppose you asked "why is there a prime less than 3 rather than no prime less than 3?" If I said "because there is a deductive proof which shows that there is a prime less than 3" that would be an answer which mathematicians would accept, even though I couldn't prove that unless I already assumed it in the sense of assuming the axioms of math. If I ask "why is there something rather than nothing?" why cant I say "because I can prove it?"
@randyhelzerman Exactly; the question in the video is impossible to answer and hence it has no meaning. This is what I was getting at in my first comment (although I approached the concept from a different angle). We might as well assume things exist and try to accept that our universe is a state that doesn't require an explanation. Trying to employ logic in order to tackle this problem is just naive and a bit silly - although ironically we have just used logic to convince ourselves of this.
When you applied existential generalization you introduced the same variable that was already captured by the universal quantifier. As I understand it, that is breaking a rule and is the source of the dilemma. You begin with x in the universal quantifier, which narrows down our subject of discussion to all things that exist. But than you apply existential generalization with the x, which implies we are now talking about the same entities as before.
Think about it. Existential import is being made when you make your first premise. When you mention all things that exist you already presume that something exists.
Existence is implied when you say "for all that exists". This is inbuilt bias... circular reasoning... a sort of assuming the consequence. And why do you do that gay little laugh? It sounds arrogant and douche-baggy.
W.R.T. this being circular reasoning, dude, the conclusion of any valid deductive argument will never give you more than what the premises already imply....otherwise it woudln't be a deductive argument. And nobody is forcing you to watch my videos; if you don't like how I laugh, there's terabytes of other videos, go watch some of them.
Hi C.E.S., on of the chief differences between aristotelian logic and modern logic is that modern logic does not give any existential import to the universal quantifier. For example, the sentence "All double-parked cars will be towed" can be true, even when there are no double parked cars. But its hard to see how the existential quantifier couldn't have, well, existential import. If the sentence "There exists a double-parked car" is true, then how could there not be a double-parked car?
I mean no offense. But you seem to think that positing existence for any one or all things, first, built into the premise, is valid proof that something has to exist. That doesnt hold. The question isnt answered. You have not proven WHY something must exist. Youve only shown that something does exist because everything already exists.
Perhaps that is a better rephrasing of my comments.
Honestly I dont know too much about the Boolean and Aristotelian controvery, their interpretations on existential import. But I do believe in the use of assumption. I believe we can posit hypothetical premises and derive truths to them with valid arguments... and whose conclusions are just as true as the premises they are based on... whose truth is contingent on the truth of the premises.... we already use assumptions for conditionals and for proof by contradiction. These dont imply existence
You start by saying "everything exists". This is true, of course, and the fact that something exists is therefore implied... because something is any subset of everything. But that doesnt prove why anything has to exist.
Okay, maybe from a technical interpretation it proves why "something" exists - given everything that does. But it doesnt prove why "anything" exists at all in the first place. Does that not make sense? The question isnt answered except in abuse of intended language meaning
Suppose nothing did exist. Then you wouldnt have a "for all" to start your argument with. So no "there exists" could be derived. Its an abuse of language, a limitation of your predicate logics descriptive ability... IMHO.
And I do think it is false to blur the lines between "for all" and "there exists" as to which implies existence and which doesnt.
You say "suppose nothing did exist. Then you wouldn't have a 'for all' to start your argument with". No--that was the whole point of the "all double parked cars will be towed" example. That sentence can be true even if there are no double parked cars. Just saying "forall x: x=x" does not have any exitential implications at all. Neither do the other premises, taken each alone, by themselves. (cont)
(cont, to CECS) Therfore, the argument is not flatly circular. Its like any other garden variety deductive proof you'll ever see--throws some premises together and derives something which no premis could do by itself, but nevertheless is implied by all of the premises together.
I dont disagree with you. Saying "for all" doesnt imply existence. So why then do you conclude with existence in your video? Starting with "for all" is meaningless. Its implies only hypothetical existence for the argument. But you conclude with a definite existence. Where does this existence get imported from?
The argument happens the same way any other deductive argument does: you start with premises, and then you use the rules of inference to deduce conclusions. The video explains in detail all of the rule of inference we use.
I know the rules of inference. My point is that there is a fallacy. Even if you follow the rules precisely, I still argue there is a fallacy. There is something fundamentally wrong with the implication of the rules youre using. And frankly I dont think you understand my point at all.
you forget that the variables such as x must be defined in a set... and you didn't take into account that the set could be empty...
therefore you could not go on with step 2.
not trying to criticise your video but formal proofs don't work that way... you can't prove anything with logic... only statements that are true!!! have to admit that you explained the "Exists" and "for All" quantifiers greatly!!! 5 *!!!
Thanks for the sub vseraph1. Well, the question is: could the set of things which x ranges over be empty? Amazingly enough, for modern logic, the answer is no. In fact, that's pretty much what the proof of this video shows: any interpretation of any theory in first order logic cannot have an empty set. Of course, this isn't my proof; its well known. Check out the wiki article on "free logic" for a fuller (and better) explanation.
Thank you for your reply, (it was to another account I have actually0 about the concern I had about you answering the THAT of the question rather than the WHY of the question. It was very informative. I really enjoyed this teaching you had. I'd like to see more if you have time. Oh and one more thing... Logic is the tool we use that makes any kind of inteligble discourse possible. Is there a tool to measure the accuracy of the tool we use called logic?
Forgive me, I am new to this so please excuse my ignorance. You did indeed prove (at least to me you did) THAT "something" exists. However, i don't believe that you've demonstrated to the satisfaction of the title of your video as to exactly WHY something exists as opposed to why something does not exist. Is there a way to demonstrate this logically? (or no) Very interesting video nonetheless.
Hi nesymiracle, suppose somebody asked "why is 1 less than 2?" A perfectly good way to answer that question is to give a little mathematical proof showing that 1 was less than 2, and then saying "that's why." Same thing here--the answer to the "why" question is to give this proof and say "that's why".
"Modern logic suggests that something must exist"?
If nothing existed then neither would logic, itself... in which case logic can dictate nothing. The question still stands.
You call yourself a logician, do you? But you are assuming logic exists independently of the universe. You posit the validity of logic, itself, as an unproven premise. We are talking about existence itself, its origins, but you presume logic predates and dictates existence, rather than existence defining logic.
If you would have listened more carefully to this video, you'd see how far off the mark your remarks are. Somebody asked me why first order logic presupposes the existence of at least one thing, and I answered their question. At the end of the video I explicitly say that whether you find this compelling or not depends upon whether you already accept it or not. You're just a pompous gasbag.
Wow... youre a real douchebag. I was just pointing out the obvious... (which you apparently agree with)... and yet youre fighting anyway? Did I attack you? I dont believe I did. Pointing out fallacy and presumption deserves an emotionally polarized attack, huh? Wow.. your rhetoric astonishes me.
Riiight....... the phrase "you call yourself a logican" wasn't attacking rhetoric. There's plenty wrong with your post. You were assuming that I was presupposing logic, that I believe that logic exists independently of the universe, etc etc etc. Backpedel as fast as you can, its not going to get you out of the hole you've dug yourself into.
You seem to have some emotional problems and trouble carrying out an conversation without resorting to personal insults. As I said before, if you don't like what I'm writing, nobody is forcing you to read it. And I don't like what you are writing either, so I won't be replying anymore. Best of luck conquring your inner demons.
So you falsely accuse me of emotional and poor rhetoric to escape continuing the debate? Awesome. Yet another fallacy on your part. Something about ad hominem. I havent used emotional ammunition on you yet. I cant help it if youre offended by the truth... and all I have said was that you dont seem to understand my point. Which is exemplified by your running away. So, congrats. I hope all your viewers see you for what you are at this point.
we both know that good or bad is subjective...or not.. really at the quatum level nothing is what it is...so lets stick to thought, to potetiality...you hate the political side of God, witch is religion. all the stuff the you are saying in your vids are trying to disprove God insted of disapproving religion. im sure we would have a good converstion if we got into it..but all im saying is, something here is beyond physical, beyond math, beyond logic. i hope you can agree!
i dont know what your trying to do.... but the more i listen to you...(and you are good) the more im sure of creationist.. and anyone who believes in a creatore will believe alot more after what you said. of course first t, they will have to understand what you said...
I'm not trying to convince anybody that God exists or that god doesn't exist. I'm just interested in the reasons they give for either believing or not believing in God, and examining them to see if they are good reasons or bad reasons. thanks for watching.
I think the confusion here is you are not defining a domain for your objects. If you ended all of your lines with "in the universe", then it wouldn't work.:
1.For every element x [in the universe], that element is equal to itself.
2. Let A be a particular element [in the universe], then using 1, A=A
3. Thus there exists an element [in the universe] equal to itself
You didn't do anything wrong but it can appear to be magic without domains of definition for the objects.
Hi TexanProgressive, this whole exercise is 100% proof theoretic, not model theoretic. As such, it imposes constraints on which kinds of universes could exist. Another way of stating the conclusion of this vid would be that any model which you specify for any first order theory whatsoever would HAVE to include at least one object.
Well sure, but only in the sense that *every* deductive argument is begging the question. The conclusion of every deductive argument is contained in its premises.
You misunderstood me. You're argument seems to be this: (1) For any X, X=X (2) There exists an object A (3) Therefore, there exists an object A so that A=A (3) Therefore, there exists an X so that X=X (4) Therefore, something exists. You begin with "There exists an object" and claim you have proven the existence of an object. Wow. Would you impressed by the following "proof"? (1) For any X, X=X. (2) The FSM = The FSM (3) Wow, I totally didn't see THAT coming.
but (2) isn't "There exists an object A". Rather, (2) is "A=A", where A is any proper name. The argument isn't *flatly* circular, in that one of its premises is copied verbatim to the conclusion. Rather, its just like any other deductive argument you'd ever see--there's some assumptions, which you may or may not agree with, and those assumptions already imply all of the conclusions you could draw deductively from them.
I don't reject your proof of the FSM. According to classical logic, it is valid. I do reject classical logic (see the wiki article on "free logic" which I think is a saner logic).
I think that given classical logic, all I have "proven" is the existence of the abstract object that is the identity of the FSM - by saying it exists.
Well, strictly speaking, you haven't proven whether it is an abstract object or a concrete object. All you have proven about it is that it exists and is equal to itself.
I don't see why a contingent object requires an explanation for why it exists. Nor do I see why a necessary being doesn't require an explanation or origin.
What is the difference between saying "The law of non-contradiction needs no explanation, because its necessarily true" and "God's existence needs no explanation, because God's existence is necessarily true"? I don't think that I relieve myself of the obligation to explain something just by decreeing, ex cathedra, that it is necessarily true. So I don't see any connection between the necessary/contingent dichotomy and the needs/doesn't need explanation dichotomy.
Sure, why not? Same as I look for an explanation for God existence. Some book tells me that non-contradiction is necessarily true. Why should I take that on faith any more than I should take on faith some other book telling me that God's existence is necessarily true? Just because somebody wrote it down doesn't make it true.
A necessary being must be omnipotent, eternal, and uncreated. otherwise it would be a contigent element in need of explanation.
only god fits that criteria, and therefore it exists.
There are several arguments from contingency besides this one. but, why do you pick on kantians? the argument has been around since Aquinas, as the third "proof" of god.
This might not be considered modern logic, but you could always use Descartes idea that "I think therefore i am" Since i am able to think, i must exist somewhere in some reality. Though the reality i perceive might be very different that the actual reality but it still proves I exist. Since I am something, some exists since i know i exist.
but doesn't imply Ex (M(x)), as one can prove by showing an appropiate model. I don't think 'the thing' is so much the actual logical axioms and rules with wich one decides to formaliza FOL, but the tarskian paradigm of truth and necessity (what imo 'IS' FOL), within which the Ex x=x can be made sense and safetly pointed out.
This was ment as a response to the "men on Mars" comment.
For deriving Ex (x=x) one doesn't actually need a proper name; there might be no proper names in the language. Imo it is precisely the fact that you can use even an open term in the introduction of an existential quantifier where the non-emptyness of the universe of discourse leaks into. Anyway, I'm realizing I should have read more of this section before posting. Sorry if this is "yet another of those comments". Really good video.
It may not be fallacious according to the definitions and properties we decided on for logic. But I still think its a fallacious argument. The very nature of logic is questionable.
Hi Cogito, Sure, I think that the real answer to this is that classical first order logic must be modified somehow. But this is why I didn't just present the proof here---I also talked about the introduction and elimination laws governing the universal and existential quantifiers, and give a brief justification of why we chose those particular laws. This is to demonstrate that whatever the flaw is in classical logic, it is a subtle flaw, not a trivial flaw. (cont)
(cont, to Cogito) so a full refutation of this argument would have to show a modification of the introduction or elimination laws of the quantifiers, and an argument as to why we should prefer the new, modified laws over the current laws.
Okay, I think I can make you follow your own advice. I want you to produce a proof, using classical, intuitionistic, minimal, free, or some another well-established first-order predicate calculus for the following proof:
"There is something that is equal to itself."
(∃x)(x = x)
...
"There is something."
(∃x)
Just emphasizing words in a sentence doesn't make the deduction for you, and you didn't (and can't) provide a proof of this. Show (∃x)(x = x) |- (∃x). Go ahead. I'll wait.
The second formula isn't well-formed, so you can make no such first-order deduction. Your now present agreement that existential instantiation from Leibniz's law cannot imply, by itself, that something exists, since such a claim is presumed, not proven within the system (existential quantifiers are primitive), then as I said earlier, you have proven nothing about ontology.
And as I've said before, you've committed an act of reification.
*sigh* theangist, If you would have watched my video with your head pulled OUT of your ass, You'll see I never reached the conclusion (Ex). Sorry, you have been insulting to me, you have misattributed your false understanding as my mistake, and you have refused to admit you were wrong. What's even worse, you are a very dull and boring conversationalist. Welcome to my blocked list.
Your logic is horribly misinformed, since your proof that something actually exists, not that some proposition applies for some possible thing, would mean you'd have to violate the rules of well-formed formulae to produce a proof from "(∃x)(x = x)" to "(∃x)." But there is no such logical move allowing this, and trying to do so violates WFF guidelines, so you've proven nothing.
Analytic tautologies don't imply the sort of ontological leaps you make. You suffer from severe reification issues.
Hi theyangist, its not "my logic" I wasn't the one who invented it. Nor is this argument my argument, this is well known. See the wikipedia article on "free logic" for another explanation of the same thing I presented in this video.
It dons on me that you don't really know what the issue of free logic is or what free logic aims to do, and nothing about free logic allows you to reify a term the way you do, nor does it allow you to violate the construction of a well-formed formula.
For that, you'd have to delve into the specifics of proof theory, which you didn't, and based on your demonstrated misunderstanding of free logic, are unprepared to do.
theyangist.....dude, I'm very tempted to conclude you are an amateur and a poser, but I'll give you one last chance. In this video I am not using free logic. I am using classical logic. Classical logic HAS existence claims, as any real logician knows. Free logic was invented specifically to exclude the kind of move I did in this video. You're never going to get anywhere if you're not willing to admit when you are wrong. Go back, actually read the wiki article this time.
Classical logic doesn't allow for this kind of reification, either. And you still can't infer (∃x), a basic existence claim, from (∃x)(x = x), not in classical logic, not in non-classical logics, not in any logic that is in common use.
Either formulate your own syntax allowing '(∃x)' to stand alone as a WFF, or revise your stance, but don't tell someone with a degree in this area to read Wikipedia articles. Be a big boy and read the real publications, jackass.
Sorry theyangist, I'm perfectly willing to talk with amateurs who are willing to learn, but I've no time for posers. The wiki article was for your convenience; if you'd like another reference take a look at James Garson's book "Modal logic for philosophers" P. 239 for another explanation. (cont)
(cont, to theangist) if you'd like to continue this conversation, you'll have to (1) demonstrate that you understand the proof of this given in Garson and (2) apologize for speaking out of turn. If you have a degree in this area, congrats, you wasted 4 years of your life, for you're just as big a fool now as you were before.
This is wrong. You can't imply an existential quantifier (the backwards E) from a universal quantifier (the upside down A). So, the rule 'All men are mortal' does not imply 'There is a mortal man'; it just means that 'If there are men, they will be mortal'.
Hi squigglesy, (upsidedown A) x implies (backwards E) x is a valid theorem in classical first-order predicate logic. See the wikipedia article on "free logic".
Okay, well I'm studying predicate calculus at university and I've been told different. Frankly, it's just common sense that a universal doesn't imply an existential anyway. Take the example 'All leprechauns are green'. So where's the leprechaun? There must be one somewhere. You might retort that this is a logical, not an empirical, system. But then you haven't really answered the question of why there is something rather than nothing, in reality. You've only answered it in a theoretical sense.
the first 1:20 cold have been summed up in one sentence. That's where I stopped.
MarkCGreer1 2 weeks ago
u never proved WHY there is something
XitonqyH 1 month ago
The fact that logic has a meaning proves that something exists, otherwise meaningfulness would vanish.
POWLIHERE22 2 months ago
Please don't ever misspell Socrates again. Never. Ever. I will hunt you down.
hogiharu 3 months ago
Ok, according to Leibniz's rule nothing should equal nothing. Therfore there should be nothing. Those other rules do not apply because at one point there was nothing.
killhorsesallthetime 4 months ago
Ridiculously flawed logic. If I say "all green unicorns are green" it doesn't follow that there are any green unicorns. And if you say my premise is wrong because there are no unicorns, then you can't use your premise either without assuming what you seek to prove (there is something), making your argument circular.
asdfaxsdgg 9 months ago
@asdfaxsdgg In first-order quantificational logic, the Law of Identity is taken as true, the inference rule of Universal elimination allows you to infer from (∀x) x = x, a = a. The inference rule of Existential Instantiation allows you to infer from a = a, (∃x) x = x. Technically speaking, the argument is sound. So, in order to challenge the argument, you must challenge the law of identity, the rule of Universal elimination, or the rule of Existential instantiation (or all of the above).
JonathanM00r3 8 months ago
@JonathanM00r3 I don't have to challenge the logical rules, it's just that they presuppose the existence of something, which is fine since in any case we don't need proof THAT there is something rather than nothing. But it means the argument is circular and does nothing to help explain the real question of WHY there is something rather than nothing.
asdfaxsdgg 8 months ago
@asdfaxsdgg The answer is given, (i.e. it would be contradictory for there to be nothing). Short of showing that the logical system is flawed or that there is a better system of logic that doesn't have (∃x) x = x as a theorem, the question is unmotivated. It would be just as silly as asking why (∀x) x v ~x or why 2+2 = 4? Our regimented theory of the world includes first-order QL. We accept the ontological commitments of QL just like we accept the ontological commitments of atomic theory.
JonathanM00r3 8 months ago
@JonathanM00r3 It's only contradictory in a logical system that presupposes existence. This doesn't mean such a logical system is flawed, it just doesn't help in giving a satisfying answer to this particular philosophical question. Of course, a better way of putting the question would be "Why is the universe the way it is and not any other way?" (The other way might be "nothingness" but also any other of an infinite number of possibilities.)
asdfaxsdgg 8 months ago
@asdfaxsdgg My point was not that you should show that the logic is flawed, rather my point was that the burden is on you to provide an alternative logic that doesn't include (∃x) x = x as a theorem but is equally powerful. If you can, for purposes of ontological simplicity, we would be obliged to accept that system of logic over classical QL. I view QL in the same light as any other theory in science (i.e. We accept for it's explanatory power as well as other theoretical virtues).
JonathanM00r3 8 months ago
@asdfaxsdgg However, if one cannot provide an alternative logic of equal power, we must accept QL like we would accept any other theory, and accepting it involves accepting it's ontology (Because, of course, that's the only way the theorems could be true). "it just doesn't help in giving a satisfying answer to this particular philosophical question." I find it satisfying. Whether an answer is satisfying is relative to the individual.
JonathanM00r3 8 months ago
@asdfaxsdgg ""Why is the universe the way it is and not any other way?" (The other way might be "nothingness" but also any other of an infinite number of possibilities.)" It COULDN'T be "nothingness" because System K of Modal Logic says that it's impossible that there be nothing. In any case though, this is a different question than the original. On any meaningful interpretation, this question appears to be a question for a cosmologist (since they study the structure of the universe).
JonathanM00r3 8 months ago
@asdfaxsdgg Presumably, the theories of the cosmologist will explain why our universe behaves in the way that it does and not in some other way. This question/problem doesn't appear to be significantly philosophical.
JonathanM00r3 8 months ago
@asdfaxsdgg "It's only contradictory in a logical system that presupposes existence." Similar things could be said like "It's only contradictory to reject electrons within a physical theory that posits electrons." While that statement is true, it only points out the need to provide an alternative theory that does not posit electrons but is equal in its explanatory power.
JonathanM00r3 8 months ago
@JonathanM00r3 Such a system of logic has explanatory power in an obviously existing world, but does not seem applicable to this particular question. There is an obvious difference between the banal "proof" of the video and a physical theory that you can test in practical experiments. As to the cosmologist, he will at best say the world is how it is because of certain physical laws, but he can't answer the more fundamental question as to why those laws are as they are.
asdfaxsdgg 8 months ago
@asdfaxsdgg "There is an obvious difference between the banal "proof" of the video and a physical theory that you can test in practical experiments." The abstractness of the question precludes a concrete answer like one we would expect in physical theory. It presumably requires an explanation/answer that is similarly abstract. Asking for a physical explanation is out of place here. Furthermore, while there is a difference, it's not obvious that it's a difference in kind (in degree, perhaps).
JonathanM00r3 8 months ago
@asdfaxsdgg "Such a system of logic has explanatory power in an obviously existing world, but does not seem applicable to this particular question." Atomic theory only has explanatory power in a world with atoms. I fail to see your point. Yes, we live in an "existing world". Our theory is supposed to explain why that is the case. In this instance, our regimented theory tells us that it would be inconsistent for there to be nothing. If we accept that theory, we should accept that answer.
JonathanM00r3 8 months ago
@JonathanM00r3 Obviously the question is profound for many people, yet you are making it into a triviality by essentially saying "Anything exists because it exists." That does not explain why. Incidentally I am not convinced the logic is even technically correct. It seems to be an existential instantiation fallacy, by which you could as well prove the existence of green unicorns. Just by common sense, "all" can be less than one; saying anything about "all x" doesn't mean there exists any x.
asdfaxsdgg 8 months ago
@asdfaxsdgg It's actually not an existential instantiation fallacy given the fact that '=' is treated as a predicate in first-order QL. Many universal statements such as "All Unicorns are Green" (∀x) (Ux -> Gx) do not imply the existence of unicorns because the structure of this sentence takes the form of a conditional involving TWO predicates. The truth conditions for the material conditional have it that it's false only when the antecedent is true and the consequent is false, else it's true.
JonathanM00r3 8 months ago
@asdfaxsdgg So trust me. It's technically correct given the rules of first-order quantificational logic. In Natural Deduction, you use the rules "Universal elimination" and "Existential Introduction" to generate the proof. In the tree method for QL, the argument with the premise and the negation of the conclusion closes, showing the original argument to be valid. It's also valid and sound in System K of Quantified Modal Logic, as I've mentioned before.
JonathanM00r3 8 months ago
@asdfaxsdgg "yet you are making it into a triviality by essentially saying "Anything exists because it exists."" I have never said this and this is not my view. My position has always been, "Something exists because it would be logically inconsistent for nothing to exist (~(Something exists)), given first-order quantificational logic." It's true that people believe the question to be profound, but that certainly is not evidence that it actually is.
JonathanM00r3 8 months ago
@asdfaxsdgg Existential instantiation fallacy cont.: So, the reason we can't infer the existence of green unicorns from the sentence "All Unicorns are green" is because that sentence is a conditional and there is an interpretation that makes that sentence true even if there are no unicorns (i.e. The antecedent is false). Statements of identity don't take that form.
JonathanM00r3 8 months ago
@JonathanM00r3 What about "all unicorns are unicorns" then? There you have an identity. Anyway, you may be right or not about the technical correctness of the argument according to any given logic system. But I'm not impressed by that, since it doesn't make sense to me on its face, and any logic system may be flawed if only for this particular case. And your stated position seems to be just a more fancy, but no more convincing, way of saying "Anything exists because it exists."
asdfaxsdgg 8 months ago
@asdfaxsdgg "What about "all unicorns are unicorns" then? There you have an identity." It's not an identity. It has this form: (∀x) (Ux -> Ux) (U(1): is a unicorn). It's true even if there are no unicorns because it's in the form of a conditional. "And your stated position seems to be just a more fancy, but no more convincing, way of saying "Anything exists because it exists." But it isn't. Those two sentences have a different semantic interpretation.
JonathanM00r3 8 months ago
@JonathanM00r3 (1) (∀unicorns x) (x = x), (2) so, for any particular unicorn, u = u, (3) therefore there exists a unicorn u for which u = u. How is this different?
asdfaxsdgg 8 months ago
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@asdfaxsdgg "(∀unicorns x) (x = x)". Improper use of the Universal quantifier. This isn't a well-formed sentence in the language of first-order logic, given the notation for universally quantified expressions.
JonathanM00r3 8 months ago
@asdfaxsdgg The universal quantifier ranges over variables. "Is a Unicorn" is a predicate that attaches to variables or constants. "(∀unicorns x)" just doesn't have an interpretation/meaning in the language of QL.
JonathanM00r3 8 months ago
@JonathanM00r3 Surely there's a way to put it. I can define U as the set of unicorns and then do ∀x ∈U (x = x) etc.
asdfaxsdgg 8 months ago
@asdfaxsdgg First-order logic doesn't include set-membership. You need second-order logic for that. But even in second-order logic, this sentence isn't well-formed (i.e. it doesn't obey the syntax of second-order logic)
If what you're trying to say is "Every member of the set of unicorns is self-identical", then you're just saying something false. Due to the axiom of extensionality, U = ∅. It would be false to say "Every member of the null set is self-identical". There are no members of ∅.
JonathanM00r3 8 months ago
@asdfaxsdgg If you're interested in an alternative logic that doesn't involve the ontological commitments that we've been talking about, then you should check out "free logic". I think you might be interested.
JonathanM00r3 8 months ago
@JonathanM00r3 That makes sense. Indeed the Wikipedia article on free logic shows an example from classical logic that proofs the existence of "Pegasus." That's what I meant. Apparently classical logic allows you to prove the existence not just of something but of anything.
asdfaxsdgg 8 months ago
@asdfaxsdgg I actually just read the Wikipedia article on free logic and it goes on to explain exactly why you can't prove the existence of "Pegasus" in standard first-order logic because one cannot substitute nondesignating constants for variables.
JonathanM00r3 8 months ago
@JonathanM00r3 Well, then the article does not really explain well what the problem with classical logic is that free logic is supposed to fix. If the assumption of the existence of "something" is the only problem, then it may make practical sense for everyday purposes to let that go, instead of complicating everything else just to cover this. But for this particular question I would indeed use a logic that is careful about existential presuppositions.
asdfaxsdgg 8 months ago
@asdfaxsdgg Go to the Stanford Encyclopedia of Philosophy article on "Free Logic". It's better and it gives an explanation of the motivations for free logic.
JonathanM00r3 8 months ago
@asdfaxsdgg "But I'm not impressed by that, since it doesn't make sense to me on its face, and any logic system may be flawed if only for this particular case." Ok, fair enough. But then we're back to what I said earlier. The burden is on the skeptic to provide an alternative logical system that has equivalent or greater power. The current system is practically indispensable for scientific reasoning and ordinary reasoning. Many philosophers work on alternative logics.
JonathanM00r3 8 months ago
@asdfaxsdgg I myself am interested in alternative logics because there are features of the current system that are counterintuitive to me as well (e.g. the truth conditions for the material conditional. See "Relevance Logic"). But, I don't take that as evidence that the system is not fundamentally correct. And until some philosopher/logician can provide a rival system, I'm compelled to accept this one. I feel the same way about scientific theories.
JonathanM00r3 8 months ago
@asdfaxsdgg "As to the cosmologist, he will at best say the world is how it is because of certain physical laws, but he can't answer the more fundamental question as to why those laws are as they are" That's a bold assertion! You might need to provide support for that claim. In any case, I think it's possible that the physical cosmologist could develop a theory that explains why the physical laws are as they are. Nothing, at this point, seems incoherent about that idea.
JonathanM00r3 8 months ago
@JonathanM00r3 Without prior restraints other than self-consistency, it is easy to imagine all kinds of possible worlds different from the one we live in. The physicist can only describe our world as it is, but he can't say it couldn't logically be any other way. So we have a fundamental philosophical question here.
asdfaxsdgg 8 months ago
@asdfaxsdgg It's also not circular in any problematic way. For instance, one can start with the assumption that nothing exists [~(∃x) x = x] and derive a contradiction (Reductio ad Absurdum). One can even do this in System K of Modal Logic with the claim "It's possible that nothing exist" [◊~(∃x) x = x] and also derive a contradiction. If this theorem is problematic, then all theorems of QL or K are equally problematic.
JonathanM00r3 8 months ago
A person asking the question is instantly answering it.
Language is the problem here.
Maybe it is better to put it in terms "Why is there Everything instead of Nothing".
Something (subset of Everything) , implies that there is also Something that doesn't exist. A concept of Selection kicks in, which triggers a concept of Choice and intelligence.
Its not as "begging" as "why is there a creation, but its close.
vdizhoor 9 months ago
A person asking the question is instantly answering it.
Language is the problem here.
Maybe it is better to put it in terms "Why is there Everything instead of Nothing".
Something (subset of Everything) , implies that there is also Something that doesn't exist. A concept of Selection kicks in, which triggers a concept of Choice and intelligence.
Its not as "begging" as "why is there a creation, but its close.
vdizhoor 9 months ago
One must start from the simple observation that something currently does exist. What exists in fact, must be possible. That means, as we extrapolate into the past, and into past states of being, we have to conclude that ever current and future state of existence must exist as a "potential" or possible state in the past.
Obviously, if the present state of existence had not been possible in the past, it could not exist now.
prodprod 10 months ago
(cont'd) (2) If one accepts this premise (and I'm not sure on what basis one could dispute it) then one would have to accept that there could never have been a point in the past at which the potential for existence, and for every actual state of existence, did not itself exist.
True nothingness -- absolute nothingness would have to be devoid of such potential (because potential is obviously *something*) -- and absent that potential, there could be no existence at all. Ever.
prodprod 10 months ago
my dick is mortal
joeodntuno 1 year ago
The best answer to this question I have come across is this:
Nothing exists except logical possibility, which necessarily exists, and our perception of material existence is an epiphenomenon of our being logical subcomponents of a logically possible universe.
I'd link you to the website where I read that but YouTube won't let me, so type into Google: "Nothing exists except logical possibility" in quote marks, & you'll be able to find the answer on the knowinghumans website among others.
MoralNihilism 1 year ago
Of course there isn't always something rather than nothing.
In fact, there are countless universes where absolutely nothing exists. Unfortunately no one is there to count them or communicate this fact to the outside.
How do I know this?
I feel it in my heart and have faith it's true.
dimbulb23 1 year ago
There is something, therefore something out there has an eternal nature, This ever existing "something" is God.
RespectMyHate 1 year ago
From Answers.com: "The implications of a proposition as to what exists. If a proposition entails the existence of something, then it has existential import. It should be noticed that in the predicate calculus the universal quantification (∀x)(Fx → Gx) has no existential import, since it is true when nothing is F."
MoonMankkkkkk 1 year ago
@MoonMankkkkkk but the existence claim didn't come from a universally quantified statement. It came from an existentially quantified statement. it came from a statement for which something must exist for it to be true.
randyhelzerman 1 year ago
@randyhelzerman
It doesn't matter. You still derived an existentially quantified statement from a universally quantified statement, which is considered an invalid inference in predicate logic.
MoonMankkkkkk 1 year ago
@MoonMankkkkkk Dude, you don't have to take my word for it; see the wiki article on "free logic" or you can look up James's Garson's book "Model logic for Philosophers". This is not my derivation; it is well known and fully accepted as a valid inference given the standard rules governing logical constants. Heck, I spent the first 1/2 of the video explaining why the rules for existential quantification are valid.
randyhelzerman 1 year ago
@randyhelzerman
In free logic, the proposition "there exists at least one x" cannot be derived solely from "far all x, x is equal to x." (The Wikipedia article shows that your method of proof is invalid in first-order logic). A logic where the former proposition can be derived from the latter must already have existential presuppositions. If that is the logic you are employing, your argument is therefore circular. If your argument is not circular, it is invalid. Which is it?
MoonMankkkkkk 1 year ago
@MoonMankkkkkk I think you need to more carefully read the article on free logic.
randyhelzerman 1 year ago
@randyhelzerman What on earth are you talking about!
From the article itself:
"Consider the following classically valid theorems. 1. ∀xA -> ∃xA"
This was the argument that you used; if there exists some predicate that is true of all entities, (you used identity), you presumed it could be inferred that there exists at least one thing that is equal to itself. Of course, this is only a valid argument in a logic that has "existential presuppositions."
MoonMankkkkkk 1 year ago
@randyhelzerman
"Classically, ∃x(x=y) is deducible from the open equality axiom y=y by particularization."
This was the logic that you used. In free logic, however:
"In free logic, (1) is replaced with 1b. ∀xA ∧ E!t -> ∃xA, where E! is an existence predicate (in some but not all formulations of free logic, E!t can be defined as ∃y(y=t))."
Again, you didn't say whether you were using free logic, but you are wrong if you are. I am quoting directly from the article you referred to.
MoonMankkkkkk 1 year ago
@MoonMankkkkkk I'm using classical logic. Thank you for going back and re-reading the free logic article.
randyhelzerman 1 year ago
@randyhelzerman
It's quite clear that the second premise had no meaning in predicate logic terms, (it wasn't in predicate logic notation and thus wasn't in well-formed formula). That is, unless you meant for "A" to be an entity, (which of course would make it improperly capitalized as capitalized letters stand for predicates). This would the inference rule of universal generalization. You then (implicitly) derived (3) from (2) using the rule of existential generalization.
MoonMankkkkkk 1 year ago
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MoonMankkkkkk 1 year ago
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MoonMankkkkkk 1 year ago
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@randyhelzerman
The problem here is that it is a specific restriction of the rule of Existential Generalization that in deriving a quantified statement from a singular statement, (as you did), the singular statement must not have been derived through universal generalization. But this is that you did. You derived "A=A" from "(x)(x=x)."
MoonMankkkkkk 1 year ago
To restate, the rule of Existential Generalization does not allow you to derive "(∃x)(x=x)" from the singular statement "A=A" because "A=A" was derived from "(x)(x=x)", a universal statement.
You have derived this proposition by misusing the rules of inference for predicate logic. Thus, the inference is invalid.
MoonMankkkkkk 1 year ago
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Of course, now that I have proved the invalidity of your argument, I, (consequently), expect you to either remove the video or make it clear you aware of the fact that the reasoning exhibited in the video is fallacious.
MoonMankkkkkk 1 year ago
While you and Lewis Carroll might (have) disagree(d) with this, he recognized that any author may take whatever policy they wish when it pertains to the creations of their own system. (As far as I am aware), the modern square of opposition affirms that universal statements lack existential import. Ergo, the proposition, "something exists", cannot be derived from the law of identity and is an axiom.
MoonMankkkkkk 1 year ago
I'm very sorry, but you're wrong here.
It has been a well-settled doctrine that in modern logic, all universal propositions necessarily lack existential import. For instance, by the rules of symbolic logic, the proposition, "All men are mortal," does not prove that there exists something which is a man, much less does it prove that there exists something that is both a man and a mortal thing.
MoonMankkkkkk 1 year ago
you answered the following question:
is there something?
the interesting, hard and diffrent question is:
Why is there something rather than nothing?
you didn´t answer that question. you neglected the: Why.
lindarajalin1 1 year ago
@lindarajalin1 Think about it this way: suppose I want to answer the question "why is there a solution to the equation 2+2=X"? A way to answer that question is "because this is a deductive proof which shows the solution is X=4". By the same token, then, why isn't a good answer to the question "why is there something rather than nothing" the same kind of answer: "because I have a deductive proof which shows it exists".
randyhelzerman 1 year ago
You never answered the title of the video lol. WHY is there something rather than nothing. You answered, prove something exists. Which I don't really understand why this needs to be proven at all.
JesusEclipse 1 year ago
@JesusEclipse hink about it this way: suppose I want to answer the question "why is there a solution to the equation 2+2=X"? A way to answer that question is "because this is a deductive proof which shows the solution is X=4". By the same token, then, why isn't a good answer to the question "why is there something rather than nothing" the same kind of answer: "because I have a deductive proof which shows it exists".
randyhelzerman 1 year ago
@randyhelzerman ah never thought about it like that. Interesting indeed :)
JesusEclipse 1 year ago
Good video, but why does logic exist? haha. Well basically for any proof of this you must assume the existence of something (logic) to determine the existence of everything. Oh well, I enjoyed the video!
HaveFaithInScience 1 year ago
If you define the quantifiers in more formal terms I think you will find that only the existential quantifier has an ontological commitment. And this is, as you sort of mentioned, only an assumption (a quite safe one, though).
I just think it's a bit weird to imply that logic can prove the existence of anything, since it's, strictly speaking, wrong.
That being said, it shouldn't be a problem to accept that there exists something. Logic isn't alpha and omega.
Tempestuphonic 2 years ago
The title of this video seems to imply that the default natural state is 'nothing'. This is indeed the stance adopted by most people, particularly religionists, and an anthropormorophic stance that is assumed due to our everyday observations of 'cause and effect'. But an equally valid question is 'why is there nothing rather than something?'
Didn't watch the video, sorry. I've seen more than enough creationist (shit-for-brains) arguments here.
C0C0nutFace 2 years ago
BWAHAHAHAHAHAHA dude I'm an atheist and this is not a creationist video.... if you are going to be a troll at least be a halfway competant one. You fail.
randyhelzerman 2 years ago
@randyhelzerman I didn't say I thought this was a creationist video, I just didn't watch it because the title seems to imply 'nothing' is default over 'something'. My comment is sound, and I'm an atheist too. If I were a troll I'd be ripping the video content to pieces and then telling you to calm down when you respond.
C0C0nutFace 2 years ago
you are so full of fail....the video is directed against people who think that is a useful question. Just as well you didn't watch the video, you probably couldn't understand it anyways.
randyhelzerman 2 years ago
@randyhelzerman ok. I'll watch the video later when I have time and then I'll let you know what I think. It is an interesting question, but I can't see much use in it (yet?). I still believe that 'something' is no more important than 'nothing', and that the only reason we're not asking the question the other way round is simply because there is 'something'. In short: that we exist is no big deal, we just 'are' and the 'reason' for this is meaningless.
C0C0nutFace 2 years ago
@randyhelzerman Ok, I've now watched your video. I found it interesting even though it doesn't answer the title question or even prove that at least one thing exists. I'm glad you mentioned this at the end though. (4 stars.)
Is it possible to prove that at least one thing exists, without first making the assumption that something exists? You might want to solve this problem and present your solution in a similar video. Please let me know when it's ready.
C0C0nutFace 2 years ago
Why don't you think I answered the title question? Suppose you asked "why is there a prime less than 3 rather than no prime less than 3?" If I said "because there is a deductive proof which shows that there is a prime less than 3" that would be an answer which mathematicians would accept, even though I couldn't prove that unless I already assumed it in the sense of assuming the axioms of math. If I ask "why is there something rather than nothing?" why cant I say "because I can prove it?"
randyhelzerman 2 years ago
@randyhelzerman Exactly; the question in the video is impossible to answer and hence it has no meaning. This is what I was getting at in my first comment (although I approached the concept from a different angle). We might as well assume things exist and try to accept that our universe is a state that doesn't require an explanation. Trying to employ logic in order to tackle this problem is just naive and a bit silly - although ironically we have just used logic to convince ourselves of this.
C0C0nutFace 2 years ago
@C0C0nutFace
You're such a fucking moron, this isn't about atheism you goddamned stupid retard, it's about mathematics and metaphysics.
NupialJungle 1 year ago
@C0C0nutFace Creationist? Haha! Go read some Russel or Wittgenstein before you go brand people things that fit your insular worldview, ignoramus.
Manusturbo 1 year ago
@Manusturbo I'm not a creationist. Go read comments properly before you go brand people to fit your insular assumptions. Oh, and nob head too.
C0C0nutFace 1 year ago
Existential Quantifiers dont imply existence. That is an existential import fallacy. Hypothetical existence does not imply actual existence.
CogitoErgoCogitoSum 2 years ago
When you applied existential generalization you introduced the same variable that was already captured by the universal quantifier. As I understand it, that is breaking a rule and is the source of the dilemma. You begin with x in the universal quantifier, which narrows down our subject of discussion to all things that exist. But than you apply existential generalization with the x, which implies we are now talking about the same entities as before.
CogitoErgoCogitoSum 2 years ago
Think about it. Existential import is being made when you make your first premise. When you mention all things that exist you already presume that something exists.
CogitoErgoCogitoSum 2 years ago
Existence is implied when you say "for all that exists". This is inbuilt bias... circular reasoning... a sort of assuming the consequence. And why do you do that gay little laugh? It sounds arrogant and douche-baggy.
CogitoErgoCogitoSum 2 years ago
W.R.T. this being circular reasoning, dude, the conclusion of any valid deductive argument will never give you more than what the premises already imply....otherwise it woudln't be a deductive argument. And nobody is forcing you to watch my videos; if you don't like how I laugh, there's terabytes of other videos, go watch some of them.
randyhelzerman 2 years ago
Hi C.E.S., on of the chief differences between aristotelian logic and modern logic is that modern logic does not give any existential import to the universal quantifier. For example, the sentence "All double-parked cars will be towed" can be true, even when there are no double parked cars. But its hard to see how the existential quantifier couldn't have, well, existential import. If the sentence "There exists a double-parked car" is true, then how could there not be a double-parked car?
randyhelzerman 2 years ago
I mean no offense. But you seem to think that positing existence for any one or all things, first, built into the premise, is valid proof that something has to exist. That doesnt hold. The question isnt answered. You have not proven WHY something must exist. Youve only shown that something does exist because everything already exists.
Perhaps that is a better rephrasing of my comments.
CogitoErgoCogitoSum 2 years ago
Honestly I dont know too much about the Boolean and Aristotelian controvery, their interpretations on existential import. But I do believe in the use of assumption. I believe we can posit hypothetical premises and derive truths to them with valid arguments... and whose conclusions are just as true as the premises they are based on... whose truth is contingent on the truth of the premises.... we already use assumptions for conditionals and for proof by contradiction. These dont imply existence
CogitoErgoCogitoSum 2 years ago
You start by saying "everything exists". This is true, of course, and the fact that something exists is therefore implied... because something is any subset of everything. But that doesnt prove why anything has to exist.
Okay, maybe from a technical interpretation it proves why "something" exists - given everything that does. But it doesnt prove why "anything" exists at all in the first place. Does that not make sense? The question isnt answered except in abuse of intended language meaning
CogitoErgoCogitoSum 2 years ago
Suppose nothing did exist. Then you wouldnt have a "for all" to start your argument with. So no "there exists" could be derived. Its an abuse of language, a limitation of your predicate logics descriptive ability... IMHO.
And I do think it is false to blur the lines between "for all" and "there exists" as to which implies existence and which doesnt.
CogitoErgoCogitoSum 2 years ago
You say "suppose nothing did exist. Then you wouldn't have a 'for all' to start your argument with". No--that was the whole point of the "all double parked cars will be towed" example. That sentence can be true even if there are no double parked cars. Just saying "forall x: x=x" does not have any exitential implications at all. Neither do the other premises, taken each alone, by themselves. (cont)
randyhelzerman 2 years ago
(cont, to CECS) Therfore, the argument is not flatly circular. Its like any other garden variety deductive proof you'll ever see--throws some premises together and derives something which no premis could do by itself, but nevertheless is implied by all of the premises together.
randyhelzerman 2 years ago
I dont disagree with you. Saying "for all" doesnt imply existence. So why then do you conclude with existence in your video? Starting with "for all" is meaningless. Its implies only hypothetical existence for the argument. But you conclude with a definite existence. Where does this existence get imported from?
CogitoErgoCogitoSum 2 years ago
The argument happens the same way any other deductive argument does: you start with premises, and then you use the rules of inference to deduce conclusions. The video explains in detail all of the rule of inference we use.
randyhelzerman 2 years ago
I know the rules of inference. My point is that there is a fallacy. Even if you follow the rules precisely, I still argue there is a fallacy. There is something fundamentally wrong with the implication of the rules youre using. And frankly I dont think you understand my point at all.
CogitoErgoCogitoSum 2 years ago
Great video.... but...
you forget that the variables such as x must be defined in a set... and you didn't take into account that the set could be empty...
therefore you could not go on with step 2.
not trying to criticise your video but formal proofs don't work that way... you can't prove anything with logic... only statements that are true!!! have to admit that you explained the "Exists" and "for All" quantifiers greatly!!! 5 *!!!
vseraph1 2 years ago
after checking out your channel I subscribed.... great videos!!!!
vseraph1 2 years ago
Thanks for the sub vseraph1. Well, the question is: could the set of things which x ranges over be empty? Amazingly enough, for modern logic, the answer is no. In fact, that's pretty much what the proof of this video shows: any interpretation of any theory in first order logic cannot have an empty set. Of course, this isn't my proof; its well known. Check out the wiki article on "free logic" for a fuller (and better) explanation.
randyhelzerman 2 years ago
Thank you for your reply, (it was to another account I have actually0 about the concern I had about you answering the THAT of the question rather than the WHY of the question. It was very informative. I really enjoyed this teaching you had. I'd like to see more if you have time. Oh and one more thing... Logic is the tool we use that makes any kind of inteligble discourse possible. Is there a tool to measure the accuracy of the tool we use called logic?
mudnyoureyes 2 years ago
Forgive me, I am new to this so please excuse my ignorance. You did indeed prove (at least to me you did) THAT "something" exists. However, i don't believe that you've demonstrated to the satisfaction of the title of your video as to exactly WHY something exists as opposed to why something does not exist. Is there a way to demonstrate this logically? (or no) Very interesting video nonetheless.
nesyamiracle 2 years ago
Hi nesymiracle, suppose somebody asked "why is 1 less than 2?" A perfectly good way to answer that question is to give a little mathematical proof showing that 1 was less than 2, and then saying "that's why." Same thing here--the answer to the "why" question is to give this proof and say "that's why".
randyhelzerman 2 years ago
Harry is mortal therefore Voldemorte is immortal.
No wait...
cyxgun 2 years ago
"Modern logic suggests that something must exist"?
If nothing existed then neither would logic, itself... in which case logic can dictate nothing. The question still stands.
You call yourself a logician, do you? But you are assuming logic exists independently of the universe. You posit the validity of logic, itself, as an unproven premise. We are talking about existence itself, its origins, but you presume logic predates and dictates existence, rather than existence defining logic.
CogitoErgoCogitoSum 2 years ago
If you would have listened more carefully to this video, you'd see how far off the mark your remarks are. Somebody asked me why first order logic presupposes the existence of at least one thing, and I answered their question. At the end of the video I explicitly say that whether you find this compelling or not depends upon whether you already accept it or not. You're just a pompous gasbag.
randyhelzerman 2 years ago
Wow... youre a real douchebag. I was just pointing out the obvious... (which you apparently agree with)... and yet youre fighting anyway? Did I attack you? I dont believe I did. Pointing out fallacy and presumption deserves an emotionally polarized attack, huh? Wow.. your rhetoric astonishes me.
CogitoErgoCogitoSum 2 years ago
Does anyone see anything fallacious in the above post? Apparently the video-poster does
CogitoErgoCogitoSum 2 years ago
Riiight....... the phrase "you call yourself a logican" wasn't attacking rhetoric. There's plenty wrong with your post. You were assuming that I was presupposing logic, that I believe that logic exists independently of the universe, etc etc etc. Backpedel as fast as you can, its not going to get you out of the hole you've dug yourself into.
randyhelzerman 2 years ago
What hole, douche? I fully admit to it... and you are still whining. Keep it coming... prove to the community how civilized and intellectual you are.
CogitoErgoCogitoSum 2 years ago
You seem to have some emotional problems and trouble carrying out an conversation without resorting to personal insults. As I said before, if you don't like what I'm writing, nobody is forcing you to read it. And I don't like what you are writing either, so I won't be replying anymore. Best of luck conquring your inner demons.
randyhelzerman 2 years ago
So you falsely accuse me of emotional and poor rhetoric to escape continuing the debate? Awesome. Yet another fallacy on your part. Something about ad hominem. I havent used emotional ammunition on you yet. I cant help it if youre offended by the truth... and all I have said was that you dont seem to understand my point. Which is exemplified by your running away. So, congrats. I hope all your viewers see you for what you are at this point.
CogitoErgoCogitoSum 2 years ago
we both know that good or bad is subjective...or not.. really at the quatum level nothing is what it is...so lets stick to thought, to potetiality...you hate the political side of God, witch is religion. all the stuff the you are saying in your vids are trying to disprove God insted of disapproving religion. im sure we would have a good converstion if we got into it..but all im saying is, something here is beyond physical, beyond math, beyond logic. i hope you can agree!
jaalul 3 years ago
ALBERT believed in God..
i dont know what your trying to do.... but the more i listen to you...(and you are good) the more im sure of creationist.. and anyone who believes in a creatore will believe alot more after what you said. of course first t, they will have to understand what you said...
well put though.
jaalul 3 years ago
I'm not trying to convince anybody that God exists or that god doesn't exist. I'm just interested in the reasons they give for either believing or not believing in God, and examining them to see if they are good reasons or bad reasons. thanks for watching.
randyhelzerman 3 years ago
I think the confusion here is you are not defining a domain for your objects. If you ended all of your lines with "in the universe", then it wouldn't work.:
1.For every element x [in the universe], that element is equal to itself.
2. Let A be a particular element [in the universe], then using 1, A=A
3. Thus there exists an element [in the universe] equal to itself
You didn't do anything wrong but it can appear to be magic without domains of definition for the objects.
TexanProgressive 3 years ago
Hi TexanProgressive, this whole exercise is 100% proof theoretic, not model theoretic. As such, it imposes constraints on which kinds of universes could exist. Another way of stating the conclusion of this vid would be that any model which you specify for any first order theory whatsoever would HAVE to include at least one object.
randyhelzerman 3 years ago
I see. That makes sense.
TexanProgressive 3 years ago
Isn't (2) beggint the question?
Deliratio 3 years ago
Well sure, but only in the sense that *every* deductive argument is begging the question. The conclusion of every deductive argument is contained in its premises.
randyhelzerman 3 years ago
Deliratio 3 years ago
but (2) isn't "There exists an object A". Rather, (2) is "A=A", where A is any proper name. The argument isn't *flatly* circular, in that one of its premises is copied verbatim to the conclusion. Rather, its just like any other deductive argument you'd ever see--there's some assumptions, which you may or may not agree with, and those assumptions already imply all of the conclusions you could draw deductively from them.
randyhelzerman 3 years ago
Then explain why you reject my proof of the FSM.
Deliratio 3 years ago
I don't reject your proof of the FSM. According to classical logic, it is valid. I do reject classical logic (see the wiki article on "free logic" which I think is a saner logic).
randyhelzerman 3 years ago
I think that given classical logic, all I have "proven" is the existence of the abstract object that is the identity of the FSM - by saying it exists.
Deliratio 3 years ago
Well, strictly speaking, you haven't proven whether it is an abstract object or a concrete object. All you have proven about it is that it exists and is equal to itself.
randyhelzerman 3 years ago
you misunderstood the argument. The proof says that the universe is contingent -could had failed to exist- yet it does exist, WHY?
can it be another limited thing? no, for that would be contingent, and would require an explanation for its existence.
only a NECESSARY being would not require an explanation or origin.
Thescotist 3 years ago
I don't see why a contingent object requires an explanation for why it exists. Nor do I see why a necessary being doesn't require an explanation or origin.
randyhelzerman 3 years ago
"Nor do I see why a necessary being doesn't require an explanation or origin."
Because they are necessary?
Deliratio 3 years ago
I don't follow, can you rephrase?
randyhelzerman 3 years ago
The law of non-contradiction does not need an explanation, because it's necessarily true.
Btw, were you saying "Contingent things don't need explanations. But necessary things do."??
Deliratio 3 years ago
What is the difference between saying "The law of non-contradiction needs no explanation, because its necessarily true" and "God's existence needs no explanation, because God's existence is necessarily true"? I don't think that I relieve myself of the obligation to explain something just by decreeing, ex cathedra, that it is necessarily true. So I don't see any connection between the necessary/contingent dichotomy and the needs/doesn't need explanation dichotomy.
randyhelzerman 3 years ago
Are you tellimg me that you are looking for an explanation of the law of non-contradiction?
Deliratio 3 years ago
Sure, why not? Same as I look for an explanation for God existence. Some book tells me that non-contradiction is necessarily true. Why should I take that on faith any more than I should take on faith some other book telling me that God's existence is necessarily true? Just because somebody wrote it down doesn't make it true.
randyhelzerman 3 years ago
A necessary being must be omnipotent, eternal, and uncreated. otherwise it would be a contigent element in need of explanation.
only god fits that criteria, and therefore it exists.
There are several arguments from contingency besides this one. but, why do you pick on kantians? the argument has been around since Aquinas, as the third "proof" of god.
Thescotist 3 years ago
This might not be considered modern logic, but you could always use Descartes idea that "I think therefore i am" Since i am able to think, i must exist somewhere in some reality. Though the reality i perceive might be very different that the actual reality but it still proves I exist. Since I am something, some exists since i know i exist.
zmod101 3 years ago
3X: X=X > 'something is equal to itself'. Therefore something exists - which is trivial: 'something exists' is self evident.
The logic does not explain 'why' something exists.
gangster3591 3 years ago
Interesting video!
qthinker 3 years ago
Doesn't this prove that 'something' exists? But the question is 'why' something exists?
qthinker 3 years ago 7
Hmmm... I don't get it....
For all humans that are currently on mars are equal to the humans that are currently on mars. Therefore there exists a human on mars.
What did I do wrong Randy?
126altf4 3 years ago
According to classical logic, you did nothing wrong :-)
randyhelzerman 3 years ago
¿?
Vx (M(x)->x=x) implies
Ex (M(x)->x=x),
but doesn't imply Ex (M(x)), as one can prove by showing an appropiate model. I don't think 'the thing' is so much the actual logical axioms and rules with wich one decides to formaliza FOL, but the tarskian paradigm of truth and necessity (what imo 'IS' FOL), within which the Ex x=x can be made sense and safetly pointed out.
excatomorfismo 2 years ago
This was ment as a response to the "men on Mars" comment.
For deriving Ex (x=x) one doesn't actually need a proper name; there might be no proper names in the language. Imo it is precisely the fact that you can use even an open term in the introduction of an existential quantifier where the non-emptyness of the universe of discourse leaks into. Anyway, I'm realizing I should have read more of this section before posting. Sorry if this is "yet another of those comments". Really good video.
excatomorfismo 2 years ago
lol thanks excat, yeah, almost everything has been raked over the coals multiple times since this vid was put up.
randyhelzerman 2 years ago
It may not be fallacious according to the definitions and properties we decided on for logic. But I still think its a fallacious argument. The very nature of logic is questionable.
CogitoErgoCogitoSum 3 years ago
Hi Cogito, Sure, I think that the real answer to this is that classical first order logic must be modified somehow. But this is why I didn't just present the proof here---I also talked about the introduction and elimination laws governing the universal and existential quantifiers, and give a brief justification of why we chose those particular laws. This is to demonstrate that whatever the flaw is in classical logic, it is a subtle flaw, not a trivial flaw. (cont)
randyhelzerman 3 years ago
(cont, to Cogito) so a full refutation of this argument would have to show a modification of the introduction or elimination laws of the quantifiers, and an argument as to why we should prefer the new, modified laws over the current laws.
randyhelzerman 3 years ago
Okay, I think I can make you follow your own advice. I want you to produce a proof, using classical, intuitionistic, minimal, free, or some another well-established first-order predicate calculus for the following proof:
"There is something that is equal to itself."
(∃x)(x = x)
...
"There is something."
(∃x)
Just emphasizing words in a sentence doesn't make the deduction for you, and you didn't (and can't) provide a proof of this. Show (∃x)(x = x) |- (∃x). Go ahead. I'll wait.
theyangist 3 years ago
What the fuck is the box? The existential quantifier? If so then the second formula isn't even well formed.
randyhelzerman 3 years ago
Then you already agree with me.
The second formula isn't well-formed, so you can make no such first-order deduction. Your now present agreement that existential instantiation from Leibniz's law cannot imply, by itself, that something exists, since such a claim is presumed, not proven within the system (existential quantifiers are primitive), then as I said earlier, you have proven nothing about ontology.
And as I've said before, you've committed an act of reification.
theyangist 3 years ago
*sigh* theangist, If you would have watched my video with your head pulled OUT of your ass, You'll see I never reached the conclusion (Ex). Sorry, you have been insulting to me, you have misattributed your false understanding as my mistake, and you have refused to admit you were wrong. What's even worse, you are a very dull and boring conversationalist. Welcome to my blocked list.
randyhelzerman 3 years ago
Your logic is horribly misinformed, since your proof that something actually exists, not that some proposition applies for some possible thing, would mean you'd have to violate the rules of well-formed formulae to produce a proof from "(∃x)(x = x)" to "(∃x)." But there is no such logical move allowing this, and trying to do so violates WFF guidelines, so you've proven nothing.
Analytic tautologies don't imply the sort of ontological leaps you make. You suffer from severe reification issues.
theyangist 3 years ago
Hi theyangist, its not "my logic" I wasn't the one who invented it. Nor is this argument my argument, this is well known. See the wikipedia article on "free logic" for another explanation of the same thing I presented in this video.
randyhelzerman 3 years ago
It dons on me that you don't really know what the issue of free logic is or what free logic aims to do, and nothing about free logic allows you to reify a term the way you do, nor does it allow you to violate the construction of a well-formed formula.
For that, you'd have to delve into the specifics of proof theory, which you didn't, and based on your demonstrated misunderstanding of free logic, are unprepared to do.
theyangist 3 years ago
theyangist.....dude, I'm very tempted to conclude you are an amateur and a poser, but I'll give you one last chance. In this video I am not using free logic. I am using classical logic. Classical logic HAS existence claims, as any real logician knows. Free logic was invented specifically to exclude the kind of move I did in this video. You're never going to get anywhere if you're not willing to admit when you are wrong. Go back, actually read the wiki article this time.
randyhelzerman 3 years ago
Classical logic doesn't allow for this kind of reification, either. And you still can't infer (∃x), a basic existence claim, from (∃x)(x = x), not in classical logic, not in non-classical logics, not in any logic that is in common use.
Either formulate your own syntax allowing '(∃x)' to stand alone as a WFF, or revise your stance, but don't tell someone with a degree in this area to read Wikipedia articles. Be a big boy and read the real publications, jackass.
theyangist 3 years ago
Sorry theyangist, I'm perfectly willing to talk with amateurs who are willing to learn, but I've no time for posers. The wiki article was for your convenience; if you'd like another reference take a look at James Garson's book "Modal logic for philosophers" P. 239 for another explanation. (cont)
randyhelzerman 3 years ago
(cont, to theangist) if you'd like to continue this conversation, you'll have to (1) demonstrate that you understand the proof of this given in Garson and (2) apologize for speaking out of turn. If you have a degree in this area, congrats, you wasted 4 years of your life, for you're just as big a fool now as you were before.
randyhelzerman 3 years ago
This is wrong. You can't imply an existential quantifier (the backwards E) from a universal quantifier (the upside down A). So, the rule 'All men are mortal' does not imply 'There is a mortal man'; it just means that 'If there are men, they will be mortal'.
squigglesy 3 years ago
Hi squigglesy, (upsidedown A) x implies (backwards E) x is a valid theorem in classical first-order predicate logic. See the wikipedia article on "free logic".
randyhelzerman 3 years ago
Okay, well I'm studying predicate calculus at university and I've been told different. Frankly, it's just common sense that a universal doesn't imply an existential anyway. Take the example 'All leprechauns are green'. So where's the leprechaun? There must be one somewhere. You might retort that this is a logical, not an empirical, system. But then you haven't really answered the question of why there is something rather than nothing, in reality. You've only answered it in a theoretical sense.
squigglesy 3 years ago