erislover, i must admit i’ve totally lost any understanding of your argument. a lot of the posts i’ve read lately seemed to be agreeing with me, except that they claimed to disagree. could you perhaps reiterate them in one organized form, independent of a rebuttal of another post? why precisely it is that language is meaningful while logic is not?
well, in trying to understand your position a bit better, i’ve collected several of what seem to be your objections. here they are, and my response to each.
it is not logic’s goal to make statements about what is “true.” logical arguments are not themselves said to be true, unless they are tautologies. they are said to be valid. a tautology is something that is true of itself, and can therefore be used to prove the validity of an argument. given the underlying assumptions. why is there no room for reality?
this statement is totally false of all logical statements other than tautologies. P->Q says nothing about its truth. (P & P->Q) -> Q is true, but says nothing about the truth of P, or P->Q, and certainly not Q. but all arguments that take this form are valid because this statement is always true. let’s take care in the future to make a distinction between validity and truth. logical validity comes from the necessary truth of tautologies. no truth value from the propositions can be gleaned from logic. that comes from reality.
no, it is created for the sole purpose of helping us understand reality, and making predictions (based on inference) about reality. but wait, that sounds like an application to me…
is there any such qualifier in english, or indeed, reality? “Hey, this one is really green. I mean it.” can that statement necessarily be true without certain assertions? again, we do not logically derive truth, we derive validity. the truth of P->Q is based on the truth of P and of Q. but P->Q is a logical statement.
what do you mean “the application is…logically true.” do you mean valid? this application doesn’t make the logical statement true either. there is nothing that can be said of the truth of the statement P->Q without knowledge of P or Q. i suppose a correspondence to reality could give those Ps and Qs some value, though.
again, where is this necessary correspondence with reality? can you give me an example of a true english statement, and its logical counterpart, and why one is said to be “true” while the other isn’t?
how bout the statement: “this statement is true or it is false.”? it certainly SEEMS to be true in any context.
additionally, i would not define logic as a language. it can be used to communicate, true, but only when we consider propositions and not variables. it is more a set of tools for analysis and inference than a language.
Of course not. Merely that the testing of such statements removes them from their own domain. I said they might as well be in English. They don’t have to be.
So you say. I have come to be of the opinion that English cannot be considered seperate from reality if it is dependent on reality for its truth conditions. Reality is not external to conversational speech.
The series of statements were to be in English. A logical argument.
** Ramanujan**
Alas, not really, as one poster insists logic finds truth, another insists it does nothing of the sort. Some find it to represent extreme generalization, others not. The summary of my argument in light of this would be, “Something that is all things to all people is meaningless,” though of course I’ve never made such an argument (and won’t). I can’t summarize my posts because they represent attacking different views of logic.
However, they all seem to focus on one point that seems awfully silly to drive home: the ability to assess the truth of a statement in formal logic is in formal logic; the ability to assess the thruth of a statement in conversational speech is in reality. Logic is determined; English is underdetermined. Finally, applications of logic to reality fail to carry over this hallmark feature of complete determination, so it is now no more expressive or powerful than English, and its use is a matter of convention, not necessity. Here logic is meaningful, but that is a cheap victory as it no longer has the form it did before. It has the symbology in common with its namesake, but without determination it is no more powerful than English. Indeed, it might as well be in English.
An assumption in formal logic is no more than the assertion of truth of some quantitiy of free variables. The free variables still have no content. The final result is still guaranteed to be correct. If your assumption is to represent an English statement then the result is no longer guaranteed. If they were no one would argue with the First Cause argument. If they were, anything that even had a logical form similar to the First Cause argument and was true would imply the truth of the First Cause argument tautologically.
Yes. Sometimes it is implicit in the inflection, sometimes people say, “And I mean it!” Most often it is implicit in the assumption that the people we talk to aren’t lying (that is, they mean what they say). I am not prepared to accept that English conversations have the same form as logical assertions. I would be willing to listen to such an argument, however.
See above.
As a response to this I will ask my own two questions. Perhaps they will shed light on why your question is not appropriate.[ul][]“This is a sentence.” What sentence?[]“This sentence makes sense.” What sense?[/ul]
Also, I do want to take a moment here to welcome the presence of Spiritus back as well. But, I must unfortunately note his return uncannily coincides with my recent flurry of spelling ‘the’ as ‘teh’. Coincidence? I think not!
So:[ul]
[li]testing logical statements against reality removes them from their domain[/li][li]but testing English statements against reality does not, because English cannot be considered separately from reality.[/ul]and you make that idstinction because . . . [ul][/li][li]logical statements must appeal to reality (perhaps filtered through another language such as English) in order to be tested for truth[/li][li]but English statements are tested for truth by appeal to reality[/ul]whcih makes logical statements meaningless and English statements meaningful because . . .[ul][/li][li]Logic is “intended to be” separate from reality, with truth delivered “automatically”[/li][li]but English is tied directly to reality with truth from observed corrspondence[/ul]and you support this distinction with the idea that[ul][/li][li]testing logical statements for correspondence to reality moves them “outside their domain”[/li][li]but testing English statements for correspondence to reality is how English statements become meaningful.[/ul][/li]Is that about right?
And also, it seems, that logic cannot be meaningful if it is dependent upon reality for its truth conditions. Good for the goose, but the gander is just a meaningless pile of feathers.
P -> Q is not an English statement. The question you asked was: Does [P -> Q] mean the same thing when doing pure logic work as when trying to analyze a specific application of it to a series of statements?
from your response to ramujan
At least 2 of us have already observed that this simple statement is simply not true.
False.
Incorrect.
Not in correspondence with reality.
Meaningless, perhaps, under your theory of meaning.
In other words:
Cite?
Nonsense. All statements of logic may be translated into other languages. So what. The power of logic comes from the rules of syntax which define which statements may validly follow from other statements. Is discrete mathematics lessened by the observation that all of the numbers can be translated into reals?
But the truth value is still wholly determined by the assumptions, which are NOT derived from logic. The acceptability of those assumptions is determined by . . . correspondence to reality.
No. The final result is guaranteed ot be logically valid. Whether it is correct depends upon the accuracy of the assumptions and the applicability of whichever formal structure was used to derive the result.
Not true. Truth is not determined by logical structure alone, but by – the accuracy of the assumptions and the applicability of whichever formal structure was used to derive the result.
Validity resides in a formal structure, not truth.
I can repeat that a few more times, but please stop simply ignoring it and provide a refutation if you disagree.
The sentence, “this is a sentence”.
The sense that “This sentence makes sense” conveys information about an English construct: depending upon context this might be information about aradoxical structures or recursive meaning or simply a syntactic illustration of grammaticla structures.
His question was appropriate. English does allow self-referential statements, and all of the paradoxes inherent in same. His statement was not a paradox, though. It was a tautology. And it was a meaningful English statement.
If you mean by “English” a language which contains all of the structures of English except those which result in certain problems of logic (such as self-referentialism and paradoxes of construction) – well, that doesn’t correspond to reality.
[quote]
and you make that idstinction because . . .
[ul][li]logical statements must appeal to reality (perhaps filtered through another language such as English) in order to be tested for truth[/ul][/li][/quote]
Logic statements do not appeal to reality to be tested for truth. Since when have they ever?
P->Q
P
Q
This is true without reality. If you want to apply this to reality and keep its generality, you might say, “This argument applies to everything it applies to.” Be my guest. I don’t know which reality you’re talking about, though. It could be any of them. When we apply logic to reality, logic becomes meaningful, but that’s because it is no longer logic but a logic-like structure (an analogy to formal logic) with underdetermined truth. Just like English. To consider the system as determined, one needs to include reality. This wasn’t necessary before.
Why would it be? It’s all a determined system.
Of course; if they were derived from logic then the whole thing would be quite circular and wouldn’t impress anyone (and “being impressed” with a proof of Fermat’s Last Theorem doesn’t make it meaningful). But if you want to keep it as formal logic you have to assert it in the way that formal logic requires, which is a binary true/false state, otherwise devoid of content. And the gap of which I discuss is just as present here for “true in formal logic” versus “true in reality”. Neither implies the other.
Which is exactly my point, and this is why attacking an argument in English on the grounds that it fails to meet the criteria imposed upon a symbolic argument in logic IS MISGUIDED AND MEANINGLESS (as you and I well know, bolding, caps, and other forms of internet “shouting” do make a person more right ;)). Careful you don’t fall in the gap seperating meaningful statements from logical ones.
An argument gains no more meaning, nor does it become more true or undeniable, given that we may compare it to a logical structure which anyone who knows logic must say is true. If this is so, then it must be because logic is meaningless.
Meaningful in any context? That was my point. As you note for my example,
Which one? And what if the conversation up to that point had nothing to do with any of those? Then what am I to use the sentence for?
[list=1][]Page 1: “why not just evaluate logic like any other scientific theory, namely by how well it models reality?”[]Page 1: “It’s not quite accurate to refer to logic as a game. It’s THE game, either higher or lower than all others depending upon how you look at it.”[]Page 1: “Logic isn’t necessarily a useful guide to the way that the world works…”[]Page 1: “Truth value is determined only by truth tables”[]Page 1: “Logic is only used for defining the validity of statements/arguments. In that capactiy, it is the be all and end all.”[]Page 1: “Reality either supports it or contradicts it.” Followed by, “The statement is true without appeal to the real world…”[]Page 1: As for your claim that logic doesn’t deal in truth–that’s just odd. Where did you get that notion?"[]Page 2: “logic is a set of things we consider “true” because they seem to be so inherently, in this reality.”[]Page 2: “also, i would like to restate that logic is based on the concept of truth.”[]Page 2: “Logic is an abstraction of the real world.”[]Page 2: “Logic, of course, is a tool that takes given knowledge and extends that to knowledge from inference”[]Page 3: “without this concept of truth, which it is the goal of logic to expose…”Page 3: “Formal logic, however, attempts to make explicit all criterion for usage without appeal to external elements.”[/list=1]That’s enough hunting.
Ah, I see the cite was not a request for showing that I was arguing with all sorts of people differently, it was to demonstrate that “the ability to assess the truth of a statement in formal logic is in formal logic.”
In that case, I will defer you to the first comment in the post above, where Q’s truth follows the two premises. And for a response, please demonstrate how I am wrong there, how the truth of that statement in logic doesn’t come from logic, but from its application to reality. Since there is no gap between formal logic and English, please do so in formal logic if you can. If not, that’s OK, too; I really am interested either way.
I will look up some references tonight to satisfy myself if no one else. Unfortunately I don’t have internet at home until this coming Saturday or later (I think it is this Saturday… chao, I can’t remember) so don’t expect them right away.
Also, Spiritus said, “Truth is not determined by logical structure alone, but by – the accuracy of the assumptions and the applicability of whichever formal structure was used to derive the result.” And I said this is my point, which it is, but now I realize that this was assuming we were talking about reality-truth, not logic-truth. If you were talking about logic-truth I still disagree.
Another note: The formal logic comment wasn’t meant to step this debate up to absurd levels, it was meant to show that logic does not have the ability to say, “In the real world…” and indeed I’ve never seen a symbol that was supposed to represent that in any logic. It was snarky, and I apologize; I do not expect this conversation to carry on in any other language than English. I(ndeed, if I am right it must, for “logic is meaningless” is a meaningful proposition and if it could be argued with logic we’d have quite the paradox.)
I don’t see the paradox Eris. I believe these are all consequences of the ‘incompletness’ theorem; or rather the understanding that resursive determinism collapses the capacity for perception (which I don’t think that theorem argues explicitly, I could be wrong). This does not however rule out determinism itself. I do agree with you that language is part of nature, logic is a part of nature and as such subject to any other aspect of nature. I personally take a ‘holographic’ approach to nature and language translation, and generally consider that more raw intelligence is required to anthropromorphise inanimate objects in order to establish a go-between for these different ‘bases’.
To the degree that rationality itself is mapped; I don’t see any conflict with free-will, simply that the conflict of consent with regards to free-will is resolved.
Why it is this way rather than not this way? I don’t know.
I do however believe that consent can be redeemed; and is most likely the sole purpose of 'the lack of determinism necessary to determine itself within the context of determinism.
I just don’t understand the necessity for variation in the instance that it causes a necessarily acute loss of consent in certain pockets. This is what troubles me about the purposefulness of ‘it all’. I do believe that it can be redeemed recursively, however that contradicts the variation clusters observed presently, as such an act would concievably fall back through the entire chain (much like determinsm itself would collapse recursively upon itself). I can simply add another ‘well it couldn’t be any other way, so that’s how it has to be’; but this is clearly not satisfactory =)
I’m about as psitive as a person can be that the hypothetical ‘Liebniz’<sp?> ‘machine’ falls in the realm of both possibility and probability; as the inability to construct it would fold reality in upon itself (what does it mean to say that though!! =); that’s my personal take on this.
erislover, i think you’ve quite missed the point of both me and Spiritus.
we both said it is not the TRUTH of a logical statement that does not depend on reality, but the validity of the argument. i guess this is what you call “logic-truth”. from your example:
P->Q
P
Q
and you claim that Q is true in any context. and therefore logic is meaningless. what about the context:
P->Q
~P
when i say you missed the point, i mean that you claim that the statement of Q in the previous proof is absolutely true. that is, “true without reality.”
but without reality, what can we say about:
P->Q
?
what can we say about:
P
?
it is these statements that the “truth” of Q in the final statement depends on. the argument is valid, because (P & P->Q) -> Q is a tautology. however, (P & P->Q)->Q says nothing about the TRUTH of P nor P->Q. the truth of Q, though not the whole statement, is dependent on the truth of those things.
also, i want to point out that with a different definition of “reality” our definition of logic would be different. it is based (whether you accept peano’s assumptions or russell’s) on certain things that are “taken as granted”. that is, it must be assumed that they exist in reality since we cannot say that they depend on any other things, so we must accept them, or we don’t accept logic.
In terms of what Ramanujan stated; I believe it can be determined as more true that our inability to translate is required in order for reality to exist at all. I’m not aware of this arguement amongst Peano or Russell however, to comment in that context.
First things first:
It is apparent that the “gap” to which you refer is simply the observation that some things can be said in English which cannot be said in formal logic. I do not contest that observation. I do not find it particularly interesting or consequential, but I certainly do not deny that it exists.
Now to the second things:
I have decided to abandon my efforts to encourage precision in your usage. I will simply note that you are wrong.
It is, however, a valid logical structure.
There are more logics on Heaven and Earth, horatierl, than are dreamed of in your argument.
You are correct that in any language a truth value must be expressed in a manner which is allowed by that language. I remain mystified at the import with which you impart this observation.
Nor does “grammatically correct in English” imply either of the above. “Truth” in formal logic is simply a property defined across relationships. I was not under the impression that either of us was addressing that property when using the English word “true”. Had I not already abondoned such hopes, I might now suggest that the symbol “T” would be un unambiguous means of delineating between the English and logical homonyms.
Now, while there is no logical implication from “T” to “truth”, the logical relationship has been very explicitely defined to map the observed behavior of “truth”. Thus, there is an English implication (which is, I gather, the only one you would find meaningful anyway.)
Only if one assumes in advance that the formal structure is not applicable to the question at hand. In English, this is known as begging the question.
No, but they are sometimes effective in getting another person to respond to a point. As such, I at times find them useful when debating with someone who responds only selectively to things that I post. Whether you find that use meaningful, I do not know.
An argument can gain substantiation by demonstrating that it conforms to a valid logical structure, which anyone who knows logic will be able to differentiate from a caim of truth.
Just to be explicit on one point, though, are you arguing that an argument contains no meaning if it is not true? Is a false statement, whether asserted by mistake or with intent to deceive, null in your theory of meaning?
Yes–a tautology in English is meaningful in any English context.
If you disagree, then please provide a counterexample for one the tautology “This is a sentence.”
This is rather frustrating.[ul]
[li]You asked for an example of a tautology in English.[/li][li]One was given. [/li][li]You declared it “inappropriate” and then offered two more tautologies, along with questions about each.[/li][li]I answered your questions.[/li][li]Now you respond with more questions which have nothing to do with the definig quality of tautologies.[/li][/ul] Which one? I truly could not care less. what if the conversation up to that point had nothing to do with any of those? What if the English language allowed for non sequitors? Then what am I to use the sentence for? Perhaps to imply an easy joke.
Again, I am going to note that if your definition of meaning in English hinges upon the idea that there are no tautologies or paradoxes in English, then your “English” is not English. Your theory does not correspond to reality.
Yes. I apologize for not making the antecedent unambiguous.
The validity of that structure comes from logic.
The truth of “Q” comes from the accuracy of the assumptions and the applicability of whichever formal structure was used to derive the result. In this case: P and modus ponens.
The demonstration that truth and validity are different things is apparently beyond the scope of this thread.
The feeling of deja vu that I experience is strangley familiar.
I was talking about “truth”, not “T”. If the above is your point, then it would help if you would stop saying things like:[ul]
[li]please demonstrate how I am wrong there, how the truth of that statement in logic doesn’t come from logic, but from its application to reality. [/li][li]Logic statements do not appeal to reality to be tested for truth. Since when have they ever?[/li][li]This is true without reality. [/li][li]The final result is still guaranteed to be correct. [/li][li]the ability to assess the truth of a statement in formal logic is in formal logic[/li][/ul]
Well, modal logics address the “real world” through inclusion. But that’s a bit of an unnecessary tangent.
No apology necessary, but I accept and thank you for offering it.
I’ve been known to snark a bit myself. That’s one reason I like to swim in the deep end.
The funny thing is that it impossible to argue that it is invalid without swimming in irony. Without the modus ponens, contradictions and tautologies merge and become indistinguishable.
If I may contribute just two things that I hope might be helpful and augment some of the points you’re making… Ramanujan might not know that, although we use the term “statement” loosely in these informal debates, there is a difference in logic between a statement and a proposition.
A proposition is a statement that is either true or false. “The lake is fifteen thousand cubic meters” is a proposition. “The lake is beautiful” is a statement. Only very specialized logics deal with statements that are not propositions.
Truth in a context of validity is called soundness. An argument is valid if its inferences follow logically from one another. An argument is sound if it is valid and all its inferences are true. So, an argument may be valid even if it is unsound.
First off; thank you for the contributions Libertarian!
Second: The Modus Ponens form I found after I read this reply (didn’t know what on earth it was)
If democracy is the best system of government, then everyone should vote.
Democracy is the best system of government.
Therefore, everyone should vote.
This has a number of troubles.
There is no evidence that we have ever had a democracy.
OR
To the degree that democracy is considered inherent; everything we do MUST be a vote ((like the absolutetization of consent without soundness (I like that word)). What I mean, is that this is the Biblical equivilent of the prayer clause “God created us to worship him. God is all powerful, so no matter what we do, we must be worshipping God if we were created to worship God”
This collapses the abstraction of consent into an embedding within ourselves which is used rhetoricly<sp?> against us by authority without the evidence of soundness. (starting to pick up some of these terms now! I used rhetorical!).
The form is susceptable to layers of abstraction in a VERY serious way; and as such cannot be sound, or as I would probably say; an axiom worthy of being an absolute.
The chief trouble with your syllogism is called audiatur et altera pars, and in this case is glaring. If the “democracy” mentioned in your first term is not refering to our government, then it should have said so.
Lib
Nice clarifications. I hate to do it, but I’m going to quibble with a couple of points.
If only logicians (and philosophers in general) were so consistent in usage. While I think that mathematicians ar epretty consistent in following this usage, one can also frequently find “statement” and “proposition” to be explicite synonyms and opposed to “sentences”. As a general rule I would say:[ul]
[li]sentences are syntactic constructs which may contain semantic content.[/li][li]propositions are sentences to which a truth value can be applied.[/li][li]statements are used synonymously with either sentences or propositions, depending upon the writer.[/ul][/li]And, of course, there is the whole issue of whether structured propositionalism is the right way to investigate truth–but as a usage guide I think the above is a good start.
Or else I’ve just muddied things up for everyone. :smack:
Actually, I think a more general way to phrase it is: a proposition is a semantic construction to which a truth value can be applied. (or which has a truth value, if one accepts truth as a poperty.)
In most propositionalist structures, there is an acceptance of indeterminate truth values as well as the T/F dichotomy. Though, if you like deflationary theory of truth I can see why you might want to exclude such structures from being propositions.
I’ll stop now. Sorry for the pedantic digression.
Oh, and I agree with you entirely that an epistemological structure can be applied to any metaphysic. I think erl’s “nothing” implied “nothing meaningful”, which rolls back into his grounding of meaning in ontological correspondence.
I will utilize, from this point, the marker “T” for what I’ve been calling “logical truth” and others call “validity”, and “truth” for whatever we find to be true here in reality.
You don’t find this point compelling? The point is: nothing that can be said in English can be said in formal logic. Logic doesn’t say anything.
And formal logic does not allow “truth” as “corresponds to reality”. In fact, it doesn’t allow “truth” at all.
I contest the latter. Its inability to hold in a vacuum is part and parcel of what gives it meaning.
I get teh subtle feeling you are right there with me, but you’re looking at the ground on the other side, the ground at your feet, and concluding that they are connected by ground in the middle.
A special case of question begging, anyway. Only one needn’t assume it in advance. The reason I have for feeling that logic is meaningless is that an English sentence gains nothing from having the form of a logical argument.
To clarify something I think you are trying to tell me, are you saying that logic is a symbolic representation of valid relationships among meaningful quantities (be they individual words or statements or whole paragraphs and concepts)? I have a few questions to ask regarding this statement, if so. If it is not worded appropriately, then I will ask for your help in correcting it. I do not want to fight strawmen here. I can tell one of our patience is coming close to an end, as well, so let’s nip this in the bud.
I see it is meaningful, but does it have the same meaning?
At times, I do not feel that I can substantively respond to one point until others are developed. Whether you find that meaningful or not, I do not know.
Not quite yet.
This would apply to modal logic as well. It would apply to any determined system. A system’s scope is where it is determined. A system is not meaningful outside of its scope. Logic is a self-contained scope. English is not. Outside of this reality, English is no longer meaningful, either.
Bold adventurers, my friend, bold adventurers.
Ramanujan
This changes the statement. Of course the result will be different if we change P to ~P. This is an application of the word “context” that I haven’t considered using before. I’ll have to think about it.
Where? In what realities is this sort of operation able to be used? I look for a point to attach these formal logic tautologies, definitions, and statements, and I don’t find anything. The moment I want to indicate attachment in formal logic, the free variable loses any indication that it is attached to reality at all. It simply has, “T”. But that could be anything. The context here is in the English application that led up to the use of symbolic logic. We’re right back to the discussion Jerevan and I were having.
total hijack Lib, I almost subscribe to the deflationary theory in that (from your link), “to assert that a statement is true is just to assert the statement itself.” But, I also go along with correspondence in that there are still certain constraints as to when we assert statements. These constraints act as the correspondence in a way analogous to a meme theoretic view of the use of propositions. Thus, reality is solely defined by inter-subjective use of language. Meaningful statements in conversational language take the form of context-dependent difference markers (the ultimate thing any word means is "there is an agreed upon difference between this [thing/word/construction] and other [things/words/constructions]), thus imposing the universal rule that difference exists (I cannot escape the transcendent implications of this, though I am not aware of how this all works ontologically as I don’t care much for ontology, leaning towards idealism over any other ontological view though I don’t like idealism proper [RE: the dualism thread]). The creation of a formal language for the purposes of understanding reality is thus completely circular and worthless, meaning-wise. The rigid flexibility and impure structure of conversational language is what allows it to be shaped by reality (if you are a realist) or what allows us to shape reality (if you are an idealist) or what allows the merging of physical reality with imagination (if you are a dualist).
