(Warning to all: this is going to be a heckuva long post, covering a lot of basic logic and the perhaps non-obvious implications thereof. If you are not too Liberal about things, you should feel no guilt in scrolling (and scrolling, and scrolling) right past it.)
Okay, I have returned, and I would like to note a few things.
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I am a male. (It doesn’t really matter to my arguments but I thought I’d clear that up anyway.)
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I fully appreciate that you are playing catch with a half-dozen people at once, from all different directions. I sympathise with the fact that you are feeling outnumbered (since you are) and that the feeling of being outnumbered by opposition can incite feelings that there is a conspiracy of enemies against you. However, being outnumbered does not make you correct, nor does it make your position immune to attack. If you do not feel like responding to these attacks, due either to the indefensibility of your position or fear that we all are out to get you, then you always have the option of departing the field. I would prefer you remain and use this as an opportunity to ferret out any errors in your position, but if you don’t want to, that’s okay. (I will of course reserve the right to interpret your departure as a concession to the correctness of my position. Wouldn’t you?)
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I am arguing only against the logical proof(s?) you present for God’s existence. Whether or not you believe Jesus came to you and told you what was moral is your business. However, you present obscure and cryptic logic as supposed proof that your positions are correct. To my eyes your logic is not as solid as you claim. If you believe it is solid, then it is my opinion that you have misled yourself and would probably benefit from having your ignorance fought. (Why else post here?) If you know your logic is false, then you must be trying to bamboozle people for some unfathomable reason. I really don’t think that’s what’s going on, but if it were it then publicly refuting you for the benefit others would be an equally, er, edifying activity to merely assisting you in correcting your misconceptions.
Of course, I could myself be wrong. Perhaps your arguments are all rock solid, and I am merely a poor fool who got As in those logic-related college courses due to the infinite pity my teachers took upon me. Or maybe I’m lying about those very classes (one must ph34r the aurgument from authority). Heck, maybe I’m actually a pedestrian hick who can barely string two words together!
Of course in that case it should be a trivial matter to prove me wrong. You wouldn’t even have to resort to debate ‘techniques’ like Ad Hominem; you could just disprove me flat. Oh, and speaking of which…
- What’s with all the ad hominems? Your last post to me was almost nothing but. Whether that sort of thing improves your position in the eyes of others I cannot say, but you can be entirely confident that calling my knowledge of basic logic into question does nothing to bolster your debating position in my eyes.
In fact, I’ve got to the point that I’m not entirely confident you even understand how logical arguments are employed. In an effort not to simply escalate the exchanges of ad hominems further, I will instead ask you to confirm whether or not you feel each of these factual points about logic is true. (I’ll start with an easy one.) Once that’s out of the way, we can maybe talk specifically about your premises and argument.
(Warning: as noted above, this is going to be a very long post, so take your time in replying. Deal with everyone else first if you like. Take all weekend if necessary. I’m in no hurry.)
(Note about symbology: In any logical arguments, premises will be numbered P1, P2, P3… Inferences that are not the conclusion will be numbered I1, I2, I3… The concludion will be marked C. The the rule of inference used to inder each non-premise will be noted at the end of the line in parentheses. Oh, and I’m going to informally use == to mean statement equivalence, since I haven’t anything better.)
So.
Point 1) Attacking the premises: A logical argument must be both valid and sound to allow you to validly reach any new conclusions from it. To be valid an argument must have no internal inconsistencies, according to the rules of that form of logic. To be sound, the argument must be valid, and also the premises must all be True (presuming a bivalent logic system).
So, do you, or do you not, agree with the above? If you don’t, we’re done. You wouldn’t be talking about logic. In fact it’s worse: all logic would be useless. I could make the following valid logical argument:
P1: If helicopters hunt down and eat children on a daily basis, then God doesn’t exist.
P2: Helicopters hunt down and eat children on a daily basis.
C: God doesn’t exist. (Modus ponens, on P1 and P2).
…and you could not dispute it, since it is valid. You don’t want that, of course.
However, if you do accept my point 1, then you must admit that your premises need to be True for your argument to be sound. It is, therefore, fair game for me to question the truth of your premises, and if you fail to demonstrate that they are true, then your argument is unsound and your conclusion, unproven.
Okay. You should be at this point vehemently denying you ever said or implied otherwise. That’s fine; this was an easy one. Moving on…
Point 2) Truth values: In a bivalent logic system, the only value that a statement in the argument can have is the value True. There are no False statements in the argument; any statement that is written down is considered True within the frame of the argument. If any written down statement in your argument can be demonstrated not to be True (for example, if you can arrive at the statement A & ~A via valid application of the logical rules) then your argument is demonstrably unsound, indicating either a logic error or that one of the premises was False. (This is done deliberately in proofs by contradiction.)
The fact that all written statements are presumed True does not, however, mean that all unwritten statements are False. If that were the case, then it would be impossible to extrapolate any further statements or conclusions, since those would already have been shown to be False by the sheer fact that they had not been stated or deduced yet. Every logic system requires it to be possible for there to be statements of unknown truth value. (So does Godel’s Incompleteness Theorem, incidentally. And where’s my whifflebat? I don’t mind beating a dead thing, equestrian or otherwise.)
Therefore, all bivalent logic systems have three values: True, False, and Not Known. (The third truth value, ‘False’, can be assumed to be the case for any unwritten statement that is the negation of a written statement.)
Because all written truth values are being asserted by the arguer as true, any statement who’s truth value is not certain to be true, either by the proof of it’s negation or by the casting of reasonable doubt upon it* must be stricken from the list of premises along with all conclusions drawn from it (lest it be misrepresented as a known true value when its truth value is in fact Not Known).
- Note that internal statements and conclusions of a sound argument are made immune from such criticism by the power of logic. All hail the power of logic!
What then, it might occur to you to ask, do you do if you find that your opponent rejects all of your premises flat, regardless of merit? Suppose that someone denies that Socrates was a man. Is it then impossible to prove to that person that he was mortal? Answer: Yes. You cannot prove anything to anyone who refuses to accept your premises despite all evidence. Common ground is indeed required for any (logical) discussion. (Alternatively you could try torture. It’s been known to work.)
So, do you, or do you not, agree with the above? If you don’t, we’re done. You wouldn’t be talking about logic. Even worse, I could create the following argument:
P1: At some unspecified time in the future, the Invisible Pink Unicorn will appear and declare that God does not exist.
P2: The Invisible Pink Unicorn is someone who never lies.
P3: If at some unspecified time in the future, someone who never lies appears and declares that God does not exist, then God does not exist.
I1: At some unspecified time in the future, someone who never lies will appear and declare that God does not exist. (Substitution into P1, from P2)
C: God does not exist. (Modus ponens, I1 and P2)
The structure of this argument is valid. But is it sound? Two of the premises are absolutely unprovable, either as True or False. I have here asserted that they are True, just as you have done with the premises to your proof. If you had to prove their negation to dispute them, then you would be unable to do so, and by default my argument would be both valid and sound, proving God’s nonexistence. You don’t want that, of course.
However if you do accept Point 2, then you must also accept that those disputing the proof of your premises (that would be me) are not required to prove their negation to dispute them. They need only successfully dispute that your proof that they are True is correct. Because, if the premise is not True, then it is not allowed to be written into the argument, because to have a non-true premise would make the argument unsound.
Point 3) The Meaning Of Things: All logical symbols have a specific, unchanging meaning, and all user-defined variables have a specific unchanging meaning for the duration of the argument. Also, there are strict suntactic rules for the use of all symbols and variables, defined by the logic system. And, based on these, in any given statement these symbols can be directly translated into english statements that convey the same meaning that the symbolic statement did.
Examples of symbols and their english translations: (in these examples, A and B are statements that are either true or false. C and D, on the other hand, are objects.)
“A & B” becomes “A and B”
“~A” becomes “not A”
“A -> B” becomes “A implies B” or “If A, then B”.
“A” becomes “it is necessary that A”
“<>A” becomes “it is possible that A”
“C = D” becomes “A equals B” or “A is B”.
(I got the <> symbol, and my newfound understanding of Modal logic, from a disreputable source.)
When expanding a logical statement out into english, parentheses may be used to avoid ambiguous statements, and minimal rephrasing can sometimes help things be easier to read. In all cases, of course, you must be very careful not to change the meaning of the sentence. (Of course.) Note that a reverse process can be used to turn english statements into logical statements, and in fact that’s how premises are generally made.
I assume you’re in agreement with me so far.
now, about those statements that are either true or false, those A’s and B’s. Assuming we’re not doing our proofs with the aim of making additional rules of inference, then all of these will be replaced by a specific statement which is constant throughout the argument. If this statement is used anywhere that one of those As or Bs is in the definitions above, it also must be the sort of statement that has a true or false value.
In the equals sign, the C and D must be objects. They cannot be statements with true or false values. (The entire statement “C = D”, however, can be used wherever a true/false statement is required.)
Thus we introduce the notion that not all symbols and variables can be used everywhere, and that some syntactical arrangements are invalid.
So, for a (cough) random exaple, let us translate the statements “G -> G” and “~~G” into english. By symbolic replacement we get:
“If G, then it is necessary that G.”
“not it is necessary that not G.” (Or, “It is not necessary that not G.”)
Okay then, what’s G? by its placement in the logical formulas, we know that it must be a statment with a true or false value. That would rule out G referring to some object, such as “God”. I mean, then you’d get sentences like “If God, then it is necessary that God” and “it is not necessary that not God.” That doesn’t make any sense. Fortunately, you’ve stated previously what “G” means in the context of your premises: “God exists”. That’s fine. So the randomly selected (cough) statements translate to.
“If God exists, then it is necessary that God exists.”
“not it is necessary that not God exists.” (Or, “it is not necessary that God doesn’t exist.”)
Similar to G, any variable that is defined at any* point in the proof retains the same value throught the proof and the discussions thereof.
- This is of course excepting variables defined with a limited scope like x in ‘Ax.(P(x))’, but then you already knew that.
So, do you, or do you not, agree with the above point? If you don’t, we’re done. You wouldn’t be talking about logic. (Heck, there would be no reason to believe that your premises or conclusion meant anything even close to what you claim they do.) Even worse, I could create the following argument:
P1: S (meaning, “Socrates was a man”)
P2: S -> M (meaning, “If Socrates was a man, then Socrates was mortal”)
C: M (Modus ponens on P2 and P1. Oh, and it means “God doesn’t exist”.)
Two true premises, and a valid argument: the conclusion’s meaning must be true, therefore proving that God doesn’t exist. You don’t want that, of course.
However if you do accept Point 3, then you must also accept the following several things:
“G”, which you have called the ‘definition’ of God, translates into “it is necessary that God exists.” On the upside, this does have a truth value, so it can be used in the proof as a premise, as we are wont to do with definitions. (Premises are the only possible way to introduce definitions formally into the argument, after al.l)
Of course you didn’t acutally use G in the proof as a premise, probably because if you did then I or most anybody else would reject it out of hand (that is, we’d refrain from asserting it to be True; Point 2). After all I don’t actually believe that god is necessary, to the point of asserting it to be True. I never even met the guy; how would I know about his necessaritude? There is no epistemic or empirical reason I should accept this statement, this ‘definition’ as being True.
If we did accept that this ‘definition’ wasn’t false, then your job would be easy:
P1: G
I1: G->G (substitution into A->A, a modal logic rule from my cite, with G for A.)
C: G (Modus Ponens and the axiom (M), from my cite.)
…No other premeses are even needed; we can prove God exists without this premise alone! This ‘definition’ as good as assumes the conclusion. Of course, since there’s no evidence for this conclusion, rejectomundo.
I will repeat: every time this ‘definition’ is used, the user of it is assuming the conclusion. It is certainly pointless to replace it into other things to get us to beleive that premises are true since it is not assumed to be true, and therefore it’s non-true value makes all arguments using it unsound, and the hoped-for conclusion rejected.
Okay, so we know that “G” translates into “it is necessary that God exists”, or perhaps “God necessarily exists” or even “God exists necessarily”. Is this synonymous with “God is necessary existence”?
Of course not. And, as one would expect, a statement with a differing meaning cannot possibly translate into the same string, unless you make a mistake in your conversion. Let us examine what the statement does mean, and how that differing meaning actually would translate into symbolic logic.
In english, “God is necessary existence” is interesting in that “necessary existence” is a nouned verb; it is nonsensical to talk about existence (necessary or not) without a referent or set of referents, stated or implied. So, this statement defines the term ‘God’ as being a nouned verb; it is therefore proper usage (by definition) to say “That helicopter Gods.” That would of course mean “That helicopter necessarily exists.” This “God” would be defined as “God(x) == E(x)” for some x, assuming that we define ‘E(x)’ to mean ‘x exists’. (No such definition has been made to date, but why not? We’re tripping the light fantastic anyway.)
Suffice to say, this ‘God’ cannot equal the God in your argument; it also (therefore) can’t equal the God in your other ‘definition’. This makes sense, since we knew the english definitions were not synonymous. Amusingly, your other definition could be written “God Gods”, or formally “God(g)”, assuming we define ‘g’ to be the object God, defined such that “G == E(g)” is true. But doing so would be quite silly, don’t you think? Almost as silly as defining God as a nouned verb in the first place.
I have gotten the impression that you found my tendency in that one post of mine to refer to your Premise 2 as “the definition of God” to be confusing, in spite of my having explained that tendency in the subsequent post. Fair enough, I will not refer to your Premise 2 as a definition again. However, as I have pointed out, and you must accept if you accept my logic Point 3, neither of the ‘definitions’ of God as G or God(x) are acceptable as non-false definitions, since the first cannot reasonably be accepted as being true and the second is basically a nonsensical mess caused by misuse of the language. (Unless you really do want to define God as a nouned verb, which cannot itself exist independently…)
So do yourself a favor and do not use either “God is necessary existence” or “God exists necessarily” as definitions when discussing your argument with me. Doing so will only make whatever point you are trying to make with them unsound, and automatically dismissed. (You probably shouldn’t use them in discussions with anyone else either, but that’s not within my power to require.)
(It may seem harsh of me to dismiss your definitions of God in a (rather hijacked) thread officially about definitions of god, but there is one key difference: you have been trying to use yours as justification for premises in a logical argument. The OP merely asks for definitions, without requiring them to be True. If I had to hold the definitions to the standard of truth that a premise requires I’d reject all the definitions of “god” that imply its existence…even the one I gave myself!)
Anyway, to get back to the point: do you accept all three Points about logic, and all that they imply? If so, then I can continue discussing your argument with you from a logical framework. If not, then you’re not doing logic at all, and I need not bother; if you are not doing logic then your streams of symbols have no persuasive power as to the conclusion. Regardless of how confusing they are.
Well, Jesus, man. Do you honestly mean to say that you’re making all this uproar over what you consider to be nothing of significance?
