Commentary on Cpt_pineapple and Fortunate Son
Offline I made this forum topic so I, and other people, can comment on the debate called Cpt_pineapple and Fortunate Son. The debate is on TAG. The argument being debated is listed below.
Okay, since I am not being allowed a topic in the debate forum, I will post my argument here and I am simply going to ignore everyone who responds except for Cpt_pineapple.
Please keep posts under 500 words.
TERMS DEFINED:
God = Intelligent being who must exist by metaphysical necessity. From his metaphysical necessity, he must also be (a) eternal, (b) the sufficient reason for his own existence, (c) theoretically unable to improve upon.
Laws of logic - principles which govern the content of our discourse and dictate proper thinking; the most obvious is the law of non-contradiction (A v ~A).
Possible worlds = states that the world could have been in given certain circumstances.
For the sake of brevity, I'm going to forego expanding the argument using the rules of propositional logic such as conjunction, modus ponens, etc.
(1) The laws of logic exist in all possible worlds.
(2) The laws of logic are ontologically dependent upon a mind
THEREFORE, an intelligent being exists in all possible worlds.
(1) is justified because given the infinite possibilities of states that the world could have been in, the laws of logic do not change. This becomes obvious when you realize someone must use the laws of logic in order to deny that they apply.
(2) is justified because the application of the laws of logic is a mental application. They cannot be located in the physical world. They only exist if someone thinks them.
The conclusion necessarily follows. If the laws of logic exist in all possible worlds and they require a mind in order to exist, then a mind must exist in all possible worlds.
In order to refute this argument, you must show the following:
(A) That there are circumstances where the laws of logic, such as the law of non-contradiction, do not have application. For example, you will have to explain how it is possible for a cat to be both a cat and not a cat at the same time.
OR
(B) That the laws of logic do not exist in all possible worlds AND that logic does not require a mind. For example, you will have to explain WHAT the laws of logic are, such that they are able to exist without a mind.
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Offline False. What you are stating requires a third element, R, to be added. So what you are actually saying is the following:
(P v R) --> Q
(~P & Q)
:.R
No!
If you posit, "P-->Q" as a premise in an argument, it does not automatically entail "~P-->~Q". That is my point. Q can still follow as a consequent from something else, even if the information is not given.
Insofar that ~P constitutes a set of multiple positive existents, we cannot know based on the information given that ~P implies nothing about Q. We can only know that P implies something about Q.
Without the R, you have the following:P = I eat too much chocolate.
Q = I get a stomach ache.
P --> Q
~P
:. Q v ~Q
Wrong again.
Under any circumstances, "Q v ~Q" cannot be inferred from ~P if the premise is "P-->Q"!
False. Implication implies the following: P --> Q
~P v Q
Umm, that's what I said, although "Implication implies" is not how I would word it.
~P v Q is not the same as ~P v Q, which is the either/or statement.
And the latter is not implied by P-->Q, so I'm not sure why you are bringing it up. See the link I've posted.
With ~P v Q, you can say "It doesn't rain or we cancel the picnic." This means that both statements can be true and the statement is valid. In other words, it may not rain and we can still cancel the picnic and the statement would be true.
Do you have a point?
"~P v Q" is the only thing implied by "P-->Q". Please show me one credible logician who says otherwise.
However, this is valid:P --> Q
~P
:. Q v ~Q
No! It is NOT valid.
The conclusion is a true statement based on the LNC, but it is inferred from only that. It is NOT inferred from "~P". The argument still has a form that is invalid. It would be like arguing:
(1) If it rains, then there is a cloud.
(2) It is not raining.
(3) Therefore, cows are either mammals or they are not.
You could actually derive "Q v ~Q" from the first argument which you've agreed is invalid. Watch:
(1) P-->Q
(2)~P
(3)~Q 1,2: Denying the antecedent
(4)~Q v Q 3; Add
(5) Q v ~Q 4; Commutation
So, all three statements can be true, and the second line is true. However, statements 1 and 2 can be true and statement three can be false and the second logical conclusion would be true. What we cannot do is assume 3 based on 1 and 2. Again, consistent to what Bob is stating.
Bob is wrong and you are wrong as well. Seriously, you guys are shooting yourselves in the foot as you've clearly never studied logic.
implication states ~P v Q, which is the same as ~P & (Q v ~Q).
No, they are not the same.
You can always get "~P v Q v ~Q" by ADD, but there is no rule of inference which allows you to get "~P & (Q v ~Q)" from "~P v Q".
I don't know how I can make this anymore clear.
If you still do not believe me, then please cite a source or something which lends credence to your testimony.
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Offline And all this means that godsperm exists and human flesh can survive rigor mortis.
"We are a nation of Christians and Muslims, Jews and Hindus -- and nonbelievers."Obama
Check out my poetry here on Rational Responders Like my poetry thread on Facebook under Brian James Rational Poet, @Brianrrs37 on Twitter and my blog at www.brianjamesrationalpoet.blog
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Offline And all this means that godsperm exists and human flesh can survive rigor mortis.
Since I do not think you understand modal logic, I'll simplify the argument for you:
(1) The laws of logic are eternal.
(2) The laws of logic require a mind in order to exist.
(3) Therefore, there exists a mind that is eternal.
God, by definition, is an intelligent being (a mind) who is eternal.
Got it?
This does not prove that Christianity is true, but it does prove that God exists.
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Offline Brian37 wrote:And all this means that godsperm exists and human flesh can survive rigor mortis.
Since I do not think you understand modal logic, I'll simplify the argument for you:
(1) The laws of logic are eternal.
(2) The laws of logic require a mind in order to exist.
(3) Therefore, there exists a mind that is eternal.
God, by definition, is an intelligent being (a mind) who is eternal.
Got it?
This does not prove that Christianity is true, but it does prove that God exists.
BULLSHIT, if you or I blow our heads off right now, the sun will still burn.
You are making cognition a prerequisite when cognition is an emergent property.
YOU falsely assume that a "WHO" is required to everything which is needlessly complicated when compared with an un-cognative "WHAT".
You are simply mentally masturbating because the idea of a super hero saving you appeals to you.
"We are a nation of Christians and Muslims, Jews and Hindus -- and nonbelievers."Obama
Check out my poetry here on Rational Responders Like my poetry thread on Facebook under Brian James Rational Poet, @Brianrrs37 on Twitter and my blog at www.brianjamesrationalpoet.blog
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Offline BULLSHIT, if you or I blow our heads off right now, the sun will still burn.
I agree. If you and I both die, the laws of logic would still remain. So you agree that the laws of logic could not have been invented by human beings?
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Offline Brian37 wrote:BULLSHIT, if you or I blow our heads off right now, the sun will still burn.
I agree. If you and I both die, the laws of logic would still remain. So you agree that the laws of logic could not have been invented by human beings?
Are you fucking brain dead?
You are confusing our cognitive observation to uncognative processes which don't give a shit, or have the ability to give a shit about us.
No wonder you believe in god sperm.
"We are a nation of Christians and Muslims, Jews and Hindus -- and nonbelievers."Obama
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Offline BobSpence1 wrote:Ok - axioms are arguably another way to describe the primary Laws, such as LNC. Theorems are NOT laws of logic, they are derived from the axioms via the application of the primary Laws and previously established theorems.
I've asked you to give me an example and you have been unable to provide.
An example of exactly what?
I could arguably have included in that statement 'pre-defined basic logic operators: negation,
Modus Ponens is a direct consequence of the primary relation of implication.
Modus tollens is also derived from the definition of implication.
and so on.
All are derived by applying the fundamental operators, or connectives:
Applying to a single statement:
negation;
Applying to a two statement - there are 16 possible fundamental binary operations, but not all are in common explicit use. Half of them are actually simple negations of the other half.
Various English words and word pairs express truth functions, and some of them are synonymous. Examples (with the name of the relationship in parentheses) are:
"and" (conjunction)
"or" (inclusive or exclusive disjunction)
"implies" (implication)
"if...then" (implication)
"if and only if" (equivalence)
"only if" (implication)
"just in case" (equivalence)
"but" (conjunction)
"however" (conjunction)
"not both" (NAND)
"neither...nor" (NOR)
as defined here.
Note the use of truth tables: if your course did not refer to those in any form, it was not a rigorous course in logic, something which continues to be apparent from your responses).
Also from that page:
In formal languages, truth functions are represented by unambiguous symbols; these can be exactly defined by means of truth tables. There are 16 binary truth tables, and so 16 different logical connectives which connect exactly two statements, that can be defined. Not all of them are in common use. These symbols are called "truth-functional connectives", "logical connectives", "logical operators" or "propositional operators". See well-formed formula for the rules which allow new well-formed formulas to be constructed by joining other well-formed formulas using truth-functional connectives.
See below:Quote:If P-->Q, then ~P implies nothing about Q
Wrong.
~P constitutes an entire set of positive existents, some of which could imply Q depending on the connotations of the individual constants.
Only if you bring in other propositions. My statement is true in reference to the statement in itself.
Quote:--> is a primary logic relationship, as with ^, v, v, which are ultimately defined in a 2 X 2 truth table, as i described previously, and which my definition is equivalent to
Quote:Demonstrating that there is no contradiction proves it is valid.
No!
Denying the antecedent can contain premises which are all true. But because the form of the argument is invalid, it cannot be considered a valid inference. Use this example:(1) If it is raining, then there is a cloud.
(2) It is not raining.
(3) There is no cloud.
There are possible worlds where all of the premises can be true. There would be no contradictions whatsoever. Would the fact that it is not raining and there is no cloud prove that this argument is valid?
For a form of argument to be valid, it must produce valid conclusions for all possible inputs. It is not sufficient to say that there is at least one possible state of affairs where all premises happen to be true.
For a form of argument to be a valid form, ie for all states of 'raining' and 'cloudy', it would require that 'raining' and 'no cloud' also be true, which contradicts (1).
Quote:So it seems pointless to continue this part of the discussion, since that while you are clearly familiar with the language and syntax of logic, you do not actually understand it.Actually, I am enjoying it, as you are physical testimony that simply because someone is good in science does not mean that they even have a passing understanding of philosophy or logic.
Seriously, the stuff we are discussing is something you learn in your intro to philosophy class. You are clearly improvising. Can you link me to any sources which say what you are saying about modus ponens?
Anyway, here's the problem:
(1) You are making up your own rules of inference. In propositional logic, the only logical implication of "P-->Q" is "~P v Q". What you are positing is the CONSEQUENT of the truth of an IF-THEN proposition, or "(P-->Q)-->[(P & Q) v ~(P & ~Q) v (~P & Q) v (~P & ~Q)]". The aforementioned consequent is not logically implied by "P-->Q", but it is a consequent if the statement "P-->Q" is true.
The expression I gave is a definition of P-->Q, not an implication. "~P v Q" is the simplest equivalent to the implication statement in terms of other operators, but "~(P & ~Q)" is another, slightly more complex, equivalent. So the first is NOT the "only logical implication" of "P-->Q".
It is an attempt to explicitly state the truth value for all combinations of P and Q where P and Q are linked by the implication operation "P-->Q".
I should have made clear to you, apparently not familiar with this fundamental definitional approach to binary propositional logic, that it assumes the operators NOT and AND and OR ('~', '&' or '^', and 'v' ) are previously defined, which would have to be by explicit truth table or equivalent.
(2) You are claiming that "~P & [Q v ~Q]" implies "~(~P & Q)". This is false. By Distribution, you can derive the following from "~P & [Q v ~Q]"; "(~P & Q) v (~P & ~Q)", but NOT "~(~P & Q)" or "P v ~Q".
I am claiming the opposite.
I am claiming that the argument { P-->Q; ~P; therefore ~Q } implies that { (P-->Q) --> "~P & [Q v ~Q]" }, which, simplifies to { (P-->Q) --> "~P" }, ie a simple negation, which, as you point out, is not equivalent to the definition of P-->Q. This is obviously one way of demonstrating that the argument is indeed fallacious - it leads to a contradiction.
(3) Let's assume that "~(~P & Q)" is a line in the argument along with "(P & Q) v ~(P & ~Q) v (~P & Q) v (~P & ~Q)". There is nothing logically inconsistent about denying an atomic sentence which is in compound sentence conjoined with other atomic sentences by the connective OR. If the atomic sentences are joined together by OR, then they do not all need to be true. In order for your argument to gain any currency, the premise would have to be: "(P & Q) & ~(P & ~Q) & (~P & Q) & (~P & ~Q)". Then denial of any one of those atomic sentences (though they are not really atomic sentences, but for the sake of brevity, we will regard them as such) would result in a contradiction.
Sorry, but if you cannot even manuever basic propositional logic, then you have no business discussing its bases.
Yet another indication that we not talking the same language.
Let me say it again: as you agree, that compound expression will be true if any one of the sub-expressions joined by OR is true. I explicitly said somewhere that P-->Q means that at least one of those sub-expressions will be true, not ALL.
If you have not come across truth tables, you have no qualification for addressing the basics of Logic.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
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Offline
No! It is NOT valid.
The conclusion is a true statement based on the LNC, but it is inferred from only that. It is NOT inferred from "~P". The argument still has a form that is invalid. It would be like arguing:
(1) If it rains, then there is a cloud.
(2) It is not raining.
(3) Therefore, cows are either mammals or they are not.
A valid analogy would have a final conclusion that "there is either cloud or not."
You could then conclude that the conclusion is always true, and by analogy to other similar statements about entirely independent propositions, as you gave about cows.
But it is not good form in a formal argument to skip that step.
(1) P-->Q
(2)~P
(3)~Q 1,2: Denying the antecedent
(4)~Q v Q 3; Add
(5) Q v ~Q 4; Commutation
Non-sequitur. Where did Q come from here? it contradicts (2).
Feel free to apply for further lessons in logic...
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
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Offline Fortunate_Son wrote:BobSpence1 wrote:Ok - axioms are arguably another way to describe the primary Laws, such as LNC. Theorems are NOT laws of logic, they are derived from the axioms via the application of the primary Laws and previously established theorems.
I've asked you to give me an example and you have been unable to provide.
An example of exactly what?
An example that a contradiction can be derived from denying the antecedent.
I could arguably have included in that statement 'pre-defined basic logic operators: negation,Modus Ponens is a direct consequence of the primary relation of implication.
[(P-->Q & P)---> Q] is not a consequence of anything. That would be saying, "R = primary relation of implication, R & {R-->[(P-->Q & P)--->Q]}" which is a presupposing modus ponens in order to prove it.
Note the use of truth tables: if your course did not refer to those in any form, it was not a rigorous course in logic, something which continues to be apparent from your responses).
I know all about them. They have nothing to do with what we are talking about. Your link was dead, by the way.
Only if you bring in other propositions. My statement is true in reference to the statement in itself.
No! Because a negative atomic sentence is not a thing in itself. It is a set of many positive existents. As I've shown in my example, you do not know what ~P implies, only what P implies.
For a form of argument to be valid, it must produce valid conclusions for all possible inputs.
I said that it was invalid, and yet it can contain no contradictions. This contradicts what you've stated earlier contradictions being the determining factor in falsifying an argument.
The expression I gave is a definition of P-->Q, not an implication. "~P v Q" is the simplest equivalent to the implication statement in terms of other operators, but "~(P & ~Q)" is another, slightly more complex, equivalent. So the first is NOT the "only logical implication" of "P-->Q".
It is not a definition. It is not an equivalent. It is a consequence.
Why is that so difficult for you to grasp?
You've conveniently ignored my request for you to cite sources. Please give me a link to a website which quotes real logicians who say what you are saying.
I am claiming the opposite.
You are claiming the opposite now. You were not claiming the opposite before. Would you like me to quote what you said back to you?
I am claiming that the argument { P-->Q; ~P; therefore ~Q } implies that { (P-->Q) --> "~P & [Q v ~Q]" }, which, simplifies to { (P-->Q) --> "~P" }, ie a simple negation, which, as you point out, is not equivalent to the definition of P-->Q. This is obviously one way of demonstrating that the argument is indeed fallacious - it leads to a contradiction.
I'm going to test that right now:
(1) P-->Q
(2) ~P
(3) ~Q
(4) ~Q v Q 3; Add
(5) ~P & (~Q v Q) 2,4; Conj
Okay. This is as far as I can get. How do I get (P-->Q)-->~P?
Let me say it again: as you agree, that compound expression will be true if any one of the sub-expressions joined by OR is true. I explicitly said somewhere that P-->Q means that at least one of those sub-expressions will be true, not ALL.
Yet your criteria of for deriving a contradiction from denying the antecedent was including "~(~P & Q)" as a line in an argument containing "(P & Q) v ~(P & ~Q) v (~P & Q) v (~P & ~Q)".
Now you've falsified your own point.
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Offline Brian37 wrote:And all this means that godsperm exists and human flesh can survive rigor mortis.
Since I do not think you understand modal logic, I'll simplify the argument for you:
(1) The laws of logic are eternal.
(2) The laws of logic require a mind in order to exist.
(3) Therefore, there exists a mind that is eternal.
God, by definition, is an intelligent being (a mind) who is eternal.
Got it?
This does not prove that Christianity is true, but it does prove that God exists.
False.
1. Logic is not a law. It is a tool, much like a hammer. A mind was needed to create it and use it, but without a mind it was never created. Just like a hammer. It exists now, but it may not have existed before humans.
2. No, logic requires a mind for it to be used, much like opposable thumbs are required to use a hammer.
3. Therefore, nothing.
Logic is a tool with a set of axioms that build into more complex theorems that were developed by humans to further cognitive thought. A hammer is a tool that is used by humans to pound nails into wood, which aids in building wooden structures. If all humans go away (say, by a deadly virus), the hammer still exists. There are simply no beings that can use the hammer (if this were to happen now). But, the hammer still exists, and it is still a tool, albeit useless to any other being on the planet. Same goes for logic. No minds left after humans go, the tool is still there, but there is no being available to use the tool.
Sorry, but unless you accept that 1 is true, the rest of the argument falls by the wayside. And for that you would have to show that there are "laws of logic" and that it isn't simply a tool of the mind. You have yet to show this.
Dolt:"Evolution is just a theory."
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Offline A valid analogy would have a final conclusion that "there is either cloud or not."
You could then conclude that the conclusion is always true, and by analogy to other similar statements about entirely independent propositions, as you gave about cows.
But it is not good form in a formal argument to skip that step.
Uh, no. The inference would be equally invalid.
Non-sequitur. Where did Q come from here? it contradicts (2).Feel free to apply for further lessons in logic...
Umm... the basic inference rule of ADD?
7. Addition (Add): from p to infer p V q.
This is a neat rule even though it may appear to be a trick. If a proposition is true, then a disjunctive statement involving that proposition is true--regardless of the truth-value of the added statement. Remember, for a disjunction to be true, only one of the disjuncts must be true. So, if you know that p is true, you can add any other statement whatsoever to it by means of the disjunctive logical operator and the resulting compound statement will also be true.
http://www.philosophy.uncc.edu/mleldrid/Logic/l10.html
I think it would be a good time for you to gracefully bow out of this discussion.
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Offline False. What you are stating requires a third element, R, to be added. So what you are actually saying is the following:
(P v R) --> Q
(~P & Q)
:.R
No!
If you posit, "P-->Q" as a premise in an argument, it does not automatically entail "~P-->~Q". That is my point. Q can still follow as a consequent from something else, even if the information is not given.
Insofar that ~P constitutes a set of multiple positive existents, we cannot know based on the information given that ~P implies nothing about Q. We can only know that P implies something about Q.
Where did you get that from my preceding statement? In fact, you are saying *exactly* what I am, that you cannot infer anything about Q when ~P exists. This is why I took your chocolate/tummy ache example and showed that what you are *now* positing is correct. Are you even reading the whole post?
Without the R, you have the following:P = I eat too much chocolate.
Q = I get a stomach ache.
P --> Q
~P
:. Q v ~Q
Wrong again.
Under any circumstances, "Q v ~Q" cannot be inferred from ~P if the premise is "P-->Q"!
Ok, you clearly have a semi-rudimentary understanding of logic. What does Q v ~Q mean? It means that Q is true or Q is false. So from ~P, you can only conclude that Q is either true or false. In the case of identity, the v doesn't apply as Q != ~Q as an axiom. Therefore, as you even stated earlier:
"Q can still follow as a consequent from something else, even if the information is not given."
means that you have Q v ~Q. Very simple, very basic.
Are you stating that there is another state besides true or false in modal logic? If so, then I wouldn't even use the term semi-rudimentary...you simply don't understand logic at all.
False. Implication implies the following:P --> Q
~P v Q
Umm, that's what I said, although "Implication implies" is not how I would word it.
No, that isn't what you said. You said is that it is the same as ~P v Q. BIG difference. This comes from your initial argument from the picnic. There is a difference between saying "Either it will rain or we will cancel the picnic" versus "It will rain or we will cancel the picnic."
~P v Q is not the same as ~P v Q, which is the either/or statement.
And the latter is not implied by P-->Q, so I'm not sure why you are bringing it up. See the link I've posted.
Because YOU made the statement about "Either it is raining or we cancel the picnic". Remember? And I said that the either/or cannot be inferred, only the or. Again, BIG difference.
With ~P v Q, you can say "It doesn't rain or we cancel the picnic." This means that both statements can be true and the statement is valid. In other words, it may not rain and we can still cancel the picnic and the statement would be true.
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Offline Where did you get that from my preceding statement? In fact, you are saying *exactly* what I am, that you cannot infer anything about Q when ~P exists. This is why I took your chocolate/tummy ache example and showed that what you are *now* positing is correct. Are you even reading the whole post?
Bob said (I forget his exact words) that if P-->Q, then Q cannot be derived from ~P. I'm saying that it can, which is why you cannot infer ~Q from ~P alone anymore than you can infer Q from ~P alone.
What does Q v ~Q mean? It means that Q is true or Q is false. So from ~P, you can onlyconclude that Q is either true or false.
That's not inferred from ~P! That's inferred from the LNC, which does not occur as a premise in the argument! It can also be inferred from the Addition rule. What you've made is an invalid inference.
No, that isn't what you said. You said is that it is the same as ~P v Q. BIG difference.
No, I never said that. Quote it back to me where I said that.... and even if I did say that undeliberately, I specifically cited Rule Implication. If you are an expert in logic, then you know what I meant.
Because YOU made the statement about "Either it is raining or we cancel the picnic". Remember? And I said that the either/or cannot be inferred, only the or. Again, BIG difference.
Where did I say it?
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Offline kidvelvet wrote:Where did you get that from my preceding statement? In fact, you are saying *exactly* what I am, that you cannot infer anything about Q when ~P exists. This is why I took your chocolate/tummy ache example and showed that what you are *now* positing is correct. Are you even reading the whole post?
Bob said (I forget his exact words) that if P-->Q, then Q cannot be derived from ~P. I'm saying that it can, which is why you cannot infer ~Q from ~P alone anymore than you can infer Q from ~P alone.
Quote:What does Q v ~Q mean? It means that Q is true or Q is false. So from ~P, you can onlyconclude that Q is either true or false.That's not inferred from ~P! That's inferred from the LNC, which does not occur as a premise in the argument! It can also be inferred from the Addition rule. What you've made is an invalid inference.
Quote:No, that isn't what you said. You said is that it is the same as ~P v Q. BIG difference.No, I never said that. Quote it back to me where I said that.... and even if I did say that undeliberately, I specifically cited Rule Implication. If you are an expert in logic, then you know what I meant.
Quote:Because YOU made the statement about "Either it is raining or we cancel the picnic". Remember? And I said that the either/or cannot be inferred, only the or. Again, BIG difference.Where did I say it?
From a previous post:
Implication (Impl.)
A rule of replacement of the form:P-->Q Example: "If it rains, then we cancel the picnic." is equivalent to "Either it doesn't rain or we cancel the picnic."
http://www.philosophypages.com/dy/i.htm#impl
Funny, it does not mention your rules of replacement.
This is simply not true. You are implying ~P v Q (either/or) as opposed to ~P v Q, which is the or statement. By saying that P --> Q is the equivalent of ~P v Q (from YOUR example, mind you), that would be incorrect. As Bob suggests, do a simple truth table, and you will see that they are not the same. If you do a truth table of ~P v Q, you will see that if ~P is true, then Q can be true or false and the statement can be true.
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Offline This is simply not true. You are implying ~P v Q (either/or) as opposed to ~P v Q, which is the or statement. By saying that P --> Q is the equivalent of ~P v Q (from YOUR example, mind you), that would be incorrect. As Bob suggests, do a simple truth table, and you will see that they are not the same. If you do a truth table of ~P v Q, you will see that if ~P is true, then Q can be true or false and the statement can be true.
EDIT: Plus, the website actually gives us the symbol ~P v Q. I was unable to paste it here because it would just show up as some weird ASCII text. Once again, if you are just focusing on the example they gave (and I do not really care enough to check if it was actually an exclusive disjunction), then you are just being nit-picky.
I can put this to bed completely right now. If what Bob says is true and denying the antecedent is an invalid form by virtue of non-contradiction, then he should be able to derive P & ~P if denying the antecedent is assumed as a premise (i.e. an indirect proof):
(1) [(P-->Q) & ~P]-->~Q
(2) (P-->Q) & ~P
Okay Bob. I've given you a head start. Now take it from here and derive a contradiction.
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Offline nigelTheBold wrote:I find I learn nothing at all from those who think highly of themselves, and perhaps not so highly of those whom they engage.That's obviously a shot at me, but allow me to clarify that I am not here to teach anyone. Atheists are unregenerate and are beyond repair. Only by the grace of God will they be converted. I am simply here to defend my theology.
Nor are you here to learn, or discuss, or actually attempt to come to some sort of understanding. No, you are here to assert your superiority, even if that requires disregarding intelligent analysis of your propositions. (I'm not referring to me, of course.) It's rather easy to see that you are not here for anything at all other than to honor yourself. That's rather pathetic in the eyes of the atheist, and dishonorable in the eyes of the Christian.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind." - PZ Myers
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Offline "P-->Q"!
TO FSON,.............SO THE FUCK WHAT?
AGAIN, what does all this mental masturbation have to do with you refusing to show your homework?
Since you have no prior data independently verified by people with no horse in the race you resort to smoke and mirrors.
YOU:
""P-->Q"=HUGE GIGANTIC PAMELA ANDERSON PUSSY GAP, THAT MAKES THE GRAND CANYON LOOK LIKE A PUDDLE=My pet claim of disembodied being exists"
"P-->Q"
Still does not show how you get from that to a brain with no brain.
SHOW YOUR HOMEWORK, other than, "God did it"
"We are a nation of Christians and Muslims, Jews and Hindus -- and nonbelievers."Obama
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Offline Quote:"P-->Q"!TO FSON,.............SO THE FUCK WHAT?
AGAIN, what does all this mental masturbation have to do with you refusing to show your homework?
Since you have no prior data independently verified by people with no horse in the race you resort to smoke and mirrors.
YOU:
""P-->Q"=HUGE GIGANTIC PAMELA ANDERSON PUSSY GAP, THAT MAKES THE GRAND CANYON LOOK LIKE A PUDDLE=My pet claim of disembodied being exists"
Quote:"P-->Q"Still does not show how you get from that to a brain with no brain.
SHOW YOUR HOMEWORK, other than, "God did it"
Okay.
If you see a pile of poopey on the ground, how do you know that there was a pooper? The poopey is absolutely proof that there was a pooper. All you need are eyes that can smell and a nose that can see.
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Offline The poopey is absolutely proof that there was a pooper.
It is not.
Knowledge of the involvement of a pooper comes from empirical data, the poop itself is not absolute proof of anything but poop.
This is the same error that I called you out on earlier in your clouds/rain example, only this time you are appealing to ignorance of epistemological steps rather than ontological ones.
Simply because we do not labour through the entire experiential learning process of a lifetime for every individual event of judgement, does not mean that knowing something you've seen a billion times happens by "god magic". And if you don't have a history of experiential data with which to form an epistemic stance on what is necessitated by X being in state Y then you just don't know. Full Stop.
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Offline It is not.
Knowledge of the involvement of a pooper comes from empirical data, the poop itself is not absolute proof of anything but poop.
Did you actually think I was being serious with this?
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Offline
observation of the history of experiential data (the contents of this thread) does allow us to form an epistemic stance that there must be at least one pooper...
"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." Max Planck
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Offline Eloise wrote:It is not.
Knowledge of the involvement of a pooper comes from empirical data, the poop itself is not absolute proof of anything but poop.
Did you actually think I was being serious with this?
You Poe'd me?
Well it looked like an i.d. argument to me.
LOL 
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Offline Wow! This philosophy thing is cool. I've been reading up on Kant. That dude says almost exactly what I was trying to say, only in sentences that convey the actual concepts. His refutation of the ontological argument is stupendously comprehensive. Importing the attribute of "existence" into the analytic concept of god is fallacious. (And that's just one of his ontological argument take-downs.)
I'm in awe.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind." - PZ Myers
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Offline Brian37 wrote:Quote:"P-->Q"!TO FSON,.............SO THE FUCK WHAT?
AGAIN, what does all this mental masturbation have to do with you refusing to show your homework?
Since you have no prior data independently verified by people with no horse in the race you resort to smoke and mirrors.
YOU:
""P-->Q"=HUGE GIGANTIC PAMELA ANDERSON PUSSY GAP, THAT MAKES THE GRAND CANYON LOOK LIKE A PUDDLE=My pet claim of disembodied being exists"
Quote:"P-->Q"Still does not show how you get from that to a brain with no brain.
SHOW YOUR HOMEWORK, other than, "God did it"
Okay.
If you see a pile of poopey on the ground, how do you know that there was a pooper? The poopey is absolutely proof that there was a pooper. All you need are eyes that can smell and a nose that can see.
Ok, if you get cancer, and everything has a designer, then your own creator must not think that much of you. And just like an abused spouse, you'd thank the abuser for teaching you a lesson.
Your idiodic premise is that complexity is the starting point when the opposite is the case.
"We are a nation of Christians and Muslims, Jews and Hindus -- and nonbelievers."Obama
Check out my poetry here on Rational Responders Like my poetry thread on Facebook under Brian James Rational Poet, @Brianrrs37 on Twitter and my blog at www.brianjamesrationalpoet.blog
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Offline Wow! This philosophy thing is cool. I've been reading up on Kant. That dude says almost exactly what I was trying to say, only in sentences that convey the actual concepts. His refutation of the ontological argument is stupendously comprehensive. Importing the attribute of "existence" into the analytic concept of god is fallacious. (And that's just one of his ontological argument take-downs.)
I'm in awe.
Most of my ideas are inspired by Kant. I do not agree with everything he says, but I agree that he was brilliant.
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But fun!
No. What you are talking about has NOTHING to do with replication and falsification. What you want me to admit to is HUMAN BEHAVIOR. Then you conflate REAL human behavior in daily life as being in the same class as emerical evidence, by scientific method through replication and falsification which filters out the bias of human behavior.
Your monster you call "faith" is nothing but wishing that a fictional super hero exists.
Walking out to my car and expecting it to start would be based on prior factors such as age, upkeep, and crime. Since I live in a good neighborhood and my car is new I have a reasonable expectation that it will start. THAT is not faith. Because like I said, if it didn't start I could merely have "faith" that it would and pray it to start. THAT is stupid. If it doesn't start I do real things to assess the problem.
Admitting that there is randomness in life doesn't mean that I should let my brains fall out and anywhere there is a sudden change or gap, insert some bullshit magical super hero into the gap.
Why don't you simply argue "You cant see air but yet you can breath" Same stupid shit.
You are high on your pet fictional god you cant see the obvious. IT IS YOU, it is not a real god, it is not magic, it is your willful ignorance and your selfish desire to want a super hero. Your belief is merely the result of mundane wishful thinking and a refusal to accept your own finite existence.
"We are a nation of Christians and Muslims, Jews and Hindus -- and nonbelievers."Obama
Check out my poetry here on Rational Responders Like my poetry thread on Facebook under Brian James Rational Poet, @Brianrrs37 on Twitter and my blog at www.brianjamesrationalpoet.blog
My position is not self-refuting because the statement "to make any statement about external reality requires making assumptions" is an assumption. It is probably one of the key assumptions in my world view. I also feel it to be a very well justified assumption.
If by self-justified you mean feeling upset is justification for believing you feel upset then you statement is wrong. Feeling upset is all the justification you need to believe you feel upset. I cannot think of anything you can be surer of then in knowing you feel what you feel.
Other people’s internal realities are for you an external reality. Your own feelings are self justified, but to make claims about other people’s feeling require some kind of assumption, evidence and justification.
All bachelors are unmarried is a definition not a statement of external reality. Definitions are parts of mental models which are internal realities.
Many things exist in multiple people's internal realities in very similar forms. By sharing certain mental models people are better able to communicate. A good example of this is language. My English is probably very similar to you r English. Because both of our English’s are similar we are able to communicate together. The same is true of math, because people use similar modes for mathematics people can understand each other.
The laws of logic are an internal reality in you, and an external reality in other people.
What I have said is not false. It is what I would describe as an internal truth.
edit: reword
Lol
Everything makes more sense now that I've stopped believing.
Apologies for not getting back earlier - work got a bit demanding.
Ok - axioms are arguably another way to describe the primary Laws, such as LNC. Theorems are NOT laws of logic, they are derived from the axioms via the application of the primary Laws and previously established theorems.
Not true.
If P-->Q, then ~P implies nothing about Q, ie ~P ==> ~Q v Q, as covered in the last two components in my expression. The implications of P implies Q and is not consistent with ~Q, as covered in the first two terms.
--> is a primary logic relationship, as with ^, v, v, which are ultimately defined in a 2 X 2 truth table, as i described previously, and which my definition is equivalent to.
And of course you can derive a contradiction when you apply that operation as part of an argument, if the argument is invalid - that is how you disprove any argument, you show a contradiction!
Demonstrating that there is no contradiction proves it is valid.
For a fallacy such as
P-->Q;
~P;
:. ~Q
to be true, implies that ~(~P ^ Q), ie that Q cannot be true if P is false. But from the definition expression for P-->Q, (~P ^ Q) is consistent with P-->Q
But (~P ^ Q) and ~(~P ^ Q) cannot both be true, by the LNC.
So it seems pointless to continue this part of the discussion, since that while you are clearly familiar with the language and syntax of logic, you do not actually understand it.
Which just shows you have no conception of my world-view, and probably aren't capable of grasping it, just as you don't 'get' logic. My thoughts and the actions of my body are aspects of one complex system, which makes such statements as you just made hopelessly simplistic.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Yeah, I believe we passed that point about around page 2.
I am reading this more out of amazement at someone's utter lack of critical thought.
Dolt:"Evolution is just a theory."
Me:"Yes, so is light and gravity. Pardon me while I flash this strobe while dropping a bowling ball on your head. This shouldn't bother you; after all, these are just theories."
I've asked you to give me an example and you have been unable to provide. See below:
Wrong.
~P constitutes an entire set of positive existents, some of which could imply Q depending on the connotations of the individual constants.
Watch:
P = I eat too much chocolate, Q = I get a stomach ache, R = I eat too much ice cream
If I eat too much chocolate, then I get a stomach ache.
If I eat too much ice cream, then I get a stomach ache.
R is included in the ~P set.
A rule of replacement of the form:
http://www.philosophypages.com/dy/i.htm#impl
Funny, it does not mention your rules of replacement.
No!
Denying the antecedent can contain premises which are all true. But because the form of the argument is invalid, it cannot be considered a valid inference. Use this example:
(1) If it is raining, then there is a cloud.
(2) It is not raining.
(3) There is no cloud.
There are possible worlds where all of the premises can be true. There would be no contradictions whatsoever. Would the fact that it is not raining and there is no cloud prove that this argument is valid?
Actually, I am enjoying it, as you are physical testimony that simply because someone is good in science does not mean that they even have a passing understanding of philosophy or logic.
Seriously, the stuff we are discussing is something you learn in your intro to philosophy class. You are clearly improvising. Can you link me to any sources which say what you are saying about modus ponens?
Anyway, here's the problem:
(1) You are making up your own rules of inference. In propositional logic, the only logical implication of "P-->Q" is "~P v Q". What you are positing is the CONSEQUENT of the truth of an IF-THEN proposition, or "(P-->Q)-->[(P & Q) v ~(P & ~Q) v (~P & Q) v (~P & ~Q)]". The aforementioned consequent is not logically implied by "P-->Q", but it is a consequent if the statement "P-->Q" is true.
(2) You are claiming that "~P & [Q v ~Q]" implies "~(~P & Q)". This is false. By Distribution, you can derive the following from "~P & [Q v ~Q]"; "(~P & Q) v (~P & ~Q)", but NOT "~(~P & Q)" or "P v ~Q".
(3) Let's assume that "~(~P & Q)" is a line in the argument along with "(P & Q) v ~(P & ~Q) v (~P & Q) v (~P & ~Q)". There is nothing logically inconsistent about denying an atomic sentence which is in compound sentence conjoined with other atomic sentences by the connective OR. If the atomic sentences are joined together by OR, then they do not all need to be true. In order for your argument to gain any currency, the premise would have to be: "(P & Q) & ~(P & ~Q) & (~P & Q) & (~P & ~Q)". Then denial of any one of those atomic sentences (though they are not really atomic sentences, but for the sake of brevity, we will regard them as such) would result in a contradiction.
Sorry, but if you cannot even manuever basic propositional logic, then you have no business discussing its bases.
Assumptions aren't statements?
EDIT: You have accused me of making assumptions about external reality without any justification and the undergirding principle to your epistemology would be the principle that "to make any statement about external reality requires making assumptions", which itself would have to be supported by assumptions which-- assuming your criteria-- you would have to justify. If you cannot justify your own principle using anything other than assumptions, then there is no reason for me to even consider that I have to follow your model.
That is why your position is self-refuting.
You "feel" this because..... ?
Sorry, you've lost me. You just said that external reality requires making assumptions, now we can justify things using external truth? How do you know it is true if external reality is based on your assumptions?
That is not what self-justification is. Any statement about your own mental state still requires you to externally verify that it is true because the statements are not a priori. Statements about your mental states have truth values which are empirically verified. Granted, this is a verified without any gaps between knowledge and perception insofar that they are predicated of the self, but immediacy and gaplessness have nothing to do with self-verification. A statement is self-verifying if it is true in all possible worlds.
http://en.wikipedia.org/wiki/A_priori_and_a_posteriori#Immanuel_Kant
Actually, "definitions" refer to conventions and conventions are external realities. You are actually referencing the law of identity. So are you saying that the laws of logic are internal realities?
Wait a minute.. you did say that, right here: "The laws of logic are internal truths and as such they don't need to be proven. A claim about external reality(i.e. external truth claims), such as the one you made, requires logical proof."
Enough with being pedantic. Let's examine this. You are claiming that the statement "the laws of logic exist in all possible worlds" is a statement about external reality. Actually, it is not.
The necessity of the laws of logic is itself a statement about the ontological nature of the laws themselves. By your own admission, these are internal truths and in accordance with this, it would be internally true that the laws of logic are necessary, since necessity is intrinsic in the notion of self-justification and intrinsic to the laws of logic themselves. Thus, in the context of our internal truth, we were able to extrapolate the ontological nature of the laws and figure out that they cannot possibly be falsified in any way. Remember, you admitted this. You said that they do not need to be proven. Therefore, without even knowing it, you are agreeing with me that they exist in all possible worlds. Thus, we've found truth about external reality in our internal reality by virtue of internal principles which inherently say something about external reality, namely that the laws of logic could not be the product of people because they are necessary and we are not.
Keep in mind that I am in no way endorsing your epistemology. As I've demonstrated, it is incredibly flawed and trades on a misunderstanding of a priority and a posteriority. I've probably made numerous contradictory statements just by pretending that I was applying it. My point is, your epistemology does nothing to undermine the argument which I've made.
EDIT: And universal statements do reference external reality. The statement "All bachelors are unmarried" can be translated: "For any person X, if X is a bachelor, then X is a bachelor." That is a statement about what would be the case in external reality if someone was a bachelor. In other words, you are saying that the law of identity will always be consistent... which would be in agreement with my point about the necessity of the laws of logic.
That does not address what I said. Please do not divert.
YOU said that the internal realities of one person would be the external realities of another, which would thus require the outside perceiver to make assumptions. Thus, by your own criteria, nobody knows anything other than what is predicated of themselves and the communication of people would just be bound up with assumptions about external reality, which ultimately would be justified in the self-evident internal truths which, between two or more thinkers, could possibly contradict one another.
So I ask you again: If one person's internal truth contradicts someone else's, how do we assess truth? ... especially since you said that we can never know external reality, we can only assume things about it.
So..... P & ~P is true for you but not true for me?
double post
False. What you are stating requires a third element, R, to be added. So what you are actually saying is the following:
(P v R) --> Q
(~P & Q)
:.R
Without the R, you have the following:
P = I eat too much chocolate.
Q = I get a stomach ache.
P --> Q
~P
:. Q v ~Q
Without R, we cannot know anything about the state of your stomach simply by implying ~P. You could still have a stomach ache by not eating too much chocolate. Without the R, ~P gives us no information, which is consistent to what Bob was stating earlier.
False. Implication implies the following:
P --> Q
~P v Q
~P v Q is not the same as ~P v Q, which is the either/or statement. With ~P v Q, you can say "It doesn't rain or we cancel the picnic." This means that both statements can be true and the statement is valid. In other words, it may not rain and we can still cancel the picnic and the statement would be true. This is the same as:
P --> Q
~P
:. Q v ~Q
~P and ~Q can both be true and have a true statement.
Which again shows that Bob's statement is corret:
P --> Q
~P
:.~Q
is an invalid statement. However, this is valid:
P --> Q
~P
:. Q v ~Q
So, all three statements can be true, and the second line is true. However, statements 1 and 2 can be true and statement three can be false and the second logical conclusion would be true. What we cannot do is assume 3 based on 1 and 2. Again, consistent to what Bob is stating.
Statement 1 is addressed earlier in the post. It shows your basic misunderstanding between ~P v Q and ~P v Q. The implication states ~P v Q, which is the same as ~P & (Q v ~Q). This is very basic, very remedial, and I must agree with Bob shows that you do not understand the basics of logic.
Dolt:"Evolution is just a theory."
Me:"Yes, so is light and gravity. Pardon me while I flash this strobe while dropping a bowling ball on your head. This shouldn't bother you; after all, these are just theories."