Symbolic Logic
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I just took my final for this class a few hours ago. Now I can relax. I'm sure I got an A in the class.
Swoop,
if you're concerned about real-world application, you should know that this (especially the examples I've given) is just an introduction. I could get into predicate logic and quantifiers, but I think it's complicated enough with just propositional logic as an intro.
Swoop,
if you're concerned about real-world application, you should know that this (especially the examples I've given) is just an introduction. I could get into predicate logic and quantifiers, but I think it's complicated enough with just propositional logic as an intro.
Symbolic logic isn't responsible for going out in the world and proving things. Rather, it is used to prove validity and invalidity, which pertains to whether or not there is a connection between premises and a conclusion, or it is used to prove consistency and inconsistency within a set of statements.
I found this series of videos that are pretty good as an introduction. However, his system is somewhat different from the one I learned. For instance, we didn't use logic trees and hypothetical syllogism wasn't one of our rules of inference. Anyway, here are those videos:
I found this series of videos that are pretty good as an introduction. However, his system is somewhat different from the one I learned. For instance, we didn't use logic trees and hypothetical syllogism wasn't one of our rules of inference. Anyway, here are those videos:
Which one of you is flaming gay?
Nah, I'm just messing with you. If you have any questions about this stuff, don't hesitate. I actually found what I feel are better videos than the series I posted, but those videos jump right into things more. So, the ones I posted are better as an intro. Not that you care, or anything.
Nah, I'm just messing with you. If you have any questions about this stuff, don't hesitate. I actually found what I feel are better videos than the series I posted, but those videos jump right into things more. So, the ones I posted are better as an intro. Not that you care, or anything.
Proof of God
Someone posted the following argument over at the IMDb.com religion board. I have to admit that it's pretty clever. First I'll state the argument in English:
Premise 1: If God doesn't exist, then it is not the case that if I pray, then my prayers will be answered by God.
Premise 2: I do not pray.
Conclusion: God exists.
Symbolic form:
The statement "God exists" will be assigned the letter G. The statement "I pray" will be assigned the letter P. And the statement "my prayers will be answered by God" will be assigned the letter A.
So, the first premise will look: ~G --> ~(P --> A)
The second premise: ~P
And conclusion: G
1. ~G --> ~(P --> A)
2. ~P ............................................................Ergo: G
3. ..........~G ..................................................Assume (for Indirect Proof)
4. ..........~(P --> A) .......................................1,3 Modus Ponens
5. ..........P & ~A ............................................4 Negated Conditional
6. ..........P ....................................................5 Simplification
7. ..........P & ~P ............................................2,6 Conjunction
8. ~~G .........................................................3,7 Indirect Proof
9. G .............................................................8 Double Negation
Alright, so...
*In line 3 we begin by assuming the opposite of the conclusion with the intent of deriving a contradiction.
*In line 4, since we now have the antecedent of the conditional in line 1 in our subproof, we can derive the consequent, namely, ~(P --> A).
*The rule for line 5 is explained as follows:
The only way for a conditional statement to come out false is if the antecedent is true and the consequent is false. Therefore, for instance, you could argue something completely absurd like, "If pigs fly, then bachelors are unmarried" and it will (as a whole) come out true. This is what we call vacuously true. But if you switch the order to, "If bachelors are unmarried, then pigs fly" it will come out false.
Furthermore, since there is only one way in which a conditional will come out false (i.e.: True --> False,) it then follows that if you have a negated conditional, the antecedent must be true and the consequent must be false. This is how we derive P & ~A from line 4.
*Line 6 is to simply isolate the P from line 5.
*Line 7 puts the P from line 6 and the ~P from line 2 together to show the contradiction.
*Since we have a contradiction, we can leave the subproof and write the negation of our assumption in line 8.
*And finally, in line 9 we get rid of the double negation and arrive at our conclusion: G.
So, what's the lesson here? It seems to be that you can prove the existence of God if you don't pray. Whoever knew the power of not praying? LOL!
Seriously though, it should be clear that this argument could work for anyone or anything. For instance, replace God in this argument with Satan, the Easter Bunny or 4-sided triangles and it will follow that each of these entities exist. So, the truth of it is rather vacuous. It fails to bring forth what "God" is. The best I think one could do here is to define God as that which answers prayers. But that's a very lacking definition; certainly not sufficient to prove the traditional view of God.
Someone posted the following argument over at the IMDb.com religion board. I have to admit that it's pretty clever. First I'll state the argument in English:
Premise 1: If God doesn't exist, then it is not the case that if I pray, then my prayers will be answered by God.
Premise 2: I do not pray.
Conclusion: God exists.
Symbolic form:
The statement "God exists" will be assigned the letter G. The statement "I pray" will be assigned the letter P. And the statement "my prayers will be answered by God" will be assigned the letter A.
So, the first premise will look: ~G --> ~(P --> A)
The second premise: ~P
And conclusion: G
1. ~G --> ~(P --> A)
2. ~P ............................................................Ergo: G
3. ..........~G ..................................................Assume (for Indirect Proof)
4. ..........~(P --> A) .......................................1,3 Modus Ponens
5. ..........P & ~A ............................................4 Negated Conditional
6. ..........P ....................................................5 Simplification
7. ..........P & ~P ............................................2,6 Conjunction
8. ~~G .........................................................3,7 Indirect Proof
9. G .............................................................8 Double Negation
Alright, so...
*In line 3 we begin by assuming the opposite of the conclusion with the intent of deriving a contradiction.
*In line 4, since we now have the antecedent of the conditional in line 1 in our subproof, we can derive the consequent, namely, ~(P --> A).
*The rule for line 5 is explained as follows:
The only way for a conditional statement to come out false is if the antecedent is true and the consequent is false. Therefore, for instance, you could argue something completely absurd like, "If pigs fly, then bachelors are unmarried" and it will (as a whole) come out true. This is what we call vacuously true. But if you switch the order to, "If bachelors are unmarried, then pigs fly" it will come out false.
Furthermore, since there is only one way in which a conditional will come out false (i.e.: True --> False,) it then follows that if you have a negated conditional, the antecedent must be true and the consequent must be false. This is how we derive P & ~A from line 4.
*Line 6 is to simply isolate the P from line 5.
*Line 7 puts the P from line 6 and the ~P from line 2 together to show the contradiction.
*Since we have a contradiction, we can leave the subproof and write the negation of our assumption in line 8.
*And finally, in line 9 we get rid of the double negation and arrive at our conclusion: G.
So, what's the lesson here? It seems to be that you can prove the existence of God if you don't pray. Whoever knew the power of not praying? LOL!
Seriously though, it should be clear that this argument could work for anyone or anything. For instance, replace God in this argument with Satan, the Easter Bunny or 4-sided triangles and it will follow that each of these entities exist. So, the truth of it is rather vacuous. It fails to bring forth what "God" is. The best I think one could do here is to define God as that which answers prayers. But that's a very lacking definition; certainly not sufficient to prove the traditional view of God.
Proof of No God
By the same trick of logic, I present the proof of God's nonexistence:
Premise 1: If God exists, then it is not the case that if my prayers are answered by God, I do not pray.
Premise 2: I do not pray.
Conclusion: God does not exist.
FORMAL PROOF:
1. G --> ~(A --> ~P)
2. ~P ............................................................Ergo: ~G
3. ..........G ....................................................Assume (for Indirect Proof)
4. ..........~(A --> ~P) .....................................1,3 Modus Ponens
5. ..........A & ~~P ..........................................4 Negated Conditional
6. ..........~~P ................................................5 Simplification
7. ..........P .....................................................6 Double Negation
8. ..........P & ~P .............................................2,7 Conjunction
9. ~G ............................................................3,8 Indirect Proof
Pretty much the same rules apply here as they did in the argument for God's existence. Isn't logic fun?
By the same trick of logic, I present the proof of God's nonexistence:
Premise 1: If God exists, then it is not the case that if my prayers are answered by God, I do not pray.
Premise 2: I do not pray.
Conclusion: God does not exist.
FORMAL PROOF:
1. G --> ~(A --> ~P)
2. ~P ............................................................Ergo: ~G
3. ..........G ....................................................Assume (for Indirect Proof)
4. ..........~(A --> ~P) .....................................1,3 Modus Ponens
5. ..........A & ~~P ..........................................4 Negated Conditional
6. ..........~~P ................................................5 Simplification
7. ..........P .....................................................6 Double Negation
8. ..........P & ~P .............................................2,7 Conjunction
9. ~G ............................................................3,8 Indirect Proof
Pretty much the same rules apply here as they did in the argument for God's existence. Isn't logic fun?
Being applied to facts means considering whether or not the premises of an argument are true.
So, for instance, if I made the statement: "If God doesn't exist, then it is not the case that if I pray, my prayers will be answered by God" would you say this is true or untrue? After all, how can my prayers be answered by God if God doesn't exist?
Of course, there is something wrong with this argument. I'm not for one second claiming this proves the existence of God. But when you say that symbolic logic has no meaning until it's applied to facts, I want to know what part of either of the above arguments aren't facts.
So, for instance, if I made the statement: "If God doesn't exist, then it is not the case that if I pray, my prayers will be answered by God" would you say this is true or untrue? After all, how can my prayers be answered by God if God doesn't exist?
Of course, there is something wrong with this argument. I'm not for one second claiming this proves the existence of God. But when you say that symbolic logic has no meaning until it's applied to facts, I want to know what part of either of the above arguments aren't facts.