3
   

In need of some logic help!!!

 
 
SS17
 
Reply Mon 11 Dec, 2017 02:25 pm
Hello all I'm in need of some help trying to figure out these logic problems. If anyone can help me with this as soon as possible it would be awesome. Please Please Please. I need help!!

Here are the problems:
(1) 1. (~F&G)->H
2. ~I->G
3. ~I&~F
.: HvJ

(2) 1. KvL
2. ~K
3. (LvL)->(~MvN)
.: ~N->~M
The next two are written out statements. You have to do translation and then solve the proof with the given variables located at the end of the statements.

(3) If Bob is morally virtuous, then he achieves heaven. But if he is not morally virtuous, then his longings are satisfied. On the other hand, if Bob doesn't achieve heaven, then his longings are not satisfied. So, Bob achieves heaven. (M,H,L)

(4)If God believes on Monday that I'll tell a lie on Tuesday, then either i have the power to make one of God's past beliefs false, or i cannot refrain from lying on tuesday. I do not have the power to make on of God's past beliefs false if either God is infallible or the past is unalterable. The past is unalterable. It follows that if God believes on Monday that I'll tell a lie on Tuesday, then I cannot refrain from lying on Tuesday. (B,F,R,I,P)
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Type: Question • Score: 3 • Views: 2,083 • Replies: 50
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jerlands
 
  0  
Reply Mon 11 Dec, 2017 02:40 pm
@SS17,
The problem is unsolvable because it's based on false assumptions.
SS17
 
  1  
Reply Mon 11 Dec, 2017 02:55 pm
@jerlands,
To which equation are you, speaking of?
jerlands
 
  -1  
Reply Mon 11 Dec, 2017 03:21 pm
@SS17,
The basis of the logic statements contain elements such as what "God" knows and what "heaven" is as proofs.
SS17
 
  1  
Reply Mon 11 Dec, 2017 04:55 pm
@jerlands,
Okay, but truly in spite of the statement . Is there a way to create a logic proof using the variables given and solve it using that statement even if it hold false assumptions? Please I need help with the formatting to solve the problem
jerlands
 
  1  
Reply Mon 11 Dec, 2017 05:14 pm
@SS17,
So where did you come by this problem?
SS17
 
  0  
Reply Mon 11 Dec, 2017 07:19 pm
@jerlands,
It’s on my homeowork. I just need help figuring out which variables go to which words in the statement to create the proof.
0 Replies
 
fresco
 
  2  
Reply Tue 12 Dec, 2017 12:51 am
@SS17,
A general method to show validity is the method of 'backward fell swoop' in which by choosing truth values which make the conclusion false, you render the conjunction of premises false.
e.g. in (2) put M=1 and N=0 which renders L=0 for 3 to be true, but that in turn makes the truth of 1 dependent on K=1. which would be contradicted in 2.
Hence the argument is valid.
Turn your worded one into symbols and try the same method.
Note that the alternative 'Truth Table' method would take up a lot of space. For example (1) would require many columns and 32 rows !
0 Replies
 
carpenters
 
  2  
Reply Tue 12 Dec, 2017 10:24 pm
@SS17,
You should spend time thinking about these problems yourself. I hope you have done so.

I do not think you are asking for a truth table “proof” of these. Truth table is too straightforward for anyone to have problem with. You are here asking for a deduction using inference rules.

The first problem

Code:1 (1) (~F & G) -> H Premise
2 (2) ~I -> G Premise
3 (3) ~I & ~F Premise
3 (4) ~I 3, &-Elimination
2,3 (5) G 2,3 modus ponens
3 (6) ~F 3, &E
2,3 (7) ~F&G 5,6 &-intro
1,2,3 (8) H 1,7 ->-elimination
1,2,3 (9) H v J 8, v-intro


The second problem

Code:1 (1) K v L Premise
2 (2) ~K Premise
3 (3) (L v L)-> (~M v N) Premise
4 (4) ~N Assumption (assume the antecedent of the conclusion)
1,2 (5) L 1,2 Disjunctive syllogism (can be proved separately if need be)
1,2 (6) L v L 4, v-Intro
1,2,3 (7) ~M v N 3,5 ->-Elimination
1,2,3,4 (8) ~M 4,7 Disjunctive syllogism
1,2,3 (9) ~N->~M 4,8 ->-intro


The disjunctive syllogism proof. A v B, ~B, therefore A
Code:1 (1) A v B Premise
2 (2) ~B Premise
3 (3) ~ A Assumption
4 (4) A Assumption
5 (5) B Assumption
2,5 (6) contradiction 2,5 ~-elimination
2,5 (7) ~~A 3,6 ~-intro
2,5 (8) A 7, double negation
1,2 (9) A 1,4,4,5,8 v-elimination


For problem three and four, I am uncomfortable with the premises of the examples you gave. They have serious flaws in them. For example, being admitted to heaven requires at least these things: believing in the Absolute Oneness of God, the Almighty AND being morally virtuous AND doing good deeds AND receiving mercy from God, the Almighty.

SS17 wrote:
Is there a way to create a logic proof using the variables given and solve it using that statement even if it hold false assumptions?


Yes, there is a way. I will give my examples which are in the same logical form as the examples you gave and work from there.

Problem three revisited

If Bob works hard, then he will succeed. But if Bob does not work hard, then he will do things that he enjoy. On the other hand if Bob does not succeed, then he will not do things that he enjoy. Therefore, Bob has to work hard.

M-Bob works hard
H-Bob succeeds,
L-Bob does things that he enjoys

To prove: M->H, ~M->L, ~H->~L therefore H

Here, we proceed by reduction ad absurdum, i.e. we assume the negation of the conclusion and derive a contradiction with the premises.

Code:1 (1). M->H Premise
2 (2) ~M->L Premise
3 (3) ~H->~L Premise
4 (4) ~H Assumption
3,4 (5) ~L 3,4 ->Elimination
2,3,4 (6) ~~M 2,5 Modus Tollens
2,3,4 (7) M 6, double negation
1,2,3,4 (8) H 1,7 ,->Elim
1,2,3,4 (9) contradiction 4,8 ~Elim
1,2,3 (10) ~~H 4,9 ~Intro
1,2,3 (11) H 10, Double negation


Problem four has issues as well. I have problems with these assumptions. Our ability to choose and God being The All-Knower is logically consistent and sound.

Freedom of choice implies absence of external coercion on the individual will. And knowledge is knowledge. How could the fact that God, the All-Knower knowing what one will chose determine that choice? For example, I might see a student, who does not study at all and he/she is always inattentive in class and does not do his homework. Then in my limited knowledge, I know that that student is going to fail. Does my knowledge determines that the student fails? I would not say that. If that student had listened to the numerous advice and encouragements of his teachers and done his/her homework and pay attention in class, he/she might have had a more brilliant future. It is in fact the student choice of not studying that determines his/her failure!

Now, God, the Almighty is the All-Knowing; there is nothing that escapes His knowledge and He has power over everything. And in no way does God’s knowledge of the future determines the choices that we make, because if we were compelled to do anything by anyone, we would not have freedom/choice. So God, the Almighty knows everything, including the future; but still, God gives us the ability to choose and the choices we make are still our choices and are not imposed on us.

Again this is a sensitive issue and too philosophically important to be taken lightly. So, I will give my examples and work from there.

Problem four revisited.

If my teacher believes on Monday that I will miss class on Tuesday, then either I make my teacher’s past beliefs false, or I miss class on Tuesday. I will not make my teacher’s past beliefs false if either my teacher is right or the past is unalterable. The past is unalterable. It follows that if my teacher believes on Monday that I’ll miss class on Tuesday, then I will miss class on Tuesday.

B=my teacher believes that I will miss class on Tuesday
F= I make my teacher’s pass belief false
R=I do not miss class on Tuesday.
I=my teacher is right
P=the past is unalterable

To prove: B->(Fv~R), (I v P)->~F, P therefore B ->~R

Code:1 (1) B->(F v ~R) Premise
2 (2) (I v P) –>~F Premise
3 (3) P Premise
4 (4) B Assumption (assume antecedent of conclusion)
5 (5) R Assumption
1,4 (5) (F v ~R) 1,4 ->Elimination
6 (6) F Assumption
2,6 (7) ~ (I v P) 2,6 Modus Tollens
3 (8) I v P 3, v-Intro
2,3,6 (9) contradiction 7,8 ~Elimination
2,3,6 (10)~R 5,9 ~Intro
11 (11) ~R Assumption
1,2,3,4 (12) ~R 5,6,10,11,11, v-Elim
1,2,3 (13) B->~R 4,12 ->-intro



A note though on the homework you were given. The last two problems are clear examples of sophistry. Sophism mean a false argument, especially one intended to deceive.

Let us analyze the statement: “I cannot refrain from lying on Tuesday.” In effect, in propositional logic, the meaning of that statement is no different from the statement: “I will not not lie on Tuesday”, i.e. “I will lie on Tuesday”. But clearly these two statements do not convey the same meaning in ordinary discourse, for the latter can be true while the former can be false, i.e. in the case where lying is a choice. If someone lie on Tuesday, it does not imply that such a person could not have done otherwise. But the statement in the problem i.e. “I cannot refrain from lying on Tuesday” intends to remove the choice of the individual in lying. This is a clear cut case of sophistical argumentation.

Moreover, use of words such as “can”, “must”, “cannot”, “possible”, “impossible” belongs to another more sophisticated branch of logic called modal logic. Which is beyond the scope of propositional logic. And that is why when I removed all modal elements of the argument, it lost all its “teeth and claws”!

I hope this helps.


fresco
 
  -1  
Reply Wed 13 Dec, 2017 12:52 am
@carpenters,
NB
The general principle on A2K is not to do the homework but to point the student in the right direction.
carpenters
 
  2  
Reply Wed 13 Dec, 2017 02:00 am
@fresco,
Thank you for the information, but I go by my own principles. When somebody is in need, then I help when I can. And besides, SS17 seemed so desperate as he/she said :"If anyone can help me with this as soon as possible it would be awesome. Please Please Please. I need help!!".

So, you do what you have to do, and I do what I have to do.
fresco
 
  1  
Reply Wed 13 Dec, 2017 06:40 am
@carpenters,
I won't labour the point, but your assumption that the student is 'advanced beyond the truth table method' is contradicted by your highlighting of 'desperation' ! ....So much for the practicalities of 'logic' when one is enjoying oneself ! Wink

carpenters
 
  1  
Reply Wed 13 Dec, 2017 10:18 am
@fresco,
fresco wrote:
I won't labour the point, but your assumption that the student is 'advanced beyond the truth table method' is contradicted by your highlighting of 'desperation' !


What you think as "a contradiction" for me translates as common sensical and proceeds from the weighing of practical considerations. Allow me to instruct you on this. Truth-table essentially involves constructing a table and populating the first row of the table with column headings consisting of the atomic sentence letters occurring in the symbolic form of the argument and the premises of that argument. Then it is just a simple matter of filling the blanks. Things are even made easier in that we only have to chose between two alternatives namely either 'true' or 'false' for the values to fill the blanks with! Then it is just a mechanical exercise with nearly no thinking involved. It could not have been more simple as a method!

Now, do I think that someone would ask about that on a philosophy forum, given such practical considerations as to the simplicity of the method and as to the boring nature of the task of actually drawing such a table in a forum post editor? Clearly that would have been an insult to the intelligence of the questioner were I to assume that, and a lost of my time were I to actually tell him to draw a truth table or give that truth table itself! Use your common sense and think about it for sometime, you might get an insight into it if you were to pay attention to practical considerations!

fresco wrote:
....So much for the practicalities of 'logic' when one is enjoying oneself ! Wink


Now, if the questioner has been enjoying himself, and has not been working on those problems and is just free-riding, then eventually he/she is going to sit for his/her exams, and I will not be there for him/her! He/she would then have to deal with the consequences for his/her negligence.

But, if the questioner has seriously been trying hard to work his/her way through the problems but still cannot find a solution and is truly in need of some help, then one day I would be held accountable for not helping someone truly in need when I could easily have done so!

So upon these considerations, I had the choice of either helping a free-rider or helping someone genuinely trying hard but is still in need. I chose to believe in the questioner's good faith. If I was wrong then only him/her loses eventually. But if I was right, then we both win and there could even be a net benefit for society as well in the long run. So logically it was better for me to help.

But in any case, it was my decision to make and it was and still is absolutely none of your business whatsoever, what I do with my knowledge or my resources or my time, or who I chose to help. On that I think we can all agree! Wink
fresco
 
  1  
Reply Wed 13 Dec, 2017 10:56 am
@carpenters,
Wrong ! We can only agree that a student will not benefit by someone doing homework for them. The rest is self indulgent blather.
carpenters
 
  2  
Reply Wed 13 Dec, 2017 11:42 am
@fresco,
It is not for you to decide who benefits from my post or not. And what you call 'self indulgent blather' is in fact precise logical argumentation which you are experiencing for the first time in your life! Smile As you took the time to reply to it, I will conclude it had an effect of trigerring a response from you. I will call it a good day! Very Happy
jerlands
 
  0  
Reply Wed 13 Dec, 2017 02:23 pm
@carpenters,
Frankly, I enjoyed the edification so thanks for the contribution!
0 Replies
 
Kolyo
 
  2  
Reply Wed 13 Dec, 2017 06:34 pm
@carpenters,
carpenters wrote:

Thank you for the information, but I go by my own principles. When somebody is in need, then I help when I can.


I have not checked your reasoning here, but assuming you're right, you have added to the informational content of a2k. Thank you, and welcome to the site.
laughoutlood
 
  1  
Reply Wed 13 Dec, 2017 08:21 pm
0 Replies
 
fresco
 
  2  
Reply Fri 15 Dec, 2017 02:35 am
@Kolyo,
' Information' is never neutral. Its definition is related to a 'choice between alternatives'. There is a line between choosing to 'help' with homework and choosing to 'do it', which has been crossed in this thread. The 'information' is freely available to any student of logic who has been to their classes or who investigates examples on the internet. Students incapable of learning by example are probably on the wrong course.
Kolyo
 
  1  
Reply Sat 16 Dec, 2017 09:15 am
@fresco,
fresco wrote:

The 'information' is freely available to any student of logic who has been to their classes or who investigates examples on the internet. Students incapable of learning by example are probably on the wrong course.


The "examples on the internet " to which you are referring, are put there by people like carpenters.

What carpenters did in this thread had 3 consequences:

1 -- It gave a lazy student an unearned quick fix.

2 -- it provided 10 to 20 honest students (Who will see it later) with an example to learn from.

3 -- it allowed carpenters to demonstrate a certain mathematical ability to those of us blessed with the same ability

Consequence #1 is negative, certainly, but I think the good effects (2 and 3) outweigh the bad (1).
 

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