Introduction to possible modal logic

[SNP1]

I am going to give a small introduction to one of the branches of modal logic. I know this should go in the philosophy section, but there are quite a few arguments for god that use modal logic. Do not expect it to be the best intro (I am not the best at articulating thoughts outside of premise and conclusion form).

When dealing with possible modal logic (I will now be calling pml) it is easier to think of it as possible worlds.

If something is possible, it exists in at least one possible world (but not necessarily our world).

There are 2 types of facts in pml:
1) Contingent
2) Necessary

A contingent fact is one that exists in one possible world, but not all possible worlds.
A necessary fact is one that exists in all possible worlds.

---NOTE---
It is a controversy among some philosopher whether the real world counts as one of the possible worlds or not
---ENDNOTE---

Think of this statement:
President Obama was assassinated January 1st, 2015.

This statement is not a true statement (as it did not happen in our world), but is a contingently true statement (as it could be true in some possible world).

Now, we can also consider this statement:
Greg and Terry are both taller than each other.

This statement is logically impossible, and thus is necessarily false (not true in any possible world).



The first step in modal logic is...

Identifying if an assertion is logically possible or logically impossible.

For this, you should learn the laws of logic. The main three, which all the laws of logic are built around, are:
1) The law of identity (example: A=A)
2) The law of non-contradiction (A cannot equal 5 and not be equal to 5 at the same time)
3) The law of excluded middle (something either is or is not, it cannot be any other option)

If you identify something as logically impossible, then it is necessarily false.
If you identify something as logically possible, then you move onto the next step...

Step 2

Identify the possible assertion as contingent or necessary.

This is one area that I still struggle in. What I do to figure it out is use this method:

P1) It is either contingent or necessary
P2) Not contingent
C) It is necessary

I, personally, assume it is contingent until I can show that it is necessary when using the above method.

Another way of identifying if something is necessary is if it is necessary by definition (you cannot have married bachelors, 2+2=4, etc.).
One exception to this is when someone defines something as being necessary in order to make it so. It has to be able to be demonstrated that it is necessary by definition.

Step 3

Formulate your argument. Make sure that the premises and conclusion(s) follow. You also need to explain how each premise follows, and how the conclusion follows from the premises.

---FINALCOMMENT---

I am still learning modal logic myself. I am only decent at possible modal logic at this point. When I have learned more, I will post more.

[PickelledEggs]

I fucking hated algebra.

edit: yes I am mocking this logic for being overly and unnecessarily complicated

[Hydra009]

A contingent fact is one that exists in one possible world, but not all possible worlds.
A necessary fact is one that exists in all possible worlds.

*looks around for other possible worlds to compare to our own*
*moves stacks of papers*
*opens drawers in sequence*
*examines dryer lint*
*shrugs*

[Solitary]

Shouldn't Modal logic be the logic of religion or neurotics? No system of logic can tell you what the truth is if the premises can't be agreed upon. Model logic attempts to show that if you don't know what is true, it could be possible. I don't know if there are aliens from Mars, but there could be. I don't know how many angels can dance on a pin on earth, but there could be a 100.000 in heaven. I don't see God on earth, but He could be in heaven. I know 2+1 is three, but it might not be in a black hole. I think our politicians and other authority figures use Modal logic.   

[Munch]

I fucking hated algebra.

edit: yes I am mocking this logic for being overly and unnecessarily complicated

Firstly, Ivy approves of your new avatar



Second, agreed, I think I can break this whole thing down to being about logical fallacy and deriving possibility from the now impossible. Might have to reread it though.

[Solitary]

PickelledEggs is tickled pink with his new avatar. 

[PickelledEggs]

Firstly, Ivy approves of your new avatar



Second, agreed, I think I can break this whole thing down to being about logical fallacy and deriving possibility from the now impossible. Might have to reread it though.

Poison Ivy is a close second for me. I have a thing for redheads in general.

[GSOgymrat]

I know this should go in the philosophy section, but there are quite a few arguments for god that use modal logic.

I see how one might attempt to disprove a god using modal logic but how would you prove a god using this method? Can you give an example?

[dtq123]

Using your quick "summary" (I'm not sure what it is,) I have concluded that I can in fact be president right now... In another world.

Am I right?

Seriously, Contingent Facts are not necessarily within our lives, so almost anything is possible.

Certain rules can be redefined... So that 15 year olds can become president.

However, I can't be 15 and remember more than 16 years of life since that would contradict each other... A Necessary Statement that one's memory can't go over their current age.

Am I getting this right so far?

[SNP1]

I see how one might attempt to disprove a god using modal logic but how would you prove a god using this method? Can you give an example?

CCF - Is a conjunct of all contingent facts in the world
P1) It is possible that a world exists where the CCF has an explanation, and that explanation is q
P2) Explanation q must be a necessary being
P3) It is possible a necessary being exists (from 1 & 2)
P4) If it is possible a necessary being exists, then a necessary being exists (via. axiom s5)
C) A necessary being exists

Using your quick "summary" (I'm not sure what it is,) I have concluded that I can in fact be president right now... In another world.

Am I right?

In a possible world, yes.

Seriously, Contingent Facts are not necessarily within our lives, so almost anything is possible.

Anything that is not logically impossible is, by definition, possible. Yes.

Certain rules can be redefined... So that 15 year olds can become president.

However, I can't be 15 and remember more than 16 years of life since that would contradict each other... A Necessary Statement that one's memory can't go over their current age.

Am I getting this right so far?

Yes, it is necessarily false to have an accurate memory of your life that goes back further than you have lived.

You are doing a good job so far.

[Desdinova]

OP, you have already tried this in another thread.  OK, we get it.  Anything is "possible".  Unicorns are "possible".  Leprechauns are "possible".  It's possible that I could wake up tomorrow with a vagina on my hand and never ever have to leave my house again.  But we all know there aren't unicorns or leprechauns or magical vaginas.  Please move on to something else.  You are beginning to embarrass yourself.

[doorknob]

"Anything that is not logically impossible is, by definition, possible. Yes"

that's like saying anything that's not a swan is by definition not a swan.

the definition of possible is...

"Capable of happening, existing, or being true without contradicting proven facts, laws, or circumstances."

That being said how then is god a necessary being and not a contingent being?

[SNP1]

OP, you have already tried this in another thread.  OK, we get it.  Anything is "possible".  Unicorns are "possible".  Leprechauns are "possible".  It's possible that I could wake up tomorrow with a vagina on my hand and never ever have to leave my house again.  But we all know there aren't unicorns or leprechauns or magical vaginas.  Please move on to something else.  You are beginning to embarrass yourself.

This is an introduction to possible modal logic so that those that want to learn it can. It isn't for idiots who do not want to learn it to comment about it.

That being said how then is god a necessary being and not a contingent being?

Based off of the argument, it cannot be contingent.

If it was contingent, it would be part of the CCF, and thus would either be explaining itself (which means the CCF does not have an explanation, but be self-contained) or would need an outside explanation (which means it doesn't actually explain the CCF).

If it was necessary, then it is not part of the CCF and can explain the CCF.

Since a contingent fact cannot logically explain the CCF but a necessary one can, the explanation (if there is one) must be necessary.

[Desdinova]

OP, answer this question.  A simple yes or no. 

Do you actually believe that the existence of a supreme sky daddy is possible?

[Solitary]

Modal logic is not logical! It's mental gymnastics trying to prove God exists, or that any other unknown can.    Solitary