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Extraordinary Claims => Religion General Discussion => Topic started by: SNP1 on January 14, 2015, 04:19:43 PM

Title: Introduction to possible modal logic
Post by: SNP1 on January 14, 2015, 04:19:43 PM
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.
Title: Re: Introduction to possible modal logic
Post by: PickelledEggs on January 14, 2015, 04:22:25 PM
I fucking hated algebra.

edit: yes I am mocking this logic for being overly and unnecessarily complicated
Title: Re: Introduction to possible modal logic
Post by: Hydra009 on January 14, 2015, 06:33:58 PM
QuoteA 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*
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 14, 2015, 07:09:59 PM
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.  :wall:  :lol:
Title: Re: Introduction to possible modal logic
Post by: Munch on January 14, 2015, 07:13:56 PM
Quote from: PickelledEggs on January 14, 2015, 04:22:25 PM
I fucking hated algebra.

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

Firstly, Ivy approves of your new avatar

(http://images6.fanpop.com/image/photos/36100000/Poison-Ivy-image-poison-ivy-36169941-300-200.gif)

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.
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 14, 2015, 07:27:42 PM
PickelledEggs is tickled pink with his new avatar.  :super:
Title: Re: Introduction to possible modal logic
Post by: PickelledEggs on January 14, 2015, 08:08:01 PM
Quote from: Munch on January 14, 2015, 07:13:56 PM
Firstly, Ivy approves of your new avatar

(http://images6.fanpop.com/image/photos/36100000/Poison-Ivy-image-poison-ivy-36169941-300-200.gif)

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.
Title: Re: Introduction to possible modal logic
Post by: GSOgymrat on January 14, 2015, 10:51:57 PM
QuoteI 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?
Title: Re: Introduction to possible modal logic
Post by: dtq123 on January 14, 2015, 11:02:16 PM
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? :eyes:

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? :redface:
Title: Re: Introduction to possible modal logic
Post by: SNP1 on January 15, 2015, 09:36:45 AM
Quote from: GSOgymrat on January 14, 2015, 10:51:57 PM
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

Quote from: dtq123 on January 14, 2015, 11:02:16 PM
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? :eyes:

In a possible world, yes.

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

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

QuoteCertain 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? :redface:

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.
Title: Re: Introduction to possible modal logic
Post by: Desdinova on January 15, 2015, 10:09:00 AM
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.
Title: Re: Introduction to possible modal logic
Post by: doorknob on January 15, 2015, 10:30:09 AM
"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?



Title: Re: Introduction to possible modal logic
Post by: SNP1 on January 15, 2015, 10:53:27 AM
Quote from: Desdinova on January 15, 2015, 10:09:00 AM
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.

Quote from: doorknob on January 15, 2015, 10:30:09 AM
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.
Title: Re: Introduction to possible modal logic
Post by: Desdinova on January 15, 2015, 12:02:54 PM
OP, answer this question.  A simple yes or no. 

Do you actually believe that the existence of a supreme sky daddy is possible?
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 15, 2015, 12:14:24 PM
Modal logic is not logical! It's mental gymnastics trying to prove God exists, or that any other unknown can.   :wall: Solitary
Title: Re: Introduction to possible modal logic
Post by: SNP1 on January 15, 2015, 12:25:49 PM
Quote from: Desdinova on January 15, 2015, 12:02:54 PM
OP, answer this question.  A simple yes or no. 

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

I think it is possible, but I think the chance of one actually existing is very low.

Quote from: Solitary on January 15, 2015, 12:14:24 PM
Modal logic is not logical! It's mental gymnastics trying to prove God exists, or that any other unknown can.  :wall:

Right, one of the accepted forms of logic isn't logical...
Title: Re: Introduction to possible modal logic
Post by: GSOgymrat on January 15, 2015, 12:39:32 PM
QuoteCCF - 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

If this can prove the existence of one god then I assume it can prove the existence of a variety gods, e.g. a god can exist that does interact with humanity, a god can exist that does not interact with humanity.
Title: Re: Introduction to possible modal logic
Post by: Desdinova on January 15, 2015, 01:00:14 PM
Quote from: SNP1 on January 15, 2015, 09:36:45 AM
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

Why does P2 have to be a "being"?  Why couldn't P2 be a set of necessary "factors"?
Title: Re: Introduction to possible modal logic
Post by: SNP1 on January 15, 2015, 02:03:46 PM
Quote from: GSOgymrat on January 15, 2015, 12:39:32 PM
If this can prove the existence of one god then I assume it can prove the existence of a variety gods, e.g. a god can exist that does interact with humanity, a god can exist that does not interact with humanity.

The argument only shows a minimalistic, deistic god.

Quote from: Desdinova on January 15, 2015, 01:00:14 PM
Why does P2 have to be a "being"?  Why couldn't P2 be a set of necessary "factors"?

For one, Occam's Razor makes it more likely that it is singular.

P2 is either one necessary factor or one necessary being. I have never before been asked if it has to be a being... I don't think so now that you point that out (no one has pointed out the "being", they usually focus on the "necessary" part). It isn't an argument that I came up with, and would have to ask the person that came up with it to find out that.
Title: Re: Introduction to possible modal logic
Post by: Desdinova on January 15, 2015, 04:56:28 PM
With all due respect SNP1, I still think it's all BS.  Sorry, if my blatant honesty offends you.
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 15, 2015, 06:19:20 PM
Quote from: SNP1 on January 15, 2015, 12:25:49 PM
I think it is possible, but I think the chance of one actually existing is very low.

Right, one of the accepted forms of logic isn't logical...
That's what I said and still mean it! Accepted by whom?  Logic is define as sound reasoning, Modal logic is not sound reasoning period! Your response is playing on words as if they are absolutes, they are not, the problem in logic and philosophy.  Solitary
Title: Re: Introduction to possible modal logic
Post by: SNP1 on January 15, 2015, 08:47:18 PM
Quote from: Solitary on January 15, 2015, 06:19:20 PM
Accepted by whom?

Forms of logic go through a process and will either be accepted or rejected by the philosophical community (philosophers). It is similar to how scientific facts get accepted by the scientific community.
Title: Re: Introduction to possible modal logic
Post by: dtq123 on January 15, 2015, 10:32:42 PM
Quote from: Solitary on January 15, 2015, 06:19:20 PM
That's what I said and still mean it! Accepted by whom?  Logic is define as sound reasoning, Modal logic is not sound reasoning period! Your response is playing on words as if they are absolutes, they are not, the problem in logic and philosophy.  Solitary

Words have a implied absolute and meaning. Without it, meanings could and would constantly shift. So Necessary facts require good definitions.

If it's still bullshit to you then at least take this away with you; Definitions are important especially when dealing with God. God can change definition very quickly, and here's a list what of people have said God is:

God is:
=The biblical god
=Love
=Truth
=etc.

And things get really weird when is goes further than the above:
=Is god material?
=Is god Omnipotent? Omnipresent?
=Is he ALWAYS benevolent? Honest? Just?
=Is he human?
=etc.

When we pin down a specific definition of God, it is easier to prevent the "No True Scotsman" Fallacy from escaping our grasp and show the fallacy of the opposing side.


For instance, Friend X says God X is just. Friend X also believes the holy book is literal fact. Friend X claims his/her god is real.

If it is possible for God X to exist in any realm, Then there must not be any contradicting factors (or so called "Necessary Facts".

The holy books contain acts of God X committing Murder.

If the holy books contain acts of God X committing Murder, Then there are contradicting factors.

Therefore, It is impossible for god X to exist in any realm due to contradicting factors.

However, if Friend X says "God works in mysterious ways" after this argument, thou must slap thy neighbor :eyes:

Seriously, It's logic wrapped in a load of algebra and tied with a long forum post. It works, but reading the whole thing is an achievement.
Edit: And the terms seem to make little sense with what they are referring to.
Title: Re: Introduction to possible modal logic
Post by: PickelledEggs on January 15, 2015, 10:49:40 PM
Here is some modal logic:


x: is boring
if you take M and multiply it by 2 and divide it by 199x you get Ness and Mr. Saturn

Now when Mr. Saturn takes a nap, 3 dogs will crap in the woods. When the smell goes away, that will reveal if the idea holds water. Just like Mr Saturn's bladder.

SNP. This "modal logic" you are trying to push on us is one of the most unnecessarily complicated attempt at trying to achieve logic I have ever seen. It's making more steps out of something that is extraordinarily more simple than you are trying to make it.
Title: Re: Introduction to possible modal logic
Post by: PickelledEggs on January 15, 2015, 11:05:11 PM
There are plenty of much more easy and simple ways to achieve the same exact result. If you want to complicate things for yourself though, go right ahead.

Also. I am in no way telling you to not try to explain it more, just putting my 2 cents in of why it shouldn't be this difficult to explain something as straightforward as logic usually is.
Just keep in mind, depending on how you go about it, your pushing of this "modal logic" on to us could possibly be considered proselytizing, which is against the rules.
Title: Re: Introduction to possible modal logic
Post by: La Dolce Vita on January 19, 2015, 03:21:39 PM
Quote from: SNP1 on January 14, 2015, 04:19:43 PMCCF - 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

This arguments is easy to destroy as it is dependent on simultaneously using two different definitions of "possible" to be convincing.

Def 1: The honest acknowledgement that everything that has not been disproved (regardless of how silly) could hypothetically "exist".

Def 2: That something is physically possible

The two definitions are in no way connected - and using them both as interchangeable means that the argument is invalid.

Sticking to a specific definition on the other hand either invalidates it (as well) or makes the argument currely irrelevant.

If we use the definition of something maybe being possible, this does in no way translate to actual existence - so the argument is invalid.

If we use the definition that something is physically possible, then we'd have to actually demonstrate that it is physically possible - empirically. Otherwise the argument has no demonstrative value. And to show that a necessary being is possible by this argument (which does not mean that a creator god is possible, but that a creator god has to exist for "all worlds") you'd have to empirically demonstrate that this being exists in our world and all others. This means that the argument can be summed up as "if there is a necessary being there's a necessary being". Which is quite laughable in terms of demonstrating such a being existing.
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 19, 2015, 04:25:59 PM
Quote from: SNP1 on January 15, 2015, 08:47:18 PM
Forms of logic go through a process and will either be accepted or rejected by the philosophical community (philosophers). It is similar to how scientific facts get accepted by the scientific community.
Not true! Science is based on facts and evidence, not opinions. Solitary
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 19, 2015, 04:29:40 PM
Quote from: dtq123 on January 15, 2015, 10:32:42 PM
Words have a implied absolute and meaning. Without it, meanings could and would constantly shift. So Necessary facts require good definitions.

If it's still bullshit to you then at least take this away with you; Definitions are important especially when dealing with God. God can change definition very quickly, and here's a list what of people have said God is:

God is:
=The biblical god
=Love
=Truth
=etc.

And things get really weird when is goes further than the above:
=Is god material?
=Is god Omnipotent? Omnipresent?
=Is he ALWAYS benevolent? Honest? Just?
=Is he human?
=etc.

When we pin down a specific definition of God, it is easier to prevent the "No True Scotsman" Fallacy from escaping our grasp and show the fallacy of the opposing side.


For instance, Friend X says God X is just. Friend X also believes the holy book is literal fact. Friend X claims his/her god is real.

If it is possible for God X to exist in any realm, Then there must not be any contradicting factors (or so called "Necessary Facts".

The holy books contain acts of God X committing Murder.

If the holy books contain acts of God X committing Murder, Then there are contradicting factors.

Therefore, It is impossible for god X to exist in any realm due to contradicting factors.

However, if Friend X says "God works in mysterious ways" after this argument, thou must slap thy neighbor :eyes:

Seriously, It's logic wrapped in a load of algebra and tied with a long forum post. It works, but reading the whole thing is an achievement.
Edit: And the terms seem to make little sense with what they are referring to.
"Words have a implied absolute and meaning. " You do realize this is a contradiction in logic don't you?  vSolitary
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 19, 2015, 04:42:32 PM
 :wall: Paraconsistent logic remains consistent even though, by definition it's inconsistent, Or putting it another way, paraconsistent logic is both consistent and inconsistent----which when you think about it, is a kind of the whole idea in a "NUT" shell. The kind of logic that nuts believe in, or irrational neurotics. It's like a lunatic that says, "war is peace," up is down, hot is cold, or God is love and hate. Give me a break, if you think like this you are a lunatic and everyone else that does!  :fU: Solitary
Title: Re: Introduction to possible modal logic
Post by: Hydra009 on January 19, 2015, 05:23:25 PM
Quote from: dtq123 on January 15, 2015, 10:32:42 PMWords have a implied absolute and meaning. Without it, meanings could and would constantly shift.
Compare a dictionary from now versus a couple hundred years ago.  The meanings most definitely do shift.
Title: Re: Introduction to possible modal logic
Post by: dtq123 on January 19, 2015, 06:34:20 PM
Quote from: Hydra009 on January 19, 2015, 05:23:25 PM
Compare a dictionary from now versus a couple hundred years ago.  The meanings most definitely do shift.

I admit this was an oversight on my part.

There are certain ideas that still are within the words though. For instance, the word "love" equates itself with "a strong liking" and that hasn't changed much as other words.

Certain ideas are held in words and both the idea and word may shift, but It is important to establish a certain idea before you start to fight about it. Like in my God example, God has many meanings, and it does shift. However, to combat shifting terms of God would be meaningless because the other individual can move the goalposts until his position is safe from scrutiny. Certain definitions for ideas give us a way to know what we are actually talking about, thus allowing us.

I think this is honest BS myself, but I want to get across the value of defining a term before continuing an argument.

Without clear definitions, we are unable to pin point when the goal posts of an argument is moving and thus weakens the point of the argument in the first place.
Quote from: dtq123 on January 15, 2015, 10:32:42 PM
Seriously, It's logic wrapped in a load of algebra and tied with a long forum post. It works, but reading the whole thing is an achievement.
And the terms seem to make little sense with what they are referring to.

Sense is all we're trying to make of reality. It works, though maybe not as well as other concepts.

But if a word could mean anything, then what am I really saying right now?  :eyes:
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 20, 2015, 10:53:11 AM
There is more than one definition of love, even the Greeks knew this. It is not an absolute word.
Title: Re: Introduction to possible modal logic
Post by: Hakurei Reimu on January 21, 2015, 10:55:54 AM
Quote from: SNP1 on January 15, 2015, 09:36:45 AM
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
Sorry, bub, that's a crock of shit.

First, by definition in modal logic, you are not considering a single world, but a multitude of possible worlds. The "conjunct of all contingent facts of the world" should only be of a world. A different world would require a different conjunct of all contingent facts (by definition, as it would be a different world that differed in some contingencies).

(1) It is possible that a world P exists where the CCF in P has an explanation, and that explanation is p.
(2) It is possible that a distinct world Q exists where the distinctly different CCF in Q has an explanation, and that explanation is q.
(3) Worlds P and Q are distinct. As such, their contingencies do not match. Therefore, the explanation q does not work for world P because q predicts contingencies that are not true in P, and vice versa for p and Q.
(4) Because P and Q are distinct possibilities for a world, it is possible for both p and q to exist as necessities for their matching world.
(5) Because both p and q are both possible necessities, then by axiom s5, both are necessary.
(6) But both p and q are mutually exclusive â€" they cannot be both true for any one world â€" but they are necessities and are thus true for all worlds from axiom s5.

(C) Axiom s5 makes modal logical incoherent.

The error in s5 is a fallacy of hasty generalization. It states, in a nutshell, that if you find some factor to be necessary in one possible world, then that factor is necessary in all possible worlds. This is an obvious error that the language of modal logic masks with its "possible"/"necessary" malarkey.
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 21, 2015, 11:18:49 AM
 :wall: No matter what kind of logic is used it cannot tell you what the truth is in this world, or any other!

Fallacy of Modal Logic

Taxonomy: Logical Fallacy > Formal Fallacy > Fallacy of Modal Logic

Exposition:
Modal logic is that branch of logic which studies logical relations involving modalities. Modalities are ways, so to speak, in which propositions can be true or false. The most commonly studied modalities are necessity and possibility, which are modalities because some propositions are necessarily true/false and others are possibly true/false.

Types of modality include:
Alethic Modalities: These include possibility and necessity, which were already mentioned, as well as impossibility and contingency. Some propositions are impossible, that is, necessarily false, whereas others are contingent, meaning that they are both possibly true and possibly false.

Temporal Modalities: Historical and future truth or falsity. Some propositions were true/false in the past and others will be true/false in the future.

Deontic Modalities: Obligation and permissibility. Some propositions ought to be true/false, while others are permissible.

Epistemic Modalities: Knowledge and belief. Some propositions are known to be true/false, and others are believed to be true/false.

Most modalities are propositional functions―that is, they are functions which when applied to a proposition produce a proposition―like negation, but unlike negation in that they are not truth-functional. That is, you cannot determine the truth-value of a modal proposition based solely upon the truth-value of the proposition it contains. For instance, from the fact that a certain proposition is true it does not follow that it is necessarily true, nor that it isn't. Some true propositions are necessary, but others are not.

Modal fallacies are formal fallacies in which modality plays a role in the fallaciousness of a type of argument.

Exposure:
Since modalities are frequent topics in philosophy―alethic modalities in metaphysics, epistemic ones in epistemology, and deontic ones in ethics―modal fallacies are quite frequent in philosophical and pseudo-philosophical argumentation. So, while students of philosophy should, of course, study logic and fallacies in general, they should pay particular attention to modal fallacies including the subfallacy below.

Subfallacy: Modal Scope Fallacy

Resources:
James Garson, "Modal Logic", Stanford Encyclopedia of Philosophy. A clear but technical survey of the field that assumes comfort with standard nonmodal logic.

G. E. Hughes & M. J. Cresswell, A New Introduction to Modal Logic (Routledge, 1996). The standard introduction, which may be too much for novices.

Modal logic is the type of logic (thinking) used by lunatics and neurotics, and why they are mental thinking everything is possible with a god or Gods. Solitary
Title: Re: Introduction to possible modal logic
Post by: SNP1 on January 21, 2015, 12:10:12 PM
Quote from: Hakurei Reimu on January 21, 2015, 10:55:54 AM
Sorry, bub, that's a crock of shit.

First, by definition in modal logic, you are not considering a single world, but a multitude of possible worlds. The "conjunct of all contingent facts of the world" should only be of a world. A different world would require a different conjunct of all contingent facts (by definition, as it would be a different world that differed in some contingencies).

(1) It is possible that a world P exists where the CCF in P has an explanation, and that explanation is p.
(2) It is possible that a distinct world Q exists where the distinctly different CCF in Q has an explanation, and that explanation is q.
(3) Worlds P and Q are distinct. As such, their contingencies do not match. Therefore, the explanation q does not work for world P because q predicts contingencies that are not true in P, and vice versa for p and Q.
(4) Because P and Q are distinct possibilities for a world, it is possible for both p and q to exist as necessities for their matching world.
(5) Because both p and q are both possible necessities, then by axiom s5, both are necessary.
(6) But both p and q are mutually exclusive â€" they cannot be both true for any one world â€" but they are necessities and are thus true for all worlds from axiom s5.

(C) Axiom s5 makes modal logical incoherent.

The error in s5 is a fallacy of hasty generalization. It states, in a nutshell, that if you find some factor to be necessary in one possible world, then that factor is necessary in all possible worlds. This is an obvious error that the language of modal logic masks with its "possible"/"necessary" malarkey.

Not exactly, the CCF refers to all contingent facts of all worlds.
Title: Re: Introduction to possible modal logic
Post by: Hakurei Reimu on January 21, 2015, 12:15:49 PM
Quote from: SNP1 on January 21, 2015, 12:10:12 PM
Not exactly, the CCF refers to all contingent facts of all worlds.
Each world will set different values to different contingencies in the CCF, hence different CCFs.
Title: Re: Introduction to possible modal logic
Post by: Solitary on January 23, 2015, 10:11:40 AM
For anyone that hasn't seen the fallacies in model logic on this thread, read this:  :wall: No matter what kind of logic is used it cannot tell you what the truth is in this world, or any other!

Fallacy of Modal Logic

Taxonomy: Logical Fallacy > Formal Fallacy > Fallacy of Modal Logic

Exposition:
Modal logic is that branch of logic which studies logical relations involving modalities. Modalities are ways, so to speak, in which propositions can be true or false. The most commonly studied modalities are necessity and possibility, which are modalities because some propositions are necessarily true/false and others are possibly true/false.

Types of modality include:
Alethic Modalities: These include possibility and necessity, which were already mentioned, as well as impossibility and contingency. Some propositions are impossible, that is, necessarily false, whereas others are contingent, meaning that they are both possibly true and possibly false.

Temporal Modalities: Historical and future truth or falsity. Some propositions were true/false in the past and others will be true/false in the future.

Deontic Modalities: Obligation and permissibility. Some propositions ought to be true/false, while others are permissible.

Epistemic Modalities: Knowledge and belief. Some propositions are known to be true/false, and others are believed to be true/false.

Most modalities are propositional functions―that is, they are functions which when applied to a proposition produce a proposition―like negation, but unlike negation in that they are not truth-functional. That is, you cannot determine the truth-value of a modal proposition based solely upon the truth-value of the proposition it contains. For instance, from the fact that a certain proposition is true it does not follow that it is necessarily true, nor that it isn't. Some true propositions are necessary, but others are not.

Modal fallacies are formal fallacies in which modality plays a role in the fallaciousness of a type of argument.

Exposure:
Since modalities are frequent topics in philosophy―alethic modalities in metaphysics, epistemic ones in epistemology, and deontic ones in ethics―modal fallacies are quite frequent in philosophical and pseudo-philosophical argumentation. So, while students of philosophy should, of course, study logic and fallacies in general, they should pay particular attention to modal fallacies including the subfallacy below.

Subfallacy: Modal Scope Fallacy

Resources:
James Garson, "Modal Logic", Stanford Encyclopedia of Philosophy. A clear but technical survey of the field that assumes comfort with standard nonmodal logic.

G. E. Hughes & M. J. Cresswell, A New Introduction to Modal Logic (Routledge, 1996). The standard introduction, which may be too much for novices.

Modal logic is the type of logic (thinking) used by lunatics and neurotics, and why they are mental thinking everything is possible with a god or Gods.  If they are an atheist and think this way (modal logic) then they are neurotic or insane, because it isn't rational to think like this.     :wall: Solitary