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Introduction to possible modal logic

Started by SNP1, January 14, 2015, 04:19:43 PM

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dtq123

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:
A dark cloud looms over.
Festive cheer does not help much.
What is this, "Justice?"

Solitary

There is more than one definition of love, even the Greeks knew this. It is not an absolute word.
There is nothing more frightful than ignorance in action.

Hakurei Reimu

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.
Warning: Don't Tease The Miko!
(she bites!)
Spinny Miko Avatar shamelessly ripped off from Iosys' Neko Miko Reimu

Solitary

#33
 :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
There is nothing more frightful than ignorance in action.

SNP1

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.
"My only agenda, if one can call it that, is the pursuit of truth" ~AoSS

Hakurei Reimu

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.
Warning: Don't Tease The Miko!
(she bites!)
Spinny Miko Avatar shamelessly ripped off from Iosys' Neko Miko Reimu

Solitary

#36
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
There is nothing more frightful than ignorance in action.