13
votes
What does □□p mean?
In general □□ p and □ p are very different. Thinking in terms of Kripke frames, they only obviously coincide if the accessibility relation is transitive. This is true for Kripke frames validating S5, ...
- 3,210
11
votes
Accepted
Are there any established logical symbols for merely possible and contingently true?
There is no established symbol, but some authors introduce their own. Girle in Modal Logics and Philosophy, p.9 uses ∇ for (derived) contingency operator, i.e. ∇p:= ◊p ∧ ◊¬p, he also has the dual Δp:= ...
- 42.5k
10
votes
What is the difference between a probability and a possibility?
On the prevailing extensional interpretation of modality the difference between possibility and probability is the diffference between quality and quantity, possibility is the quality quantified by ...
- 42.5k
10
votes
Accepted
Is it consistent to say "X is possible but false"?
Well, in English you would use the subjunctive tense and say, "possibly I could have had a cat in my room, but in fact I do not." That's a reasonable statement to make. "I could have ...
- 11.1k
10
votes
Is there a system of logic which denies DNI?
Yes there is. As you say, intuitionistic logic has DNI but not DNE. There are also dual-intuitionistic logics whose connectives operate in a fashion that is dual to those of intuitionistic logic. Dual-...
- 22.8k
9
votes
Does this modal ontological argument prove the existence of God?
I understand your argument as follows:
A maximally great being possibly exists.
If a maximally great being possibly exists then it necessarily exists.
If a maximally great being necessarily ...
- 6,456
9
votes
Accepted
Is the problem of logical omniscience intractable?
Logical omniscience was always only a technical problem related to formalization of epistemic logic in terms of possible worlds. Since classical possible worlds are supposed to be consistent and ...
- 42.5k
8
votes
Why did many valued logic fail in describing modal logic?
So the three valued logic of Łukasiewicz has three truth values {1,i,0}. Łukasiewicz was trying to solve the problem of future contigents with this logic.
His view is that statements about the past ...
- 852
8
votes
Should truth entail possible truth?
If we're talking about metaphysical possibility, then normally yes. If you reject the claim that "if P then possibly P", you must also reject the claim that "if necessarily P then P". Proof: suppose ...
- 3,784
8
votes
Accepted
Is every world accessible to itself?
You are correct about the relationship between □P → P and the reflexivity of the accessibility relation. As to whether you want to take this as an axiom, it depends entirely on your intended ...
- 22.8k
7
votes
What is the explanation for inferring existence in every possible world from existence in some in Plantinga's Ontological Argument?
This looks like a "lame terms" redux of Plantinga's "victorious" ontological argument from The Nature of Necessity. Here is Plantinga's explanation of why if a maximally great ...
- 42.5k
7
votes
Accepted
How does the concept of the 'virtual' (Deleuze) relate to 'counterfactuals' (Lewis)?
In a sense, Deleuze's virtual and Lewis's possible worlds compete to provide the "right" conception of the possible. The descriptions are indeed similar but this is deceptive, Deleuze and ...
- 42.5k
7
votes
Accepted
How to prove the completeness of S5?
Hughes and Cresswell's proof proceeds roughly as follows:
They show that any sentence of S5 is logically equivalent to a modal conjunctive normal form (MCNF) in which a sentence takes the form of a ...
- 22.8k
7
votes
How to be skeptical of transcendental arguments?
The argument form that you quote is straightforwardly valid in standard logic. It might be symbolised as
1. ◇Y → X
2. Y
3. Y → ◇Y
therefore,
4. X
You give 1 and 2 as premises, and 3 is the T axiom ...
- 22.8k
6
votes
Why did many valued logic fail in describing modal logic?
The specific quotation you gave about Łukasiewicz refers to the fact there was an attempt to understand intuitionistic logic as a many-valued logic, but this failed because Gödel proved in the early ...
- 22.8k
6
votes
Does this modal ontological argument prove the existence of God?
The proof does not work, I think. Your problems are premises 1 and 2.
My main problem is with premise 1: it is possible for a maximally great being to exist. Why should we accept this?
There is the ...
- 1,956
6
votes
What is Plantinga's "trivial property"?
Plantinga uses the concept of non-trivial properties in his transworld depravity defense of God's benevolence, see How does free will defense of God's benevolence work? Ciprotti in Theological ...
- 42.5k
6
votes
Where is the fallacy in Seth Yalcin's counterexample to the modus tollens?
The use of modus tollens is valid only when used with propositions containing valid logical predicates. And here it is not.
A logical predicate is commonly understood as a boolean function P: X → {...
- 380
6
votes
What does □□p mean?
To add to the existing answer, there's also epistemic logic, where □ is interpreted as knowledge (relative to a given subject).
Possible worlds in such a system are worlds that are consistent with ...
- 6,456
6
votes
Accepted
Obligation and material implication
Neither □(p → q) → (□p → □q) nor □(p → q) → (p → □q) really work. Both run into the problem pointed out by Chisholm with his contrary to duty paradox. The problem is that the simple version of deontic ...
- 22.8k
5
votes
What are the practical applications of modal logic?
A very practical application of modal logic is the control of traffic lights. Some approaches use fuzzy logic, but there are also Prior-Kripke based traffic lights.
- 136
5
votes
Accepted
How does Plantinga's free will defense of God's benevolence work?
Geirsson and Losonsky, in Plantinga and the Problem of Evil (from your "P.S." statement) fail at least two ways in attempting to address Plantinga's argument:
Counter-Factuals (CFs) are possible ...
- 956
5
votes
Accepted
Is it possible to not know that one knows p?
Everything hinges on how you understand "knowing."
First off, you're going to need to decide whether there's a distinction between episteme, techne, and phronesis (or if you prefer Gilbert ...
- 24.6k
5
votes
Accepted
Why do “L” and “M” name the strong and weak modal operators in modal logic?
From the Polish logician and philosopher Jan Łukasiewicz who invented the Polish notation for logic (named after his nationality) :
M ϕ for możliwość : possibility
L ϕ for konieczność : necessity [...
- 36.1k
5
votes
Does this modal ontological argument prove the existence of God?
The proof fails in the very first step. You try to justify this step in your initial explanation, but let's just put this explanation as part of the proof.
Nobody has successfully disproven the ...
5
votes
Accepted
Why substitutivity doesn't work in an intensional context?
As a quick aside/introduction, this answer might be better served as an answer to "what is meant be 'intensional context' in the philosophy of language?" because I go over more than just the ...
- 2,841
5
votes
The difference between indicative conditional and counterfactual
The difference is expressed by the late David Lewis in terms of two examples ('Counterfactuals, 1973) :
Indicative conditional : 'If Oswald did not kill Kennedy, then someone else did'.
...
- 35.4k
5
votes
Is □(□A→B) v □(□B→A) provable in S5? If it's not, I am having trouble coming up with a countermodel
This statement is provable. You can turn it into an equivalent implication: ¬□(□A → B) → □(□B → A)
Then make the hypothesis that the first term is true and show that the second follows.
The first ...
- 5,830
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