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Question: Can you direct me to resources about modal logic and complexity!?
I would like to gain an understanding of modal logic including S5 (Kripke semantics)!. also, I would like to understand complexity theory (as in NP completeness)!. I think these might be related in some way!. Ultimately, my understanding of these things will help me better understand and assess logical alethic and epistemic arguments in philosophy, particularly theodicies, where logical arguments are propounded for or against God's existence in the face of evil facts!.
Widely available material is preferred, that is, a book that is not expensive and obscure, or freely accessible internet resources!. I am rather poor ATM!.
also, since this is introductory, I would like to avoid a ton of math and favor simple English with illustrative examples!. I am already reading the Wikipedia material and the resources their articles offer toward the ends of the articles!.
Thank you!.Www@QuestionHome@Com
Best Answer - Chosen by Asker:
Can I be impertinent !?
Having spent over twenty years studying philosophy and theology [with a main slant on ethics] [although I did teach an introduction to logic course - basic square of opposition aristotelian syllogism , lucasziewiczian and logic gates etc, fallacy, smullyan etc]
alethic arguments , modal logic !?
dude, you're wasting your time if you honestly think these will assist you in any way regarding theodicies and the problem of evil!.!.!.because they are not what you're looking for !
modal logic is not a means of constructing an argument,
modal logic is a means of expressing a subjective judgment call and the presumptive relation between phenomena and predicates!.
If you really want to learn , including learning how to argue; start with predicate logic and learning from the argumentative style of geniuses - I'd say chesterton would be your first stop - if you don't believe me try this link http://www!.cse!.dmu!.ac!.uk/~mward/gkc/book!.!.!.
and scroll down to the man who thinks backwards;
then move onto his book 'heresies'!.
sound daft !? trust me - it's diamond dust and worth a lifetime of reading the most profound tomes and failing to realise the fallacious ,spurious or downright false nature of the inherant arguments!.!.!.!.
The problem is not our thinking - it's the way we delude ourselves into believing our thinking is not subject to all manner of prejudices and non-epistemic doxa!.
when it comes to Theology - i'd start with a check-up that one is fully aware of the christian-based positions [they are the most technical and non-pragmatic and the most capable of having a decent rational argument with countering philosophies - walter kasper's 'the God of Jesus Christ' is a brilliant tool - of course there's aquinas and all the riches and von balthasar is the best modern catholic theologian by far ]
But if you're resolute and determined to go along the modal logic path - please ensure your other logical education is up to par or it will be like swimming through mud - even 'logic for dummies' is a good starting block!.
You were right to start with wikipedia but to be frank - if maths is not your forte and you shrink away from it - why bother with something that is really going to frustrate you beyond imagining just so that you can find a technical shorthand for arguments you have to construct yourself in order to express your understanding of alethic arguments !?
possible, probable, most likely are not the means of trying to validate positions - one ends up enmeshed in subjunctive clauses and pragmatism!.
If aquinas seems a little daunting - a good little book from the 1920's is still available on amazon - 'God and Intelligence in modern philosophy' by Fulton Sheen - it might help a great deal in readying yourself for applying the modal logic and avoiding the confusion of realising you've pre-selected contradictions on false premises grounded on antinomies - Think kant's critique of practical reason [square circle isn't round and is round] [God is XY/God isn't XY]
Good luck but move slowly - if you're screaming out for modal logic instruction read the book reviews on amazon before you buy - believe or not the reviewers really do know what they're talking about in this issue - it's not the same as the viewpoints on a grisham or dan brown!.Www@QuestionHome@Com
I don't think either theory is understandable without a good deal of math!. I recommend the book "Modal Logic: An Introduction" by Brian Chellas!. I used it in my modal logic class in college!. You need a basic mathematical understanding of 1st order logic before you can hope to tackle modal!. Otherwise, even if you understand the basic idea, you'll never be able to use it to investigate complexity or any other purpose!.
http://www!.amazon!.com/Modal-Logic-Introd!.!.!.
We had a little computational complexity theory in my differential equations class, but there is another complexity theory that always interested more!. (It's related to chaos and we discussed it in the same class)!. I mainly took that class because of the intro to chaos theory and I don't really remember much else!. Again, though, it's not really understandible without a good background in the math!. That was by far the hardest math class I ever took!. I barely got through it!. I don't know any good books for that, sorry!.Www@QuestionHome@Com