Question for Frank

[da_chicken]

1078439385[/unixtime]]Your construct was based "logically" on using Contraposition on sets of directives - which is painfully invalid. Consider, Contraposition gives us things such as:

If you roll a 20 on your attack roll, you hit your opponent. Therefore: If you miss your opponent, you did not roll a 20 on your attack roll.

It just doesn't work. The fact that this thread has featured various so-called philosophy majors saying that it did, simply proves that the power of ignorance is all pervasive or something.

Er, Frank, that statement is true. If I missed my opponent, then I didn't roll a 20, did I? The statement "If you roll a 20 on your attack roll, you hit your opponent." is true if you roll a 19. Similarly, "If you miss your opponent, you did not roll a 20 on your attack roll." is also true. Because if I had rolled a 20, I would have hit.

"But I can roll a 19 and hit!"

So what? Neither premise deals with the instance of rolling a 19. The premise is predicated on rolling a 20. Those premises are not in any way saying "If you do not roll a 20 on your attack roll, you cannot hit your opponent." That would be the fallacy of leaping to conclusions. Or hasty generalization. One of the two.

Contrapositive is:
P -> Q becomes ~Q -> ~P
Not:
P -> Q becomes ~P -> ~Q

The former two statements are logically equivalent. Thet latter two are not.

Code: Select all

[br]Contrapositive Truth Table[br]--------------------------[br]P  Q   P->Q   ~Q->~P  ~P->~Q[br]T  T    T       T       T[br]T  F    F       F       T[br]F  F    T       T       T[br]F  T    T       T       F[br]

Column 4 is the contrapositive of 3. Column 5 is the negation of each side of the condititional in 3.

In order for the statement "If you roll a 20 on your attack roll, you hit your opponent." to be false, you must "roll a 20" AND "not hit". In order fot the stament "If you miss your opponent, you did not roll a 20 on your attack roll." to be false, you must "not hit" AND "roll a 20".

If you want to handle the case of rolling a 19, then P becomes false and both statements are always true.

The point is that logic doesn't prove exclusivity. The "truth" of a logical premise is constrained by the system it pertains to.

Edit: Added clarifications.

[da_chicken]

1078364066[/unixtime]]And looking back at the argument before, I have this to add:

Rules are fundamentally different form bivalent sentential logic. In Sentential Logic we assume that all of the statements are true and then work from there.

In a system of rules, we have a series of rules which are essentially implications which we apply to a series of given Ps and ~Ps as applies to the certain situation. Then, since it is entirely possible that one or more of these rules will be conflictory based on our actual set of circumstances, we have a priority system.

What you can't do is infer what other situations are based on the rules alone. In this circumstance,

P ) Q
~R ) ~Q
.: P ) R

does not follow at all.

In whose universe?

Premises:
1. P -> Q
2. ~R -> ~Q

Find: Relationship between P and R.

3. ~Q -> ~P (1, Conditional Contrapositive)
4. ~R -> ~P (2, 3, Transitive Conditional)
5. P -> R (4, Conditional Contrapositive)

If (5) is not the case, then P -> Q is actually false OR ~R -> ~Q is actually false. Which is to say P is actually false OR ~R is actually false.

In other words, your premises are flawed in spite of your sound logic. Doesn't mean your argument isn't still sound.

If you are a Monk, you gain your Wisdom Modifier as a bonus to AC.

does not also mean

If you do not gain your Wisdom Modifier as a bonus to AC, you are not a Monk.

Of course it doesn't. Your premises are flawed because you've ignored part of the rules. Both sentences are false. Using just the core rules (since more material simply complicates the matter), the correct statements are (in pseudocode):

Code: Select all

IF[br]{[br]  Class == Monk AND[br]  Armor == None AND[br]  Shield == None AND[br]  Encumbrence == None AND[br]  Character != (Immobilized OR helpless)[br]}[br]THEN[br]{[br]  Wisdom bonus applies to AC[br]}

The contrapositive of that is:

Code: Select all

IF[br]{[br]  Wisdom bonus does not apply to AC[br]}[br]THEN[br]{[br]  Class != Monk OR[br]  Armor != None OR[br]  Shield != None OR[br]  Encumbrence != None OR[br]  Character == (Immobilized OR helpless)[br]}

There is no case where one statement is true and the other is false.

Note that in the contrapositive, the negation turned all the ANDs into ORs. That's why your statement appears correct upon mere casual inspection.

[fbmf]

[The Great Fence Builder Speaks]
Please refrain from personal attacks and "sniping".
[/The Great Fence Builder Speaks]

Game On,
fbmf

[Username17]

You are demonstrating that you do not understand some logical concepts.

No. I understand the logical concepts obviously much better than you do, because I know when they do and do not apply, and you clearly don't. There are lots of rules of Logic. There's Sentential Logic, there's Fuzzy Logic, there's Consequential Logic, there's C++ Logic, etc. Each applies to a different sphere. Each breaks down when applied to different things.

Sentential Logic does not apply to directives, exclamations, or questions. Period. Not ever, not even once. It's as invalid as trying to parse your Cheerios box with Pascal.

Those two sentences say the exact same thing.

No they don't. One is a directive, and the other is a conclusion about the results of applying that directive. The first doesn't have a Truth value because it is a directive. The second has a truth value that will be contingently True or False depending upon what other directives you are and are not following.

If you apply the rules of Sentential Logic to any system of potentially conflictory directives, you run into big probelms. Specifically, you find yourself in the position where you can logically prove anything at all.

And it goes like this:

Consider the result where I have the rule "If you are a Monk, you gain your Wisdom Modifier to AC", and I also have the rule "A Monk wearing armor does not gain a Wisdom Modifier to AC." And I'm playing a Monk who happens to be wearing armor. I can logically deduce that I can summon Tiamat as a free action - provided that I continue to use sentential logic on this problem despite the fact that the rule statements are directives.

The symbolization looks like this:
M = "I am a Monk"
A = "I am wearing armor"
W = "I get Wisdom bonus to AC"
T = "I can summon Tiamat as a free action"

The premises are:

1. M . "I am a Monk"
2. M * A . "I am a Monk wearing armor."
3. M => W "If you are a Monk, you gain your Wisdom Modifier to AC"
4. (M * A) => ~W "A Monk wearing armor does not gain a Wisdom Modifier to AC."
---
5. W . 1,3 MP
6. ~W . 2,4 MP
7. W v T . 5 Addition
.: T . 6,7 MT

You see, if you have any true statement, then "this true thing or any other thing no matter how absurd" is still True. If you have any true statement of one thing or another thing, and you know that one of them is false, the other must be True by definition. So if there's any contradiction in Sentential Logic, I can summon Tiamat as a Free Action.

In any system of rules, there are contradictions all over the place. For one thing, when there are complex concepts and things which happen and do not happen contingently, this is expressed in multiple statements each of which is a separate directive (not to be confused with an implicatory sentence). This does not mean that you get to summon Tiamat as a free action, this means that you have to keep track of the priority given to each directive in the set to keep your head from exploding like a James T Kirk robot.

Use the correct form of Logic for the purpose. Use of the incorrect form of Logic will let people summon Tiamat as a free action or otherwise get you meaningless and trivial results. Do not use 10 shade fuzzy logic for explicating attack rolls - you either hit or don't hit. Do not use sentential logic on questions, directives, or exclamations, they don't have Truth values implicitly and will lead to contradictions if for some reason truth values are arbitrarily assigned to them.

-Username17

[Username17]

Of course it doesn't. Your premises are flawed because you've ignored part of the rules. Both sentences are false. Using just the core rules (since more material simply complicates the matter), the correct statements are (in pseudocode):

That's quite a chicken/egg problem you've just introduced.

It is, of course, perfectly possible to convert all of the results of a set of directives into a single (often extremely complex) statement which can then follow ruls of sentential logic.

What's the problem? The problem is that you can only do so from the results, not from the individual statements in the consequential logic set you began with.

Which is to say, you first have to figure out the priority assigned to every single directive, and then apply all of the possible cases and then map a unity statement of sentential logic which puts a conjunction of all possible values of inputs which would lead the pachenko machine of directives to give an output against that output.

So in order to put the Dex Bonus to AC into sentential logic:

* First we have to find all the variables which can lead to directives regarding Dex bonus to AC (concealment, uncanny dodge, blindfighting, rough terrain, balance ranks, climbing, climb ranks, running, run feat, flat footed, feinting, quicker than the eye, blink, etc.)

* Then we have to prioritize all of it as per the original consequential logic it was written in (for example, concealment beats the rule that you get your dex bonus; blindfighting beats concealment when you are being attacked in melee).

* Then we have to run all possible scenarios which can lead to the Dex bonus being available (or unavailable, it's not important).

* Finally, we set up an enormous equation of sentential logic in which every single set of circumstances wherein the directives would lead us to have our Dex bonus to AC are conjoined together and made equivalent to having Dex bonus to AC.

---

Then and only then we have a statement in Sentential Logic. It's going to now be available for use with the rules of sentential logic (for example, an equivalency can be broken into two implications, which can then be contraposed).

But what have we really gained? Not a whole hell of a lot. In order to get to that point we had to prioritize all of the directives successfully and run them all out in every possible circumstance. So before we can use Sentential Logic we already have to not need it any more.

Woot.

-Username17

[Crissa]

Frank, I think the construct you wrote would be easier to parse if you did not include the Tiamat statement unless you have a results matrix stating the actual results.

-Crissa

PS: I certainly think the logical discussion wasn't going anywhere, but another thread for them to hash it out in perpetuity seemed harmess enough. Like the game in the basement of Weird Pete's: Let them play where it won't trip the rest of us over. ^-^

[Mole_2]

The term elemental has multiple meanings in 3E DND.

a) It is a creature (see monster manual under elemental,fire etc).

b) It is also a type e.g. thoqqua. Included within the type is the elemental template.


The wording of Wildshape does not unambiguously state wether it is referring to the type or the creature (although the brackets containing reference to the elements are circumstancial evidence that the designers were thinking of a) ). No logic will get to the correct answer based on the wording.


Mod edit: Rest of post deleted. Any old feud or argument on another board should stay on that board,per the rules thread.

Any old feud you have with another poster should be resolved via PM, e-mail, or pretty much any other method except my message board.

[Username17]

Mole2:

To put the record straight, that is not what I did, and that isn't what they did.

The game designers said that the literal wordings of the Sorcerers and metamagic description prevented their use of Quicken. As written that was not true. I pointed out the logical error in their description and they stuck to their guns. And then they modified the 3.5 PHB to fit what I said it would have to say if they wanted Sorcerers to be unable to use Quickened Spells.

I was right. They pretended that no such error had been made right up until they corrected it. Part of the whole "I'm the Pope, STFU!" syndrome that Skip Williams seems to always be struggling with.

-Username17

[User3]

Post edited by Administrator

[The Great Fence Builder Speaks]

Lee, I appreciate your concern, but there is a Report to Mod function for a reason. If it doesn't work for Unregistered Guests,email me at the address in my profile.

...and your "give him his meds" comment constitues a personal attack that will not be tolerated.

[/The Great Fence Builder Speaks]

[Oberoni]

I'll go on record as saying that "Sorcerers can't quicken" is ghetto.

Not ghetto fabulous. Just ghetto.

[Mole_2]

1078749097[/unixtime]]

Mod edit: Rest of post deleted. Any old feud or argument on another board should stay on that board,per the rules thread.

Any old feud you have with another poster should be resolved via PM, e-mail, or pretty much any other method except my message board.

Fair enough, but I am curious why you also deleted text that was specifically referring to this debate and made no mention of anything outside this thread.

Just for the record I have no feud with Frank.

Mod edit: Rest of post deleted as potentially inflammatory. Check your PM for my explanation.