When Lurking, can you "charge" now?

[nurglitch]

I think what you have to understand is that it's not about convincing me. Nobody can be convinced of anything they don't want to be convinced of themselves. It's a waste of time trying to convince coredump of anything because he honestly believes he is right, and that people that disagree with him need to be convinced otherwise.

Yet working out disagreements is valuable for its own sake, as well as getting to the truth of the matter. The trick, so it seems, is to work together Sometimes that's as simple as finding a page number, and other times differing opinions are so sophisticated and complex they require re-establishing common assumptions about math, logic, and grammar.

So rather than trying to convince coredump that he's somehow wrong about something, I prefer to use the opportunity to demonstrate arguments for and against a particular position, and let the audience decide for themselves (or at least be aware of the disagreement so it can be handled without interrupting a game).

[acmemyst]

coredump said:

But if you want to play formal logic... lets do that.
Under Onslaught
No Assault unless Fleet
so
If No Fleet then No Assault
so
If Not P then Not Q
P
Therefore.... nothing....

This is correct. In an attempt to resolve the ambiguity a bit further, here's how I worked it out:

Let X denote a unit, and <name>(X) be its abilities/effects:

Onslaught(X) -> ((not fleet(X)) -> (not assault(X)))
Assume Onslaught(X):
(not fleet(X)) -> (not assault(X))
Rewrite:
(not not fleet(X)) OR (not assault(X))
Simplify:
fleet(X) OR (not assault(X))
Assume fleet(X):
TRUE OR (not assault(X))

At which point, the truth value of assault(X) is undecided by this proposition. Thus, the Onslaught rule does not affect whether a unit can assault, and thus, play by BGB (no assault).

Nurglitch's latter point is an invalid construction of "unless", in which he translates to "IF fleet THEN assault", which is invalid. Here's a formal logic definition of the concept after a quick Google search:

"the form “Unless P, Q” means that if P is absent (or false), Q is surely present (or true), though it does not really tell us whether in the presence of P, Q is necessarily or just possibly absent. Thus, this form implies “if not P, then Q” – and “if P, not-then Q”, though possibly (in some cases) also “if P, then not Q”."

Thus, again, Onslaught+Fleet does not unambiguously determine the truth value of Assault, and thus, play by BGB (no assault).

Source: www.thelogician.net/5b_ruminate/5b_chapter_04.htm

[nurglitch]

Jul 12, 2012 14:25:27 GMT acmemyst said:

Onslaught(X) ->; ((not fleet(X)) ->; (not assault(X)))

That's the nice thing about logic, it helps to clarify things. You've mucked up converting the sentence to pseudo-code. Which is sort of the argument to begin with, and the hard part, so to speak, so let's talk about the logic stated by the sentence, and particular the structure of "unless".

What is "unless"?

Dictionary.com
un·less   /ʌnˈlɛs, ən-/ Show Spelled[uhn-les, uhn-] Show IPA
conjunction
1. except under the circumstances that: I'll be there at nine, unless the train is late.
preposition
2. except; but; save: Nothing will come of it, unless disaster.

Merriam-Webster
un·less conjunction \ən-ˈles, ˈən-ˌ\
Definition of UNLESS
1: except on the condition that : under any other circumstance than
2: without the accompanying circumstance or condition that : but that : but

The term 'Unless' indicates a conjunction, and we can replace "unless" in "A unit under the effect of Onslaught may not assault unless it also has the Fleet ability" with:

1. A unit under the effect of Onslaught may not assault except on the condition that it also has the Fleet ability.

2. A unit under the effect of Onslaught may not assault under any other circumstance than it also has the Fleet ability.

3. A unit under the effect of Onslaught may not assault except under the circumstances that it also has the Fleet ability.

So 'unless' indicates that there is a conjunction of Onslaught and Fleet, specifically the effect and the rule, respectively, particularly in combination with the words "may not."

So where does the material conditional come from, where these rules are the conditions, and the option to charge is the effect? It's pretty straight-forward, from the use of the word "may not".

Dictionary.com
may1    /meɪ/ Show Spelled[mey] Show IPA
auxiliary verb, present singular 1st person may, 2nd may or ( Archaic ) may·est or mayst, 3rd may; present plural may; past might.
1. (used to express possibility): It may rain.
2. (used to express opportunity or permission): You may enter.
3. (used to express contingency, especially in clauses indicating condition, concession, purpose, result, etc.): I may be wrong but I think you would be wise to go. Times may change but human nature stays the same.
4. (used to express wish or prayer): May you live to an old age.
5. Archaic . (used to express ability or power.

Written as "may not", the sentence prohibits units without the conditions, the effects of Onslaught and possession of the Fleet rule, from charging. Which brings us to how such a prohibition against units without Onslaught and Fleet means a permssion for units with Onslaught and Fleet. The easy part, if you will.

We could write it thusly, where O is the effect of Onslaught, F is the Fleet rule, and A is the charge. I'll also introduce the logical operators NOT as '~', OR as 'v', AND as '^', IF...THEN as '->'

1. ((O ^ F) -> C) assumption
2. O ^ F assumption
3. ~(O ^ F) v C material implication (1)
4. C disjunctive syllogism (2, 3)

CORRECTED: So basically it's that "may not...unless" means the same thing as 'may if', rather than "may not".

As a note, I'll mention the 1st assumption is the sentence in Onslaught prohibiting charging unless the unit also has Fleet as well as Onslaught, and the 2nd assumption is that a unit has Onslaught manifested upon it, and the Fleet rule.

A person with an understanding of symbolic logic may not buy this argument unless also they have the Extract Logical Content from Natural Language ability.

EDIT: Corrected for an embarrasing lack of consistency.

[acmemyst]

Jul 12, 2012 16:01:42 GMT nurglitch said:

We could write it thusly, where O is the effect of Onslaught, F is the Fleet rule, and A is the charge. I'll also introduce the logical operators NOT as '~', OR as 'v', AND as '^', IF...THEN as '->'

1. ~((O ^ F) -> C) assumption
2. O ^ F assumption
3. ~((O ^ F) v ~C) material implication (1)
4. ~(O ^ F) v ~~C distribution (3)
5. ~(O ^ F) v C double negation (4)
6. C disjunctive syllogism (2, 5)

This derivation seems incorrect no?
Step 3 should be:
3. ~(~(O ^ F) v C) (Rewrite 1)

Also, Step 4 looks like a misconstrued application of De Morgan, i.e., it should look like
4. ~~(O ^ F) ^ ~C (DeMorgan)

So that we get
5. (O ^ F) ^ ~C (double negation)
6. TRUE ^ ~C (2, 5)

Which would mean that, under your translation, the rule explicitly states that you cannot charge..

[coredump]

Under the effects of Onslaught:
Not Charge unless Fleet. (This means "you may not charge"... unless you have fleet. So what does it mean if you do have fleet?? We don't know yet, it hasn't said. It has only said what happens if you don't have fleet.)

But, 'Not Charge unless Fleet' does mean that 'you can't charge, if you don't have fleet'...right?

Not Charge if Not Fleet

So,

If Not Fleet, then Not Charge

Which is the correct way to codify this statement.

[coredump]

Nurglitch, the fact that you are including O means you are not codifying this correctly. The entire situation is based on "IF" you cast Onslaught, so it is all prefaced by
If O, then..... the new conditional

If O, then (If not fleet, then not charge).

The way you are codifying it requires that you cast onslaught in order to charge. Your methodology is predicated on these being the only rules in the game.

[nurglitch]

acmemyst:

Yup, I definitely got the translation wrong. The 1st assumption reads: "It is not the case that the combination of Onslaught and Fleet allows charges."

Which is not semantically equivalent the sentence in question. Basically I forgot that it's "may not...unless", or in other words: 'may if'. Which is embarrassing considering how much I wrote to make that point. It's like "Hey kids, don't smoke." *blows smoke ring*

Mind you, whether 'may not...unless' and 'may if' mean the same things seems to be the point of contention.

Corrected Version:
1. ((O ^ F) -> C) assumption
2. O ^ F assumption
3. ~(O ^ F) v C material implication (1)
4. C disjunctive syllogism (2, 3)

[nurglitch]

coredump:

Glad to have you back. But wrong as usual, which is unfortunate because acmemyst has me on the right track, it seems. Including Onslaught as a condition is necessary because it is the combination of the effect of Onslaught and Fleet that allows a unit to charge after running. That's the whole "may not...unless" bit.

I certainly made a mistake, which was translating "may not...unless" as both a conjunction of Onslaught and Fleet, and a negative conditional. Turns out the proper translation is a conjunction of antecedents to a conditional. Mea culpa. So:

A unit under the effect of Onslaught may not charge. Unless it also has the Fleet rule.

In which case, it may charge.

[acmemyst]

Jul 12, 2012 16:56:52 GMT nurglitch said:

But wrong as usual, which is unfortunate because acmemyst has me on the right track, it seems.

Not quite.
I pointed out the flaw in your formal derivation, but didn't comment on the validness of the translation. To infer from that my agreement with the latter is, ironically, quite like the problem we are discussing.

I second Coredump that the correct translation is
O -> (~F -> ~C)

From which (TRUE v ~C) can be derived, as by my first post.

Your new derivation is correct, but I cannot agree that
(O ^ F) -> C

is the correct way to translate. Again, see my earlier referenced source on the codification of "unless" in terms of formal logic.

[nurglitch]

acmemyst:

Yes, quite. The flaw in my formal derivation stemmed from the invalidity of the translation. Basically garbage in, garbage out. No inference regarding your agreement was intended.

So it's back to discussing how one might codify "unless" in the context of "may not...unless".

[coredump]

Nurglitch, you keep saying things like "you're wrong", but never show why? You tend to ignore what you don't want to deal with.

I 'came back' to give you the benefit of the doubt, and even more fully explained what I was saying, and why. Unfortunately, you again respond with 'you're wrong' and keep plowing ahead.

How am I wrong? Which step is incorrect? What statement is false?
Why do you insist that a car without tires can go 200mph??

[nurglitch]

So, following the expert, Avi Sion, there are three possible interpretations of "may not...unless" in the Onslaught sentence:

1. ~(A -> B)
2. ~A -> B
3. A -> ~B

Avi says: "Thus, the form “Unless P, Q” means that if P is absent (or false), Q is surely present (or true), though it does not really tell us whether in the presence of P, Q is necessarily or just possibly absent. Thus, this form implies “if not P, then Q” – and “if P, not-then Q”, though possibly (in some cases) also “if P, then not Q”."

From which we can noodle:

1. If a unit is Fleet, then it may not charge.
2. If a unit is not Fleet, then it may not charge.
3. If a unit is Fleet, then it may not-charge.

Of these, #2 seems to be the favoured interpretation of coredump and yourself. Not much room for unless, unless we say that it is a consequent of Onslaught. As you say:

O -> (~F -> ~C)

So, it seems that you believe that:

'A unit under the effects of Onslaught may, if not Fleet, may not charge.'

Is that correct?

[nurglitch]

coredump:

Why, your exegesis, premises, and conclusion are wrong. And that's why we're having this discussion. Not because you're wrong, but because we're trying to work out what is right, and in doing so I'm trying to show you what you're getting wrong.

I mean, if you noticed how I was showing you that you were wrong, we wouldn't be having this conversation.

[acmemyst]

The full translation, using that definition of "unless", should probably be:

1. O -> ( (~F -> ~C) ^ (F -> (C v ~C)) ) (Assumption)
2. O (Assumption)
3. F (Assumption)
4. ( (~F -> ~C) ^ (F -> (C v ~C)) ) (MP, 2)
5. ( (~~F v ~C) ^ (F -> (C v ~C)) ) (rewrite first implication)
6. ( (F v ~C) ^ (F -> (C v ~C)) ) (double negation)
7. ( (TRUE v ~C) ^ (F -> (C v ~C))) (3)
8. ( (TRUE v ~C) ^ (C v ~C) ) (MP, 3)
9. (TRUE) ^ (C v ~C) (drop second or-clause)
10. (C v ~C)

Again, the rule simply does not itself explicate whether a unit with Onslaught and Fleet can charge or not.

[nurglitch]

Under that translation. I contest that your translation is valid. Please explain how you get:

O -> ( (~F -> ~C) ^ (F -> (C v ~C))

"A unit under the effect of Onslaught may not assault unless it also has the Fleet ability."

Because what you have says:

"A unit under the effect of Onslaught may not assault when it does not have the Fleet ability, and may either assault or not assault if it has the Fleet ability."

Because the meaning of the sentence is this:

1. A unit under the effect of Onslaught may not assault.
2. Unless it has the Fleet ability.
3. Therefore, a unit with Onslaught and Fleet may assault.