Logic and Rules: Part 2

So I find myself putting off my readings for my USSR history class. Then I remember that I’ve left readers in the dust with my logic articles. Well, here we take off once more! If you remember, last time I went over the basic logic gates that construct arguments, as well as the basic methods by which to appraise those arguments. In hindsight, I forgot some definitions:

Valid- This means that it is impossible that we have all premises true and the conclusion is false.

Invalid- It is possible to have all premises true and the conclusion false.

Sound- An argument is valid and has every premise true. Please note that these are incredibly hard to find outside of mundane statements.

You probably need to refresh your memory, so here's the link to my last bout of insanity:

Moving on, we’ll start with the S-rules, which deal with basic inferring from the logic gates.

AND S-Rule:

If it is the case that you have two items linked by an AND symbol, then you can infer each part.

Banana and chocolate

(B*C)

B

#C

Please note, however, that if it is negated ~(B*C), then you cannot infer a thing.

OR S-rule:

If you have the negation of an OR statement, then you can infer the opposite of both.

Not-either banana or chocolate

~(BvC)

~B

#~C

In the case of a negation of the negation of an OR statement, you cannot infer anything.

IF-THEN S-rules:

If you have the negation of an IF-THEN statement, then you can infer the first part and deny the second. Please note the original definition of an IF-THEN “it is not the case that we have A true and B false.” This negation means that we do have A true and B false.

Not if banana, then chocolate

~(B>C)

B

#~C

As has been usual so far, if there is a positive IF-THEN, it is the case that we cannot infer anything.

These should be rather obvious in their usage, and you may find yourself using these rules to infer things about what another person is saying. Now, let us move on to the I-Rules, which are just referred to as the Inference rules, and while those last rules were technically inferring, they’re just called the Simplification rules.

AND I-rule:

If we have the negation of an AND gate, we can affirm one and deny the other.

It is NOT the case that we have A true AND B true

~(A*B)

A

#~B

Remember, if there is a denial of the first, we cannot infer anything.

OR I-rule:

If we have an OR statement, and deny one of the two premises, then we can affirm the other.

Chainsaw or shotgun

(CvS)

~S

#C

Remember that you can only infer when you have a denial of one of them. If one is affirmed, the other can be true or false…we don’t know!

IF-THEN I-rule:

So, we’re back to this complicated prick. This gate actually has two I-rules, so ‘ere we go!

If we have an IF-THEN statement, and affirm the first premise, then we can affirm the second.

If chainsaw then shotgun

(C>S)

C

#S

If we have an IF-THEN statement, and deny the second, then we can deny the first.

If chainsaw then shotgun

(C>S)

~S

#~C

So yeah, this one proves to still be quite wretched as a logic gate.

Now, I can certainly understand that all this is rather dry, so I’m going to shoot something out to the community: Give me a rules situation that you are having trouble with, and I will apply these principles to it to find meaning, and it will be in the next segment of this…not necessarily frequent series regarding Mr. Spock.

As always, shoot me an email at dominobi@gmail.com

I will be waiting to see what you guys have questions on!

Regards, Ishamael

Criteria of a Deep Thought.

Everyone knows Bell of Lost Souls. As a website, it is quite possibly the most public, active, and well-known combination of people that enjoy miniature wargaming, and it updates every single day. That's a bitch. It could very well be considered the "face" of 40k online. In this segment, I want to comment on their headlines with the title of "Deep Thought", beginning with the article this day on the Chaos Space Marines codex.

As stated in the title, what should be the criteria of these Deep Thought articles? This CSM one is but one example, and doesn't count for much, but its lack of length does not warrant such a designation. This normative statement presupposes that for a "deep thought" to occur, a worthwhile analysis must occur, in which benefits and disadvantages are adequately explored to paint a more full picture of how a unit is; not just "It's good!" without due recourse to disadvantages with the unit. As such, I will give my own example of what a "Deep Thought" should include, the example of which will be my own take on the units concerned in the aforementioned article.

Basic Chaos Space Marines- Has the ubiquitous statline of a marine, and comes with a better selection of basic wargear than their equivalents in the generic Marine codex, as well as a slightly-higher leadership score. At ten models, two special weapons can be bought, or one special and one heavy. As most know, they have the options for Icons, which give a boost to a particular statistic as they dedicate themselves to a God, or to the pantheon of Chaos. In comparison to their brothers in the Marine codex, their lack of a multi-melta for their heavy weapon hurts them as a choice for Troops, and their one-higher leadership is deceptive; And They Shall Know No Rules is by far greater than this, as even if they run away they may still regroup. They can assault with some hope of success, but if they lose combat against any dedicated cqc unit, odds are they will be running away, even with the Icon of Glory. Compared to the cult troops, which already have that basic stat increase, as well as different options, purchasing any Icon is questionable.

"perhaps the most solid troops choice in the game"- Someone has not looked at that Space Wolves codex, otherwise he might have noted the Grey Hunters being a wonderful combination of CSM and Space Marine rules. For a cheap "not good, not bad" unit for your Troops, one could go with a CSM squad, yet the endurance, cqc ability, and Fearless options available by the Cults in their different specializations gives one the option to have a better unit for a specific job.

For a deep thought to occur, the unit must also be compared to the other units available for the same slot in other armies. This comparison allows one to consider which choice will be the best overall for a balanced army.

I would hope my point is clear. I could go on to give my take on the other "best" units available in the codex, of which I only agree with two (Lesser Daemons and Oblits). Think on that. I, the resident Khorne player, do not think that they are better than Plague Marines. MSU Plague Marines have the special weapons of a full CSM squad, endurance, some cqc ability, and are quite cheap. Compare the 185 for 5 Plaguies, 2 meltaguns, and an Extra Armor Rhino, to a 270 point unit of CSM to have the same stat line, transport, and special weapons, as well as that Icon.

I am a product of being a philosophy major in college, and applying it to 40k is helping me to consider the full picture of a unit. As a quick example, the article in question would not be worth the small time investment to read it, as it does not consider any opposing issues regarding the units. Struggle in reviewing is key here.

As usual, if you have any questions or requests, shoot me an email at dominobi@gmail.com

Post Script: Logic and Rules: Part 2 is in the works! I'll be taking a step backwards to speak on validity, invalidity, and incoherency (being over 2" away lol), and a step forwards by going over the Simplification and Inference rules of Logic. To see the use of logos with the rules, see this article on the Blood Angels. If you don't read it already, add www.yesthetruthhurts.com to your normal reading list!

Logic and Rules: Part 1

So, more and more I see people putting “I feel that…” into conversations regarding the rules of this game. An example of which is the INAT FAQ, where the organizers change and make up rules to suit themselves. If you don’t believe me, look at their Tyranid section, then how they go around to define weapons as “hull-mounted” when the codex does not, the difference being a huge change in line of sight of the weapon. So I am here today to lay some ground rules to go by when assessing whether or not something is supported by the rules. To begin this multi-segmented article, I will show the four basic gates of logic, as well as their relevant truth tables. Ambiguity cannot be tolerated, for logic necessitates absolutes; all terms that people consider ambiguous will be defined for the purposes of examples.

For those unfamiliar with binary, 1 means true, 0 means false.

Generally, A and B will be used for examples.

AND- defined as * symbol

00 = 0

01 = 0

10 = 0

11 = 1

Essentially, this gate boils down to that both sides of the symbol must be true in order for the sentence as a whole to be true. For it to be true I had a burger and a drink (A*B), I really do have to have a burger and a drink, for it is false otherwise.

OR- defined as “v” for our purposes

00 = 0

01 = 1

10 = 1

11 = 1

An OR gate claims that at least one of the pieces are true. I have either a quarter or lint in my pocket (AvB). Turns out that I had lint, but it is still true.

IF- THEN - defined as >, or Wakka Wakka Man

00 = 1

01 = 1

10 = 0

11 = 1

This is the trickiest of them thus far, for it states that we do not have A true and B false. If I eat a burger, then I will get fat (A>B).

IF AND ONLY IF- Well, for simplicity’s sake, we’ll just use +

00 = 1

01 = 0

10 = 0

11 = 1

This gate states that it is true only in the case that both parts are either both true or false. I am awesome if and only if I can prove it. (A + B)

For the purposes of “not”, ~ will be our requisite symbol.

For the conclusion I will use “#” as the symbol

The import:

OK, now that I’ve done all this, what the hell is the use?

Unlocking language, in a sense.

Let’s look at Pedro Kantor’s Chapter Tactics rule to start:

If you include Pedro Kantor, then your guys exchange Combat Tactics for Stubborn and your Sternguard gain the Hold the Line! Special rule.

So, how does this reduce to logic?

If Pedro, then Stubborn and Hold the Line! (P > S * H)

Yet, players have stated that you can combine Vulkan and Pedro to form the Wonder Twins!

If Vulkan, then Awesome (not going to write all the rules) (V > A)

Continuing on, the rules state that if you have more than one character, then you must choose which of their Chapter Tactics will be used. This reduced in to logic in this fashion: It is not the case that if you take Pedro and Vulkan that you gain both Chapter Tactics.

~( P * V)

Say I take Pedro and Vulkan, and wish to cheat by saying that I can use the TL-awesome rule and Hold the Line! Can an argument be made for this:

If I take Pedro and Vulkan, then I can have both TL-awesome, and Hold the Line

I have Pedro

I have Vulkan

Therefore, I gain TL-awesome and HtL

(P * V > A * H)

P

V

# A * H

Why, this only shows that any twit can get away by not reading all the rules! Let’s look at the real way in which this works:

(P > S * H)

(V > A)

~(P * V)

At this point, we must affirm one, or deny the other to get any result at all!

I want Vulkan!

V

# A

The key is that it is true that I took Vulkan, and therefore it is true that I gain TL-awesome

Now, there were some things I did in here that I will be covering next time in my quest for the Holy Grail of rules lawyering, and these are called the Simplification and Inference rules!

If there are any questions, send me an email at dominobi@gmail.com