Blogical Symbols

geomodal

Here are some symbols I’ll be using from time to time:

L = “it’s necessary that”

M = “it’s possible that”

(x) = “all x’s are such that”

(3x) = “there exists an x such that”

& = “and”

v = “or”

-> = “implies that”

~ = “it is not the case that”

<-> = “if and only if”

Capital letters stand for whole sentences. For instance,

R = “it is raining”

C = “there are clouds in the sky”

so that

R -> C

says “It is raining implies that there are clouds in the sky”.

pleven

We need logic to understand that?

geomodal

It’s just an example. Duh.

I’ll use lowercase letters to stand for objects or people, and stick them to the right of uppercase letters to signify relationships between things. When I do that, I’m not using uppercase letters for whole sentences, but rather for words or phrases that express relationships between things. For example, if

K = “kisses”

b = “Sarah”

and

s = “Jodie”

then Lbs says that “Sarah kisses Jodie”.

pleven

You like that example, don’t you, Geo?

geomodal

I have no idea what you’re talking about, Pleven.

I’ll express properties of things in a similar way. For example, if

P = “piece of crap”

b = “Brad’s car”

then Pb says “Brad’s car is a piece of crap”.

It should always be clear whether an uppercase letter is a whole sentence or just a relationship/property phrase, because in the latter case the uppercase letter will always be followed by one or more lowercase letters. I am also using the particular letters L and M to mean “it’s necessary that” and “it’s possible that”. Usually a little drawing of a box is used instead of L and a little drawing of a diamond instead of M, but it’d be damned hard to put a little picture of a box or a diamond up every time I wanted to use it!! So I’m going to use L and M, and trust context to disambiguate.

I can’t believe you’re going to use modal logic. Pfft! How pedestrian. Everyone knows that modality contributes nothing to logical content.

pleven

Кой е това? And besides, who asked you?

Майка ти. Вчера в леглото.

pleven

Hey! You know what? Screw you buddy!!


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