Modal logic. Let’s talk about it. Anyone here have any real experience w/ this stuff? I humbly ask that you exhaustivley explain it to me. I’m not trying to debate, just trying to categorize what I do know about this properly, and fill in the gaps in my understanding.
Relate it any way you can.
Here’s a few resources.
en.wikipedia.org/wiki/Modal_logic
plato.stanford.edu/entries/logic-modal/
This thread is probably a good opportunity for anyone else new to modal logic (or logic entirely) to exchange their knowledge. Remember, learning is not like a debate. Unlike argument, learning is more beneficial to you, the less you know and the more mistakes you make.
I’m fairly new to modal logic, but I think the best place to start is for us to all share our understanding of the following terms in propositional logic. Unlike math, the symbols in propositional logic are less important than the meaning behind them. As long as everyone agrees what symbol means what.
conditional - “X causes y.” commonly an arrow from x to y.
negation - “NOT x” commonly a squiggly negative sign “~” some might have an easier time remembering by just putting a circle with a line across
Conjunct - “X & Y” - just remember, don’t use “+” it’s too confusing once involving math.
Dysjunct - “X OR Y” - Some like “/” to symbolize a fork in the road.
I’ve left out a lot of things (eg: biconditional, proof and theorems, existential and universal symbols - quantifier logic). It’s better to have those core symbols thoroughly before getting allover the place.
Another important understanding is how brackets work. They’re just like in common language (I use a bracket here to say something on its own that’s part of a greater sentence). However: It’s important to always use them wherever you can to subdivide everything you say properly.
Someone new to this please tell me how I can use propositional logic to tell people that the cat can chase either white mouse or black mouse if it rouses. Here’s the letters and their meaning.
R - “cat rouses”
W - “cat chase white mouse”
B - “cat chase Black mouse”
Gaia -
R > W v B
This is what would be used in propositional symbolic logic. Any statement can be rendered this way, but many are better served elsewise.
Thank, faust. I was actually offering a test for anyone looking to learn it from a fresh perpective. I know you’re thorough in this discipline. Textbooks tell me the more proper way is
R > (W / B)
But it doesn’t matter. If you want to post a tough english statement for someone to translate, faust, I’d like to try it.
Oops. Your version is correct, of course. My bad. Was in a rush. The way I wrote it is ambiguous, which is, of course, the reason for the parenths.
I dunno. Mebbe I’ll give it some thought.
I don’t know about this.
What do the parentheses do? I thought I got it without them.
stranger - You could easily get it without the parens. But you could also read it as (R > W) v B. You see, you already knew where the disjunction was. The way I just now wrote it, it says "If the cat rouses, it chases the white mouse OR the cat chases the black mouse (without rousing). It’s a matter of the distribution of the rousing of the cat. Or, in other words, a matter of just what is conditional.
Ah, ha. Thank again. I am sooo not bearded.
One more question. Is there a point to it?
Actually 2 more. Will you throw down a sentence to try and work using the symbols already put forth? (If the answer to the first question is yes, of course.)
Is there a point to what? It’s just a premise in an as yet nonexistent argument. In other words, it’s a (compound) statement, put into symbols. Doing this makes it ever so much easier to perform operations on such statements.
The specific symbols don’t really matter, except for some common conventions. The capital letters are chosen because they are easy to remember - R for Rouse, etc. If gaia had said “Cat gets up”, we might choose G (for “gets”), or we might choose C (for cat).
If my Father goes to bed soon, I’ll either Smoke some more dope or I’ll download some Porn.
F > (S v P).
Isn’t symbolic logic fun?
=D> Excellent.
If you smoke dope, you won’t download porn but you will either sleep or eat a lot.
S > (~P) (Sv E) ?
You need a conjuctive symbol between the parens - I learned a “.”, except that it was higher. I don’t know what is usually used - oh, gaia is using “&”. So, S > (~P) & (S v E).
You don’t strictly need the “~” here, unless other premises make using it clearer. I suppose the way you wrote it is the way it’s usually done, though. But “P” could stand for “you won’t download porn”.
Also - I could actually do both - smoke dope AND download porn. While the way I wrote it sounds like one would exclude the other - that I have to choose, logically, I don’t. I am only stating that I will do at least one of those. I actually added the “either” for clarity. But I could have said - and it is a logical equivalent to what i did say - I will smoke dope or download porn. As long as it’s possible to do both, both are allowed. This is one reason we use symbols. It’s just easier, in the long run. But we must transcribe the written statements carefully.
Oh crap - I did it again. It should be S > [~P & (S v E)]
Ah.
Unsound modal logic! Yikes. I see the point a little more, I think. So far we have symbols to represent can, must, can’t, both, one or the other.
Impressive stuff guys. Tell me some more…
No, we don’t have a symbol that represents “can”. We can symbolise the disjunction - if that’s what you mean - “I can do this or I can do that” - but that’s not really symbolising “can”. I suppose that if we don’t have a contradiction, we have “can”. But there is no symbol for it, unless i misunderstand you.
“Must” is a little different. “P > Q” may mean this, but it doesn’t always, so that symbol won’t be used that way. However, here Q is a necessary condition that P, just not the other way 'round. The relationship between P and Q is not causal, in other words.
I see what you mean. We can represent potentials as potentials (by their symbols), implying can.
Hmm. I was thinking backwards, I think. But still…
X > Y
X has to be there for Y, but X can exist without Y?
No, it’s the other way around. I know that this is counterintuitive at first, but, in a material implication (which is what the symbol represents), the antecedent (first term) is a sufficient condition of the consequent. But not a necessary one.
When (if) I snort a line of smack, (then) I get high.
But that’s not the ONLY way I get high.
BUT, I get high every time I do snort a line of smack (I don’t like needles). So, the high is a consequence of the smack - smack always gets me high. It always happens - doing the smack is actually “necessitated” by the high. Or it isn’t smack. Or, the implication isn’t true.
Who wrote that quote? That was a mistake.
X > Y
X is a sufficent for Y.
X always does Y.
It doesn’t have to be X that causes Y, but when X, always Y.
Is it backwards, or is the “necessary” wrong?
The necessary is wrong.