Whoa Pardner! Turn that horse around and come back to where I am still getting my foot in the stirrup.

r=ATOM 2?

SpeedOfSound wrote:

Code: Select all

val A = ATOM true;
val B = ATOM false;
val C = ATOM false;
val D = ATOM true;
val E = ATOM true;
     

See? This is one world. There are 32 possible worlds given that we have no constraints. Very simple.

This is the wrong usage. The argument to ATOM should be a symbol in the alphabet, not a boolean value. The alphabet can be anything (I choose ints above), but it would be traditional to use characters. So if you want propositional variables a, b, c, d and e, you could define:

Code: Select all

val a = ATOM #"a"
val b = ATOM #"b"
val c = ATOM #"c"
val d = ATOM #"d"
val e = ATOM #"e"


Each of these values has type "char term", meaning that we have terms in the alphabet of characters. The next thing we want to do is assign true and false to each of these. To get an idea of how, look at the type of the evaluation function after instantiating 'a to char:

Code: Select all

eval : (char -> bool) -> char term -> bool

This should give you a clue as to how we assign true and false to our propositional variables. It's in the first argument of eval, where we see that it's literally just a mapping from the alphabet "char" to the datatype "bool". I choose to name the argument "e" because these assignments are sometimes called environments.

In my above example, I used "fn x => Int.rem (n,2) = 0" as the environment. This is because I had chosen integers for my alphabet, and here I assign all the even numbers the truth-value "true" and all the odd numbers the truth value "false".

Talk of an assignment of truth values to the alphabet is standard when discussing the formal semantics of propositional logic. If you want to call these assignments worlds, I won't stop you. But this has nothing so far to do with modal logic.

SpeedOfSound wrote:- eval e2;
stdIn:5.1-5.8 Error: operator and operand don't agree [tycon mismatch]
operator domain: 'Z -> bool
operand: bool term
in expression:
eval e2
-
Did I do some dumb shit here?

"eval" takes two arguments. The first argument is a function, which is the environment in which you wish to evaluate the term given as the second argument.

In your example, you've chosen to base your propositional language on an alphabet of booleans. This gives you just two possible atoms, not five as you might have intended (in your example, a=d=e and b=c.) But a simple environment in which to evaluate terms in this language would just be to use the identity function:

Code: Select all

- eval (fn x => x) e2

Going back to a char alphabet, if you've set the characters #"a", #"d" and #"e" to true and everything else to false, then a simple evaluation is just:

Code: Select all

- eval (fn c => c = #"a" orelse c = #"d" orelse c = #"e")

For very large alphabets, you might prefer to start with a binary tree implementation of a set, store all atoms that are to be assigned true in the set, and then pass the membership function in as the environment.

I didn't realise you'd only just started SML. Hopefully, you've seen some examples of functions taking functions as argument (higher-order functions). But if you're not fully comfortable with polymorphism, you can change the datatype definition to:

Code: Select all

datatype term = ATOM of string | NEG of term | IMP of term * term

Yes. Very new to SML. Just a few weeks ago that I even heard of it. Let me play with some stuff here and catch up.

I see what you are doing and it is more general than what I tired to use it for. But I need to go back to my course and find out how I got lost. Battling a bout of depression right now too so baby steps. That usually lasts for three days.

SpeedOfSound wrote:Yes. Very new to SML. Just a few weeks ago that I even heard of it. Let me play with some stuff here and catch up.

I see what you are doing and it is more general than what I tired to use it for. But I need to go back to my course and find out how I got lost. Battling a bout of depression right now too so baby steps. That usually lasts for three days.

Feel free to throw me any other ML questions you have while doing the course, either by PM or in the maths forum.

Hope you feel better soon.

Thanks. I will. I'm playing with a few things.

I feel great actually. I'm just depressed so I'm running slow. I have come to enjoy my depressive vacations in the midst of my manic mainstream.

Still working on it. SML. Holy Fucking Hell! I'm in love.

http://confreaks.com/videos/1287-rubyco ... rogramming
Thought you might like this foray into ruby and lambda calculus.

SpeedOfSound wrote:Still working on it. SML. Holy Fucking Hell! I'm in love.

http://confreaks.com/videos/1287-rubyco ... rogramming
Thought you might like this foray into ruby and lambda calculus.

I had the Y-combinator as my signature for a bit.

But if we're talking about Y-combinators, then we're not talking about SML or any typed lambda calculii. The Y-combinator isn't well-typed.

It's a cool talk though. I love his intro.

Is this thread a discussion on existence, or MSL?
Dont want to waste my time if the latter, as I dont talk that lingo.
(edit to add - not being facetious, its a serious question - I dont want to rerail the derail if its drifted onto MSL)

Yes, hamsters exist.
(As does the Large Hadron Collider, although I saw a hamster, but only saw photos of the (alleged) LHC)

Little Idiot wrote:Is this thread a discussion on existence, or MSL?
Dont want to waste my time if the latter, as I dont talk that lingo.
(edit to add - not being facetious, its a serious question - I dont want to rerail the derail if its drifted onto MSL)

Yes, hamsters exist.
(As does the Large Hadron Collider, although I saw a hamster, but only saw photos of the (alleged) LHC)

As I recall it is about the meaning of the utterance "x exists" and a little about extension. A a side dish about SML and some logic related programming items.

Ok, then if I may pass on the side, skip the starter and head straight into the main - isnt it simply a case of the word existence being context specific?

If I say 'Peter Pan can fly, but Captain Hook cant' I mean they exist with constant characteristics in the context of the story.
So, then in the context of that story, a child would be quite correct (and only in that context) if I started talking about Captain Hook flying. At least I'd have to justify how and why he could do so - where as no need to justify myself if it was Peter Pan flying.

If I say the integer '3' exists, then this is different to saying the integer 3.1 exists, as 3.1 is obviously not an integer.
I dont mean I can get a sack of 3 and bring it home.
Context specific.

If I say trees exist, the context is general, if I say the mango tree in my back garden, I am being specific about an instance of a tree - context specific.

Based on this, you cant give a definition of the word exist without relating a context for the word. Changing the context changes the 'definition' of the word because its a context specific word, like many others.
But that doesn't mean we cant use it - in general or philosophy - just gotta be careful and clear about our context.

Does the world exist?
Yes.
But this does not mean I am a physicalist or that the world is observer-independent material object 'out there' in space.

To me, the world exists within the context of my experience of it, as I assume it exists in your experience. This 'experienced world' which is forced upon me in the format I know as experience is a construction from many sources, including but not limited to my senses. Because the construction is a 'mental construction' I describe the world as mental.
One does not have to ascribe an observer independence upon the world to allow it to exist - and idealism does not need to declare 'the world does not exist' - we just provide the context (mental experience) in which the world is said to exist.

Little Idiot wrote:Does the world exist?
Yes.
But this does not mean I am a physicalist or that the world is observer-independent material object 'out there' in space.

To me, the world exists within the context of my experience of it, as I assume it exists in your experience. This 'experienced world' which is forced upon me in the format I know as experience is a construction from many sources, including but not limited to my senses. Because the construction is a 'mental construction' I describe the world as mental.
One does not have to ascribe an observer independence upon the world to allow it to exist - and idealism does not need to declare 'the world does not exist' - we just provide the context (mental experience) in which the world is said to exist.

My bold.

But, if the context in which the world is said to exist is ‘mental’, then how does this differ from the context in which the world is said to be physical? If the context ‘mental’ implies that the observer is in some fundamental way distinct in nature from the observed material phenomenon, then how is that possible? How can that which is assumed to be distinct in nature from the system have any possible affiliation or means of contact with the system?

Little Idiot wrote:Ok, then if I may pass on the side, skip the starter and head straight into the main - isnt it simply a case of the word existence being context specific?

If I say 'Peter Pan can fly, but Captain Hook cant' I mean they exist with constant characteristics in the context of the story.
So, then in the context of that story, a child would be quite correct (and only in that context) if I started talking about Captain Hook flying. At least I'd have to justify how and why he could do so - where as no need to justify myself if it was Peter Pan flying.

If I say the integer '3' exists, then this is different to saying the integer 3.1 exists, as 3.1 is obviously not an integer.
I dont mean I can get a sack of 3 and bring it home.
Context specific.

If I say trees exist, the context is general, if I say the mango tree in my back garden, I am being specific about an instance of a tree - context specific.

I might say that Peter Pan does not exist and pretty much get agreement from everybody. For the same reasons that pretty much everyone agrees that birds exist.

Little Idiot wrote:Based on this, you cant give a definition of the word exist without relating a context for the word. Changing the context changes the 'definition' of the word because its a context specific word, like many others.
But that doesn't mean we cant use it - in general or philosophy - just gotta be careful and clear about our context.

I would it call it the situation or usage rather than context. Context doesn't quite cover it. It has some affect on the truth value of the statement.

As for a definition of course we can do that without all the context or the individual situation. That's how words work. We can't do away with how words work.

Little Idiot wrote:Does the world exist?
Yes.
But this does not mean I am a physicalist or that the world is observer-independent material object 'out there' in space.

To me, the world exists within the context of my experience of it, as I assume it exists in your experience. This 'experienced world' which is forced upon me in the format I know as experience is a construction from many sources, including but not limited to my senses. Because the construction is a 'mental construction' I describe the world as mental.
One does not have to ascribe an observer independence upon the world to allow it to exist - and idealism does not need to declare 'the world does not exist' - we just provide the context (mental experience) in which the world is said to exist.

You believe in some kind of True Nature that's all hooked up with magic and theism. I might get on just fine with you if we are talking about some species existing or some class of numbers but why should I listen to you talk about the world existing? I would sooner take my lead from Peter Pan.

The simple way to see this is for instance, if you say Peter Pan exists and I say prove it then you get Peter Pan to make a house call or show me some convincing documentation. If you say a cup of coffee exists between us while we sit at the cafe I expect to be able to see the cup and drink the coffee. That isn't going to change for us if we move to a bar. It will still be the case even if it's our uncles having the conversation.

So context dependent doesn't quite describe it. The object and everything around it and lots of structure and knowledge also partake in the determination. Situation is a bit improved.

Destroyer wrote:

Little Idiot wrote:Does the world exist?
Yes.
But this does not mean I am a physicalist or that the world is observer-independent material object 'out there' in space.

To me, the world exists within the context of my experience of it, as I assume it exists in your experience. This 'experienced world' which is forced upon me in the format I know as experience is a construction from many sources, including but not limited to my senses. Because the construction is a 'mental construction' I describe the world as mental.
One does not have to ascribe an observer independence upon the world to allow it to exist - and idealism does not need to declare 'the world does not exist' - we just provide the context (mental experience) in which the world is said to exist.

My bold.

But, if the context in which the world is said to exist is ‘mental’, then how does this differ from the context in which the world is said to be physical? If the context ‘mental’ implies that the observer is in some fundamental way distinct in nature from the observed material phenomenon, then how is that possible? How can that which is assumed to be distinct in nature from the system have any possible affiliation or means of contact with the system?

The physical is a form of the mental, it is fundamentally no different to the physical, because what we call the physical world is just how we experience the mental world. You cant show me a piece of something physical in any way other than as part of my (mentally constructed) experience.
The physical is a subset of the mental.