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Modal logic and free will. Keith, Bob, Swartz, Dave, Tim: a bunch of guys.

121 posts in this topic

Posted

Oh yeah, and I almost had big bloomin blighter talking about swartz's logic in the chatroom but I had to dash. If you're out there BBB I'd still like to hear what you were going to say.

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Posted

As I've already explained, a "possible world" in this heuristic is simply a logically possible world. All a "possible world" means in this context is that some state of affairs may possibly exist provided that the state of affairs in question does not bring about a logical contradiction.

Of course this means that most of these possible worlds are not the ACTUAL world. The number of non-actual but possible worlds greatly outstrips the actual world. There are innumerable counterfactuals for every actual existent. There is a possible world at which pigs fly and donkeys talk. There is a possible world at which Keith leaves his cell and goes to Hawaii. And there is a possible world at which Bob declines to put on his hat.

What I have said, from a strictly logical point of view, is that all these counterfactual states of affairs have a logical connection, viz. : They are propositions about possible but non-actual worlds. And I have said that if you inquire as to WHY something did not occur, you are then going beyond the formalism of the modal logic, which is fine, but these inquiries are not necessary for the formal logical structure and have no bearing on it. To repeat: We know why the possible world "pigs fly" is nonactual: pigs never evolved wings. We know why, very likely, the possible world, "Keith goes to Hawaii," will turn out to be non-actual: Keith is in prison. What we DON'T know, because you won't tell us, is why Bob isn't free to refrain from putting on his hat!

You say Keith and Bob are disanalogous but then you contradict yourself by demanding that any free will argument I provide for Bob must also go through for Keith. But this isn't so. From a purely logical standpoint, what Keith ends up not doing, and what Bob ends up not doing, count as "possible but non-actual worlds." Again, when we inquire WHY these worlds are non-actual, we discover that Keith is in prison! What prison is Bob in that he can't do other than put on his hat?

Again, I invite you to answer the question: Why can't Bob refrain from putting on his hat?

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Posted

All a "possible world" means in this context is that some state of affairs may possibly exist provided that the state of affairs in question does not bring about a logical contradiction.

Yeah and I still don't understand "who" says that the state of affairs in question is or is not a possible contradiction.

I think if we sort this out :

Quote

making a distinction between kinds of 'possible'

problem solved.

Critical thinking is the process of thinking that questions assumptions

so basically, on what assumptions is what anyone saying "based", and why are those assumptions true?

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Posted

A classic example of an impossible state of affairs

Necessarily, all bachelors are unmarried

Bert is a bachelor

Bert is married

Hence, there is no possible world in which Bert exists.

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Posted

David, the implication of possible contradiction is nonsensical, as such a contradiction would only occur in at least one world, where you meant it to occur in all possible worlds (not the contradiction, per se, but the fact that it is a contradiction).

If logical impossibilities were fixed in some possible worlds and not, necessarily, in others, then they would hardly be logically impossible.

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Posted

David, the implication of possible contradiction is nonsensical, as such a contradiction would only occur in at least one world, where you meant it to occur in all possible worlds (not the contradiction, per se, but the fact that it is a contradiction).

If logical impossibilities were fixed in some possible worlds and not, necessarily, in others, then they would hardly be logically impossible.

Where did I use the phrase "possible contradiction?" If I did I either misspoke or it exists in some wider context. We might speak sensibly about possible logical contradictions if we lack knowledge as to whether some proposition really is logically contradictory. As it happens, though, I think we can tell easily enough, as your bachelor example shows. Anyway, I await Timothy's next response.

Wait, it was Inzababa who used the phrase, "possible contradiction."

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Posted

Yeah and I still don't understand "who" says that the state of affairs in question is or is not a possible contradiction.

It's based on logic, not on "who" says it.

Logically, there are no married bachelors. Logically, there are no square circles. Logicially, 2+2 never equals five. And so on.

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Posted

Yeah and I still don't understand "who" says that the state of affairs in question is or is not a possible contradiction.

It's based on logic, not on "who" says it.

Logically, there are no married bachelors. Logically, there are no square circles. Logicially, 2+2 never equals five. And so on.

that's what you say, ie it's an assumption.

I'm inclined to believe that, however, I'd like to know on what basis you assume this.

"criticism" and "critical thinking" is a process that seeks to question assumptions.

Now if that is true, I'd like you to "prove to me" that what you say is true.

I'm not concerned with you or anything personal, I'm only concerned with the following question :

why, logically, are there no married bachelors?

why, logically there no square circles?

when a square and a circle is in the first place something that we define and assign a meaning to.

IE : it is an abstract symbol.

I'd like to know who, and why that symbol was assigned and related in this way, not whether "who" is a nice guy or not.

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Posted

Where did I use the phrase "possible contradiction?" If I did I either misspoke or it exists in some wider context. We might speak sensibly about possible logical contradictions if we lack knowledge as to whether some proposition really is logically contradictory. As it happens, though, I think we can tell easily enough, as your bachelor example shows. Anyway, I await Timothy's next response.

Wait, it was Inzababa who used the phrase, "possible contradiction."

Yeah it was me, because I see a possible contradiction in this phrase :

All a "possible world" means in this context is that some state of affairs may possibly exist provided that the state of affairs in question does not bring about a logical contradiction

and, the OP would like, in fact he has requested, that we "focus" on this

Quote

Quote

making a distinction between kinds of 'possible'

David, the implication of possible contradiction is nonsensical, as such a contradiction would only occur in at least one world, where you meant it to occur in all possible worlds (not the contradiction, per se, but the fact that it is a contradiction).

If logical impossibilities were fixed in some possible worlds and not, necessarily, in others, then they would hardly be logically impossible.

exactly my thought.

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Posted (edited)

A classic example of an impossible state of affairs

Necessarily, all bachelors are unmarried

Bert is a bachelor

Bert is married

Hence, there is no possible world in which Bert exists.

yes, but it's not "necessary" is it?

Unless you specify an absolute "domain" in which it is absolutely necessarily true.

"Bert is a bachelor and Bert is married" is only a contradiction if this is true :

"Necessarily, all bachelors are unmarried"

question :

why is that phrase "Necessarily, all bachelors are unmarried" true?

Edited by Inzababa

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Posted

why is that phrase "Necessarily, all bachelors are unmarried" true?

Because, by definition, it's a logical contradiction. If a man were married, he wouldn't be a bachelor. If a man were a bachelor, he would be unmarried. Once the bachelor marries, he is, by definition, no longer a bachelor.

Stop wasting everybody's time with your inane and pointless questions!

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Posted

For fuck sake!

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Posted

Erm, these propositions are true in virtue of their definitions. This is basic stuff.

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Posted

Where did I use the phrase "possible contradiction?" If I did I either misspoke or it exists in some wider context. We might speak sensibly about possible logical contradictions if we lack knowledge as to whether some proposition really is logically contradictory. As it happens, though, I think we can tell easily enough, as your bachelor example shows. Anyway, I await Timothy's next response.

Wait, it was Inzababa who used the phrase, "possible contradiction."

Yeah it was me, because I see a possible contradiction in this phrase :

All a "possible world" means in this context is that some state of affairs may possibly exist provided that the state of affairs in question does not bring about a logical contradiction

and, the OP would like, in fact he has requested, that we "focus" on this

Quote

Quote

making a distinction between kinds of 'possible'

David, the implication of possible contradiction is nonsensical, as such a contradiction would only occur in at least one world, where you meant it to occur in all possible worlds (not the contradiction, per se, but the fact that it is a contradiction).

If logical impossibilities were fixed in some possible worlds and not, necessarily, in others, then they would hardly be logically impossible.

exactly my thought.

You were the one who coined the phrase "possible contradiction," not I. I have already explained my position. I have NOT said that "logical impossibilities were fixed at some worlds and not at others. That would be absurd. I have said just the opposite. That a logical impossibility MEANS that it is not possible to be true at ANY world. If it were possibly true at some world, it would by definition not be logically contradictory!

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Posted

why is that phrase "Necessarily, all bachelors are unmarried" true?

Because, by definition, it's a logical contradiction. If a man were married, he wouldn't be a bachelor. If a man were a bachelor, he would be unmarried. Once the bachelor marries, he is, by definition, no longer a bachelor.

Stop wasting everybody's time with your inane and pointless questions!

who says "it's a logical contradiction"?

If it were, you could demonstrate it.

Stop wasting everybody's time with your inane and pointless questions!

thanks again for your personal advice, made a note of this and will try not to waste your time :)

Erm, these propositions are true in virtue of their definitions. This is basic stuff.

definition defined by who?

Where did I use the phrase "possible contradiction?" If I did I either misspoke or it exists in some wider context. We might speak sensibly about possible logical contradictions if we lack knowledge as to whether some proposition really is logically contradictory. As it happens, though, I think we can tell easily enough, as your bachelor example shows. Anyway, I await Timothy's next response.

Wait, it was Inzababa who used the phrase, "possible contradiction."

Yeah it was me, because I see a possible contradiction in this phrase :

All a "possible world" means in this context is that some state of affairs may possibly exist provided that the state of affairs in question does not bring about a logical contradiction

and, the OP would like, in fact he has requested, that we "focus" on this

Quote

Quote

making a distinction between kinds of 'possible'

David, the implication of possible contradiction is nonsensical, as such a contradiction would only occur in at least one world, where you meant it to occur in all possible worlds (not the contradiction, per se, but the fact that it is a contradiction).

If logical impossibilities were fixed in some possible worlds and not, necessarily, in others, then they would hardly be logically impossible.

exactly my thought.

You were the one who coined the phrase "possible contradiction," not I. I have already explained my position. I have NOT said that "logical impossibilities were fixed at some worlds and not at others. That would be absurd. I have said just the opposite. That a logical impossibility MEANS that it is not possible to be true at ANY world. If it were possibly true at some world, it would by definition not be logically contradictory!

I know I coined that phrase, I said so in my previous post.

I also know and understand your position.

I would like you to "prove" it.

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Posted

OK, since Inzababa clearly struggles with English (and, I suspect, every other traditional language), maybe we should try a different style of communication.

Hence,

Let Ax stand as the universal symbol, such that AxFx is equivalent either to 'All x's that have the property F' or 'For any x that has the property F'

Let Fx stand for 'x has the property of being a bachelor'

Let Gx stand for 'x has the property of being unmarried'

Let any lower case letter 'a' - 't' denote a token, the type, or collective, of which is shown as a lower case letter 'x' - 'z'.

In this case the type is personhood.

Hence, 'Gx' denotes that any token with the group 'x' has the property of being unmarried. 'Ga' denotes that some 'a' (call him 'Bill') is unmarried, therefore 'Gx' can be rewritten 'There is an unmarried person'. and 'Ga' can be rewritten 'There is a person, called Bill, who is unmarried'

Since we're dealing with bachelors, and there are no female bachelors (as a female 'bachelor' is not called as such), we can reduce the scope accordingly, such that the type applies to men.

Therefore, 'Gx' denotes 'There is an unmarried man'.

Ax(Fx > Gx) All bachelors are unmarried men

Fa Bill is a bachelor

_________________

Ga Bill is unmarried

This also works the other way

Ax(Gx > Fx) All unmarried men are bachelors

Ga Bill is unmarried

______________

Fa Bill is a bachelor

The above arguments have shown that we can reduce the general rule to a specific incidence whether we determine bachelors to be unmarried men, or unmarried men to be bachelors. That is, in any such case we present such that the assumption, rule, or definition applies universally, there is no specific case that can possibly ignore or subvert the initial rule/definition/assumption. This is evident when one considers that the token 'a' can be replaced with any specific person (including Bill).

Focussing, for the moment, on the universal rule, and combining the above arguments, we can show that the property of being a bachelor and the property of being unmarried are logically equivalent, thus

Ax(Fx > Gx)

Ax (Gx > Fx)

___________

Ax (Fx <> Gx)

The <> symbol denotes that the conditional path can go either way, thus 'If F then G and if G then F' is equivalent to 'G only if F' and to 'F only if G'

The conclusion above can, therefore, be written

Ax((Fx > Gx) & (Gx > Fx))

Consequently, it is logical (not an assumption) that, in all cases that something is a bachelor, that thing is also unmarried, and in all cases where something is unmarried, that thing is a bachelor.

Let's see what happens when we try to apply the property of one without applying the property of the other.

Ax(Fx <> Gx)

Fa

_________

~Ga

The ~ symbol denotes negation

Hence, we have

All bachelors are unmarried, and all unmarried men are bachelors

Bill is a bachelor

Bill is married (negation of being unmarried)

Extending this, through reductio, we get

Ax(Fx <> Gx) (From definition of 'bachelor')

Fa (Assumption 1)

~Ga (RAA assumption)

Ex(Fx & ~Gx) (from P2 and P3) ('Ex' denotes any token. It is not the same as 'Ax' as it refers only to a specific, though nonspecified, thing)

Ex (Gx & ~ Gx) (from P1 & P4)

Ex(Gx) (from P1 & P5

___________________

Ex(Fx & Gx)

We have therefore shown that, for any specific man, to state that that man can be a bachelor without being unmarried (or vice versa), is to state a contradiction. Hence, it logically follows that any given bachelor is an unmarried man, as the denial of this logic entails a contradiction.

I have, therefore, shown that all bachelors are unmarried men, and that to claim otherwise is to contradict oneself. One doesn't even have to use 'bachelors' and 'unmarried men'. The symbols above can denote anything such that F is defined by G (All circles are round, all triangles have 3 angles totally 180 degrees, etc).

The only way, therefore, to deny that no bachelor is unmarried is to attack the definition, and present a case for the existence of a bachelor that is married. But this is self-defeating, as the above reductio shows. And, since the reductio establishes a contradiction between being married and being a bachelor, it follows necessarily that no bachelor is married, therefore it is impossible for there to exist a married bachelor, there, there exists no possible world containing a married bachelor.

And I'm not interested in there being some possible world where the definition of bachelor is different, or the properties of being unmarried subserve differently in that world than in this world, because explaining basic logic is a fucking chore in this thread, so damned if I'm going to get into internalism vs externalism of mental thoughts and properties!

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Posted

Let Ax stand as the universal symbol

(that's one of the basic "assumptions")

which means what?

A symbol which represents "all that is possible"?

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Posted

Rob, that's an excellent post, but at the end of the day, you're trying to explain logic to somebody who would ask, "How do we know that a brick wall is made from bricks?" or, "How do we know that a man who was born exactly 60 years ago is 60 years old today?" or, "How do we know this blatantly five-sided shape is not a quadrangle?"

IOW, you're wasting your time on an idiot.

Let Ax stand as the universal symbol

(that's one of the basic "assumptions")

which means what?

A symbol which represents "all that is possible"?

He told you in the same line, doofus!

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Posted

Let Ax stand as the universal symbol

(that's one of the basic "assumptions")

which means what?

A symbol which represents "all that is possible"?

That's the best you can do?

I give you undeniable proof that there is no possible world in which there exists a married bachelor, and your best retort is to pick up one 'assumption' and attack that, with the entire crux of your attack depending entirely on your obtuse choice to ignore that explication of the assumption, which I gave on the same line!

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Posted

Rob, that's an excellent post, but at the end of the day, you're trying to explain logic to somebody who would ask, "How do we know that a brick wall is made from bricks?" or, "How do we know that a man who was born exactly 60 years ago is 60 years old today?" or, "How do we know this blatantly five-sided shape is not a quadrangle?"

IOW, you're wasting your time on an idiot.

Let Ax stand as the universal symbol

(that's one of the basic "assumptions")

which means what?

A symbol which represents "all that is possible"?

He told you in the same line, doofus!

so someone who asks how do we know something is an idiot?

why? how does that work?

Oh, and you're assuming I don't know about logic, which might be a mistake.

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Posted (edited)

It's not so much an assumption as a reasoned inference.

Ax is a universal quantifier. It was created specifically for that purpose. To state 'Ax denotes that for all x or for any given x' is no more an assumption than to state 'The letter B is the letter B' or 'The colour red is not blue'.

But no, I'm tired of this, we'll ask the bloody questions.

Give us an axiom, or an argument, in predicate format, using modal logic if you wish, that demonstrates your grasp of logic. Use predicate format and the English vernacular to facilitate your demonstration.

Edited by Big Blooming Blighter

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Posted

Let Ax stand as the universal symbol

(that's one of the basic "assumptions")

which means what?

A symbol which represents "all that is possible"?

That's the best you can do?

I give you undeniable proof that there is no possible world in which there exists a married bachelor, and your best retort is to pick up one 'assumption' and attack that, with the entire crux of your attack depending entirely on your obtuse choice to ignore that explication of the assumption, which I gave on the same line!

no, it's not the best I can do, it seems it's the best we can do.

I just wanted to know what your logic was based on, ie, what were the assumptions.

This :

with the entire crux of your attack depending entirely

says a lot also about what you think of "ME"

if I tell you I'm not attacking "you", or anything for that matter, you wouldn't believe me would you?

Here's a tip :

Critical thinking is the process of thinking that questions assumptions

It's just a process ok? Nothing personal.

Not attacking YOU, not trolling YOU, not insulting YOU, simply attempting to reply to the OP's question, which was

"different kinds of possible".

possible means what and functions how under what assumptions?

This :

Is personal :

But if "you" and "anyone else" don't want to think critically, and prefer to resort to character assassination, no problem, I'll leave you to your childish games. You might get a job on Fox News.

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Posted

There comes a point where 'questioning assumptions' becomes akin to being utterly obtuse.

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Posted

Nice post, Blighter, which is why you should be posting here more often. :yup:

Now, after that post, it will be just absurd to fruther explain why a bachelor necessarily is not married (there are no married bachelors at any possible worlds in modal logic heuristic) and hopefully we can return to the thread's actual topic.

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Posted

Oh, but I was SOOOOOOOO ready to pull out some truth tables(!)

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