h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

psi

With == reflexive

p == p=>p; p=>p == p

Hi Bx4,

Sorry I phrased my last post badly because I implied that I think C' is valid and I don't think it is, I meant to put a 'not' in there.

I deny C' as well, so that simplifies things because we don't have to consider the alethic bit.

It cannot be the case that p == p=>p. Have another look at it and consider what happens when p is false.

Do you now agree that to assert p is not the same as to assert p=>p ?

psi

'I deny C' as well, so that simplifies things because we don't have to consider the alethic bit.'

I don't see the relevance of the alethic modality here. It is smply a consequence of the 'modern' approach of mapping the Lewisian strict conditonal to the alethic/mater implication form.


'It cannot be the case that p == p=>p. Have another look at it and consider what happens when p is false.'

True. Though my error was to accept your use of material implication. It is inadequate to deal with the Principle of Identity.

http://www.earlham.edu/~peters/courses/log/mat-imp.htm

Lewis developed strict implication to deal with these paradoxes. Hence material implication is not sufficiently strong to deal with the Principle of Identity. You need strict implication for this.

'Do you now agree that to assert p is not the same as to assert p=>p '

Yes but this is because you are using material implication.

hi psi

Bin thinking about with a An Ardbeg free brain. I think we are both wrong:

1. I cant assert the equyivalenc of the strict implication

p->p==p

2. Tou are wrong to claim that there is a crypto MSF since I don't need tthe supposed equivalence to get to @p all I need to do is to show that I can show that the conditional is one of strict implication and not simply a material conditional which I have since it is consistent with the Lewis definition of strict implication

Once I have my strict implication it is easy to get to @p

pa->pc==pa == @(pa=>pc) == @pa=>@pc;@pa|-@pc

So having /shown/ that 'if p then p is a strict implication the I can by modus ponens that p is a necessary prpsition.

Here the the tuth value of p is immaterial to p being a necessary proposition, the truth valus of p only determines whether p is necessarily true or necessarily false.

So while I agree with your President of France argument that I can't get to @p by asserting that

@p == @p=>@p

I disagree with your conclusion

'However, to assert @p would be to say that, necessarily psiomniac is the president of France at t1, which is false.'

Since I have shown that I can get to 'it is necessarily true that psiomniac is the PoF at t1' if it is a /fact/ that at ti. If it is not a fact that you were PoF at t1 then I get to 'it is necessarily false that psiomniac is the PoF at t1'

However it is that p is necessary and not contingent that is important.

*** I had reservations about your definition of the omiscience
condition:

@p=>@Kc(p)

The difficulty is that you cannot simply /assert/ that 'if p then Kc(p)' is a strict conditional you have to /show that it is and since you /cannot/ show that if your antecedent is true your consequent must be true.

However there is nothing in p if necessarily true that entails that Kc(p) is necessarily true so you can't get to your conclusion necessarily.

Contrariwise I can show in my omniscience codition that 'if Kc(Y) then Kc(E), is a strict implication.

Not sure how much I'll be on today, fun and profit in the world.
bsy

Hi Bx4,

"Bin thinking about with a An Ardbeg free brain. I think we are both wrong:"
Well, let's not be hasty.

"1. I cant assert the equyivalenc of the strict implication

p->p==p"
I'm glad you say that because to persuade you of that was my next task.

"Once I have my strict implication it is easy to get to @p"
I disagree for the reasons set out below.

In this:

"pa->pc==pa == @(pa=>pc) == @pa=>@pc;@pa|-@pc"

...we've just agreed that the first bit, pa->pc==pa, cannot be asserted so it is probably best to edit that out.

But now we are left with:

@(pa=>pc) == @pa=>@pc;@pa|-@pc

This is valid, but where did '@pa' come from?

Did you assume that @(pa=>pc) == @pa? If so this is a modal version of the same error isn't it?

"So having /shown/ that 'if p then p is a strict implication the I can by modus ponens that p is a necessary prpsition."
No you can't for the reasons above, and if you think about it this doesn't even make sense because it yields that all propositions are necessary.

"Here the the tuth value of p is immaterial to p being a necessary proposition, the truth valus of p only determines whether p is necessarily true or necessarily false."
I don't think so, otherwise:

@p == @p v @¬p

Which gives:

@p == @(p v ¬p)

Which is false because in the case that @p is false, @(p v ¬p) is still true since the rhs is the law of the excluded middle.

"Since I have shown that I can get to 'it is necessarily true that psiomniac is the PoF at t1' if it is a /fact/ that at ti. If it is not a fact that you were PoF at t1 then I get to 'it is necessarily false that psiomniac is the PoF at t1'"
Given the above, I hope you can now see that this is wrong. You can say necessarily(psiomniac is the PoF at t1' if it is a /fact/ that at ti psiomniac is the PoF) but to do what you've done above is the MSF with less of an emphasis on the 'crypto'.

"*** I had reservations about your definition of the omiscience
condition:

@p=>@Kc(p)
The difficulty is that you cannot simply /assert/ that 'if p then Kc(p)' is a strict conditional you have to /show that it is and since you /cannot/ show that if your antecedent is true your consequent must be true."

But it was you who correctly pointed out that some things are properly part of the definition (although I disagreed with your particular case). So I can just /stipulate/ it is a strict conditional. I can justify doing this by pointing to the properties of what I'm defining: if G is omniscient then /by definition/ it is not possible for p to be the case and G not know about it. I can't see why you'd have a difficulty with that.

"However there is nothing in p if necessarily true that entails that Kc(p) is necessarily true so you can't get to your conclusion necessarily."
The necessity comes from omniscience, not from the content of p.

"Contrariwise I can show in my omniscience codition that 'if Kc(Y) then Kc(E), is a strict implication."
But then, as ever, you are left with having to assert @Kg(Y), which is false.

ttfn

hi psi

Just to let you know I think I'm done on 'Compatibilism'.

I just had a quick shufti and I see that stephen is now claiming despite his 'I am typing at t0' argument he was /not/ trying to use supposedly contingent facts to generate ontological alternate possibilities.

Now he has gone all empirical with his weird science of the headache pill and that's so incoherent it's not even wrong.


I just can't be arsked......
bsy

Hi Bx4,

Well that's up to you of course, but I think it would be a shame if we couldn't resolve the @Kg(Y) issue, which let's face it, is nothing to do with stephen.

I agree with you that the logic is not going to settle questions about the ontology of alternative possibilities, I agree about the indexing and the validity of all the arguments, and reference to tenseless facts, but there is that one dirty plate left, @Kg(Y), or @p .

Maybe we can sort that out here.

ttfn

hi psi

'Up to you'

Perhaps you would like to distenangle stephen's weird science for him?

'but there is that one dirty plate left, @Kg(Y), or @p .'

A starter or ten:

The assumption of possible world semantics is a 'fudge factor' to allow modal model theories to be built. They are not needed for Lewis strict implication.

Hi Bx4,

'Perhaps you would like to distenangle stephen's weird science for him?'
Don't know whether I'm up to that.

'A starter or ten:

The assumption of possible world semantics is a 'fudge factor' to allow modal model theories to be built. They are not needed for Lewis strict implication.'
Let's accept that for the sake of argument for now. How does that give you what's needed? What is it about Lewis's strict implication that you think warrants @Kg(Y)?

hi psi

'Let's accept that for the sake of argument for now.'

Why not accept it because it is a fact?

'The basis of the theory is the set-theoretical idea that reality -- the sum of the imaginable -- is a universe composed of a plurality of distinct elements. This universe is hierarchically structured by the opposition of one well-designated element, which functions as the centre of the system, for all the other members of the set. The resulting structure is known as ‘modal system’, or M-model (Kripke). The central element is commonly interpreted as ‘the actual world’, and the satellites as merely possible worlds. For a world to be possible it must be linked to the centre by a so-called ‘accessibility relation’. The boundary between possible and impossible worlds depends on the particular interpretation given to the notion of accessibility '
(Possible-worlds theory, Marie-Laure Ryan, the Routledge Encyclopedia of Narrative Theory)

Is one citation enough or do you require more?

Since Kripke (and in a slightly different form Hintikka) did not develop modal model theory until some /25/ years /after Lewis ( Introduction to Symbolic Logic, Lewis and Langford, 1932) specified strict implication in /his/ 'strictest' B-variant system S1 which does not involve model theory then arguments from possible world semantics seem not only anachronistic but irrelevant.

'How does that give you what's needed? What is it about Lewis's strict implication that you think warrants @Kg(Y)?'

It's simple in S1 Lewis' defines strict implication, P->Q as ¬#(P.¬Q), colloquially, 'it is impossible that P can be true and Q false. So

1)def(omniscient observer: an observer g who knows every event in Y, the set of all events (Y) in the universe; Kg(Y))

http://images.elfwood.com/art/g/e/georgepappas/tralfamadore1_copy.jpg

now from 1) I can assert the /material/ conditional:

2)If observer g knows every event in Y then observer g knows any arbitrary event E in the universe; Kg(Y)=>(Kg(E)

Now I can show from ¬#(P.¬Q) that 2) warrants the stronger implication:

3)Strictly, If observer g knows every event in Y then observer g knows any arbitrary event E in the universe; Kg(Y)->(Kg(E)

Which I can since is logically impossible that g can know every event in U but not know an arbitrary event E in U. From 3) by the usual means:

Kg(Y)->Kg(E) == @(Kg(Y)=>Kg(E)) == @Kg(Y)=>@Kg(E); @Kg(Y)|-@Kg(E)

What 'warrants' &K(g) is that it appears in the first premise of the modus ponens, as the strict conditional, @Kg(Y)=>@Kg(E), and as far as I am aware normal practice in modus ponens is to use the antecedent as the second premise.

Now you have claimed that @Kg(Y) is false but how without recourse to possible world semantics (though I think your argument even allowing it, is problematic) will you show it so?

It would be interesting to see how you get to your own dirty plate @p using an argument akin to the above.

bsy

hi psi

On the basis that tou might argue that 'one swallow do
does not a summer make':

'The insight of Kripke and Hintikka was that [modal K] /can/ be given a semantics using `possibilities' and a relation of accessability between these possibilities. The accessability relation obtains between possibilities w and v exactly when v is compatible with what is believed in w . One can then define that a sentence of the form K P is true in a world w just in case P is true in all /models that are compatible with what is known in w .' [my emphases]
(Bisimulations on Planet Kripke, Jelle Gerbrandy,Ph. D. Thesis, University of Amsterdam (ILLC Dissertation series DS-1999-01, 1999)

Note /can/ be given not /must/ be given. In order to invoke Kripke- Hintikka semantics in attempt to show that my second premise is false you have to show that I cannot derive my strictly implicative modus ponens without needing to invoke K-H semantics.

Hi Bx4,

"Why not accept it because it is a fact?"
Because it isn't a fact. 'Fudge' is an evaluative term rather than an accurate description, and not one that I agree with. So you can give any number of citations and they'll conclude that possible world semantics is a model, but I didn't say it was Camelot did I?

"Since Kripke (and in a slightly different form Hintikka) did not develop modal model theory until some /25/ years /after Lewis ( Introduction to Symbolic Logic, Lewis and Langford, 1932) specified strict implication in /his/ 'strictest' B-variant system S1 which does not involve model theory then arguments from possible world semantics seem not only anachronistic but irrelevant."
Adhering to a strict chronology and only using contemporaneous theoretical instruments in order to criticise seems unwise to me, so I don't feel that the criticism 'anachronistic' holds water here. I also think 'inconvenient' is more accurate than 'irrelevant'.

"It's simple in S1 Lewis' defines strict implication, P->Q as ¬#(P.¬Q), colloquially, 'it is impossible that P can be true and Q false."
I assume the convention is to use '.' for the untypable logical AND symbol and so I agree with the above.

I have already agreed on 1)-3), it really is logically impossible for G to know every event in Y and not know E, this is not problematic.

So we get uncontroversially to the matter at issue, which is:

Kg(Y)->Kg(E) == @(Kg(Y)=>Kg(E)) == @Kg(Y)=>@Kg(E); @Kg(Y)|-@Kg(E)

which is valid, the only point of dispute being where @Kg(Y) came from. Your latest answer is that Modus Ponens uses the antecedent of the first premise as the second premise. I agree, that's what MP does.

But here's the thing, for some reason I can't fathom, you think that the structure of Modus Ponens gives you a warrant to /assert/ the second premise.

Getting back to the children to illustrate why this isn't satisfactory, we have:


p = stephen has no children at t0
q = stephen has less than 3 children at t0

A strict implication is warranted here, so:
p -> q == @(p => q) == @p => @q

So we have a warrant for:

1) @p => @q

However, you now tend to apply an MP, for which you need:

2) @p

Where is the warrant for that? You have said that this is normal practice. That's true if you are going to do an MP. However, the MP though valid if you follow normal practice, will not be sound unless you have some independent reason to suppose that 2) is true. Remember, 2) @p says that necessarily stephen has no children at t0.
So it seems to me that what is needed is that you provide some justification that it is /logically/ necessary that stephen has no children at t0. That's where it got really strange because your argument seemed to be that /if/ it is a fact that p then @p, but that can't be right can it? There is nothing /logically/ contradictory about stephen having a child at t0, even if it happens to be the case that he doesn't. It is factually incorrect, yes. It would be logically contradictory for him to have no children at t0 and have a child at t0, yes. But all propositions are logically necessary if made true by reference to a tenseless fact? Is that your argument?

"Note /can/ be given not /must/ be given. In order to invoke Kripke- Hintikka semantics in attempt to show that my second premise is false you have to show that I cannot derive my strictly implicative modus ponens without needing to invoke K-H semantics."
The above is intended to get us to the start of that task, I appeal to your patience therefore.

hi psi

'Because it isn't a fact. 'Fudge' is an evaluative term rather than an accurate description, and not one that I agree with. So you can give any number of citations and they'll conclude that possible world semantics is a model.

Except I did not say 'fudge' I said 'fudge factor' which isn't a value judgement but a mathematical technique and one I use all the time.

http://www.answers.com/topic/fudge-factor

More evidence of the risks of 'interpretation' when allied to a misapprehension of actual content, perhaps

Stuff to do in the world- Catch you later

Hi Bx4,

I had a possible light bulb moment and wondered whether your Quinian tendencies might explain your view of @p, specifically the rejection of the a priori/a posteriori distinction. What do you think?

"More evidence of the risks of 'interpretation' when allied to a misapprehension of actual content, perhaps"
I think 'fudge-factor' is no better than 'fudge' in this context, so I still don't agree. The 'fudge' element in both is meant to imply an imprecision either accommodated or introduced for expediency in order to get a result. I think that's no more true of possible world semantics than it is of material implication.

ttfn

....or indeed strict implication.

his psi

'I had a possible light bulb moment and wondered whether your Quinian tendencies might explain your view of @p, specifically the rejection of the a priori/a posteriori distinction'

Why Quinian? I thought his concern was more about the supposed distinction between analytic and synthetic propositions.
But its not that issue thats relevant here, rather that I align myself with Frege and Quine's doubts about the legitimacy of the whole modal programme.

I had thought that what divided me from you and stephen was differences about necessity and contigency but in my own light bulb moment I think its a much more fundamental difference of actualism versus possibilism

'Actualism:The belief that actuality and existence are co-extensive - i.e., that only actual things exist, that there are not, in addition to the actual, any possiblia (possible entities)'

I am an actualist which I have just realised makes notions like contigent facts and necessary facts irrelevant.

It seems to me that our positions are fundamentally irreconcilable.

bsy

Hi Bx4,

The supposed distinction between analytic and synthetic propositions might do actually. The reason is that I am talking about things which are true by definition as opposed to what is actually true in the world and all the complications about whether other things could have been actual if an indeterministic process had turned out differently are separate to my beef with @Kg(Y) .

I'll have a look at actualism versus possiblilsm because I haven't followed the argument, but on the face of it, that only actual things exist should not preclude the possible as a matter of logic, that's metaphysics, and I would have thought you would be more of the 'consign them to the flames' tendency in that regard.

ttfn

psi

'The supposed distinction between analytic and synthetic propositions might do actually.'

I suspect this /presupposes/ that synthetic propositions are contigent. I have never seen a persuasive account that they must be.

' The reason is that I am talking about things which are true by definition as opposed to what is actually true in the world and all the complications about whether other things could have been actual if an indeterministic process had turned out different'

Something of a petitio principii here. A synthetic proposition could have been otherwise (contigent) if it is is the correlate of a fact that is the outcome of an indeterministic process and so could have been otherewise.

There are a number of problems here in addition to the petitio principii.
First what makes a process ontologically indeterministic?

Second,assuming an indeterministic interpretation (and there are deterministic ones) of quantum mechanics then once the wave function has collapsed (or whatever) there is only the /actual/ /existing/ outcome unless you can demonstrate that the alternative outcomes exist as possibilia in the world.

'separate to my beef with @Kg(Y)'

Indeed remind me of /precisely/ what your beef is again?

'I'll have a look at actualism versus possiblilsm because I haven't followed the argument'

I wouldn't bother to much I'm a very primitive empirical sort of actualist and so have no interest in the filosofickal twitter, woo-woo and one-upmanship that 'professional' (i.e. paid) filosofickals indulge in to impress each other.

My position is really straight forward I can in principle, if not in practise, establish the actual existence of putative states of affairs in the world. If someone can explain how I can /empirically/ establish the /existence/ of possibilia in the world.

'that only actual things exist should not preclude the possible as a matter of logic'.

Well, this certainly true of logicians of the modal tendency though as I pointed out I lean towards the Frege-Quine non-modal tendency. However, the fact that one can build modal logics and generate possible world semantics that allows model theory to be applied to them does not entail that these semantics represent existent possiblia.

'that's metaphysics, and I would have thought you would be more of the 'consign them to the flames' tendency in that regard.'

In pointing out not only the absence of any /empirical/ evidence that would demonstaate the existence of possiblia but also the lack of any instrumentalties that would allow such evidence to be gathered, surely, doing just that?

Hi Bx4,

"I suspect this /presupposes/ that synthetic propositions are contigent. I have never seen a persuasive account that they must be."
You suspect wrongly. I just haven't seen your argument that they are necessary.

"Something of a petitio principii here. A synthetic proposition could have been otherwise (contigent) if it is is the correlate of a fact that is the outcome of an indeterministic process and so could have been otherewise."
There is nothing of the petitio principii here. In talking about things that are true by definition we avoid such complications, by which I mean /whether/ other things could have been actual if an indeterministic process had turned out differently. Nothing in that statement warrants an interpretaion that I'm assuming that there are such processes as far as I can see.

"There are a number of problems here in addition to the petitio principii."
Apart from there being no petitio principii, the problems you mention seem to me to stem from your interpretation of actualism. What makes a process ontologically indeterministic? The fact that what is actual was not causally necessitated by antecedent events (if such processes exist). Then you have the idea that since only the actual outcome exists, well what? That other outcomes don't? So what? If I program a robot car to react to traffic signals, I am encoding the possiblity that they will be red or green into computer language. Even if there is only ontologically speaking, the actual, my program would be a manifestation that this is not the case logically speaking.

"Indeed remind me of /precisely/ what your beef is again?"
I set out my beef with @Kg(Y) in #557 and #558 on the thread.

"My position is really straight forward I can in principle, if not in practise, establish the actual existence of putative states of affairs in the world. If someone can explain how I can /empirically/ establish the /existence/ of possibilia in the world."
I wonder whether you are assuming that the possible can have no role in our deliberations if they don't have the ontological status of the actual? If so, what about my car program?

"In pointing out not only the absence of any /empirical/ evidence that would demonstaate the existence of possiblia but also the lack of any instrumentalties that would allow such evidence to be gathered, surely, doing just that?"
I don't think a possiblility 'exists' in the sense you are using that term, otherwise it wouldn't be a possibility, it would be an actuality.

psi



'There is nothing of the petitio principii here'

The fact that your your de dicto definition of an indetereministic processes /assumes/ a particular /interpretation/ of indeterminacy as a premise that is consistent with your conclusion suggests otherwise. I could assume an indeterministic 'many worlds' interpretation or a deterministic 'hidden variable' inteptetation as premises which would result ia quite different conclusions. So your conclusion is assumed in your premise.

'In talking about things that are true by definition we avoid such complications, by which I mean /whether/ other things could have been actual if an indeterministic process had turned out differently.'

Ok then first begin by formally laying out your /de/ /dicto/ definition and then show how it has any material relevance to /actual/ events.

'Nothing in that statement warrants an interpretaion that I'm assuming that there are such processes as far as I can see'

If so then what is the relevance of you definition to an actual event in the world and why did you introduce it since 'could have been actual' says nothing about the /actual/ event in the world. What does 'could have been actual' mean if anything?

'Nothing in that statement warrants an interpretaion that I'm assuming that there are such processes as far as I can see'


If so then nothing in that statement is of /any/ relevance to events in the /actual/ world. So what is the point of your de dicto definition?

'the problems you mention seem to me to stem from your interpretation of actualism.'

Ah! the 'intepretation' gambit. It's not /my/ interpretation:

"The fundamental thesis of actualism is: Everything that exists (i.e., everything there is) is actual." (SEP)

'What makes a process ontologically indeterministic? The fact that what is actual was not causally necessitated by antecedent events (if such processes exist).'

The phrase 'if such processes exist' means you are advancing a hypothetical argument. Of what relevance is your brain state to an actual event in the world whether produced by a deterministic or an indeterministic process?

'Then you have the idea that since only the actual outcome exists, well what?'

That the onus is on anyone who asserts the existence of non-actual possibilia to provide an account of how one /can/ show that this is so.

'That other outcomes don't? so what?'

the is rather that when someone claims that possibilia (in some non-actual sense) exist then they have to specify precisely what they mean by 'exist'.

'So what? If I program a robot car to react to traffic signals, I am encoding the possiblity that they will be red or green into computer language. Even if there is only ontologically speaking, the actual'

A computer program is a set of instructions which may include branching conditionals. Your program merely encodes instructions on that determine behavior the car on encountering a predetermined layout of traffic lights. In fact you dont need ann actual car or an actual layout all you need is a version of your program which contains variables that when replaced by constants that specifies the state of of each traffic light. When this is done the state of the system is /fixed/ as is the behavour of the car. The variable do not represent 'possibilities' they simply allow one not to have to rewrite the progra each time it is run with different constants hard-coded.

'my program would be a manifestation that this is not the case logically speaking.'

Actually it doesn't because ther is nothing in the logic of your program that requires the inclusion of modalities in its instructions.

'I set out my beef withd @Kg(Y) in #557 and #558 on the thread.'
I was referring to your dodgy possible worlds 'rebuttal'.

'I wonder whether you are assuming that the possible can have no role in our deliberations if they don't have the ontological status of the actual?'

Given, that I have pointed out elsethread that that I accept that there are brain states that hypothesise alternate possibilities why would you assume this? However, the brain state can be about another brain state that has no actual correlate in the world, think pink unicorns.

'If so, what about my car program?'

What about it? See above.

'I don't think a possiblility 'exists' in the sense you are using that term, otherwise it wouldn't be a possibility, it would be an actuality.'

You need to take that point up with those who assert that possibilities exist in any sense. Feel free to argue that possibilities in any sense 'exist' that does not involve a humptydumptyist redefinition of the meaning of 'exist'.