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A Technical Refutation Of Determinism

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Below is a technical refutation of determinism by Alvin Plantinga taken from his recent book Science, Religion, & Naturalism.  Where the Conflict Really Lies.  He shows that determinism is necessarily false.  He starts with a premise about the laws of nature which states that the laws of nature are as they are provided God doesn't act to change them.    Of course you do not need to believe in God in order to believe this because it is a conditional statement that doesn't presuppose the existence of God.  He then goes on to assume the truth of determinism, and then deduce a falsehood.  Given that determinism entails a falsehood, determinism must be false.

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(LN) When the universe is causally closed (when God is not acting specially in the world), P.

For example, Newton's law of gravity would go as follows:

(G)  When the universe is causally closed, any two material objects attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Note that on (LN), the currently canonical account of determinism implies that determinism is false.  According to that account, determinism holds just if the natural laws conjoined with the state of the universe at any one time entails the state of the universe at any other time.  A bit more exactly: let ''L'' be the conjunction of the natural laws, and S(t) and S(t*) be the states of the universe at any times t and t* : then,

Necessarily, for any t and t*, if L & S(t), then S(t*).

It is worth noting that if the above account of natural laws is correct, determinism so understood is false and indeed necessarily false.  For suppose determinism is true.  According to (LN), a natural law is of the form

If the universe (U) is causally closed, the P.

Take the conjunction of the natural laws to be

If U is causally closed, then P,

where now P is the conjunction of the consequents of all the laws.  Let ''PAST'' denote a specific past state of the universe.  Now suppose determinism is true.  Then

(1)  (If U is causally closed, then P) and PAST

entails

F (the actual future)

that is, (using 'N' to mean 'Necessarily'),

(2) N (If (1) then F).

(2) is equivalent to

(3) N [if (if U is causally closed, then P) and PAST, then F],

that is,

(4) N [if (either U is not causally closed or P) and PAST, then F],

that is,

(5) N {if [(PAST and P) or (PAST and U is not causally closed)] then F}

(5) is of the form

N if (p or q) then r;

but then each of p and q entail r; hence

(6) N [if (PAST and P) then F] and N [if (PAST and U is not causally closed) then F].

But the right hand conjunct of (6) is obviously false: clearly there is a possible world that (i) shares its past with the actual world, (ii) is not causally closed (because, perhaps, God acts specially in it) and (iii) does not share its future with the actual world.  Therefore determinism, which entails (6), is false.  Indeed, given the usual view that propositions of the form necessarily p are non-contingent, either necessarily true or necessarily false, (6) is necessarily false; hence determinism, which entails it, is also necessarily false.

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(bismillah)

(salam)

This is a very good argument. I have the following reaction to it. See if you agree.

I concede the conclusion he draws, i.e. that a causally-closed determinism is false, but I deny that the argument proves that.

The argument proves that if a causally-open universe is possible then a causally-closed determinism is false.

I believe it is possible, obviously. But a cc-determinist need not.

They may wish to believe a causally-open universe entails an inconsistency (not unlike people who think that the notion of 'God' is inconsistent). They'd have to prove it, of course.

But until the argument merely stipulates the possibility of a causally-open universe, then the argument does not entail that a cc-determinism is false.

(wasalam)

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On 11/7/2013 at 9:47 AM, guest102317 said:

(bismillah)

(salam)

This is a very good argument. I have the following reaction to it. See if you agree.

I concede the conclusion he draws, i.e. that a causally-closed determinism is false, but I deny that the argument proves that.

The argument proves that if a causally-open universe is possible then a causally-closed determinism is false.

I believe it is possible, obviously. But a cc-determinist need not.

They may wish to believe a causally-open universe entails an inconsistency (not unlike people who think that the notion of 'God' is inconsistent). They'd have to prove it, of course.

But until the argument merely stipulates the possibility of a causally-open universe, then the argument does not entail that a cc-determinism is false.

(wasalam)

Could you explain why it requires that an open universe be possible?

Is it because of 6?

I disagree that the argument requires the possibility of a causally open universe.  Someone may believe that (6) is true while also holding that its antecedent is impossible.  I.e. they may view it as a true contrapossible.  For example, 'If the law of excluded middle is false, then classical logic is flawed'.  This is a true conditional with an impossible antecedent (assuming that the law of excluded middle is necessarily true).  You can run an argument using it, accepting it as true, whilst taking its antecedent to be necessarily false.  Similarly, you may take an open universe to be broadly logically impossible (Id love to see proof of this) whilst taking (6) to be true.

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(bismillah)

(salam)

A conditional would be False iff the antecedent is True but the consequent False, and otherwise it is True.

A strict conditional would be False iff there is no possible world in which the antecedent is True but the consequent False, and otherwise it is True.

But suppose one disputes that there is a possible world in which the antecedent is True. Hence, they dispute that the strict conditional is False.

Following (6), Plantinga mentions that the right conjunct, which is in the form of a strict conditional, is False. But if one disputes that there is a possible world in which the antecedent is True, they thereby dispute that the strict conditional is False. Hence, they dispute that the right conjunct is False. It follows that they dispute the conclusion Plantinga draws from the argument.

-------

Quote
they may view it as a true contrapossible. For example, 'If the law of excluded middle is false, then classical logic is flawed'.

I concede that any [strict] conditionals with a False antecedent is True, such as your example. I deny that any [strict] conditionals with a False antecedent is False. If Plantinga does not prove his antecedent True, but he merely asserts it, there is nothing in the way of a cc-determinist to assert the antecedent False.

To be clearer, Plantinga's conclusion declares that his argument - as it stands - entails the falsity of cc-determinism on the grounds that the right conjunct is False. But without proof that there is some possible world in which the antecedent is True and the consequent False, the right conjunct is not proven False. Thus, the conclusion he draws is logically invalid.

How do you see my response?

(wasalam)

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On 11/7/2013 at 3:58 PM, guest102317 said:

(bismillah)

(salam)

A conditional would be False iff the antecedent is True but the consequent False, and otherwise it is True.

A strict conditional would be False iff there is no possible world in which the antecedent is True but the consequent False, and otherwise it is True.

But suppose one disputes that there is a possible world in which the antecedent is True. Hence, they dispute that the strict conditional is False.

Following (6), Plantinga mentions that the right conjunct, which is in the form of a strict conditional, is False. But if one disputes that there is a possible world in which the antecedent is True, they thereby dispute that the strict conditional is False. Hence, they dispute that the right conjunct is False. It follows that they dispute the conclusion Plantinga draws from the argument.

-------

I concede that any [strict] conditionals with a False antecedent is True, such as your example. I deny that any [strict] conditionals with a False antecedent is False. If Plantinga does not prove his antecedent True, but he merely asserts it, there is nothing in the way of a cc-determinist to assert the antecedent False.

To be clearer, Plantinga's conclusion declares that his argument - as it stands - entails the falsity of cc-determinism on the grounds that the right conjunct is False. But without proof that there is some possible world in which the antecedent is True and the consequent False, the right conjunct is not proven False. Thus, the conclusion he draws is logically invalid.

How do you see my response?

(wasalam)

Salam

Thanks for the reply. 

I said 'contrapossible' but what I should have said was counterpossible (a counterfactual with an impossible antecedent).  I havent been differentiating between strict conditionals and subjunctives.  I would need to read up more on strict conditionals to be able to appreciate your post.  What stops you from taking the premise as a subjunctive?

Quote
To be clearer, Plantinga's conclusion declares that his argument - as it stands - entails the falsity of cc-determinism on the grounds that the right conjunct is False. But without proof that there is some possible world in which the antecedent is True and the consequent False, the right conjunct is not proven False. Thus, the conclusion he draws is logically invalid.

The argument that I would make is that we ought to believe that this is possible.  We can see no logical contradiction in the concept of an open universe and the concept of an open universe does not contradict any metaphysical laws.  It does not require the existence of a God, so typical arguments against the logical possibility of God are not relevant here. 

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(bismillah)

 

(salam)

 

I don't disagree with your argument to accept the possibility of a causally-open universe. But I believe it would remain an assumption any diehard cc-determinist will have to do deny.

 

If we take Lewis' analysis, apparently subjunctives are conditionals with variable strictness, where the scope of the modal operator is determined by the accessibility relation. A strict conditional would be when the scope is at its widest, i.e. inclusive of all possible worlds.

So, treating it as subjunctive, it would still be the case that Plantinga's argument is, on its own, unable to disprove cc-determinism conclusively. What follows is why I see this to be the case.

 

Since a subjunctive is a conditional, to be False the antecedent would have to be True. Since they are modal, i.e. expressed in possible world semantics, the antecedent would have to be True in some possible world.

 

Thus, if the cc-determinist believes the antecedent to be impossible because inconsistent, then the only way an argument can compel them to withdraw this belief is if it proves that the antecedent is possible.

 

Does that make sense? There is another way I could argue this, I think. A different route altogether. But I believe this route is correct. Perhaps you'll agree.

 

(wasalam)

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On 11/7/2013 at 10:39 PM, guest102317 said:

(bismillah)

(salam)

I don't disagree with your argument to accept the possibility of a causally-open universe. But I believe it would remain an assumption any diehard cc-determinist will have to do deny.

If we take Lewis' analysis, apparently subjunctives are conditionals with variable strictness, where the scope of the modal operator is determined by the accessibility relation. A strict conditional would be when the scope is at its widest, i.e. inclusive of all possible worlds.

So, treating it as subjunctive, it would still be the case that Plantinga's argument is, on its own, unable to disprove cc-determinism conclusively. What follows is why I see this to be the case.

Since a subjunctive is a conditional, to be False the antecedent would have to be True. Since they are modal, i.e. expressed in possible world semantics, the antecedent would have to be True in some possible world.

Thus, if the cc-determinist believes the antecedent to be impossible because inconsistent, then the only way an argument can compel them to withdraw this belief is if it proves that the antecedent is possible.

Does that make sense? There is another way I could argue this, I think. A different route altogether. But I believe this route is correct. Perhaps you'll agree.

(wasalam)

Salam,

Quote
Since a subjunctive is a conditional, to be False the antecedent would have to be True. Since they are modal, i.e. expressed in possible world semantics, the antecedent would have to be True in some possible world.

Im following what you are saying.  From the little I have read on strict conditionals, it seems to me that what you are saying (about the argument requiring possibility) is true, if it is the case that the conditionals are meant to be read as strict conditionals.  If you have time, I would like some clarifications.

1.  According to wiki, a strict conditional is a material conditional plus modal operator.  But a material conditional isnt a subjunctive... or am I wrong?

2,  It doesnt seem that a subjunctive conditional needs a true antecedent to be false.  For example, 'If Cameron wasnt the Prime Minister, I would have been'.  The antecedent is false, but the conditional is true.

btw, what texts did you use to study logic? 

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(bismillah)

 

(salam)

 

 


1.  According to wiki, a strict conditional is a material conditional plus modal operator.  But a material conditional isnt a subjunctive... or am I wrong?

 

I understand you to be correct. A subjunctive is not a mere material conditional. The distinction between a subjunctive and a strict conditional seems to be a matter of degree, not of kind, and so the strict conditional would be the limiting case of a subjunctive, i.e. the maximum degree of a subjunctive.

To be specific, a strict conditional states that a material conditional holds in all possible-worlds simpliciter -- so it is the highest modal rigidity -- while a subjunctive states that a material conditional holds in all possible-worlds accessible by the actual-world -- so it does not hold in possible-worlds not accessible by the actual-world.

In your Cameron example, that is a subjunctive but not a strict conditional, because there is some possible-world, accessible to the actual-world or not, in which you become the Prime-Minister. Had it been a strict conditional, there would be no possible-world, accessible to the actual-world or not, in which neither you nor Cameron would be Prime-Minister.

 

 


2,  It doesnt seem that a subjunctive conditional needs a true antecedent to be false.  For example, 'If Cameron wasnt the Prime Minister, I would have been'.  The antecedent is false, but the conditional is true.

 

I believe you mean: the antecedent is false, but the conditional is false too. Am I right or have I misunderstood?

 

 

 


btw, what texts did you use to study logic?

 

I learnt the basics of formal logic rather sporadically and from different sources, because at that time I was not being tutored in logic.

I learnt and am still learning from T Sider's Logic for Philosophy which is quite broad, deep and rather mathematically precise. I have had a look at, and hope to study in earnest soon enough, Burgess' Philosophical Logic, which is basically an engagement with alternative logics. For mathematical logic, it was Boolos' et al Computability and Logic.

 

(wasalam)

Edited by Jebreil
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correction:

In your Cameron example, that is a subjunctive but not a strict conditional, because, supposing it were true there would be some possible-world, accessible to the actual-world or not, in which you don't become the Prime-Minister. Had it been a true strict conditional, there would be no possible-world, accessible to the actual-world or not, in which neither you nor Cameron would be Prime-Minister.

 

(wasalam)

Edited by Jebreil
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On 11/8/2013 at 3:39 PM, guest102317 said:

(bismillah)

(salam)

I understand you to be correct. A subjunctive is not a mere material conditional. The distinction between a subjunctive and a strict conditional seems to be a matter of degree, not of kind, and so the strict conditional would be the limiting case of a subjunctive, i.e. the maximum degree of a subjunctive.

To be specific, a strict conditional states that a material conditional holds in all possible-worlds simpliciter -- so it is the highest modal rigidity -- while a subjunctive states that a material conditional holds in all possible-worlds accessible by the actual-world -- so it does not hold in possible-worlds not accessible by the actual-world.

In your Cameron example, that is a subjunctive but not a strict conditional, because there is some possible-world, accessible to the actual-world or not, in which you become the Prime-Minister. Had it been a strict conditional, there would be no possible-world, accessible to the actual-world or not, in which neither you nor Cameron would be Prime-Minister.

I believe you mean: the antecedent is false, but the conditional is false too. Am I right or have I misunderstood?

I learnt the basics of formal logic rather sporadically and from different sources, because at that time I was not being tutored in logic.

I learnt and am still learning from T Sider's Logic for Philosophy which is quite broad, deep and rather mathematically precise. I have had a look at, and hope to study in earnest soon enough, Burgess' Philosophical Logic, which is basically an engagement with alternative logics. For mathematical logic, it was Boolos' et al Computability and Logic.

(wasalam)

correction:

In your Cameron example, that is a subjunctive but not a strict conditional, because, supposing it were true there would be some possible-world, accessible to the actual-world or not, in which you don't become the Prime-Minister. Had it been a true strict conditional, there would be no possible-world, accessible to the actual-world or not, in which neither you nor Cameron would be Prime-Minister.

(wasalam)

Thanks for the explanation.

Yes I meant false.

Do you think Sider's book can be effectively studied without a tutor, assuming basic propositional and predicate knowledge?

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(bismillah)

(salam)

Quote

2,  It doesnt seem that a subjunctive conditional needs a true antecedent to be false.  For example, 'If Cameron wasnt the Prime Minister, I would have been'.  The antecedent is false, but the conditional is false too.

I don't think I'm wrong in saying, for this [and any] subjunctive to be false, one would locate a possible-world w in which: (i) Cameron wasn't the Prime Minister [i.e. the antecedent is True in w] and (ii) you were not the Prime Minister either [i.e. the antecedent is False in w]; and (iii) w would be accessible to the actual-world.

Quote

Do you think Sider's book can be effectively studied without a tutor, assuming basic propositional and predicate knowledge?

It's a tough text, because it's very condensed, concise and rather mathematical. Yet, it's rather good at not assuming things as it proceeds, so, as long as one takes every step of the way as a substantial step in its own right, and is prepared to think it through until it's suitably grasped, the terseness shouldn't be a hindrance inshallah.

There's some amount of metalogic, but if you're happy to concede to the experts that the systems are consistent and (in)complete, you might as well ignore or leave for later. 

As for the more philosophical parts, if you're patient with it and are happy to read and re-read next week and come back in a month and read the same section again, and perhaps google any particular section which you find confusing, I believe it's manageable for purposes of philosophy. I've been maturing into this textbook rather than having it fed to me. It's an interesting experience. Every time I open the book, I treat it as a challenge, and hope to improve that bit more.

Have you come across Logic with Trees by Colin Howson? I have that book too, but I haven't studied much of it yet. It covers much less material, and it is more discursive, but no less rigorous. It seems to be the perfect bridge between Elementary Logic and Intermediate Logic.

(wasalam)

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(bismillah)

(salam)

Quote

2,  It doesnt seem that a subjunctive conditional needs a true antecedent to be false.  For example, 'If Cameron wasnt the Prime Minister, I would have been'.  The antecedent is false, but the conditional is false too.

I don't think I'm wrong in saying, for this [and any] subjunctive to be false, one would locate a possible-world w in which: (i) Cameron wasn't the Prime Minister [i.e. the antecedent is True in w] and (ii) you were not the Prime Minister either [i.e. the antecedent is False in w]; and (iii) w would be accessible to the actual-world.

Quote

Do you think Sider's book can be effectively studied without a tutor, assuming basic propositional and predicate knowledge?

It's a tough text, because it's very condensed, concise and rather mathematical. Yet, it's rather good at not assuming things as it proceeds, so, as long as one takes every step of the way as a substantial step in its own right, and is prepared to think it through until it's suitably grasped, the terseness shouldn't be a hindrance inshallah.

There's some amount of metalogic, but if you're happy to concede to the experts that the systems are consistent and (in)complete, you might as well ignore or leave for later. 

As for the more philosophical parts, if you're patient with it and are happy to read and re-read next week and come back in a month and read the same section again, and perhaps google any particular section which you find confusing, I believe it's manageable for purposes of philosophy. I've been maturing into this textbook rather than having it fed to me. It's an interesting experience. Every time I open the book, I treat it as a challenge, and hope to improve that bit more.

Have you come across Logic with Trees by Colin Howson? I have that book too, but I haven't studied much of it yet. It covers much less material, and it is more discursive, but no less rigorous. It seems to be the perfect bridge between Elementary Logic and Intermediate Logic.

(wasalam)

Quote

(bismillah)

(salam)

I don't think I'm wrong in saying, for this [and any] subjunctive to be false, one would locate a possible-world w in which: (i) Cameron wasn't the Prime Minister [i.e. the antecedent is True in w] and (ii) you were not the Prime Minister either [i.e. the antecedent is False in w]; and (iii) w would be accessible to the actual-world.

Im not sure exactly what you mean by accessible.  In order to be false, (1) there would have to be a possible world at which the antecedent is true, and the consequent is false, and (2) there is no other possible world closer to the actual world at which the antecedent is true and the consequent is true.  Maybe by accessible you mean (2)?  So whilst the conditional is false, it has a false antecedent, but in order to demonstrate its falsity one would have to locate a possible world in which the antecedent is true.  So you are right that a false conditional requires a true antecedent (but not necessarily true in the actual world - this is what confused me).

Quote

It's a tough text, because it's very condensed, concise and rather mathematical. Yet, it's rather good at not assuming things as it proceeds, so, as long as one takes every step of the way as a substantial step in its own right, and is prepared to think it through until it's suitably grasped, the terseness shouldn't be a hindrance inshallah.

There's some amount of metalogic, but if you're happy to concede to the experts that the systems are consistent and (in)complete, you might as well ignore or leave for later. 

As for the more philosophical parts, if you're patient with it and are happy to read and re-read next week and come back in a month and read the same section again, and perhaps google any particular section which you find confusing, I believe it's manageable for purposes of philosophy. I've been maturing into this textbook rather than having it fed to me. It's an interesting experience. Every time I open the book, I treat it as a challenge, and hope to improve that bit more.

Have you come across Logic with Trees by Colin Howson? I have that book too, but I haven't studied much of it yet. It covers much less material, and it is more discursive, but no less rigorous. It seems to be the perfect bridge between Elementary Logic and Intermediate Logic.

Howson's book looks very interesting.  I think I will be revisiting Sainbury's Logical forms initially, and then maybe take a look at logic with trees.  For the time being Sider's book is probably too heavy.  If I started reading it there is a high chance that I will get annoyed at slow progress and lose interest.  Thanks for rekindling my interest in the subject!

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