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What is the difference between Logical necessity, and Metaphysical necessity?

 
 
troyjs
 
Reply Fri 10 Jun, 2011 12:50 am
After reading a little on the distinction between logical necessity and metaphysical necessity, this is how I understand it:

Logical necessity – A proposition is logically necessary, by virtue of equivalence.
All bachelors are unmarried men.
Bachelors is equivalent to unmarried men.

Metaphysical necessity – A proposition is metaphysically necessary, by virtue on entailment.
A man can not be in two places at once.
The word ‘man’ is not equivalent to ‘not be in two places at once’. Therefore it is not a logically necessary proposition. However, the meaning of the word ‘man’, entails not being able to be in two places at once, by virtue of fact.

Where it starts to become more interesting, is when a predicate is involved:
All German men are men.
The phrase ‘German men’, is not equivalent to the word ‘men’, yet this sentence seems to be analytic, or logically necessary.
This, I believe, is because the atomic nominative ‘men’, includes all predicates which can be attached to the word ‘men’ – the phrase ‘German men’ being a subset of the category ‘men’. With this in mind, it would seem that the predicate is not important, and can be ignored as regards to attaining the logical truth of the proposition.

My contention, however, is that metaphysically necessary propositions are in the same logical category.
A man can not be in two places at once.
The meaning of the phrase ‘not be in two places at once’ does not contain the meaning of the word ‘man’, and there is therefore no logical equivalence. But it would seem that the word ‘man’ is equivalent to another word or phrase, which is equivalent to the phrase ‘not be in two places at once’, in the same way that the phrase ‘German men’ is logically equivalent to the word ‘men’. If the predicate ‘German’ can be ignored in the case of the ‘German men’ proposition, then all irrelevant descriptions of the word ‘man’ can be ignored in the case of being in two places at once.

I hold that a name, if it is meaningful, is equivalent to its complete definition.

It would seem that this must be true, if we were to affirm that a proposition is metaphysically necessary. My argument is that a complete definition of the word ‘man’, will include the descriptive proposition, ‘not be in two places at once’.
If we designate this descriptive proposition as, ‘p’, then we have as follows:

If (p)(x) then (p) .. where x is all other descriptive propositions of the word ‘man’.

Does this mean that all true propositions can be translated into logically necessary propositions? If the relevant descriptive proposition is not part of the definition of a word, then how could we even have metaphysical necessity?
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igm
 
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Reply Fri 10 Jun, 2011 10:10 am
@troyjs,
troyjs wrote:

After reading a little on the distinction between logical necessity and metaphysical necessity, this is how I understand it:

Logical necessity – A proposition is logically necessary, by virtue of equivalence.
All bachelors are unmarried men.
Bachelors is equivalent to unmarried men.

Metaphysical necessity – A proposition is metaphysically necessary, by virtue on entailment.
A man can not be in two places at once.
The word ‘man’ is not equivalent to ‘not be in two places at once’. Therefore it is not a logically necessary proposition. However, the meaning of the word ‘man’, entails not being able to be in two places at once, by virtue of fact.

Where it starts to become more interesting, is when a predicate is involved:
All German men are men.
The phrase ‘German men’, is not equivalent to the word ‘men’, yet this sentence seems to be analytic, or logically necessary.
This, I believe, is because the atomic nominative ‘men’, includes all predicates which can be attached to the word ‘men’ – the phrase ‘German men’ being a subset of the category ‘men’. With this in mind, it would seem that the predicate is not important, and can be ignored as regards to attaining the logical truth of the proposition.

My contention, however, is that metaphysically necessary propositions are in the same logical category.
A man can not be in two places at once.
The meaning of the phrase ‘not be in two places at once’ does not contain the meaning of the word ‘man’, and there is therefore no logical equivalence. But it would seem that the word ‘man’ is equivalent to another word or phrase, which is equivalent to the phrase ‘not be in two places at once’, in the same way that the phrase ‘German men’ is logically equivalent to the word ‘men’. If the predicate ‘German’ can be ignored in the case of the ‘German men’ proposition, then all irrelevant descriptions of the word ‘man’ can be ignored in the case of being in two places at once.

I hold that a name, if it is meaningful, is equivalent to its complete definition.

It would seem that this must be true, if we were to affirm that a proposition is metaphysically necessary. My argument is that a complete definition of the word ‘man’, will include the descriptive proposition, ‘not be in two places at once’.
If we designate this descriptive proposition as, ‘p’, then we have as follows:

If (p)(x) then (p) .. where x is all other descriptive propositions of the word ‘man’.

Does this mean that all true propositions can be translated into logically necessary propositions? If the relevant descriptive proposition is not part of the definition of a word, then how could we even have metaphysical necessity?



I understand it like this:

If a proposition cannot be false, the proposition is a metaphysically necessary truth. In your example the proposition cannot be false. A proposition is logically necessary if it is not logically possible for it to be false e.g. Socrates could have been a hippopotamus is logically possible but not metaphysically possible. Whereas everything that has shape has size is a metaphysically necessary truth. If a proposition is logically necessary it is only a metaphysically necessary truth if it cannot be false in addition to this and in the particular way described above.

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