Kripke’s argument –
(1) take any objects x and y such that x is identical with y - then if x has a certain property F - y also has F
(2) take any object x- necessarily x is identical with x
(3) take as in (1), any objects x and y such that x is identical with y - and let F be the property of necessarily being identical with x - applying premise (1), we see that if x has this property - y has this property
But (2) tells us that any object x has the property of being necessarily identical with x
Hence:
(4), given any objects x and y such that x is identical with y - not only does x have the property of being necessarily identical with x [by (2)] but y has it also [by (3)] - that is, any object y which is identical with x is necessarily identical with x
my argument -
(1) is true if x and y are identical
the question is can x and y be identical? – if x and y are identical on what basis do we distinguish x and y – that is how is it that we are talking about two things and not one?
if we are talking about two things – x and y are not identical
if x and y are identical we are not talking about two things
on the face of it identity is a relation – a possible relation between things – i.e. ‘x is identical with y’
for a relation of any kind to hold – the entities must be distinguishable – otherwise there is no relation
therefore there cannot be any identity relations
(2) take any object x – x is necessarily identical with x
x cannot be distinguished from x – therefore there is no possibility of a relation of x with x
for x to be identical with x (necessarily or not) x would have to be x and not x
this is logically impossible – if not just plain stupid
and then you would have to argue an identity relation – which I have already shown makes no sense – even in the case where you have distinct entities
(3) if x and y are identical and x has the property F which is the property of necessarily being identical with x – then y has this property too
x and y cannot be identical – there is no identity – the concept is false – or we might say a common mistake of language if not perception – the kind of illusion philosophers were meant to dispel – not propagate
necessity is generally contrasted with possibility – a necessary property is one which cannot be other than it is –
any such description is an ‘epistemologically fatal description’ – that is behind it is the decision to regard the property as fixed –
that is to say ‘necessity’ is an epistemological decision to end inquiry – to reject possibility –
the desire for such ‘fixedness’ – for certainty – is very understandable – and may indeed have some pragmatic value at times – generally though it is the mark of a weak intellect
(4) if y is identical with x it is necessarily so
there is nothing to be said for this argument
necessity is just passed from premise to conclusion
yes it is a valid argument
but the argument would be valid if instead of ‘necessarily x is identical with x’ (2) asserted that ‘x is contingently identical with x’ etc.
‘necessity’ in this argument has no content – and therefore no value
which perhaps is the truth after all
Kripke distinguishes three types of identity statements
A. identity statements that join two individuating descriptions –
‘The first postmaster general of the United States is identical with the inventor of bifocals’ – ‘the x which is G is identical with the x which is H’
Kripke argues this is a contingent identity statement
an entity may be described in any number of ways – i.e. ‘x is the first postmaster general of the United States’ and ‘x is the inventor of bifocals’ – and whatever other descriptions might be used
in a logical sense the entity is truly an ‘x’ – an unknown – in the absence of description
description makes known – not in any absolute sense – but rather in an operational sense – that is we can ‘operate with x’ – when x is described – that is to say description enables -
the x which is G and the x which is H – is the x described as G and described as H
there is only one x – variously described
that is in the above example – there are not two entities – the first post master general of the United States – and – the inventor of bifocals
there is only one entity to which these descriptions have been applied
so there is no question of identity – if indeed it was regarded as a genuine question
furthermore
the descriptions themselves are clearly not ‘identical’ – they are distinct -
they can have the same reference point
but the logic of this is a decision to say x is G and H and I and J etc. –
that is the one entity x is given multiple characterizations
what - is x outside of these characterizations?
x
B. identity statements which join two proper names – ‘Cicero is Tully’ (‘a = b’)
Kripke holds if B is true – it is necessarily true
a proper name is an identification mark - it is a reference place for description
it is actually just an indicator that sets up the possibility for description
any entity can be named – and variously named
to say ‘Cicero is Tully’ is really only to say x is named C and x is named T
will the two reference points be identical?
that is to say will the C-point descriptions be identical to the T- point descriptions?
this is really a contingent question
there may be parallels – even family resemblances – or indeed strangely - no apparent relation
it all depends on the facts of the matter – I’m sorry to say
but do we have identity?
if there are multiple reference points (proper names) there just simply is different description lines from these points
parallel lines – possible – but distinct - therefore not identical
and the ‘distinction’ is contingent – a matter that is of place and time at the very least – not to mention the indeterminacy of perception and the possibilities of conception
but just back to the statement ‘Cicero is Tully’ for a moment –
it as actually a meaningless use of terms – unless different description lines are presumed – which would usually be the case
on the question of proper names Kripke makes a distinction between rigid and non-rigid designators –
consider the question – might someone else have been the inventor of bifocals?
and the question might someone else have been Richard Nixon?
Kripke says yes to the first and no to the second
the first instance of proper name usage is regarded as non-rigid and the second as rigid
in relation to the first the answer is not ‘yes’ it is rather that we do not know
it is a contingent matter – bifocals may been invented by another – or they may never have been invented – if they hadn’t been invented by the turkey who invented them
in so far as they were invented and invented by ‘the first Postmaster General of the United States’ (formerly known as ‘x’) then we can say that the designator – is active
that is we can use it – at least until the ‘real inventor’ comes forward –
the idea of Richard Nixon as ‘a rigid designator’ – opens up the possibility of a whole dimension of logic devoted to horror
and who can doubt it – Nixon did rigidly designate Vietnam Cambodia the Constitution of the United States and finally mercifully – himself
the logical question being asked here is – might someone else have been Richard Nixon – someone other than the man he is?
the proper name Richard Nixon – is a reference place for many and varied lines of description
we ‘know’ Richard Nixon in terms of those descriptions
so the question is might Richard Nixon be described in a manner – different from the lines of description already active
the answer is yes
‘Richard Nixon’ is a reference point for description
outside of these descriptions - Richard Nixon is an unknown -
(or was) even to himself
the name is only a point for reference
it designates the logical space for description
to name is the decision to apply description to the unknown
the identification involved in naming is logically speaking uncertain
if it is the unknown that is identified – in a logical sense – how is it identified?
how do you make a reference point in the unknown?
first up in actual reality as distinct from logical reality we come to the making of descriptions – in a world already described –
I can’t imagine any situation where the pure (as in logical) unknown is what we face
any phenomenon no matter how novel will be describable to some extent
so we always begin our description on some basis of accepted or given description
we do as a matter of practical necessity – signify - in whatever manner - the logical place to be described
this only works given that others recognize this signification
how that occurs is a question for science
C. theoretical identifications – ‘heat is the motion of molecules’ or ‘pain is a certain state of the brain’
firstly – ‘heat is the motion of molecules’
‘heat’ here is a description of a phenomenon
‘motion of molecules’ – is a theoretical explanation
different types of description
a correct logical analysis of this statement would be x is described as H (heat) and H is described as M (motion of molecules)
which of course means x is also described as M
two different accounts or descriptions of x
this is not to suggest that the x in question is not real until described
it is rather to say that description provides a platform for dealing with it –
that is it gives us identifiers
the two descriptions are different accounts of the one thing
they emerge essentially from the need to deal with it in different ways
the description ‘heat’ may be an explanation of sensation – and that may be all that is being asked for
the description ‘motion of molecules’ comes from a need to account in terms of the laws of physics
the entity or phenomenon being so described as ‘heat’ or ‘motion of molecules’ is logically speaking - independently of these or any other descriptions – unknown
‘pain is a certain state of the brain’
‘pain’ – we shall say is a description of an event
‘a certain state of the brain’ – likewise a description
x is described as P and x is described as BS (a certain brain state)
the event itself is only known in terms of the descriptions applied to it
to argue that P is BS - can only mean that one description can function for another
and if that was the case why two descriptions?
clearly one does not function for the other
for if it did then science would not need the description BS – P would do the job
the descriptions P or BS fulfill different functions
the event itself – independent of its description - is unknown
to argue i.e. that P can be replaced or should be replaced by BS is only to argue for a change of usage
good luck
© greg. t. charlton. 2009.
