Spinoza: Concerning God

Spinoza's Ethics
First Part
Concerning God


I present Spinoza’s axioms definitions and propositions and follow each with my response



DEFINITIONS:


D.I. I understand that to be CAUSE OF ITSELF (causa sui) whose essence involves existence and whose nature cannot be conceived unless existing.


'cause in itself' is that which has no explanation - in other words it is the unknown

as it is used in D.I. ‘cause of itself’ is a description of the unknown as if it is known – in other words it is a fraudulent notion



D.II. The thing is said to be FINITE IN ITS KIND (in suo genere finite) which can be limited by another thing of the same kind. E.g., a body is said to be finite because we can conceive another larger than it. Thus a thought is limited by another thought. But a body cannot be limited by a thought, nor a thought by a body.


how a thing is described will dictate what it is and what it is not

i.e., a physical description will be at odds with a non-physical description –

the thing itself is unknown – in itself it has no definite description

its description is a question of utility

description is always an open question


D.III. I understand SUBSTANCE (substantia) to be that which is in itself and is conceived through itself: I mean that, the conception of which does not depend on the conception of another thing from which it must be formed.


a substance is that which is undefined – that which is undefined is unknown


D.IV. An ATTRIBUTE (attributum) I understand to be that which the intellect perceives as constituting the essence of a substance.


an attribute is a primary description of a substance


V. By MODE (modus) I understand the Modifications (affectiones) of a substance or that which is in something else through which it may be conceived.


a modification or mode is a secondary description


VI. GOD (Deus) I understand to be a being absolutely infinite, that is a substance consisting of infinite attributes, each of which expresses eternal and infinite essence.

I say absolutely infinite, but not in its kind. For whatever is infinite only in its kind, we may deny the attributes to be infinite; but to the essence of what is absolutely infinite there appertains no negation.


‘God’ is a name for the unknown –

(any proper name is a ‘description place’ – that is an identification of the logical place for description – a proper name has no meaning – except as a mark for description – its status is syntactical)


VII. The thing is said to be FREE (libera) which exists by the mere necessity of its own nature and is determined in its actions by itself alone. That thing is said to be NECESSARY (necessaria), or rather COMPELLED (coacta), when it is determined in its existence and actions by something else in a certain fixed ratio.


to describe a thing as free or compelled is to characterize it – and to characterize it in relation to other things

the utility of these characterizations is determined by the uses the are put to

either characterization fits within a broader descriptive framework or world view

there is no essential world view – there are only options

a free conception and a compelled conception are two such perspectives

in itself the world is unknown


VI. I understand ETERNITY (aeternitas) to be existence itself, in so far as it is conceived to follow necessarily from the definition of an eternal thing.

Explanation. – For such existence is conceived as an eternal truth, just as is the essence of a thing, and therefore cannot be explained by duration or time, although duration can be conceived as wanting beginning and end.


time is the space between events – which is to say it is the making of a measurement of the relation of events

eternity is the absence of the measurement of events

it has no use



AXIOMS


A.I. All things which are, and are in themselves or in other things.


a thing can be described independently or in relation to other things


A.II. That which cannot be conceived through another thing must be conceived through itself.


a thing may be conceived in relation to another thing or independently of other things


A.III. From a given determined cause an effect follows of necessity, and on the other hand, if no determined cause is granted, it is impossible that an effect should follow.


the relation of things can be described in terms of cause and effect


IV. The knowledge of an effect depends on the knowledge of a cause, and involves the same.


our knowledge of cause and effect is based on the decision to relate things in such a manner


V. Things which have nothing in common reciprocally cannot be comprehended reciprocally through each other, or, the conception of one does not involve the conception of another.


things can be related in terms of each other or they can be known or described independently of other things


VI. A true idea should agree with its ideal (ideatum) i.e., what it conceives.


an idea of a thing makes that thing known –

truth is a question of function – does the idea enable action in relation to the thing in question?


VI. The essence of that which can be conceived as not existing does not involve existence.


a thing exists in terms of its description



PROPOSITIONS


P.I. A substance is prior in it nature to its modifications.


a substance is its modifications – that is its descriptions –

apart from its descriptions it is unknown


P.II. Two substances, having different attributes, have nothing in common between them.


two substances having different attributes – that is different primary descriptions have in common that they are (apart from their attributes) unknown


P.III. Of two things having nothing in common between them, one cannot be the cause of the other.


the cause or reason for anything is unknown –

any causal proposal is a conjecture –

the validity of any such explanation depends on the broader theoretical descriptions in which it is embedded

how things are and how they related to each other is a matter of description –

description is the ground for action

what action or end is being contemplated determines description


P.IV. Two or three distinct things are distinguished one from the other by the difference of the attributes of the substances or by the difference of their modifications.


things are distinguished by their definitions – by their descriptions


P.V. In the nature of things, two or more substances may not be granted having the same nature or attribute.


we do not apply the same description to two things in principle because to do so renders the act of description useless

in practise the question of meaning is the question of deciding how and when a description does or does not apply


P.VI. One substance cannot be produced by another.


how things are described determines their relation

a substance outside of definition is an unknown –

how a substance is defined will determine its relation with other substances –

the production of substances is a theory of how nature works –

for any such theory to function substances must be defined and defined in relation to each other

anything can be related to anything else – the issue is to find the appropriate description –

such is the task of science


P.VII. Existence appertains to the nature of substance.


if a thing exists it exists

the real question is what descriptions apply to it –

and this is a question of how something is to be understood –

the question is not if x exists – it is rather how x is described – which is to say how x exists

ultimately there is no unique existential description


P.VIII. All substance is necessarily infinite.


the unknown is not necessary or infinite – it is – unknown

substance is made known in description

to describe x as infinite is to describe it as being without limits

this is a false description

for x to be – x must be distinguished from ~x

that is x must be described as what it is - as distinct from what it is not

any description is the drawing of limits

there is no infinite description


P.IX. The more reality or being a thing has, the more attributes it will have.


a thing may be described variously –

the more descriptions that can be applied to a thing – the more utility it has


P.X. Each attribute of the one substance must be conceived through itself.


there is no definite description of any thing –

any description is based on a prior description –

so no attribute (description) can be conceived through itself (be based on itself)


P.XI. God or a substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists.


God or a substance consisting of infinite attributes each of which expresses eternal an infinite essence is a thing without definition –

the act of definition is an act of distinction –

that is the point of the act is to distinguish x from ~x

that which cannot be defined cannot be described –

that which cannot be described cannot exist

our knowledge of what exists just is our descriptions of the world –

beyond description the world is unknown


P.XII. No attribute of a substance can be truly conceived, from which it would follow that substance can be divided into parts.


an attribute is a definition or description of a substance –

the substance itself is unknown outside its definition –

definition is a question of utility –

a substance may be described as having parts – if this description is deemed useful


P.XIII. Substance absolutely infinite is indivisible.


substance absolutely infinite – is indefinable

that is to say if x cannot be distinguished from ~x – then x itself cannot be determined

definition requires negation – that which cannot be distinguished in terms of its negation cannot be defined

to define substance as absolutely infinite is to deny the logic of definition


P.XIV. Except God no substance can be granted or conceived.


a substance is that which prior to description is unknown –

the unknown is described variously –

‘God’ is one among many possible descriptions of the unknown

‘God’ as a proper name is a logical place for description – it is an identification mark


P.XV. Whatever is, is in God, and nothing can exist or be conceived without God.


the unknown is the ground of all description


P.XVI. Infinite things in infinite modes (that is, all things which can fall under the heading of infinite intellect) must necessarily follow from the necessity of divine nature.


the unknown is the object of consciousness –

it is only determined by description –

the unknown is the ground of possible description –

the only necessity is the necessity to act –

description is the basis of action


P.XVII. God acts merely according to his own laws, and is compelled by no one.


the ground of description is the unknown –

different pursuits require different forms of description

there is no universal description

the question of the logic of description is always an open question

it is itself a matter for description


P.XVIII. God is the indwelling and not the transient cause of things.


'God' is a name for the unknown

in asking ‘what is the cause of things?’ –

we can say we do not know in any final sense

but this is not to say the unknown is the cause of things –

and this is what Spinoza’s view comes to

any theory of the cause of things is a response to the unknown

it is an attempt to provide a theoretical platform that will enables us to act rationally in the world


P.XIX. God and all the attributes of God are eternal.


all descriptions (attributes) have value – all value is a question of utility – utility is a question of contingency – that is time place - need


P.XX. God’s existence and his essence are one and the same thing.


the unknown’s existence and its essence are one and the same thing - unknown


PXXI. All things which follow from the absolute nature of any attribute of God must exist forever and infinitely, or must exist eternally and infinitely through that same attribute.


any description of the unknown has value only in terms of its utility


PXXII. Whatever follows from an attribute of God, in so far as it is modified by such a modification as exists of necessity and infinitely through the same, must also exist of necessity and infinitely.


whatever follows from a description has value in terms of its utility

any description of the unknown is an attempt to determinate it

the determination will be successful or not depending on the task it is put to - and the criterion for success that is adopted


P.XXIII. Every mode which of necessity and infinitely exists must of necessity have followed from either the absolute nature of some attribute of God, or from some attribute modified by a modification which exists of necessity and infinitely.


any description is a description of the unknown or a description of a description of the unknown –

the existence of any description is a question of its utility –

there is no necessity in utility – utility is uncertain


P.XXIV. The essence of things produced by God does not involve existence.


the essence of things is the unknown – the unknown is the ground for existential statements


PXXV. God is not only the effecting cause of the existence of things, but also of their essence.


the unknown is the ground of any explanation – the cause of things is unknown – as is their essence


P.XXVI. A thing which is determined for the performing of anything was so determined necessarily by God, and a thing which is not determined by God cannot determine of itself to do anything.


action is the immediate ground of description –

an action is determined or not in description –

outside of description any action is unknown


P.XXVII. A thing which is determined by God for the performing of anything cannot render itself undetermined.


God or the unknown is undetermined –

a determination is a description –

a description is the ground for action –

there is no definite description –

the unknown is only ever provisionally determined


P.XXVIII. Every individual thing, or whatever thing that is finite and has a determined existence, cannot exist or be determined for action unless it is determined for action and existence by another cause which is also finite and has a determined existence; and again, this cause also cannot exist nor be determined for action unless it be determined for existence and action by another cause which also is finite and has a determined existence: and so on to infinity.


a thing is determined by description –

natural determination – or veridical perception is a function of the relation of consciousness to it object –

to describe a thing as finite is to assert it is definable –

to speak of the cause of any thing is to offer an existential explanation of it –

determinism is a form of description which is consistent with the idea that all things are determined –

such a view has itsuses


P.XXIX. In the nature of things nothing contingent (contingens) is granted, but all things are determined by the necessity of divine nature for existing and working in a certain way.


the unknown is neither necessary or contingent – it is unknown –

any determination of the unknown – that is any description of it is uncertain

so called ‘necessary’ descriptions may prove useful depending on the task to be performed

necessity is a decision to stop inquiry – to establish a foundation

its value is pragmatic

contingency is the way of things


P.XXX. Intellect, finite or infinite in actuality (actus), must comprehend the attributes of God and the modifications of God and nothing else.


the object of knowledge is the unknown – the intellect determines the unknown for action


P.XXXI. The intellect in actuality, whether it be finite or infinite, as also will, desire, love, etc., must be referred not to active but passive nature.


the intellect or the action of consciousness refers to that outside itself –

the unknown can be characterized as active or passive or uncertain or in any number of ways –

the object of consciousness does not dictate its characterization or description


P.XXXII. Will can only be called a necessary cause, not a free one.


will is a conscious determination of the body –

an action can be described as free or not free


P.XXXIII. Things could not have been produced by God in any other manner or order than that in which they were produced.


the origin of things is unknown –

we make speculative theories in response to any such question –

the question itself is open to question i.e. perhaps there is no origin


P.XXXIV. The power of God is the same as his essence.


the essence of reality is that it is unknown –

any action in response to this reality is an act of power –

that is in the face of the unknown –

any action is powerful -

action is power


P.XXV. Whatever we conceive to be in the power of God necessarily exists.


the unknown is powerless


P.XXXVI. Nothing exists from whose nature some effect does not follow.


we can conceive the world in terms of cause and effect – such an idea is natural to human consciousness – and as such is useful



© greg. t. charlton. 2009.

Chomsky's reflections on 9-11

Chomsky asks three questions:

(1) who is responsible?
(2) what are the reasons?
(3) what is the proper reaction?
(4) what are the longer term consequences?

in response to (1) he accepts the CIA analysis –

‘that the guilty parties were Bin Laden and the Al-Qaeda network’

Chomsky says no one knows more about them than CIA.

Chomsky goes on to mention the attack on the World Trade Centre and that the ‘FBI director Robert Mueller testifying to Congress could only say that U.S. intelligence now ‘believes’ the plot was hatched in Afghanistan though planned and implemented elsewhere’

he goes on -

‘And long after the source of the anthrax attack was localized to U.S. government laboratories, it has still not been identified’

his conclusion is that ‘despite the thin evidence the initial conclusion about 9-11 is presumably correct’

thin evidence?

Chomsky notes the evidence has been ‘hard to find’

none of the perpetrators or material witnesses survived the attacks and no useful forensic evidence survived

so my question is – what evidence?

the CIA argument is speculation

it is a case of finding a criminal to fit the crime – in the absence of any direct evidence

the argument seems to be –

Al- Qaeda ‘attempted to blow up the World Trade Centre and many other targets in a highly ambitious campaign in 1993’

therefore

Al-Qaeda is responsible for the atrocities of 9-11

this is not a valid argument and as Chomsky notes the FBI cannot endorse the first premise

the conclusion may well be true but as far as I know to date there is no direct evidence for it

the U.S. government set up Guantánamo Bay prison – with the intention of obtaining ‘intelligence’ and ‘evidence’ in relation to 9-11 and the activities of Al-Qaeda – from all reports it is a torture chamber – and any information obtained would have no value in an independent court of law

if you accept the Chomsky-CIA argument as indeed most everyone has - then you can go on to (2) – why?

what were the reasons for the attack by Al-Qaeda?

Chomsky says –

‘Turning to (2), scholarship is virtually unanimous in taking the terrorists seriously at their word, which matches their deeds for the past twenty years: their goal, in their terms, is to drive the infidels from Muslim lands, to overthrow the corrupt governments they impose and sustain, and to institute an extremist version of Islam’

this is an argument based on the authority of scholarship

he also notes that Eisenhower and his staff discussed ‘the campaign of hatred against us’ in the Arab world ‘not by the governments but by the people’

the National Security Council advised that the basic reason is that the U.S supports corrupt and brutal governments that block democracy and development in order ‘to protect its interests in Near East oil’

this may well be a correct answer to George Bush’s question “Why do the hate us?’

and if you accept the argument of (1) then it could well be a reason for the atrocity of 9/11

but the question really needs to be asked – from this so called Arab point of view - how did the attacks of 9-11 advance their cause against the U.S.?

it was a hit – and in that sense a successful attack on America – but what were the consequences in terms of the above reasons?

as a result Bin Laden it would seem is no closer to expelling the infidels in Saudi Arabia and assuming power in that region

if anything the effect of 9-11 on the Muslim world has been catastrophic

the U.S. response was to wage a war of terror on Afghanistan and Iraq – which resulted in the mass murder of Muslims and the destruction of their societies and cultures

my point is if you accept the Chomsky-CIA argument that Al-Qaeda was responsible for 9-11 and further that it acted for the reasons given by Eishenhower’s National Security Council –

then at the very least you would have to conclude Al-Qaeda failed

this of course assumes that the attack on the US was designed to weaken the US position in Muslim lands

and it also assumes that the 9-11 attack was in some sense rational – that at the very least it was motivated by some goal beyond just mass murder and destruction

political leaders are adept at using religious groups for their own political purposes –

it has been claimed i.e. that George Bush used the Christian right to gain power

has anyone considered the possibility that Bin Laden has done the same kind of job on the Muslims – that is used them for his own purposes?

and as to what they might be – let me just say be careful not to automatically assume that his reasons are or were rational

and I hasten to add the same warning applies to any assessment of the actions of Bush and his gangsters

now to (3)

from an epistemological point of view the question is – in the absence of any hard evidence and in the absence of an independent judicial process what is the proper response to the atrocity of 9-11

first up it needs to be made clear that it has never seriously been put that on 9-11 the U.S. was attacked by a nation state

from the outset – the money was on Al-Qaeda

it is my recollection that in response to the claim by the Bush administration that Bin Laden and his gang were in Afghanistan – the Taliban government said they would hand him over but only to an international court

the U.S. rejected this proposal

not long after they attacked

the successful overthrow of the Taliban and the failure to capture Bin Laden was followed by another attack on a nation state – Iraq

we need not go into all the lies and slide shows that precipitated this war

the point is that as with Afghanistan – if you accept the Chomsky-CIA argument it was the wrong target

it was not only the wrong target – it was the wrong type of target

9-11 – on the Chomsky-CIA argument was not an attack by a nation state on a nation state

it was rather an attack by a terrorist group on the U.S.

the Americans got it wrong – in terms of their own argument

their response was illogical

Chomsky argues

‘What about the proper reaction, question (3)? The answers are doubtless contentious, but at least the reaction should meet the most elementary moral standards: specifically, if an action is right for us, it is right for others; and if wrong for others, it is wrong for us’

the argument is – what’s right for me is right for you – what’s wrong for me is wrong for you –

if you accept that then the converse is true –

what’s right for you is right for me – what’s wrong for you is wrong for me

OK let us say from the point of the view of the perpetrators it was right to attack the U.S. and cause the destruction of innocent lives

there were people in the Bush administration that believed the U.S. was therefore licensed to attack and cause the destruction of innocent lives

what’s right for them is right for us

presumably the perpetrators were of the opinion that to do nothing was wrong – hence 9/11

was the Bush administration therefore justified in taking the same view?

in terms of the principle Chomsky enunciated above the answer it seems is ‘yes’

Chomsky does not put forward a definition of what is right – what is wrong

and surely this is the most important of issues – it is left open

fill in the blanks –

what you believe is right – is what is right for others – and what you believe is wrong is wrong for others

the perpetrators of 9-11 would most likely fully endorse that view

and the Bush administration would not be troubled by it either

Chomsky’s principle has no moral content -

so what should have been the proper response?

this was the very real dilemma facing President Bush

now you may not agree with or support what turned out to be his response – but I don’t think anyone would doubt he faced an almost impossible moral dilemma

no response was not an option

but what is the correct response?

my reading of Bush immediately after 9-11 was that he faced this issue head on – and was not just concerned with a response – but indeed with the proper response

I really felt for him during that period

however he is not the first person to be in this dilemma –

a wrong has been committed – and there is no clear evidence as to who the criminals are or where they are

ordinary citizens fall back on a system of justice – with the knowledge that even if it functions correctly and due process occurs – there is no guarantee that they will get satisfaction

as a matter of definition they get justice – but in the case of murder for instance – even if there is a just conviction and sentence – the loved one’s of the victim will never have retribution – it is not possible

and as they say if you want revenge – dig two graves

what I am getting at here is that the proper response to crime is a legal response

now in the case of a nation state – how is this possible?

what is clear is that it is only possible if a nation state that has been wronged is prepared to submit to an international court of law

now to cut to the quick – as far as I know there was no international court and international force that would have been able to address the atrocity of 9/11

yes we have war crime tribunals and United Nations courts of arbitration - but really no international justice system to deal with a terrorist attack on a nation state

at the very least it seems to me that the U.S. should have moved to establish a legal framework that was designed to deal with such crimes

there is no doubt in my mind that had this been the response of the Bush administration – they would have received enormous if not unanimous support from the nations of the world

and I am pretty sure there would have been an out pouring of resources – and an international determination to right the wrong and to achieve justice

an international justice framework for dealing with terrorism was lacking then and it still is - and everyone everywhere is less secure because of this fact

now to (5) what are the longer term consequences?

let us be perfectly clear – the 9-11 attacks were attacks on the U.S.

decent people all over the world felt for America and its citizens on that day

and there was no doubt in their minds that the perpetrators of the crimes should be brought to justice

America had more allies on that day than they have ever had

and then George Bush put the proposition “you are either with us or against us”

it was just then that they lost the argument

there was absolutely no need to play the stand over man – to do the strong arm

and furthermore one of the assumptions of his threat was that the attack on the U.S. was an attack on ‘all freedom loving people’

his argument was that 9-11 was not just an attack on the US – but rather an attack on all countries and governments that were not pro-terror

so from the word go Bush misrepresented the fact

the attack was an attack on America – no one else was attacked on 9-11

and either out of fear of the U.S. or the belief that God was on their side countries lined up – to fight the good fight

and this of course meant that those in the ‘coalition of the willing’ had to sell the misrepresentation to their citizens

I am assuming here of course that collaborators like Blair and Howard actually realised that they were being conned – and then passed it on

this may not have been the case – it is possible that they were just stupid

the result though was atrocities being perpetrated on innocents in the name of freedom and democracy

that is the systematic commission of war crimes

the question though is what will be the long term consequences of 9-11?

Chomsky concludes –

‘the basic issues of international society seem to me to remain such as they were, but 9-11 surely has induced changes, in some cases, with significant and not very attractive implications’

what is clear is that the U.S. is weakened – not by the attack of 9-11

but by the lies it told post 9-11

there was no need to lie –

and the fact of the lies being told was a sign of the moral weakness of the U.S. government - the governments that fell in with them – and the governments that remained silent

one result of this is that the moral authority of government has been eroded

when people question the truth of their governments they question the truth of government


© greg. t. charlton. 2009.

Saul Kripke - identity and necessity

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.

Russell on mathematics XVIII

Russell: introduction to mathematical philosophy:
mathematics and logic


according to Russell mathematics and logic are one –

logic is the youth of mathematics and mathematics the manhood of logic

after a survey of all that has come before in his book Russell asks the question

‘What is this subject, which may be called indifferently either mathematics or logic? Is there any way we can define it?’

to begin Russell says

in this subject we do not deal with particular things or properties –

we deal formally with what can be said to be any thing or any property

logic does not deal with individuals – because they are not relevant or formal

in the syllogism the actual truth of the premises is irrelevant – all that is important is that the premises imply the conclusion

a syllogism is valid in terms of its form – not in virtue of the particular terms occurring in it

and we are therefore faced with the question – what are the constituents of a logical proposition?

if we take a relation between two terms we may represent the general form of such propositions as xRy – i.e. x has the relation R to y

in the assertion ‘xRy is sometimes true’ i.e. there are cases where dual relations hold – there is no mention of particular things or relations

we are left with pure forms as the only possible constituents of logical propositions

the form of a proposition is that which remains unchanged when every constituent of the proposition is replaced by another

logic is concerned only with forms – and stating that they are always or sometimes true

in the proposition ‘Socrates is human’ – the word ‘is’ is not a constituent of the proposition – but merely indicates the subject predicate form

in the proposition ‘Socrates is earlier than Aristotle’ ‘is’ and ‘than ‘ merely indicate form

however form can be the concern of a general proposition even when no symbol or word in that proposition designates form

Russell argues we can arrive at a language in which every formal belonged to syntax and not vocabulary

in such a language we could express all the propositions of mathematics even though we did not know one word of the language

we should have symbols for variables such as ‘x’ an ‘R’ and ‘y’ arranged in various ways – and the way of arrangement would indicate something was being said of all or some of the values of the variables

there are symbols with constant formal meanings – these are ‘logical constants’

‘logical constants’ will always be derivable from each other - by term for term substitution

and that which is in common is ‘form’

all constants that occur in pure mathematics are logical constants

logical propositions are those that can be known a priori – that is without study of the actual world

logical propositions have the characteristic of being tautologous – as well as being expressed in terms of variables and constants

this gives us the definition of logic and pure mathematics

Russell says he does not know how to define tautology

and in a note to this matter says –

‘The importance of “tautology” for a definition of mathematics was pointed out to me by my former pupil Ludwig Wittgenstein, who was working on the problem. I do not know whether he has solved it, or whether he is alive or dead.’

yes – one gets the impression here that Russell was not all that keen on the tautology

or at the time of his writing the above all that keen on the student who introduced the ‘importance’ of it to him

for he doesn’t even bother to give a definition of tautology

we are left wondering – perhaps indeed it is just a bad smell

also one would imagine a query here a word there could have settled the question of whether Wittgenstein was alive or dead –

perhaps though the first world war was the reason for placing Wittgenstein in a disjunction


my view on all this is -

all propositions are actions – we can say propositional actions

their basis is necessity – practical necessity

that is we propose descriptions of the world – so as to be able to operate effectively in the world –

we can therefore say any proposal is a proposal for order

we need order so as to operate effectively

this is a premise for any propositional behaviour

logic is a description of the possibilities of propositional order

that is logic displays the order inherent in propositional behaviour

so my first point is that logic is a descriptive action

the propositions of logic describe what is possible with propositions – that is how they can be ordered – how they can be related

i.e. a proposition can be put – and its opposite can be put

the second proposition is negation of the first - the relation here is negation

two propositions can be conjoined – and in such a case their relation is conjunction

propositions can be disjoined – and their relation is disjunction

implication is a relation where one proposition is said to imply another

describing the relations between propositions (negation conjunction disjunction implication) tells us not only how propositions are used – but also if the question arises – how they can be used - in relation to each other

in this sense logic is the study of propositional relations

and it is an account or description of propositional behaviour that applies to any propositional usage – mathematical or empirical

mathematics is primarily concerned with calculation

that is to say it is a particular or specialized propositional usage –

this is not to suggest that mathematics is in any way limited –

for it is clear that any kind of experience can be made the subject of calculation

logic though is not an activity of calculation – even though there is calculation in logic

it is a description of the possibilities of propositional behaviour – one form of which is mathematical action

and it is in that sense a description or a proposal about what actually occurs

for this reason it makes no sense to speak of it as being a priori

logic as a descriptive activity only exists because propositional behaviour exists –

because that is how the world is in terms of human beings and their actions

the propositions of logic are descriptions of what occurs or can occur when people use propositions

Russell mentions the law of self-contradiction as a logical proposition – and somewhat reluctantly the tautology

‘it is raining and it is not raining’ is a self-contradiction – it is a proposition that contradicts itself – it is a logically false statement

which to my mind means quite simply it has no use

‘it is raining and it is raining’ – is tautologous – it is a proposition which takes the value true for all assignments of truth values to its atomic expressions

again it like the self-contradiction is a propositional form that has no utility – no use

now I make this point to raise the question whether it makes any sense to speak of ‘propositions of logic’

if as Wittgenstein argues and Russell comes along for the ride – the propositions of logic are all tautologous –

then as a set of propositions they are useless

but they are only useless in this sense because they are being treated in an artificial manner

they are being taken out of any context – even out of the world

and then the question is asked – well what is their significance or their meaning?

well the answer of course is that they have none – they’ve been placed in a void –
and the very point – theoretical point of a void is that it has no significance

this bizarre result is a consequence – firstly of regarding propositions as in some sense special entities – when in fact all they are is the expression of the human need to make known – which is I would suggest the most basic of human needs

and they are therefore actions in the unknown – actions of defiance if you like

now to describe these actions – the propositional actions – to get an idea of how they do and can work is just another propositional action designed to shine some light into the darkness

logical activity is just the same action as any other propositional action – it has no specials status

it is a descriptive activity

its subject is propositional behaviour

so it is a propositional account of propositional behaviour

its an ‘in house’ activity – or action within the action

it’s ground if you like is all propositional behaviour

and the ground of all propositional behaviour is simply the unknown

for it is the unknown that is the object of all propositional behaviour

through our propositions we make platforms for action

it is on such platforms that we get about the business of living

logic is simply a way of seeing how we do this



© greg. t. charlton. 2009.

Russell on mathematics XVII

Russell: introduction to mathematical philosophy:
classes


as to the nature of classes –

Russell’s goal here is to define class in such a way that eliminates mention of class

so that the symbols for classes are mere conveniences – not representing objects called classes – but are rather logical fictions – incomplete symbols


it needs to be said from the outset that a class is an action – an action of classification

any reference to class in an a substantive or non-active sense is merely a reference to the representation of the class (of the act)

so i.e. when logicians are talking about classes in the manner that Russell does – what they are actually – or should I say logically referring to is a representation of the act of classification

that might be in whatever form – i.e. diagrammatical or symbolic – in the sense of logical symbols

now the point of this is that actions are not fictions – not incomplete symbols

their meaning may be ultimately unknown – or in practice indeterminate - nevertheless they are as real as any natural event

the guts of the problem for Russell is that he never considered that classes are actions

he has from the beginning been hoodwinked into this idea of ideal entities – even though his own analysis shows they don’t make sense – they don’t function – but he soldiers on – I think because of an entrenched metaphysics and epistemology – which never really comes up for question in his discussion of pure logic or the logic of mathematics

it’s as if there is a template and mathematics has just got to fit – and that the metaphysics justifies the making of any devise or argument that serves the unstated purpose of a correct fit

anyway

Russell’s view is that classes cannot be regarded as part of the ultimate furniture of the world

this notion of ‘ultimate furniture’ really needs to be given some scrutiny

yes we have in Western philosophy various theories of the ultimate furniture – from Thales onwards

the problem with ‘ultimate furniture’ as the idea is usually understood – is an epistemological problem

who is to know what is ultimate – if indeed the notion of ‘ultimate’ makes any real sense?

the truth is any proposition can function as an ultimate proposition – if so constructed –

in short if given that status

what is clear is that systems of thought – radically different systems will produce very different accounts of the ‘ultimate furniture’

so from a straight out epistemological point of view – one would have to conclude there just is no ultimate account

unless you want to go down the path of epistemological facism – and claim there is one true account and the rest are false

most Western philosophers have indeed taken this course –

some have even managed to fit freedom pluralism and tolerance into their absolutism –
nice job that

in general I would have to say it’s just been a parade of charlatans and hucksters – all with the same mask – truth

or perhaps it’s all just a misunderstanding

and yes the notion of ultimate and ultimate furniture – does play a role in how we think act and construct our world

and that therefore such notions even though they do not have the epistemological credentials that have been claimed for them – are in fact useful and in that sense necessary

all very well –

I guess my point is that when it comes to logic and the logic of mathematics – we are better off with an open mind

the activity has indeed produced theory and technique – these are tools to begin with – to work with

and in that sense it is the activity itself that is basic – and indeed you may come up with any number of theories as to why this is so – but that is just structuring the unknown

killing the beauty really –

back to Russell –

his argument is –

‘If we had a complete symbolic language, with a definition for everything definable, and an undefined symbol for everything indefinable, the undefined symbols in this language would represent symbolically what I mean by “the ultimate furniture of the world”. I am maintaining that no symbols either for “class” in general or for particular classes would be included in this apparatus of undefined symbols.’

as to definition –

it is the act of definition which defines – there is no other basis to it – but the act of singling out and describing –

any act of definition presumes that a term can be translated into other terms

the point of definition is utility –

a term is made active – in terms of a definition

and a term may be defined in innumerable ways

that is there in no essential definition

so there is no limit on definition – which is to say – any term or any symbol that requires definition can be defined

Russell clearly has a notion of the indefinable –

I can’t really imagine what he thinks it is

except to say that if you are talking in terms of an essential or ultimate definition – then indeed – any symbol is indefinable

this is not how it works in practise however –

if you get yourself tangled up as Russell has with bizarre notions like his idea of class – and his theory of infinite numbers

then you do find yourself stuck – or as he so politely puts it ‘indefinable’

but the key point of the above is just that he thinks that class is a definable

another way of putting is to say that in his view ‘class’ is not some kind of ultimate category

which might be to say – even though it does define – it too is definable

all of which is to get us ready for the move where class will be defined as ‘something else’

and Russell will be able to say – yes I have defined class without using ‘class’

and with this idea that some or all of the problems associated with his idea of class will melt away

my bet though is that in fact it will be the notion of class as Russell understands it that will dissolve

he’s an old fox

but the question will be – what’s left and what was all this for?

no sick sparrows flew into his cell – so we got this run around?

what I will point out again is that if you understand class as the act of classification and the markings of any such act – none of these issues emerge

we are not dealing with entities – we are dealing with actions

back to Russell –

he argues classes cannot be regarded as a species of individuals – on account of the contradiction about classes that are not members of themselves and because he thinks we can prove that the number of classes is greater than the number of individuals

as I have argued a class can only be a ‘member’ of another classification – another class - and in such a case what you have is an act upon an act

to ascertain the number of individuals – you have to first determine them – this is an act of classification

a classification is not an individual – therefore there is no question of one being greater than the other –

to suggest such is to compare apples and oranges – or to commit what Ryle called a category mistake

also Russell says we cannot take classes in the pure extensional way as simply heaps and conglomerations – he says – if we did this we could not account for a null class

again as I have argued in other posts in this sequence – there is no null class – that is there is no ‘classification of nothing’

I would argue there is no ‘nothing’ to classify

and further the act of classification is at the very minimum an act about something

an act on something

what all this is leading to is –

‘We shall come nearer to a satisfactory theory if we try to identify classes with propositional functions.’

not exactly a grand finale – would you say?

nevertheless this is the argument – classes as propositional functions

it’s a risky course – for if it is successful you might just end up with – propositional functions - and classes as a nostalgic memory –

prime facie though – what is the situation here?

that is intuitively what are we to say of the relation of classes and propositional function?

firstly the propositional function is a structure for propositions –

Russell uses the statement ‘all men are mortal’ and says it involves the functions ‘x is human’ and ‘x is mortal’

in these functions the subject of the predicate is unknown –

the subject is left undefined –

now Russell’s argument is that every class is defined by some propositional function – which is true of the members of the class – and false of other things

so propositional functions define classes

it does seem to me that the x’s in the above functions may well function as places for classes – i.e. ‘x’ is the class of those things that satisfies the function –

this works on the level of pure verbalism –

that is we can refer to the unknown represented by x – as the place of classes

but to do this with any logical significance we need to have the notion of class to begin with

that is functions provide ‘places’ for classes – if classes exist

so what I am getting at is that the two notions ‘class’ and ‘propositional function’ are independent concepts

and furthermore quite different

a classification per se is not a propositional function

and even though you may choose to determine your propositional function in the language of classes – there is no necessity here

x is x – is unknown

if you have as a part of your theory of propositional functions the axiom that all propositional functions are determined by classes – then yes class terminology fits

but the other side of the coin is not so intuitive

a classification may be written up in terms of a propositional function – in propositional logic

that is the idea of class may be applied in the context of propositional logic

even so this would not be the only valid use of the notion of class

so in general the point is – a classification is one thing

and a propositional function is not a classification –

though it may be how a class is used – that is it may be a context for the use of the idea of class

propositional functions are logical apparatus – tools to enable logical process

classification is not an action dependent on propositional function

Russell goes on to say –

‘But if a class can be defined by one propositional function, it can be equally defined by any other which is true whenever the first is true and false whenever the first is false. For this reason classes cannot be identified with any one such propositional function..’

yes – propositional function is a definition tool

a particular propositional function will define a class in a particular manner

another propositional function will define it in another manner

if what you are after is a theory of the nature of class – the theory of propositional function is not relevant

the propositional function is a tool that can be used to define particular classes

it is not a meta theory of the nature of class

at this point of the story Russell has pretty much written off his own argument –

“For this reason the class cannot be identified with any one such propositional function rather than any other…..’

he goes on –

‘When we have decided that classes cannot be things of the same sort as their members, and that they cannot be just heaps or aggregates, and also that they cannot be identified with propositional functions, it becomes very difficult to see what they can be, if they are to be more than symbolic fictions. And if we can find any way of dealing with them as symbolic fictions, we increase the logical security of our position, since we avoid the need of assuming there are classes without being compelled to make the opposite assumption that there are no classes. We merely abstain from both assumptions. This is an example of Occam’s razor, namely “entities are not to be multiplied without necessity”. But when we refuse to assert that there are classes, we must not be supposed to be asserting that there are none. We are merely agnostic with regard to them: like Laplace, we can say “je n’ai pas besoin de cette hypotheses.’

it strikes me as an early instance of the British axiom ‘don’t mention the war’

Russell bites the bullet and gets pragmatic – in the attempt to resurrect the idea of the propositional function as the definition of class

but this is really the argument you have when you haven’t got an argument

he wants to set forth the conditions that a symbol must fulfil if it is to serve as a class

he lists five –

(1) every class is rendered determinate by a propositional function
(2) two formally equivalent propositions must determine the same class
(3) we must find some way of defining not only classes – but classes of classes
(4) it must be meaningless not false to suppose a class a member of itself
(5) it must be possible to make propositions about all classes that are composed of individuals or about all classes composed of objects of one logical type

yes we can accept that a propositional function defines a class

and that two formally equivalent propositions determine the same class

these two ‘conditions’ are no more than just applying the apparatus of propositional logic to classes - and that has never been in question

and asserting these conditions does not address the issue of the logic of classes

classes of classes – is no more than classification of classification – action on action

no problem if you understand that a class is an action

there is no sense in the idea that an act of classification is performed on itself

if we speak of ‘all classes’ we are really only referring to the function of classes – that is what a classification does – classify – so no more than a trivial and unnecessary statement

of course we can speak of our classifications - in the same way as we can refer to and make propositions concerning any of our actions


© greg. t. charlton. 2009.