Of course, what I have recently been primitively grasping at is the fundamental notion Wittgenstein was expressing the Tractatus: I have come to understand that the only truths that matter (and thus, the only accurate aim of philosophy) are the personal; the subjective. The truths of logic (which are what all external, or scientific, investigations lead to) are essentially meaningless: they every one reduce to tautology. Leibniz's A=A. Logic, science, mathematics...all are investigations of different ways of expressing this single principel which is their sole axiom. The arts (in the broadest sense) however, refuse any requirement of axiom. They begin from the individual, that is, life, with all the contradictions and irresolutions that implies.
This is why the philosophy that matters has to be carried out as an art. I want, I need, to say more than A=A.
Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts
Friday, 22 August 2008
Friday, 15 August 2008
Popular Misconceptions of Descartes' Cogito
It seems that the true meaning and intention of Descartes' famous principle has been somewhat misunderstood. Some have understood it but I think its true intent has often been obfuscated. I want to examine this.
Cogito Ergo Sum is usually translated as I think therefore I am. This in itself may be misleading. We can see this if we deconstruct it:
Cogito Ergo Sum is usually translated as I think therefore I am. This in itself may be misleading. We can see this if we deconstruct it:
(i) think... therefore ...(i) am
translates as
"i" possess the quality/activity "thoughts"... therefore ..."i" am a stateable bearer of properties
It should be obvious that if we accept the condition "'i' think" then the conclusion "'i' am" follows; no further logic is necessary to extract this from the conditional. If it is true that 'i think' then we know immediately that 'i am'. The second half is in fact the hidden axiom upon which the conditional first half is based. In order to 'think', I must 'be'. If it is true that 'i think' then clearly (without any more logical steps), i must be. I cannot think if I am not.
Of course, one needs to understand: if there are thoughts (which we know there are) then the existence of thoughts is apparent. If Descartes is wholly identifying 'i' and 'thoughts' then his logic is secure. Could it be that all he intended to say in the first step was that, these thoughts, these phenomena which are all that I am, exist. Existence is apparent and this I can give the handy label 'i'.
In Descartes' reply to Mersenne, he establishes that existence is not found from thought by any logical proces or manipulation: existence is already present within the axiom of "i think". 'i think' being a self-evident assertion (notwithstanding the separation of 'i' and 'think' into separate ontologies via grammatical obfuscation), 'i' (that is, existence) is already apparent - it has already been stated and does not need to be deduced.
Thus, the cogito ergo sum (much clearer in Latin) is merely an articulation of identity, of A=A.
Thus, I believe that Descartes is not setting out to prove the existence of a mental, cohesive, self...but to establish a criterion of truth. Cogito ergo sum makes it clear that there is, despite scepticism, ascertainable, definite, knowable and self-evident truth. That this truth is contentless is not the issue. The fact is, that truth can be established where there is no room for doubt. This is Descartes' gift: the grounding of solidity and the establishment of a basic epistemological principle. "is". There are thoughts. If there are thoughts, and those thoughts are me, then i am.¹ A=A is not effaceable. If "there are thoughts", then "there is a definite criterion of truth". The conditional statement at the beginning of the formula, "if 'i think'..." leads immediately, without application of logic or any other data, to "then there is such a thing as existence, for existence need not be any (cannot be any) more established than the fact we already know "i think". Perhaps a better translation would be:
thoughts? -> existence
¹Although the cogito can in this way be expressed as a syllogism, we must still understand that its conclusion is not really an extrapolation: it is already present in the first condition.
Post-Script. Since first posting this it has been brought to my attention that Descartes originally formulated the cogito in French, and it does in fact contain the personal pronoun. Perhaps then I am confounding my own intention with Descartes. My point in general however, still stands.
Saturday, 17 February 2007
Truth, Logic and Meaning in the World
Here I'm addressing the status of logic, material reality and the human mind in respect of their distinct natures and relationships.
Karl Popper (in his book Conjectures and Refutations, p266) divides all meaningful statements into three types:
1)Logical or Mathematic
2)Empirical and Scientific
3)Philosophical or Metaphysical
Logical statements are a priori, based solely on abstract reasoning; they rely only on correct thought. Empirical statements are 'facts' about the world, statements about matter, if you will, which are based on sense data. Philosophical statements are speculation/extrapolation, making strictly untestable claims based in the inner world of the human mind.
By means of example, a logical statement would be 'if all x are y then all x are z' (where 'x' and 'y' and 'z' can stand for anything we want: objects, statements, whatever). The rules for determining the truth of this depend on the rules of logic and the categories of maths, ie given the definitions of the terms used either the statement is true or it is not.
An empirical statement would be 'There are two swans on the lake', or 'The earth orbits the sun'. To discover if these are true or false, we would conduct an experiment based on observation (empirical data), to ascertain whether the world correlates with the statement.
The difference between logical and empirical statements may be more clearly understood if we use objects as examples: for instance, 'all rocks are heavy' is an empirical statement, as we must examine the objects which we call 'rocks' and see if they indeed all have the quality we call 'heavy'. 'All rocks are rocks' however, is a logical statement as whatever the objects we call rocks are, it is true that they are rocks.
Therefore we can replace the word rocks with a placeholder such as the term 'x' , as whatever we are referring to, it is true that 'x'='x'. All of the investigations in logic are based on working out equivalence. We can only find if a logical statement is true by working out if the terms used mean the same thing. In the syllogism used above for example, 'if all x are y then all x are z' it is true only if all y are z.
A philosophical statement would be 'All action is predetermined' or 'God exists'. This kind of assertion cannot be subjected to measurement in the scientific sense, and are generally considered irrefutable as they are not subject to testing. Rather, they express a sense of 'soft' meaning which affects primarily the way we approach the world, and our place in it. Newton's theory of gravity is as much a philosophical statement as the two examples given because while its predictions can be tested, the claim of gravity as a force within objects cannot be experienced: only its effects. We do not 'see' the force of gravity, we simply see events such as an apple falling, which happens to correlate with the postulation that there is a force attracting objects to each other.
So it seems clear that we can assign Truth to the categories in the following manner:
1)Logical statements have an Absolute Truth value, as they are either True or False, and only false when incorrectly formulated. There is no inbetween and when true they are absolutely True.
2)Empirical statements have Contingent Truth as valid statements can be made ('today is monday') whose truth value is dependent on the conditions present in the material world.
3)Philosophical statements have no truth value, as they are merely speculation; they have nothing to say about the world outside of the subject - instead, they are a framework by which we understand the world and our place in it. They are subjective, personal and irrefutable as they make no solid claims; what they in fact describe is an individual's approach to the world. They are generated from within, and tackle the interface between the mind and matter. This should be more clear when we consider that the two opposing statements 'God exists' and 'God doesn't exist' make no impact on the facts about the world around us: The chair I'm sitting on is green, whichever one is the case. There are still two swans on the lake, whether or not I believe in God, and even if I have a vision and change my belief while looking at the swans, the empirical data remains precisely the same (although my feelings about it may now differ).
Something interesting comes to light when we examine this: Philosophical statements make no claim on truth. They are metaphor, and their value is purely pragmatic. Empirical statements, while approximating truth, can never be True in a whole sense, as in approaching a precisely accurate representation of any state of affairs, the statement nears an infinite complexity: To say there are two swans on the lake does not come close to the actual material facts, as we have said nothing about their precise position; their size; their motion; the ripples on the lake, the wind that is causing them, the atomic interaction of the water with the feathers of the swans; etc. In order to accurately represent reality, the statement would need to be as complex (and as unbound by human category judgments such as 'swan') as reality itself. The term 'the lake' has no objective meaning: more must be stated about the subject's perspective in order to comprehend the intention behind the statement (for otherwise the statement is both true and false, depending on one's point of view - ie, the particular 'lake' we are looking at). The inclusion of this subjective data makes the statement more specific and therefore more accurate but correspondingly more difficult to formulate and thereby increasingly difficult to assess. Therefore empirical statements can only approximate Truth in the same way that objects can approach lightspeed, but find their mass increasing exponentially as they do so.
Logic however, stands apart from these two. The laws of logic are all tautological: they bear no informaton content. All logically true (that is, necessarily true) statements are reducible to the single guiding principle of logic, the Law of Identity. This is the axiom which no logical system can do without. It states "A=A". For if A is not itself, if A is not A, then no other statement can be understood to be either true or false. From this we can see how all logical truth is a restatement of this single axiom (Other logical systems may include additional 'unquestionable' axioms but these tend to be deviant logics developed with particular practical uses in mind). Wittgenstein claimed that all logical statements say the same thing, towit nothing (Tratatus Logico-Philosophicus 5.43), and we can see clearly now how this is the case.
So now we can see in our tripartite description, that logical statements have absolute truth, Truth with a capital 'T'; but completely lack meaning. Philosophical statements have no truth but are entirely meaningful. Empirical statements stand inbetween these two, their accuracy being in negative correlation with the amount of meaning (or unstated subjective background) they carry.
Although Popper originally postulated these categories as a practical means of testing assertions, it seems to me that reality could also be neatly divided along these lines.
1)Logic, the transcendent ideal which has no place in the world, but can be thought of either as generator or abstraction from reality.
2)Matter, the physical 'stuff' of perception.
3)Mind, the interior mental world of thought, emotion and experience.
Ergo, Truth is not of the world. The stuff of the world we experience is Meaning, which is in direct negative correlation to Truth. The more Meaning, the less Truth and vice versa. Truth stands above and beyond the world, being a single unitary transcendent; in fact even beyond time. Truth is Eternal; Meaning is Ephemeral, based entirely in the 'Now' of subjective experience.
This I think is the point I was trying to make in my earlier blog, 'Matter': Logic is a transcendent principle which can be seen as both generative and an abstract of matter. Matter and Mind are co-generative, standing as two sides of the same coin. As Minds cannot exist without Matter to work upon, to mold, so Matter cannot exist without Minds to imbue perspective into it.
As a footnote, I would ask Kabbalists and those familiar with scriptural exegesis to contemplate the similarity between God's self-revelation to Moses as "Ehyeh Asher Ehyeh", I Am That I Am, and the single abstract Truth of A=A. There is a reason that the Kabbalists give Kether (the primary sefirah of the Tree of Life, known as Ehyeh) the alternative title "concealed of the concealed", and claim it as the primordial divine thought which generates all else in existence.
Karl Popper (in his book Conjectures and Refutations, p266) divides all meaningful statements into three types:
1)Logical or Mathematic
2)Empirical and Scientific
3)Philosophical or Metaphysical
Logical statements are a priori, based solely on abstract reasoning; they rely only on correct thought. Empirical statements are 'facts' about the world, statements about matter, if you will, which are based on sense data. Philosophical statements are speculation/extrapolation, making strictly untestable claims based in the inner world of the human mind.
By means of example, a logical statement would be 'if all x are y then all x are z' (where 'x' and 'y' and 'z' can stand for anything we want: objects, statements, whatever). The rules for determining the truth of this depend on the rules of logic and the categories of maths, ie given the definitions of the terms used either the statement is true or it is not.
An empirical statement would be 'There are two swans on the lake', or 'The earth orbits the sun'. To discover if these are true or false, we would conduct an experiment based on observation (empirical data), to ascertain whether the world correlates with the statement.
The difference between logical and empirical statements may be more clearly understood if we use objects as examples: for instance, 'all rocks are heavy' is an empirical statement, as we must examine the objects which we call 'rocks' and see if they indeed all have the quality we call 'heavy'. 'All rocks are rocks' however, is a logical statement as whatever the objects we call rocks are, it is true that they are rocks.
Therefore we can replace the word rocks with a placeholder such as the term 'x' , as whatever we are referring to, it is true that 'x'='x'. All of the investigations in logic are based on working out equivalence. We can only find if a logical statement is true by working out if the terms used mean the same thing. In the syllogism used above for example, 'if all x are y then all x are z' it is true only if all y are z.
A philosophical statement would be 'All action is predetermined' or 'God exists'. This kind of assertion cannot be subjected to measurement in the scientific sense, and are generally considered irrefutable as they are not subject to testing. Rather, they express a sense of 'soft' meaning which affects primarily the way we approach the world, and our place in it. Newton's theory of gravity is as much a philosophical statement as the two examples given because while its predictions can be tested, the claim of gravity as a force within objects cannot be experienced: only its effects. We do not 'see' the force of gravity, we simply see events such as an apple falling, which happens to correlate with the postulation that there is a force attracting objects to each other.
So it seems clear that we can assign Truth to the categories in the following manner:
1)Logical statements have an Absolute Truth value, as they are either True or False, and only false when incorrectly formulated. There is no inbetween and when true they are absolutely True.
2)Empirical statements have Contingent Truth as valid statements can be made ('today is monday') whose truth value is dependent on the conditions present in the material world.
3)Philosophical statements have no truth value, as they are merely speculation; they have nothing to say about the world outside of the subject - instead, they are a framework by which we understand the world and our place in it. They are subjective, personal and irrefutable as they make no solid claims; what they in fact describe is an individual's approach to the world. They are generated from within, and tackle the interface between the mind and matter. This should be more clear when we consider that the two opposing statements 'God exists' and 'God doesn't exist' make no impact on the facts about the world around us: The chair I'm sitting on is green, whichever one is the case. There are still two swans on the lake, whether or not I believe in God, and even if I have a vision and change my belief while looking at the swans, the empirical data remains precisely the same (although my feelings about it may now differ).
Something interesting comes to light when we examine this: Philosophical statements make no claim on truth. They are metaphor, and their value is purely pragmatic. Empirical statements, while approximating truth, can never be True in a whole sense, as in approaching a precisely accurate representation of any state of affairs, the statement nears an infinite complexity: To say there are two swans on the lake does not come close to the actual material facts, as we have said nothing about their precise position; their size; their motion; the ripples on the lake, the wind that is causing them, the atomic interaction of the water with the feathers of the swans; etc. In order to accurately represent reality, the statement would need to be as complex (and as unbound by human category judgments such as 'swan') as reality itself. The term 'the lake' has no objective meaning: more must be stated about the subject's perspective in order to comprehend the intention behind the statement (for otherwise the statement is both true and false, depending on one's point of view - ie, the particular 'lake' we are looking at). The inclusion of this subjective data makes the statement more specific and therefore more accurate but correspondingly more difficult to formulate and thereby increasingly difficult to assess. Therefore empirical statements can only approximate Truth in the same way that objects can approach lightspeed, but find their mass increasing exponentially as they do so.
Logic however, stands apart from these two. The laws of logic are all tautological: they bear no informaton content. All logically true (that is, necessarily true) statements are reducible to the single guiding principle of logic, the Law of Identity. This is the axiom which no logical system can do without. It states "A=A". For if A is not itself, if A is not A, then no other statement can be understood to be either true or false. From this we can see how all logical truth is a restatement of this single axiom (Other logical systems may include additional 'unquestionable' axioms but these tend to be deviant logics developed with particular practical uses in mind). Wittgenstein claimed that all logical statements say the same thing, towit nothing (Tratatus Logico-Philosophicus 5.43), and we can see clearly now how this is the case.
So now we can see in our tripartite description, that logical statements have absolute truth, Truth with a capital 'T'; but completely lack meaning. Philosophical statements have no truth but are entirely meaningful. Empirical statements stand inbetween these two, their accuracy being in negative correlation with the amount of meaning (or unstated subjective background) they carry.
Although Popper originally postulated these categories as a practical means of testing assertions, it seems to me that reality could also be neatly divided along these lines.
1)Logic, the transcendent ideal which has no place in the world, but can be thought of either as generator or abstraction from reality.
2)Matter, the physical 'stuff' of perception.
3)Mind, the interior mental world of thought, emotion and experience.
Ergo, Truth is not of the world. The stuff of the world we experience is Meaning, which is in direct negative correlation to Truth. The more Meaning, the less Truth and vice versa. Truth stands above and beyond the world, being a single unitary transcendent; in fact even beyond time. Truth is Eternal; Meaning is Ephemeral, based entirely in the 'Now' of subjective experience.
This I think is the point I was trying to make in my earlier blog, 'Matter': Logic is a transcendent principle which can be seen as both generative and an abstract of matter. Matter and Mind are co-generative, standing as two sides of the same coin. As Minds cannot exist without Matter to work upon, to mold, so Matter cannot exist without Minds to imbue perspective into it.
As a footnote, I would ask Kabbalists and those familiar with scriptural exegesis to contemplate the similarity between God's self-revelation to Moses as "Ehyeh Asher Ehyeh", I Am That I Am, and the single abstract Truth of A=A. There is a reason that the Kabbalists give Kether (the primary sefirah of the Tree of Life, known as Ehyeh) the alternative title "concealed of the concealed", and claim it as the primordial divine thought which generates all else in existence.
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