Tuesday, 6 December 2011

The Philosophy of Logic

It is remarkable that we have descriptions of the laws of logic but few descriptions of the nature of logic itself.  Wittgenstein, often a last resort for our debunking needs, describes the nature of logic "logic is trancendental". That is, logic provides a foundation or ground, in this case, as it happens, for the world "structure". He also identifies this ground as "necessary" when describing the propositions of logic as tautologies. A tautology is necessarily true - "either it is raining or it is not raining". This confuses the transcendental with the transcendent* for conditions or grounds are only necessary for the objects they ground or identify. To make those grounds absolute or self-justifying is to confuse the grounds for an object with the object itself. But then commentators on logic, including Wittgenstein, suffer from that over-familiarity that paints its cultural totems into a self-evident or transcendent, corner.

Logic is a contingent element in the ad infinitum of legitimacy. Logic, or rather a logic, portrays an arbitrary mix or empty fusion of both  i) ontologies, and ii) moral injunctions. Its description in terms of its content or of its transcendency arises from a failure to perceive these. As such Logic is neither a ground, nor transcendent.

i) The ontology of a logic is given through its syntax; specifically through the behaviour of the elements of the syntax. An ontology describes a particular behaviour of objects (or syntactical elements). Logic offers a physical ontology and its syntax behaves in that way. Not all objects behave in the same way. For example, only the logic or object behaviour of physical objects is incorporated in mathematics where the elements of mathematical syntax never vanish or appear without redress being made within the whole mathematical application.

Elsewhere, a phenomenalistic "logic" is employed in the use of colour in the arts. Artists change the hue of an intended colour to compensate for the visual influence of the colours of its surroundings. In this case the elements of the syntax (a particular colour) vanish or appear with no redress or compensation in the application (as in e.g., a painting).

Thus the  "laws" of logic, such as the law of contradiction, inference, fallacy, form, syllogism, etc., are not transcendent or absolute but reflect only a particular ontology or behaviour of elements in the syntax of a system. In any case it was always a philosophical awkward moment to apportion "law" to a description of a self-evident or transcendent form, the term really being meaningful for only local physical systems.

ii) These terms in the logical lexicon - "right reason", "rational", the "logical" (as in "right thing to do") offer privileged binaries (after Derrida) in a reductionist system, in this manner. A physical ontology operates most of logic today where its perceived transcendency or inevitability privileges it over other logic ontologies. This same privileging agent operates on other, non-logical systems, such as the mental or moral, where a reductionist or quasi-mechanistic or -physical judgement is seen to be inevitably superior to one based on the physically unmeasurable, such as the immediately perceivable, feelings or experience.

Today's Logic, then, is an ontological montage offering a false unity through a prescriptive, privileging transcendent status.

There are two major classes of logics that underpin all its forms:
1) transcendentally real,
2) transcendentally ideal.
The syntax of both appears the same.

Logic is a description of an ontology, but an ontology requires a condition for the identification of its elements (see the example of a TV, below). The syntax of a logic cannot display which of these identificatory conditions (Tr. ideal or Tr. real) underpins it; that is, all syntactical forms of both 1) and 2) are indistinguishable. Each logical system or syntax has these two unrevealed frameworks that are a condition for the appearance of its elements or objects. This deposes the very idea of a transcendent, absolute or self-justifying logic. Systems operating under particular object behaviours are absolute and incommensurable: colours behave like colours - vanishing and appearing, and materials behave like materials - they do not vanish or appear without redress, yet each system has these two, mutually exclusive, frameworks that announces its syntax.

1) transcendentally real logic is a description of ontology as the behaviour of objects. Transcendentally real logic acknowledges existence as the condition for the appearance of the elements of a syntax, or objects and their behaviour. Existence is prior to identification in that existing objects identify themselves or prescribe their own limits. For example, an electron is subject-independent and identifies its own limits, these being its physical extent because its ontology, its logic, is physical. Existence refers to objects that identify themselves. Object existence is a transcendentally real doctrine.

2) transcendentally ideal logic is a description of ontology as the framework for, and the behaviour of, objects. Transcendentally ideal logic acknowledges identification as the condition for the appearance of the elements of a syntax or objects, and their behaviour. Because identitification is prior to existence objects do not identify themselves and so are neither absent nor present. Absence and presence are thus values of existence.

Quine treats logic as pragmatic, and not transcendent or absolute. This seems to drop the need to describe logic as having an absolute or transcendent object behaviour by replacing it with a logic that has a variety of behaviours or ontologies. Yet the same confusion arises as to the nature of the Quinean logic, logic still appears as transcendent or as absolute in some form or other.

Then again, the move to a pragmatic description does not address the transcendental status of a logic. A pragmatic logic is a transcendentally real logic, whose syntax self-identifies. No such self-identification accrues from that other, transcendentally ideal, perspective where a pragmatic logic identifies objects and their behaviours according to an anthropomorphic identifying condition or perspective ("pragmatic").  The pragmatics of entertainment prescribe limits in the physical ontological domain, such limits can identify a  T.V., for example. A carpet on which the T.V. rests would not fall within those pragmatic limits.  In other words the T.V. is not an object (from the transcendentally ideal view of it) until it is constructed from the identifying conditions of entertainment, which sets its physical parameters.

A pragmatic logic becomes a tool of science when a particular logic is ditched or taken up depending on the outcome of experiment or to meet the needs of theory. This means that the syntax accomodates different object behaviours.   Different logics have been mooted to meet maverick object behaviours, such as quantum. Probability theory is an artifice that attempts to prevent that change, to keep the elements of the syntax within a physical ontology. A pragmatic entity, whether logically prescribed or through some other stipulate, comes and goes, without redress. Such a logic places all ontologies under the umbrella of phenomenalism, where objects vanish and appear without any redress (colours, for example, display this ontology or logic).

By adopting 2) a transcendentally ideal view, there is no single pragmatic logic, or any number of pragmatic or non-pragmatic logics that are identified by their object behaviours, that self-identify. As indicated in 1) and 2), above, logics describe ontologies, and ontologies can be either transcendentally real or ideal.

Finally, logic(s) is not the terminus of rational thought, unless we take rational thought to be addressing our familiarity with the behaviour of objects in a morally prescriptive context or other identifying condition. Rational thought is a false terminus, more a mixed bag of expectations, morals, needs and object ontologies.

* Transcendental, a term taken from Kant, is not to be confused with transcendent. Transcendental refers to “the conditions under which objects can be experienced or known by the human mind”, as Henry Allison says. This is almost there, but we need to add ... under which objects can arise. I often write - objects can be "identified" or "constructed" but I do not mean to presuppose the object as given by the use of such terms.On the other hand, transcendent refers to

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