The Pagan Agenda

This is a continuation, perhaps a summation, of some strands of thoughts that have existed piecemeal in comments and philosophic posts recently.

In his ‘Philosophical Investigations’, Wittgenstein writes:

“(108) We see that what we call “sentence” and “language” has not the formal unity that I imagined, but is the family of structures more or less related to one another. — But what becomes of logic now? Its rigor seems to be giving way here. — But in that case doesn’t logic altogether disappear? — For how can it lose its rigor? Of course not by our bargaining any of its rigor out of it. — The preconceived idea of crystalline purity can only be removed by turning our whole examination around. (One might say: the axis of reference of our examination must be rotated, but about the fixed point of our real need.)”

In the above quotation Wittgenstein talks about having to fix our investigation of logic around our true need. I interpret this to mean that rather than suppose logic to be a precondition, we must examine logic enacted through use in order to determine its meaning. The following investigation is an attempt to show an example of logic-in-use in order to show a grammatical aspect of the term ‘logic’. The example is treated within the context of an analytical debate, a language game where the participants attempt to prove or disprove the validity of a position on the basis of a contradiction.

When we say that “Socrates is a man because he is not a woman” what is being expressed? We suppose that a tacit understanding of logic enriches the syntactic meaning of the statement, much the same way that we infer 2 + 2 = 4 to be qualitatively different than 2 + 2 = 5, in that underlying the first case the signs take on certain attributes which because the terms are arranged in a certain way bring to mind an implicit set of rules (known categorically as ‘logic’) which the second case transgresses. If this were not the case we would sense no difference between 2 + 2 = 4 and 2 + 2 = 5 beyond the formal one. Logic as guiding principle is implicit in order for the proposition to function within the analytical debate, there is a particular sensibility to the proposition ‘Socrates is a man because he is not a woman’ that we for the sake of convenience tend to term ‘logical’. This proposition could be expanded to “’Socrates is a man because he is not a woman’ is a logical proof’, in which case logic is explicitly expressed now as the embodiment of the aforementioned principle in a particular concrete argument. Both versions of the proposition treat logic as a substantive, first as a guiding principle, and second, as an embodiment of that principle in a particular concrete argument.

Herein I will look at two possible ways in which the proposition (in either form) may be used (these are not the only two ways, nor do I propose them to be isolated ways, part of both may in fact intermingle in the decision-making process). In the first case (1) the nouns may refer to real things with fixed attributes which can be put in self-identical relationships in order to express a bivalent fact. In the second case, (2) the nouns, and indeed the proposition as a whole, may possess only a crude resemblance to real things, in the way knights and kings in a chess game do, so as to emphasize particular attributes that serve the needs of the immediate language game; the language game of truth-discerning in an analytical debate.

With respect to use (1), what is perhaps considered a conventional view of how logic operates, the proposition ‘Socrates is a man because he is not a woman’ is understood by the participants by looking into the syntax of the sentence, and treating the nouns as representative of actual things: so that for the first part of the proposition to be sensible at all there must first be in the language game an acceptance that things can be expressed in self-identical relationships (Socrates IS a Man). If our language consisted only of unique words representing unique things and the rules were followed systematically in this fashion, there could be no such comparison made; however because that which is signified can be both ‘Socrates’ and ‘man’ in common use, the implicit acceptance of the rule of self-identical relationships between things, in this reading, facilitates understanding. Furthermore, the syntax of using ‘because’ identifies a causal relationship which in this case comes in the form of an either/or condition. Sense is understood as either Socrates is a man or either he is a woman, and inversely, if he is not a woman he therefore must be a man. The context through which this can make any consistent sense is whereby all propositions have truth-value, which I denote as the ‘law of bivalence’.

The dependence on ‘thingness’ and ‘bivalence’ in the above syntactic reading of the use of the proposition requires, as Nietzsche has previously discovered, an inhibited form of reasoning (with untouchable first axioms) in order for the assumptions of meaning to be upheld. As Nietzsche first posited: ‘thingness’ is a convenient conflation of a bundle of shared effects, which if we were to take each of these effects away one by one, there would be no ‘thing’ left-over. What is a chair but the sum of its effects? The convenience of denoting thingness to a bundle of effects is that it benefits our want of communication, to share the same words for a bundle of effects expedites communication, thus the use of ‘thingness’ has a pragmatic purpose. The fallacy of a logician, Nietzsche argues, is that he/she takes these abbreviations of effects as wholly representative of the bundle of effects they are meant to refer to: to mistake what is pragmatically used as what is absolutely implied.

To return to the example of the proposition, it is supposed that there is in reality a sharp distinction between man and woman, enforced by the belief in bivalence. At any point of use of the word ‘man’ we are referring to a limited fixed group of attributes that can at no time encompass the meaning-potential of what is signified. This becomes increasingly problematic when we suppose self-identical relationships between things and in the process come to describe contingent things as a result. Thus interpretation (1) of the game of truth-discerning is based on selective interpretations of things which can at no time be representative of what is ostensibly signified. Therefore my picture of ‘man’ may not share the same bundle of effects that your picture of ‘man’ may, yet the proof is so fashioned as if to suggest there was only one picture, one fixed way in which the word operates. This is a logical shortcoming that the ‘deed’ of analytical debate overlooks.

As with the case of ‘thingness’, Nietzsche argues, the law of bivalence is likewise perpetuated through traditional expressions of logic. By ‘law of bivalence’ I mean the notion that every proposition has a truth-value. For example, the proposition ‘Socrates is a man because he is not a woman’ assumes that there is such a thing as ‘Socrates’ and such a thing as a ‘man’ and that they can be related in a self-identical relationship on the basis of the bivalent fact that Socrates is not a woman. The thingness of bivalence, that is to say, the notion of bivalence as an absolute attribute which transcends the rules of logocentric language games, I believe is one of the greatest grammatical errors to have come from our use of language. Bivalence demands proof, but cannot give such proof for its own essential claims.

The familiarity of ‘logic’ and ‘logical proofs’ as substantives in common usage has the potential to bewitch our intelligence into supposing these substantives to exist as preconditioned standards for the meaning of the proposition, passively guiding, rather than as actively involved coefficients in the truth-making. This is to say the ‘thingness’ of logic, as it resonates in our usage of the concept as substantive, may unwittingly influence our conceptualization of truth in any particular expression of it. In this reading, ‘Socrates is a man because he is not a woman’ may exist as proof in a purely superficial sense, satisfied by a recognition of pattern in the phrase with a preconceived entity known as logic. As Wittgenstein himself pointed out, the decision to form metaphysical concepts as substantives begs to ask unnecessary questions: What is logic? What is knowledge?

The concept of ‘logic’ as a substantive does not by any ‘logical’ means become a genuine thing (i.e. beyond the scope of its arbitrary rules) because of the logical proofs that may be conceived; nor do the logical proofs as substantives become genuine things because of their conformity to the rules of logic. Their uses succeed only within the particular language game participants belong to.

With respect to use (2), which more resembles acts of rule-following described in Wittgenstein’s Philosophical Investigations, the terms described do not need to be processed by the participants as representative of actual things, but may be used in themselves as signs of logic. In the same way one may say a knight piece is not a horse but a tool in order to enact some activity within the larger game context, so may the proposition ‘Socrates is a man because he is not a woman’ be used as a tool, either in fragments or as a whole as cashable pieces of argument based on a prior repositiory of analytical uses. In this case it does not matter to the participant whether or not a ‘man’ exists with fixed attributes in the actual world, but only that in order to facilitate the need of the language game the participant can convince the other with familiar uses of logic in order to win the argument. To serve the pragmatic purpose of winning, each side may behave in the same manner, in an interest of finding the sequence of words that serves to exclude the other’s argument. For example the noun ‘man’ in the proposition may be limited to ‘what science deems man to be’ and working with a shared implicit context as such the interest is less about ‘man’ in its fullest potential of meanings, but as it fits in the narrow scope of analysis immediately under scrutiny. Additionally, ‘Socrates is a man because he is not a woman’ may have symbolic resonance in the dialogue, a token example of a logical proof through which neither party has a vested interest in analyzing deeper.

The two uses I have described each treat the concept of logic as a substantive. This is evident if we ask how is the thing we refer to as ‘logic’ enacted in the proposition “’Socrates is a man because he is not a woman’ is a logical proof”? One possibility is that an individual grasps an implicit acceptance of the rule of bivalence and of the existence of things with fixed attributes that can be arranged in self-identical relationships that makes up the conditions for the statement being logical; another possibility is that ‘logical proof’ as substantive influences use as a mitigating framer of the truth-making by the very phrasing of it as a substantive. In the first case logic-as-substantive is implicit in the use of syntax, without explicit mention of the concept of logic at all. In the second case logic-as-substantive is implicit in the use of semantics, in the formal semantic constraints that are put on the words in order to serve some particular purpose within the game of truth-discerning. If logic is used as a substantive it is by habit of communication treated on par as a thing, and its thingness when inputted into a truth-discerning calculus, I believe, bewitches our understanding of how we play the game of truth-discerning.

What I feel is neglected by the presumption of logic is the pragmatic inclination of individual will in choosing a version of ‘truth’ that best satisfies his/her immediate end. I believe in the end the individual decides.
This is very tentative, and any faults in reasoning that one may notice please let me know (I am still playing within the confines of a game of logic).