Logic and reason are not the sole domain of one Culture, Race, or Gender (Judy, 1993). It has also been said that the problem of the Negro is a problem for thought (Chandler, 2013). From this it follows that a model for Black thought, a Black logic, is required in order to move past a reactive stance that assumes without critically assessing the mechanisms and the conditions within which a system of thought was constructed (Jones, 2013).
By Black logic, I do not intend to create a logic of Black identity. On the contrary, I am very much opposed to that project. A logic as a model of a system of thought, for me, is indicative of a form of life, a mode of producing thought appropriate to the contexts in which they arise. The method revealed and the products it produces are not random but also not necessarily caused by the context either, meaning its arrival in this context does not negate its existence or success in others. Thus, a logic modeling the relations between thoughts and the frame organizing a particular world in which those thoughts are obtainable indicates a mechanism for creating thought. This mechanism serves as evidence of the subjectivity of a group of individuals; entities that are individual but not necessarily mutually exclusive from one another because of a form of life that obtains between them. Their way of being is modeled by their mode of expression. If it is possible that this mechanism produces output that obtains a particular context, then it is necessarily possible in contexts outside of ones in which a system has been installed in which those expressions may be derided or negated (Lewis, 1973). Below, I aim to demonstrate the validity of blacknessâ modes of being qua mode of expression, the method by which those subjects irrefutably reason.
To make a start, we begin with current Pessimist logics within Black studies (see Mbembe, 2001; Patterson, 1982; Sexton, 2011; Wilderson, 2008; etc.). It will be shown that because the Pessimist maintains a âtranscendent,â (Wilderson, 2008) external stance while forming studies on blacknessâ form of life, the framework developed to analyze the Black identity they have created obtains no subject and, therefore, is either incomplete or contradictoryâSee Appendix I to III. A transcendent position can only be obtained by stipulations seeking evidence for previously held belief and deeming this as evidence for that belief. The insertion of a universal statement into one's study in order to deduce an analysis of the inner structure of a state of affairs and organize an opaque contextââopaqueâ because the stance is transcendent to that contextâultimately fails (Quine, 1956). By âbaseâ we mean an epistemic foundation such that the relation that holds between a reason and a belief obtains if and only if the reason is a reason for which that belief is held.
The object founding the Pessimist's school of thought comes out of a particular translation of Frantz Fanon's Black Skin, White Masks. âThe black man is not. Any more than the white man.â Regarding analyses of White supremacy and Afro-Pessimismâthe school whose adherents we challenge belowââthe black man is not,â full stop. This unusual construction of Fanon's proposition encourages one to consider the deep structure of the phrase. The black man is not and, so, neither is the white man. This is an epistemic qua psychological proposition on Fanon's part, not an ontological one. Unless we conflate what can be the case with what we know. The full stop at the center of the phrase functions as an inclusive NOR operator. The distinction between White and Blackâcapitalized here in order to emphasize that they are names and as such are used as identities, not individuals in and of themselvesâis asserted by Fanon. They are constructions whose semantic content is a function of their being indexed to a particular reference frame. There is a logic to these constructions and a rationale for their maintenance, even if what they maintain is an irrational attitude. Revealed as such by Fanon, it becomes rational to propose a method counteracting the mode with which these concepts organize the articulation of a particular, representational, surface structure of our state of affairs.
By proposing a logic that undoes the normative erasure of alternatives qua standards of reason, we attend to the problem posed by blackness to thought by actually revealing that logic and rationality are not of the sole purview of one race or another. In so doing, this act necessitates a development of the logic underlying that seen as the superior while combatting an anti-intellectual intellectualism entrenched in the study of Black folk. Black logic is not only possible but becomes the basis for articulating a logic at all since without it, neither is the White. As both are based on what they're not, the distinction of a dominant and subordinate logic becomes irrational. This begs the question, why has this irrational belief been maintained, even by those who by doing so further their own subordination?
From here on we consider language as a capacity to produce expressions, not solely by output. As such, this capacity has been shown to be a mechanism for creating thought. Along these lines, language is not necessarily constituted by the ability to communicate said thoughts (Chomsky, 2016). However, the sonic or ânon-logicalâ symbolic strings articulated out of one's mouth serve as the empirical basis for a study that does not presuppose their method of construction nor their meaning themselvesâhere their function within a form of life. The function those constructions obtain with respect to the circumstances of their utterance reveals that underlying the surface structure of âsentencesâ is a generative syntax that utilizes sentences as the vehicle for the statements, objects, of thought produced. It has been maintained that a Black identity, articulated in a manner relevant to the conditions in which it is used, introduced from one context for use in another reveals the precariousness of normative functions presumed and set to strings that are retroactively defined as correct based on a sort of dictionary that standardizes their use in order to manage discourse. It follows that we cannot differentiate the Black and the White by virtue of output alone, as Black-ness appears differently dependent upon the material within a particular context it has at its disposable in order to produce an identity that is not interchangeable regardless of context but functionally equivalent, i.e., whose operation expresses a Black form of life within those conditions.
In managing discourse, one manages the modes of being qua modes of expression possible in that context. As language capacity has been defined within linguistics by infinite use of finite means, producing expressions that are not random but never the less appropriate, i.e. dependent on but not necessarily caused by, conditions or context (Chomsky, 2016; Humboldt, 1836), Black English reveals the sonic well-formed strings articulated out of one's mouth are not directly correlated to meaning. Semantic content is discerned by the use of those outputs obtained within states of affairs, which indicates a mechanism producing and later mapping that finite set of sonic elements to the thoughts produced. A single word can denote multiple objects or their parts and a single object can be denoted by multiple words. Just as well, concepts for which we have words do not necessarily denote something in the extra-mental world. For example, infinity is not an object in the âphysicalâ world but a real concept nonetheless. Modes of expression, then, are the ways in which one is in the world (Wittgenstein, 1953; Jones/Baraka, 1963). âBlack Englishâ can be considered immanently philosophical as it takes a generative syntax across contexts and utilizes the finite means in those contexts to articulate alternative states of affairs, utilizing the semantic interpretations determined to correspond to the linguistic material therein (Baldwin, 1979; Dillard, 1973). This is accomplished along syntactic transformations rather than following the extra-âgrammaticalââby way of a grammar book or dictionaryârules blindly (Kripke, 1980; Wittgenstein, 1922).
Black English is fluid until external parameters are imposed upon it (Dillard, 1973). The object of the study to follow is an alternative syntax embodying the principles of constructing the propositions of a subject that generates a smooth running semantics by way of the framework of related functions composing the objects of thoughts that obtain within the form of life structured by those expressions. From there decision procedures determining the appropriate interpretations of these expressions can be formulated and we can provide proofs of the method embodied by this thought-producing mechanism. In doing so, a theory of subjectivity emerges. In this is the capacity to produce thought from the finite lexicon available along certain transformational rules, whose interpretations are critical of the state of affairs, reality, constructed in such a way that is not random but appropriate to the context. Our goal is to reveal the method of constructing propositions rather than an all-encompassing statement that dictates what counts and what does not as a valid expression. A universal statement fails to capture all of the output of an infinitely recursive procedure under a finite set of parameters. In this way, Afro-Pessimism or White supremacy is shown as self-defeating as evidenced by the logic embedded within those critical propositions. Evidence of a mechanism for creating thought, thus the subjectivity in the deep structure producing Black identities will be developed below. Black, then, is an identity; blackness represents subjectivity as a recursive function producing various discreet identities dependent upon the conditions and contexts in which that subject finds as well as creates itself.
By illustrating a system of thought which does not presume the mechanism creating it, we show the validity of statements made regardless of the surface structure of what has been articulated. Articulation, then, is indicative of a form of life. In what follows, blacknessâ method and mechanism of producing thought, thereby revealing its subjectivity, is proven valid. By making the generative syntax to within subjectivity explicit, without recourse to any other means of justification requiring further justifications leading to either ambiguity or antinomies of various sorts, what is stated from that form of life cannot be discounted and if it is, justification lies on the side of the one that disregards what has been expressed, not the one creating the thought.
Let's propose a system (N, 0) for a Black logic and from which the form of thought articulated expresses blackness. In order to illustrate a logic, we formalize the use of certain symbols so that the statements constructed are: i) not ambiguous; and, ii) are able to be represented without recourse to material with which their operation becomes ambiguous, i.e., words.
I will use lower case letters: x, y, z equivalent to x, xâ, xââ, etc. in the same order representing the objects of statements. The apostrophe is to show that the object is the successor of and other than the base letter to which it is affixed. A successor, the object recursively produced by some operation, will become important to us later as their use suffices in representing the result of a particular operation we will develop in section II called articulation.
Upper case letters: R, A, Aâ, B, etc. represent a relation obtained between objects or an object and the context of which it is a part. A statement as a whole is a relation between object(s) and a predicate whose function expresses a description of those objects that obtains the conditions represented by that upper case letter. The scope of those conditions is denoted by the use of parentheses which determines the extension of the domain consisting of the objects obtaining that set condition. For example, A(⌠xâŚ) states that x obtains the conditions set by A which makes A the predicate of x. We hope to show that predicates as a description of the conditions of which x is a part, behave in the same way as a function, positing a relation between x as argument and the interpretation it produces, i.e., the solution to that function. So, A(x) is the same as A(x,x) which is to say that A is a function of x, i.e., x is A related to itself in the conditions which A represents.
Letters other than x, xâ, y, z, such as a, c, etc. represent constants or names.
I use the term object insofar as we speak of a term's objective use, the âobjectâ of a function. In fact, a function is an object of thought insofar as how they are traditionally defined. Let a function be defined by the following:
If one has an object in a domain and another object in a sub/co-domain, the pair of those objects are elements of a function. In this way, a function becomes an abstract object, an object of thought.
We can quantify these abstract objects even if its output is 0, for as yet applied. As the content of an identity ascription names the co...