New Approaches to the Circle of Sense and Nonsense
Abstract
:1. Introduction
2. Results: In a Search for Deeper Meanings—Navigating the Circle of Sense and Nonsense and, in Turn, Describing Logical Varieties as Knowledge Illuminators
To apply logic to dealing with nonsense and studying processes of nonsense transformation into sense, we need sufficiently powerful logical systems. These systems are called logical varieties [10]. They represent the new higher than before level of the development of formal or mathematical logic including many-valued logics (sometimes also called multi-value logics), fuzzy logics, relevant logics, and many other novel logical systems [10].Burgin provided the following explanation:Mathematical theories, such as group theory, category theory or set theory consist of many axiomatic theories, i.e., of many syntactic logical calculi. Systems of these syntactic logical calculi are organized in a definite way, which is formalized by the construction of syntactic logical varieties, quasivarieties, and prevarieties [13].Mark provided the following definition of logical prevarieties in our paper’s appendix, for mathematicians:Now we can give the exact definition of a syntactic logical prevariety.Let us take a class K of syntactic calculi with a language L of logical expressions and a language R of logical rules of inference and fix a class F of partial mappings from L to L.Definition 10[9]. A triad A triad M = (A, H, M), where A and M are sets of expressions that belong to L and H is a subset of R, is called:
- (1)
a projective syntactic (logical) (K,F)-prevariety if there exists a set of calculi Ci = (Ai, Hi, Ti) from K and a system of mappings fi: Ai → L and gi: Ti → L (i ∈ I) from F for which the equalities A = ∪i∈Ifi(Ai), H = ∪i∈IHi and M = ∪i∈Igi(Ti) are valid (it is possible that Ci = Cj for some i ≠ j); each calculus Ci = (Ai, Hi, Ti) is called a component of M and the set R(M) of all calculi Ci = (Ai, Hi, Ti) is called the representation set of M.- (2)
a syntactic K-prevariety if it is a projective syntactic (K,F)-prevariety where all fi and gi are inclusions, i.e., A = ∪i∈IAi and M = ∪i∈ITi;- (3)
a projective syntactic (K,F)-quasivariety with the depth k if for any i1, i2, i3, …, ik ∈ I either the intersections ∩j=1kfij(Aij) and ∩j=1kgij(Tij) are empty or there exists a calculus C = (A, H, T) from K and projections f: A → ∩j=1kfij(Aij) and g: N → ∩j=1kgij(Mij) from F where N ⊆ T;- (4)
a projective syntactic (K,F)-variety with the depth k if it is a projective syntactic (K,F)-prevariety and for any h, k, i1, …, ik ∈ I either the intersections ∩j=1kfij(Aij) and ∩j=1kgij(Tij) are empty or there exists a calculus C = (A, H, T) from K and projections f: A → ∩j=1kfij(Aij) and g: T → ∩ j=1kgij(Tij) from F;- (5)
a syntactic K-variety with the depth k if it is a projective syntactic (K,F)-quasivariety with depth k in which all f and g are bijections, i.e., A = ∩j=1kfij(Aij) and T = ∩j=1kgij(Tij).The calculi Ci are called the components of the variety (prevariety) M.When classes K and F are not specified such a triad M = (A, H, M) is simply called a syntactic logical variety, syntactic logical quasivariety or syntactic logical prevariety depending on what conditions it satisfies [13].
There is a poignant irony to the fact that the computer, a mechanism entirely predicated on symbolic logic, can be used to explore non-sense as well as illogical and elusive resonant artistic content. A work of art can be seen as an organism- like vehicle of content that is both generated and experienced through interaction [6].I point out the following related to my artistic work:If we look historically at the use of nonsense in literature and other forms of art, we find a fertile realm of creative exploration. How can our understanding of nonsense be applied to the realm of interactive art as well as symbolic logic? Here, Lewis Carroll becomes an interesting subject for investigation in that he both authored texts about logic (as Charles L. Dodgson) as well as texts exploring nonsense. Deleuze states in his book entitled The Logic of Sense:The work of Lewis Carroll has everything required to please the modern reader: children’s books or rather, books for little girls; splendidly bizarre and esoteric worlds; grids; codes and decodings; drawings and photographs; a profound psychoanalytic content; and an exemplary logical and linguistic formalism. Over and above the immediate pleasure, though, there is a play of sense and nonsense, a chaos-cosmose... Deleuze continues: The privileged place assigned to Lewis Carroll is due to his having provided the first great mise en scène of the paradoxes of sense–sometimes collecting, sometimes renewing, sometimes inventing, and sometimes preparing them [14,15].One goal of the use of computer systems is to come to better understand ourselves. Computers can function as mechanisms of discourse, enabling the exploration of embodied models made operative through interactive mechanisms. Within this computer-based context, through the exploration of nonsense, one can witness a contrasting critique of sense [16]. The subtle displacement of a particular element from a selected context can actually help to illuminate aspects and/or qualities of functionality [6].
Rather than becoming embroiled in the controversies which surround the nature of human intelligence, the practitioners of artificial intelligence have generally chosen to define their goals in empirical or operational terms rather than theoretical ones … The researcher simply chooses a task that seems to require intelligence (playing chess say or recognising visual images) and tries to build a machine that can accomplish it [17].
- Obtain results suggesting prospective directions for future research in this area;
- Study psychological processes generating transitions in the sense/nonsense triad and the circle of sense and nonsense;
- Study how the sense/nonsense triad and the circle of sense and nonsense function in science;
- Study how the sense/nonsense triad and the circle of sense and nonsense function in art, music, and literature;
- Study how the sense/nonsense triad and the circle of sense and nonsense function in technology and engineering [13].
3. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Seaman, B. New Approaches to the Circle of Sense and Nonsense. Philosophies 2024, 9, 40. https://doi.org/10.3390/philosophies9020040
Seaman B. New Approaches to the Circle of Sense and Nonsense. Philosophies. 2024; 9(2):40. https://doi.org/10.3390/philosophies9020040
Chicago/Turabian StyleSeaman, Bill. 2024. "New Approaches to the Circle of Sense and Nonsense" Philosophies 9, no. 2: 40. https://doi.org/10.3390/philosophies9020040