Boolean Logic, Fregean Logic, Wittgensteinian Logic and the processing of natural language

with No Comments

Gottlob Frege (1848-1925) transformed the field of logic from what it had remained since the days of Aristotle. Regarded as the founder of modern logic and much of modern philosophy [1], Frege laid the foundations of predicate logic, first-order predicate calculus and quantificational logic – formal systems central to computer science and mathematics (also modern philosophy and linguistics). Not only did Frege bring rigor to ‘analysis’, laying the foundation for ‘analytical philosophy’ [2], Frege was not satisfied with the ambiguity and imprecision of ordinary language. He created a new ‘formula language’ with elaborate symbols and definite rules, focused more on conceptual content than rhetorical style, which he called Begriffsschrift – a formal language for ‘pure thought’ [3].

Before Frege, George Boole (1815-1864) created what later became known as ‘Boolean logic’, he stated that:

“No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form” [4].

Boolean logic is the system behind the operations of computers. Claude Shannon applied Boolean logic (algebra) to solve problems using two symbols “1” and “0”. This formulation first appeared in Shannon’s 1937 master’s thesis, “A Symbolic Analysis of Relay and Switching Circuits [5].” This thesis is credited with launching modern switching theory, the foundation for digital computers today. It has been described as “possibly the most important, and also the most famous, master’s thesis of the century [6].”

An application of Wittgensteinian logic to online content analysis[7], could help filter authentic information from information disorder (non-information, off-information, mal-information and mis-information). Wittgensteinian logic applied in natural language processing technology (if possible) via automation could transform the quality of information online. Many challenges remain.

Pinker [8] explains how English and other natural languages are “hopelessly unsuited to serve as our internal medium of computation.” Pinker states that ‘thought’ carries more information than ‘words’ and the speaker may not be able to fully articulate to the receiver the full intentions of her thoughts through words alone. The receiver has to decode what he believes the speaker is trying to articulate. Some challenges of the English language  include: “ambiguity”, “lack of logical explicitness”, “co-reference”, “deixis” and “synonymy.” For the time being only human analysts (not artificial intelligence) can consistently and reliably filter authentic information from the inauthentic.

Ultimately, the hope is that effective natural language processing (NLP) applications will be developed to analyze online content and filter out misinformation effectively. This is an area of further research, within artificial intelligence field, that must be regarded as urgent today.

 

Notes

[1] Chomsky, N. Personal communication with author, 2021.

[2] Demopoulos, W. Frege and the rigorization of analysis. J Philos Logic 1994;

23, pp.225–245

[3] van Heijenoort, J. From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931. Massachusetts: Harvard University Press, 1967, pp. 1-82

[4] Boole, G. Studies in Logic and Probability. London: Watts & Co., 1952, p.273.

[5] Shannon, C. A Symbolic Analysis of Relay and Switching Circuits. Massachusetts Institute of Technology. https://dspace.mit.edu/handle/1721.1/11173 (1937, accessed 08 September 2021).

[6] MIT News.  MIT professor Claude Shannon does; was founder of digital communications, https://www.newsoffice.mit.edu/2001/shannon   (2001, accessed 08 September 2021).

[7] Omoregie, U. Online misinformation analysis through Wittgensteinian lens. SocArXiv (2021).  https://osf.io/preprints/socarxiv/c9ynd/

[8] Pinker, S. The Language Instinct: How the Mind Creates Language. New York: Harper Collins, 1994, pp. 69-72.

Leave a Reply

Your email address will not be published. Required fields are marked *