Title: Origin and value of the phrase “universe of discourse”
Date: March 3rd 2011

*Original Research by: Damian C. Koshnick [if using, please cite]


On the “universe of discourse

Historians of logic (C.S. Lewis, 1918; Heath, 1966; Mofti, 2008) typically indicate that the first use of the term “universe of discourse” was by Augustus De Morgan (1846). However, Hobart and Richards (2008) suggest that De Morgan used the phrase “universe under consideration,” but never, in fact, used the exact phrase “universe of discourse” as was actually coined by George Boole in 1854. Additionally, Hobart and Richards cite Corcoran (2003) who was confident about this revised point of origin stating, in the introduction to a reprint of Boole’s “The laws of thought” (1854), that Boole authored the term for, “the first time in the history of the English language” (p. xx).

Reading Boole’s term in the originating context is, I was pleased to find, utterly surprising. Although his book is on formal logic, he presents notions on the nature of discourse that seem both highly advanced for the date, 1854, and that echo several of the principles by which English as a subject was expanded in the mid-1960’s (particularly through Moffett’s book by the title, “Teaching the Universe of Discourse”). Consider, briefly, the content within which Boole first employed the phrase “universe of discourse”:

In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. … Now, whatever may be the extent of the field within which all objects of our discourse are found, that field may properly be termed the universe of discourse. (The laws of thought, p. 42)

That Boole’s pre-Vygotskian conception of discourse correlates thought as self-dialogue (though not precisely as the social-internalized), and further that he does so in a manner that equates 1. inner “conversing,” (i.e. dialogue) with 2. expressed dialogue shaped for others, this is a critical part of the “expansive” view of English that Moffett championed in the 1960’s, and which only came to broadly influence theories and instruction in the language arts thereafter.

What also echoes so much of what Moffett concerns himself with (in his book using the same phrase), is this formative concept that the potential of -a given “discourse”- is made finite by the assumed boundaries of the “universe” in/for which we imagine ourselves to be operating/conversing.

In a following chapter, Boole uses the term “universe of discourse” in a more formal, logician’s sense to be n(1), where 1 stands for all that is assumed in a given universe. 1, of course, could technically be everything in total, but as Boole notes above “usually we confine ourselves to a less spacious field.” He also clarifies at some length that:

As in primary propositions the universe of discourse is sometimes limited to a small portion of the actual universe of things, and is sometimes co-extensive with that universe … The office of any name or descriptive term employed under the limitations supposed is not to raise in the mind the conception of all the beings or objects to which that name or description is applicable, but only of those which exist within the supposed universe of discourse. (p. 166-167)

At times then, we may understand the degree to which we have intentionally drawn down the set or class of objects in a given universe, but very often too, as Boole puts it, “antecedent implied undertandings” limit the nature of a universe about which we speak. The main job of the logician is to determine everything stated, or assumed in a given universe + discourse. This is done through (another Booleen invention) the identification of primary propositions –x, y, and z, followed by an analysis of secondary propositions which are the probable-relations between them.

Concluding thought: What is amazing to me is how often we intuit the primary propositions -the z, y, and z, and nearly instantaneously also the secondary propositions -the how- when we think to ourselves, when we speak with others, and when we sit down to write to an audience. Of course, it is also the case that these primary, and secondary propositions are not clear, and so much of determining this corresponds to what it takes to be a “good” writer, or a useful teacher of writing.

Put simply: “To whom am I writing?” – “What do they need to know?” – “How can I make myself clear?” … and thus the “universe of discourse” is drawn and redrawn over and over again, and never -really- in precisely the same manner, or according to the same boundaries.

Damian C. Koshnick
March 3rd 2011 / Santa Barbara, CA

Knapp’s Castle, with photo by: [Kate Koshnick]
In the hills above Santa Barbara, George Knapp, built Knapp’s Castle in 1916. The mansion was destroyed by a forest fire in 1940, and now only these sandstone foundations, several fireplace pillars and walls remain … with a view of the Santa Ynez Mountains, Los Padres National Forest, Paradise Road, and Lake Cachuma.
[http://www.independent.com/news/2011/jan/06/knapps-castle-construction/]

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2 thoughts on “Origin and value of the phrase “universe of discourse”

  1. Many thanks for this elegant recapitulation of Boole’s thought. I had thought that the extensive treatment in the Laws were the original of the phrase, and I was looking to get a confirmation of this from someone else.

    An intriguing thought for you may be that there is a potential derivation for both Boole and de Morgan (and also Babbage) from conversations with their friend the Indologist Henry Colebrook, who was Boole’s brother-in-law (and who wrote a splendid series of expositions of Indian logic recorded in the Transactions of the Asiatic Society in 1823).

    Mary Boole (Boole’s wife, Colebrook’s sister) was convinced of this and described it in 1901: Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan and George Boole on the mathematical atmosphere of 1830-1865

    de Morgan himself said The two races which have founded the mathematics,those of the Sanscrit and Greek languages,have been the two which have independently formed systems of logic

    I myself hadn’t heard of Moffett but will now read him

    Again, many thanks

  2. I found this quite helpful. The American philosopher Charles Peirce wrote a short paper on the concept of universe of discourse. He wrote that “The term was introduced by De Morgan in 1846 (Cambridge Philosophical Transactions, viii, 380) but De Morgan never showed that he fully comprehended it.” (CP 2.536; Cross-Ref:††) This part is especially interesting: “In every proposition the circumstances of its enunciation show that it refers to some collection of individuals or of possibilities, which cannot be adequately described, but can only be indicated as something familiar to both speaker and auditor. At one time it may be the physical universe, at another it may be the imaginary ‘world’ of some play or novel, at another a range of possibilities.” (CP 2.536) Since I stumbled upon this topic via Roman Jakobson, I am now considering how this tidbit could be applied to improve his communication model. Just like you said, “the “universe of discourse” is drawn and redrawn over and over again” in the process of communication. In any given exchange we are constantly referring to something in different “worlds”. Thus, Jakobson writes that “from a linguistic point of view the verb of existence remains elliptic as far as it is not accompanied by a locative modifier: ‘unicorns do not exist in the fauna of the globe’; ‘unicorns exist in Greco-Roman and Chinese mythology’, ‘in the tapestry tradition’, ‘in poetry’, ‘in our dreams’, etc.” (Jakobson 1985[1956]: 120). It’s a neat concept and a lot has been written about this, which is why I appreciate your exposition of this concept in Boole.

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