Ordinary language contains imprecisions and ambiguities. The structures and mechanisms of natural language have caused confusions and disputes. One example centers on the nouns ‘space’ and ‘time.’
Consider these sentences:
Is there enough space in the suitcase for a pair of shoes?
He has space in his car for two more passengers.
How much space is in the storeroom?
Because we often take nouns as names for objects or substances, these sentences give the impression that ‘space’ names something which is found in suitcases, cars, and storerooms. This impression could give rise to the formation of sentences like these:
Can I take the space out of the suitcase and put it into the car?
Can an astronaut bring some space back to earth with him?
There’s a quart of space in the car, and a quart of space in the storeroom; can we exchange them?
This same type of confusion occurs with nouns like ‘time’ and ‘nothing’ and can be traced through the writings of many philosophers. Fridugis (also spelled Fredegis or Fredegisus) wrote an essay titled “On Nothing and Darkness” around 804 A.D.; Hegel and Sartre wrote extensively about nothing.
Likewise, the verb ‘to be’ causes confusion. Examples like the following lead the reader to infer that ‘be’ has the algebraic property of transitivity:
Fred is a teacher.
Fred is here.
A teacher is here.
But applying transitivity becomes problematic in examples like this:
My car is red.
My car is capable of going 75 MPH.
Red is capable of going 75 MPH.
These examples, and many others, have led some philosophers to seek a clearer and more precise mode of expression. It was thought that a more rigorous mode of expression would solve, or resolve, some of the questions and problems in philosophy.
This line of thought can be traced back at least as far as Aristotle (ca. 330 B.C.). His work on syllogisms, and his investigation of the verb “be” with its competing senses, manifest the hope that clarified language would lead to clarified thinking and understanding.
The next step is seen in the medieval Scholastics and their development of formal logic, including quantified and modal logics. William of Ockham (also spelled Occam) was among the most noted logicians of the early 1300s.
Gottlob Frege built on the work of John Venn, Charles Lutwidge Dodgson, and others. Frege developed symbolic logic in the 1870s, leaving behind the words and letters of natural language entirely. Symbolic logic raised hopes for higher levels of precision in the expression of propositions and of relations between propositions.
By the early twentieth century a clearly defined group of philosophers was working on language and logic as the keys for solving the major problems of philosophy. Bertrand Russell’s Principia Mathematica, Wittgenstein’s Tractatus Logico-Philosophicus, and the works of logicians like Kurt Gödel and Georg Cantor exemplified this shared project.
Of course, not all philosophers were part of this movement, and among those who were part of the movement, there were substantial variations and disagreements. As Garth Hallett writes:
For Frege, Russell, and others, a perfectly precise and regular linguistic calculus was a desirable possibility or goal; for young Wittgenstein it was a fact and had only to be revealed through an appropriate notation.
An optimism and enthusiasm surrounded some philosophers in this movement. They figured that it was only a matter of time until most, or even all, of philosophy’s major questions would be finally and permanently answered by rigorous logical analysis. Logic would avoid the ambiguities of natural language, and it was those ambiguities, they thought, which had created the questions in the first place.
As the exploration of logic continued, however, questions about topics like completeness emerged. Slowly the analytical program unraveled. Logic might end up posing more riddles than it solved.
The movement’s initial hopefulness, and even naivety, withered under the discoveries of logicians. A new question emerged: Was the anticipated level of rigor and specificity possible?
Even more: was such an idealized formalism even desirable?
The early phase of Wittgenstein’s career was not, strictly speaking, “formalist,” in the sense that formalism is a view in the philosophy of mathematics which denies much meaning to mathematical expressions and treats them rather merely as exercises in symbol manipulation according to a set of arbitrarily stipulated rules.
While the early Wittgenstein was not a formalist, he relied to some extent on an analogy between mathematics and natural language, and relied even more on structures and forms to communicate meaning.
As is well known, an entire industry has arisen around the activity of comparing the earlier and later phases of Wittgenstein’s career. Garth Hallett argues that Wittgenstein’s later work
is directed against the supposed ideal which underlay both positions and against the pointless proposals and unrealistic analyses to which it gave rise. Ordinary language is no such calculus, nor need it be. In fact the ideal of absolute precision and regularity is ultimately unintelligible.
On Hallett’s view, then, Wittgenstein is rejecting both the view that “a perfectly precise and regular linguistic calculus was a desirable possibility or goal,” and the view that such a calculus was already latently present “and had only to be revealed.”
Among the competing views of the relationship between the early Wittgenstein and the late Wittgenstein, one central question is the extent to which the late views reject the early views, and the extent to which the late views see themselves as somehow continuing, or being founded on, the early views.
In any case, the late Wittgenstein in general, and much of later twentieth century philosophy with him, continued to see great importance in language, but sought to explore language less along the lines of an analogy between language and mathematical logic, and more along the lines of language as a social and anthropological phenomenon.
