Notes on Truth, Beauty, and Goodness -- Phil A231

William Jamison - Instructor

The Rejection of Logical Atomism

William Jamison - Instructor

Since Chapter 2 does not have a numbering system as does the Tractatus, I will refer to page and paragraph.

In this chapter Wittgenstein initiates his rejection of the logical atomism of the Tractatus. Essentially, Wittgenstein is recognizing that issues of reference and denotation, or how a word or phrase pictures a fact, is much more complicated than logical atomism assumes. Notice how the importance of this shift has been described: (from The Flight from Reality in the Human Sciences by Ian Shapiro):

"The interpretive turn thus went hand in glove with the ascent of ordinary language philosophy associated with the later Wittgenstein and J. L. Austin in the 1950s and with developments in literary hermeneutics in which understanding social processes was modeled on the interpretation of texts.7 It was but a small step from this to the view that society should be conceived of as a text, whose meaning is best recovered by exploring the web of linguistic conventions within which social agents operate as collective authors. We are locked within a prison-house of language, as Frederick Jameson colorfully put it, the implication being that it is better to try to understand linguistic reality from the inside than to indulge vain fantasies of escape.8 Different theorists had different views of how such understanding is best achieved, but they all agreed that the point of the exercise is to elucidate social meanings by exploring the linguistic conventions--the language games, as Wittgenstein had it--within which people inevitably operate. Social reality arises out of conventional linguistic usage, and the key to understanding it lies in recovering the conventions so as to see how people use them to act in the social world."

Back to the notation:

Much of the notation used in chapter 2 is from logic books written by Bertrand Russell and Gotlob Frege. Apart from being aware what this notation is basically being used to do there is no need to become too familiar with it for this course. This sort of notation is explained in either logic courses or some mathematics courses.

To give you a basic idea of what it means think of the following as a guide:

When we discussed the four atomic types of statements, what Aristotle calls standard form categorical statements, I drew them on the board this way:

A  All S are P E  No S is P
I    Some S is P O  Some S is not P

Keep in mind that all statements you can make are going to have either the form of one of these four types of statements or will be a combination of two or more of them. So you can analyze any set of statements by breaking them down into a string of these -- which is essentially what a computer programmer is doing while writing code.

Imperatives, exclamations, and questions are not statements in this sense, since they are neither true nor false.

Here is the same table with the logical notation for each:

A  All S are P


(x) ( Sx Px )

E  No S is P


(x) (Sx ~Px)

I    Some S is P


($x) (Sx . Px)

O  Some S is not P


($x) (Sx . ~Px)

It might not at first be obvious that everything we say turns out to be one or a combination of these four statement types. Pick something you might say that is true or false and see if you can break it down into the subject and predicate sets, and see how those sets are being related in the complex statement you made.

For example: "Classical music includes the music of Mozart and some of the early music of Beethoven, but lot's of people think of all full orchestral music as classical also."

What sets are included in the complex statement? The list would include: "Classical music", "Mozart's music", "early music of Beethoven", "lot's of people". "full orchestral music", and a second sense of the set "classical".

Breaking the complex statement down into the atomic elements, the standard form categorical statements, we have the following:

1. All the music of Mozart is classical music.

2. All the early music of Beethoven is classical music.

3. Some people are people that think all full orchestral music is classical music. (That is that some people are in the set of things that consist of people that think all full orchestral music is classical music.)

The complex initial statement includes statements 1, 2, and 3 all conjoined with one another. For the complex statement to be true, all three statements, 1, 2, and 3, have to be true.

Try this technique and you will see that all statements that are either true or false can be treated this way.

Another point in reading the text is noting that there are only three ways we connect statements together. We can add them with "and" (which includes all words that do the same thing -- for example "but" or "also"). These are conjuncts. We can connect them with "either-or". These are disjuncts. We can use negation - "not".

So the three logical connectors are: "and, or, not."

The symbols used to represent these are ".", "v", "~". For reasons of economy, there are other connector symbols that represent various combinations of these three. But this is enough to get on with for now.


This page is maintained by William S. Jamison. It was last updated August 14, 2012. All links on these pages are either to open source or public domain materials or they are marked with the appropriate copyright information. I frequently check the links I have made to other web sites but each source is responsible for their own content.