My reading of this work arose from a reference to it during conversations about language and its nature with someone whom I consider a friend, with whom I enjoy discussing these topics. This is the English version of the revision of Ludwig Wittgenstein’s work that arose from the notes and correspondence he maintained with Bertrand Russell (his doctoral advisor) and other thinkers¹. There is a parallel revision based on the Spanish version, done to address potential translation issues given the age of the treatise.

Perhaps, I imagine, the initial thoughts behind all this reasoning were driven somewhat by the commotion that Russell’s «Principia Mathematica» caused in Wittgenstein circles at the beginning of the last century. Wittgenstein presents a dense and very brief work, without a doubt. But it is also very prose-like; for my taste, it lacks rigour and formalisation.

The format Wittgenstein followed isn’t beneficial either, and at first glance, it seems nothing more than a bunch of unconnected good wishes. The English version I obtained has a note indicating that the numbering of the propositions in the work suggests their importance. The second level of numbering, i.e., n.1, n.2, n.3, … corresponds to comments on the Ith proposition; the third-level propositions n.m1, n.m2, n.m3, … are comments on those of the higher level, and so on. This is not indicated in the Spanish version, and it is essential to understand what was going through Herr Wittgenstein’s mind. I will resort to that numbering for some references.

The «Tractatus Logico-Philosophicus» was published years before the formulation of the Entscheidungsproblem², more than a decade before its answer (to the Entscheidungsproblem), more than a decade before the already well-known works of Herr Dr. Kurt Gödel³, and many decades before Chomsky’s work on linguistics (and in particular his hierarchy⁴), so we may forgive Herr Wittgenstein for some of his assertions. Herr Wittgenstein would have a long way to go today for him to see how much man has achieved in understanding the «laws of thought.»

As a computer scientist, one can’t help but be drawn to Proposition 2 and its reference to the philosophy behind object-orientation in the fields of analysis, design, and programming. As a computer scientist, one is drawn to the incipient allusions to formal grammars in Proposition 3.

The notation used by Wittgenstein (reminiscent of that used by Frege and Russell) is not very helpful. What he wrote as x.fx, we express today:

which makes it challenging to keep up with some logical expressions.

There are two points about the fact that this work was suggested to me by a psychologist that «boggled my mind» for a while. There are certainly a couple of references in Wittgenstein’s work to the field of psychology and to specific topics falling within its domain; Russell also mentions it in his introduction:

“[…]the problem what actually occurs in our minds when we use language with the intention of meaning something by it; this problem belongs to psychology. Secondly, there is the problem as to what is the relation subsisting between thoughts, words, or sentences, and that which they refer to or mean; this problem belongs to epistemology.[…]”

Wittgenstein mentions psychology in his propositions 4.1121, 5.541, 5.5421, 5.641, and 6.423. But, in light of what generative artificial intelligence has been showing us over the past five years, there are some things on which psychology no longer has the final say regarding language today.

The other point is the references to «language.» For example, Russell notes in the introduction:

“A logically perfect language has rules of syntax which prevent nonsense, and has single symbols which always have a definite and unique meaning.[…]”

and like this there are several other mentions of language, its function and nature in the introduction, in Wittgenstein’s preface and his propositions in terms of a medium of expression of logic (3.032), on meaning and signifier (3.323, 4.1121, 4.121, 5.4732; I’m sure Sassure would have an opinion here); the nature of language (4.001, 4002, 4.0031, 5.4731). But I think there is a confusion here about the phenomenon of language and formal grammars (and here I have no doubt that Chomsky would have something to say).

Propositions 5.6, 5.62 reminded me of what Orwell postulated in «1984», on the importance of language to be able to manifest our mind in the reality that surrounds us. Still, I think that Herr Wittgenstein exaggerates about the properties of language (6.12), its consistency (6.124, 6.233) and the timid (although nice, nonetheless) attempt at defining numbers that he gives in 6.02 and 6.241 (I do not doubt that Herr Dr. Gödel would have an opinion here).

Discussing Herr L. Wittgenstein's "Tractatus Logico-Philosophicus" with @MiauMiauMoi

We agree, and his look says it all. pic.twitter.com/LfVNHszfTf

— Dr. Edu 🐾 (@dreduphd) August 21, 2025

In the end, Herr Wittgenstein does not follow his own proposition number 7.

References

1. «Tractatus logico-philosophicus«, Wikipedia, web. Visited: 20205.08.20. URL: https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus.
2. «Entscheidungsproblem«, Wikipedia, web. Visited: 20205.08.20. URL: https://en.wikipedia.org/wiki/Entscheidungsproblem.
3. «Gödel’s incompleteness theorems«, Wikipedia, web. Visited: 20205.08.20. URL: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems.
4. «Chomsky hierarchy«, Wikipedia, web. Visited: 20205.08.20. URL: https://en.wikipedia.org/wiki/Chomsky_hierarchy.