Science and The Logic of Legibility.

By Robert Hanna

“The only thing you absolutely have to know, is how to read.” (Albert Einstein, slightly but relevantly misquoted.[i])


You can also download and read or share the complete longer essay from which the short essay directly below has been extracted, “Caveat Lector: Six Investigations in The Philosophy of Reading,” HERE.


For us it is the circumstances under which he had such an experience that justify him in saying in such a case that he understands, that he knows how to go on….This will become clearer if we interpolate the consideration of another word, namely “reading.”… The use of this word in the ordinary circumstances of our life is of course extremely familiar to us. But the part the word plays in our life, therewith the language-game in which we employ it, would be difficult to describe even in rough outline. (Wittgenstein, 1953: p. 61e, §§155–156)


In four recent short essays, available online HERE, HERE, HERE, and HERE, I’ve explored some of the important epistemological and metaphysical features of the act or process of reading.

Since it’s self-evidently true that you, the reader of this very sentence, are reading this very sentence, then we can safely assume that you already know how to read and also what reading is — at least, as the later Wittgenstein rightly puts it in the text quoted as the epigraph of this essay, in a way that suffices for “the ordinary circumstances of our life,” even if the phenomenon of reading is philosophically “difficult to describe even in rough outline.”

But, fully allowing for the fact that the philosophy of reading is difficult, nevertheless it’s passing strange that, with the notable exception of fifteen sections in the Philosophical Investigations (Wittgenstein, 1953: pp. 61e-70e, §§ 156–171), even during the heyday of the “linguistic turn“ to “linguistic philosophy” (Rorty, 1967) that was enacted by the tradition of classical Analytic philosophy from 1880 through the 1970s, and equally during the post-classical, post-linguistic-philosophy period spanning the philosophy of language-&-mind, the philosophy of mind per se, and Analytic metaphysics, from the 1980s into the 2020s — so, for the last 140+ years — Analytic philosophers have paid surprisingly little attention to the phenomenon of reading — indeed, one can correctly say that they’ve consistently or even relentlessly avoided thinking, talking, and writing about it.

Now, since Analytic philosophers — like all other philosophers — live, move, and have their being as thinkers, talkers, writers, and above all, as readers, then perhaps this general pattern of philosophical avoidance is simply an instance of the widespread cognitive pathology that one might call young fish syndrome, whereby those who are everywhere surrounded by and ensconced in a certain intellectual, theoretical, affective or emotional, moral, sociocultural, or political transparent medium by means of which they encounter themselves, each other, and their world, nevertheless blithely fail to recognize the necessary and obvious existence of that all-encompassing medium:

There are these two young fish swimming along and they happen to meet an older fish swimming the other way, who nods at them and says “Morning, boys. How’s the water?” And the two young fish swim on for a bit, and then eventually one of them looks over at the other and goes “What the hell is water?” (Wallace, 2012)

To be sure, this wouldn’t be the only occurrence of young fish syndrome in the 140+ years of the Analytic tradition (Hanna, 2021: esp. chs. XVII-XVIII).

In any case, against the grain of Analytic philosophy’s avoidance of the phenomenon of reading,[ii] in this essay I want to explore some of the important logical features of the phenomenon of reading, in relation to the nature of science, where “science“ is understood in the maximally broad sense of “an organized body of knowledge,” so that it includes not only the formal sciences (e.g., logic, mathematics, and computer science) and the natural sciences (e.g., physics, chemistry, and biology), but also the social sciences, the “human sciences” or “moral sciences” more generally, and philosophy itself.

For convenience and ease of expression, in what follows I’m going to use the terms legible, legibility, illegible, and illegibility, respectively, as synonyms for the terms readable, readability, unreadable, and unreadability, respectively.

As per the fourth of the four recent short essays I mentioned above, let’s call any sentence that is (i) specifically about the act or process of reading, and that is also (ii) self-referring by means of the 2nd-person indexical description “you, the reader,” and the indexical description “this very sentence,” a caveat lector sentence.

Such sentences are so-named by me after the latin phrase “caveat lector,” meaning let the reader beware; but I’m interpreting that phrase broadly enough so as also to include the meaning let the reader be self-consciously aware.

And from a philosophical standpoint, here’s the paradigmatic example of a caveat lector sentence:

You, the reader of this very sentence, can’t either coherently or self-consistently deny that it’s self-evidently true that you’re reading this very sentence.

For convenience, I’ll call the sentence I displayed in large boldface text immediately above, The Lector Sentence, and for the purposes of this essay, it won’t matter whether The Lector Sentence is a universal sentence-type or a particular sentence-token.

Above all, for the purposes of this essay, we must recognize that The Lector Sentence is a caveat lector sentence that’s self-manifestingly true.

Then it’s highly instructive logically to compare-&-contrast The Lector Sentence with the classical Liar Sentence, i.e.,

This very sentence is false.

which, as self-manifestingly false, is not only a contradiction but also paradoxical, since necessarily, if it’s true then it’s false and if it’s false then it’s true, hence necessarily, it’s true if and only if it’s false.

The Lector Sentence and The Liar Sentence are (i) each of them reflexive, i.e., self-referring, (ii) each of them self-manifesting, and (iii) mutually antithetical.

More specifically, The Lector Sentence is reflexive, non-contradictory, true, and furthermore self-manifestingly true, whereas The Liar Sentence is reflexive, contradictory, self-manifestingly false and paradoxical, and furthermore both true and false, i.e., a truth-value glut.

In these ways, The Lector Sentence shows us the foundations of all science, truth, sound proof, and knowledge (Hanna, 2022d), whereas, as Alfred Tarski so brilliantly showed, The Liar Sentence shows us the limits of all science, truth, sound proof, and knowledge (Tarski, 1943, 1956).

For the purposes of this essay, I’ll define a text as any sequence of one or more characters (with a one-character sequence as the limiting case) where, as per the Oxford Encyclopedic English Dictionary, “character” is defined as

a printed or written letter, symbol, or distinctive mark. (Hawkins and Allen, 1991: p. 247)

Then, a text is illegible if and only any of the perceptible, syntactic, or semantic features that are either individually or conjointly required for reading that text cannot be discerned.

Some important and even leading or paradigmatic sciences contain contradictions or even paradoxical sentences.

For example, as per Gödel’s first incompleteness theorem, the Principia Mathematica-style formalization of Peano Arithmetic contains undecidable, unprovable, self-contradictory, and indeed paradoxical sentences, if that formal system is assumed to be not only sound but also complete (Gödel, 1967).

But no science can contain nothing but contradictions or paradoxes, on pain of explosion, or logical chaos, whereby not only is it the case that every sentence follows from every other sentence, but also that every sentence is a truth-value glut.

So, the fact that no science can contain nothing but contradictions or paradoxes is a direct implication of what I’ve called, following Hilary Putnam, the minimal principle of non-contradiction: not every sentence is both true and false (Putnam, 1983; Hanna, 2006: ch. 2, 2015: ch. 5).

Correspondingly, and now zeroing in on the logical features of reading in relation to science, all sciences must be at least minimally legible, i.e., there cannot be a science that’s completely illegible.

Let’s call that the principle of minimal legibility.

The principle of minimal legibility obtains because (i) every science must be communicable, but if no one can read any of it, then obviously it can’t be communicated and (ii) in order for a science to be, taken as a whole, meaningful, truth-evaluable, and knowable, then at least some of the sentences of that science must be completely legible.

Can there be an illegible sentence?

Yes, if that means a sentence that’s partially but not completely legible: a sentence that contains some but not all-&-only illegible characters could still be otherwise legible.

Let “BLAH” stand for an illegible character within a sentence.

Then, the sentence

The cat is sitting on the BLAH.

is partially but not completely legible, and therefore it’s illegible to that extent.

But there’s no such thing as a sentence made up of nothing but illegible characters; for example, the text


is not a sentence: it’s gibberish.

Can there be an illegible word?

Yes, if that means a word that’s partially but not completely legible: a word that contains some but not all-&-only illegible characters could still be otherwise legible.

Let “#” stand for an illegible character within a word.

Then, the word


is partially but not completely legible, and therefore it’s illegible to that extent.

But there’s no such thing as a word made up of nothing but illegible characters; for example, the text


is not a word: it’s gibberish.

Obviously, all sciences must be ideally aimed at truth, sound proof, and knowledge, even if they do in fact fall short of that, but always only within the limits of the minimal principle of non-contradiction: otherwise, they’re logical chaos.

Correspondingly, all sciences must also be ideally aimed at complete legibility, even if they do in fact fall short of that, but always only within the limits of the principle of minimal legibility: otherwise, they’re gibberish.

Therefore, The Lector Sentence, complete legibility, and the principle of minimal legibility should also be explicitly and fully recognized by all philosophers and scientists as taking their rightful logico-normative places alongside the classical logical norms of truth, sound proof, knowledge, and the minimal principle of non-contradiction.


[i] The original quotation is: “The only thing you absolutely have to know, is how to locate the library.”

[ii] Apart from later Wittgenstein, and now outside the Analytic tradition, another notable exception to this philosophical avoidance of the phenomenon of reading is the Polish phenomenologist Roman Ingarden’s 1968 book, The Cognition of the Literary Work of Art (Ingarden, 1973).


(Gödel, 1967). Gödel, K. “On Formally Undecidable Propositions of Principia Mathematica and Related Systems.” In J. van Heijenoort, (ed.), From Frege to Gödel. Cambridge MA: Harvard Univ. Press. Pp. 596–617.

(Hanna, 2006). Hanna, R. Rationality and Logic. Cambridge: MIT Press. Available online in preview HERE.

(Hanna, 2015). Hanna, R. Cognition, Content, and the A Priori: A Study in the Philosophy of Mind and Knowledge. THE RATIONAL HUMAN CONDITION, Vol. 5. Oxford: Oxford Univ. Press. Also available online in preview HERE.

(Hanna, 2021). Hanna, R., The Fate of Analysis: Analytic Philosophy From Frege to The Ash-Heap of History. New York: Mad Duck Coalition. Affordably available in hardcover, softcover, and Epub at URL = <>.

(Hawkins and Allen, 1991). Hawkins, J.M. and Allen, R. (eds.), The Oxford Encyclopedic English Dictionary. Oxford: Clarendon/Oxford Univ. Press.

(Ingarden, 1973). Ingarden, R. The Cognition of the Literary Work of Art. Trans. R.A. Crowley and K.R. Olson. Evanston IL: Northwestern Univ. Press.

(Putnam, 1983). Putnam, H. “There is At Least One A Priori Truth.” In H. Putnam, Realism and Reason: Philosophical Papers, Vol. 3 Cambridge: Cambridge Univ. Press. Pp. 98–114.

(Rorty, 1967). Rorty, R. “Introduction: Metaphilosophical Difficulties of Linguistic Philosophy.” In R. Rorty,(ed.), The Linguistic Turn. Chicago, IL: Univ. of Chicago Press. Pp. 1–39.

(Tarski, 1943). Tarski, A. “The Semantic Conception of Truth and the Foundations of Semantics.” Philosophy and Phenomenological Research 4: 342–360.

(Tarski, 1956). Tarski, A. “The Concept of Truth in Formalized Languages.” In A. Tarski, Logic, Semantics, and Metamathematics. Oxford: Oxford Univ. Press, 1956. Pp. 152–278.

(Wallace, 2012). Wallace, D.F. “This is Water.” farnam street/fs blog. Available online at URL = <>.

(Wittgenstein, 1953). Wittgenstein, L. Philosophical Investigations. Trans. G.E.M. Anscombe. New York: Macmillan.


Mr Nemo, W, X, Y, & Z, Monday 12 September 2022

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Mr Nemo

Mr Nemo

Formerly Captain Nemo. A not-so-very-angry, but still unemployed, full-time philosopher-nobody.