Are There Some Legible Texts That Even The World’s Most Sophisticated Robot Can’t Read?, #1–Introduction, & and The Logic of Legibility.
By Robert Hanna
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)
’Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe. (Carroll, 1988)
TABLE OF CONTENTS
2. The Logic of Legibility
3. Necessary and Sufficient Conditions for Legibility and Reading
4. Legibility, Reading, and The Falsity and Impossibility of Strong AI
This essay will be published in three installments; this first installment contains sections 1 and 2.
You can also download and read or share a .pdf of the complete text of this essay HERE.
The strong thesis of artificial intelligence, aka the strong AI thesis, is the two-part thesis which says (i) that rational human minded animal intelligence can be explanatorily and ontologically reduced to Turing-computable algorithms and the operations of digital computers (aka the thesis of formal mechanism, as it’s applied to rational human minded animal intelligence), and (ii) that it’s technologically possible to build a digital computer that’s an exact counterpart of rational human intelligence, such that this machine not only exactly reproduces (aka simulates) all the actual performances of rational human intelligence, but also outperforms it (aka the counterpart thesis) (see, e.g., Block, 1980: part 3; Kim, 2011: ch. 6). If the strong AI thesis is true, then, at the very least, necessarily, some robot must be able to do anything that any ordinary rational human minded animal can do. Correspondingly, the standard strategy in the strong AI program is to start with some accomplishment, act, or task that any ordinary rational human minded animal can already achieve or perform, and then reverse-engineer a digital computer program and either a stationary digital computer or a mobile digital computer — a robot — that can perform the same accomplishment, act or task, at least as well as, or better than any ordinary rational human minded animal. Now, robots can do some things that no stationary digital computer can do. So, the leading question I’ve asked in the title of this essay is whether there some legible texts that we — i.e., ordinary rational human minded animals — can read, but even the world’s most sophisticated robot — can’t read? If so, then the strong AI thesis is false and the strong AI program is impossible.
But in order to answer my leading question, which I’ll do in the concluding section 4, we’ll need to have at least the basic sketch of a plausible theory of legibility and reading already in place, which I’ll do in two stages, in sections 2 and 3 respectively.
2. The Logic of Legibility
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 first 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” (Wittgenstein, 1953: p. 61e, §§155–156).
But, fully allowing for the fact that the philosophy of legibility and reading is difficult, in this section I want to explore some of the important logical features of the phenomena of legibility and 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 (for example, logic, mathematics, and computer science) and the natural sciences (for example, 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. Moreover, 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.
Here’s what I take to be 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 the purposes of this essay, I’ll call the sentence I displayed in boldface text immediately above, The Lector Sentence, and also 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, however, 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.
The Liar Sentence, 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, 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 lower-bound limiting case, and there’s no upper bound on the number of characters, 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 Kurt 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, 1931/1967).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: necessarily and a priori, 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
BLAH BLAH BLAH BLAH BLAH BLAH BLAH.
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 — i.e., necessarily and a priori, not every sentence is both true and false — and its De Morgan equivalent, the minimal principle of excluded middle — i.e., necessarily and a priori, some sentences are either true or false with no third value and no value-gap, i.e., necessarily and a priori, not every sentence is neither true nor false with a third value or a value-gap — 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 and/or minimal principle of excluded middle.
[i] The original quotation is: “The only thing you absolutely have to know, is how to locate the library.”
Mr Nemo, W, X, Y, & Z, Monday 30 January 2023
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