Tuesday, May 31, 2022

Indeterminacy and Borges’ infinite library

Jorge Luis Borges’ “The Library of Babel” (from his collection Labyrinths) famously describes an infinite library, comprising books which together represent every possible combination of characters in the alphabet in which they are written.  Most of the books are gibberish, just as, if you emptied a bag of Scrabble letters onto the floor and looked at the patterns that resulted, almost none of what you’d see would count as a genuine word or sentence.  But because every possible combination is there, many intelligible books are there too.  In fact, every possible such book is there, so that the library contains all knowledge, every truth there is about everything.  For any of these truths, though, the trick is to find it somewhere in this infinite, bewildering Babel.

That’s the idea, anyway, and Borges’ narrator’s description of the library, its history, and its denizens is arresting.  But would such a library really contain all knowledge?  Yes and no.  Unusual as the library is, it is nevertheless made up of books, more or less as we know them – that is to say, physical objects with marks whose semantic meaning is a matter of linguistic convention.  And as I have discussed many times over the years in various books, articles, and here at the blog, systems of material representations (words, pictures, or what have you) are, considered just by themselves, inherently indeterminate, inexact, or ambiguous in their content.  Given their physical properties alone, there is no fact of the matter about exactly what meaning they convey.

The indeterminacy of the physical

This is a truth acknowledged by philosophers of widely divergent commitments, from W. V. Quine to James F. Ross, and the conclusions they draw from it are no less divergent.  I follow Ross in holding that, since we have thoughts which do have determinate, exact, or unambiguous content, the lesson we should draw is that thought cannot be identified with any system of material representations.  For example, it cannot be identified with representations encoded in brain activity, in the electrical circuitry of a computer, or the like.  (I develop this line of argument in detail in my ACPQ article “Kripke, Ross, and the Immaterial Aspects of Thought” and have defended it against various objections here at the blog, for example in this post.)

Quine’s famous example involves a linguist trying to interpret a native speaker’s utterance of “Gavagai” in the presence of a rabbit, where the utterance is in some heretofore unknown language.  The linguist could translate it as “Lo, a rabbit!”, but might also produce translations that, instead of making reference to a rabbit, referred instead to either a temporal stage of a rabbit or an undetached rabbit part.  Which translation is to be preferred would depend on what beliefs the linguist thought he should attribute to the native speaker.  Does the speaker and the community he comes from fundamentally conceive of the world in terms of persisting substances?  In that case, the first translation would be preferable.  Or do they conceive of it instead in terms of ephemeral events?  In that case, the translation that made reference to a “temporal stage of a rabbit,” however odd to our ears, would be the one to go with.  And so on.

Deciding between the options would require appeal to other utterances of the speaker, along with the speaker’s behavior in general and the physical surroundings in which the conversation takes place.  But these other utterances, and the behavior as well, are also all susceptible of various alternative interpretations.  Suppose that the linguist is able to put together three different manuals of translation of the native speaker’s language, all of which are equally useful in allowing him to communicate with the speaker, but none of which is consistent with the others (since, for example, they translate “gavagai” in the three different ways described).  Then, Quine says, if behavior, facts about physical surroundings, and the like are all we have to go on, then there just is no fact of the matter about what the speaker really means.  The choice of which translation manual to use is a pragmatic matter.

Since Quine thinks that is all we have to go on, he draws the radical conclusion that there is indeed no fact of the matter about what the speaker means.  And since the scenario he describes differs only in degree from the situation we’re all in with respect to each other, he concludes that there is no fact of the matter about what any of us means either.  Other philosophers, judging (quite rightly in my view) that this position is incoherent, conclude instead that behavior, physical surroundings, and the like are not all that we have to go on. 

Now, it turns out that if the rest of what we have to go on is just more in the way of physical facts, then that will not suffice to change the outcome of Quine’s argument in the least.  For example, as Saul Kripke showed, appealing to computer programs purportedly being implemented in the brain makes no difference at all, because exactly which program any machine (or the brain) is running is itself indeterminate from the physical facts alone.  Thus does Ross conclude that the semantic content of our utterances, and the conceptual content of our thoughts (which is the source of the content of our utterances) is not to be identified with any physical or material properties at all.  (Again, see the articles linked to above for detailed exposition of the argument, responses to various objections, and so on.)

Infinite, schminfinite

Note that adding material representations (words, computer code, whatever) to a system of representations ad infinitum doesn’t change things in the least.  Even an actually infinite series of material representations will, considered just by itself, be as indeterminate or ambiguous in its semantic content as a finite series.  To see this, consider the following series:

…-4, -3, -2, -1, 0, 1, 2, 3, 4 …

Suppose that in some infinite corridor of Borges’ library, you can find this series written on a wall, extending forever in both directions.  Wouldn’t that unambiguously represent the series of integers?  Given our conventions, sure it would.  But given only the physical properties of the representations, it would not.  For the physical properties do not themselves have any inherent connection to the numbers represented.  There is, for example, no inherent connection between “4” and the number 4, any more than there is an inherent connection between “IV” and the number 4 or between “IIII” and the number 4.  That they are related is merely a matter of our conventions.  Suppose that “4” instead stood for cheeseburger, that “7” stood for carburetor, that “18” stood for collapse of the wave function, that “47” stood for Stan Lee’s sunglasses, and so on.  Then the infinite series written on the corridor walls would not represent the integers, but rather some bizarre sequence of disconnected concepts.

This is in fact why most of the books in Borges’ library would be gibberish.  Linguistic representation involves layers of conventions.  For example, there is in English the convention by which “a,” “b,” “c,” etc. count as letters.  But there is the further convention by which the sequences of letters “dog” and “cat” count as words.  There is, by contrast, no convention by which “rbxzt” or “ZZggTT” counts as a word.  So, putting limits on what counts as a letter only goes so far in excluding meaningless marks.  In English, the conventions will allow in “a,” “b,” “c,” etc. but not, say, “ȸ” or “Ж.”  But “a,” “b,” “c,” etc. will still yield meaningless combinations of marks.  Languages are in this way inefficient, allowing for the possibility of enormous amounts of nonsense unless some special conventions exclude it, but where (given the indeterminacy of the physical) there is no way to exclude all of it.

Could there be a system of representations that contains no gibberish?  And, for that matter, no indeterminacy of meaning?  Yes, but it would have to comprise what the Scholastic philosopher John Poinsot (also known as John of St. Thomas) called “formal signs,” which are signs that are nothing but signs.  To explain the idea by way of contrast, consider again the written word “dog.”  This is a sign that is more than a sign.  It is, in particular, a sequence of physical shapes and on top of that it is a representation of dogs.  A formal sign that represented dogs would be one that has no such double nature.  It would be a representation of dogs and nothing more than that – it would not, for example, also be a sequence of shapes, or of noises, or the like.  Concepts, according to Scholastics like Poinsot, are formal signs in this sense.  (For a bit more on this notion, see pp. 27-28 of “Kripke, Ross, and the Immaterial Aspects of Thought,” linked to above.)

But a system of signs that are nothing but signs would not be a system of material representations.  For to be a material representation just is to have some additional nature over and above being a representation (for example, the nature of having such-and-such a shape, such-and-such a chemical composition, or what have you).  So, if there could be a system of representations that contained no gibberish, and also no indeterminacy or ambiguity of content, then that too would not be a system of material representations.  It is because material representations have this dual nature – of being representations and also, on top of that, material things of a certain kind – that material properties and meaning can “come apart” from one another in a way that entails either gibberish or ambiguity.

Hence, a system of representations containing no gibberish or indeterminacy of meaning would not be Borges’ library which, qua library, comprises material representations (books, written words, etc.).  Borges’ library could contain all possible knowledge only if there is something distinct from the library, by reference to which (some of) the linguistic marks contained in the books by convention count as representations of all possible knowledge.  Borges’ narrator recognizes that the library by itself does not suffice to determine exactly what any book within it represents, saying:

An n number of possible languages use the same vocabulary; in some of them, the symbol library allows the correct definition a ubiquitous and lasting system of hexagonal galleries, but library is bread or pyramid or anything else, and these seven words which define it have another value. You who read me, are You sure of understanding my language? (p. 85 of the Penguin books edition)

Beyond the library

Of course, the denizens of Borges’ library, who read and interpret the books, are distinct from the library itself, and they assign meanings to the linguistic representations contained therein.  But they are not the ultimate source of the information said to be contained in the library, and could not be, since in none of their minds (considered either individually or collectively) is all of that information to be found.  That’s precisely why Borges describes some of them as searching the library for books that would contain certain secrets they would like to know.  In some way, then, there must be something distinct not only from the library, but also from the minds of its inhabitants, that determines the meaning of the (subset of) representations contained in the books that count as all possible knowledge.  What would this be?

One possible answer is implied by mathematician and science fiction writer Rudy Rucker’s notion of the “Mindscape,” which I discussed in a post some years back.  The Mindscape is essentially the collection of all the possible concepts, propositions, and inferences that a mind might entertain, considered as something analogous to Plato’s realm of the Forms.  But as the Neo-Platonic/Augustinian tradition argued – and as I argue too, in chapter 3 of Five Proofs of the Existence of God – ultimately we can make sense of the Platonic realm only if we understand it as comprising ideas in the divine intellect.  (Though as I explain in the post just linked to, Rucker’s Mindscape is not itself to be identified with the divine intellect, but rather as something that ultimately presupposes the divine intellect.)

Though Borges’ infinite library does not exist, something analogous to it – in particular, analogous to it in its being a repository of all knowledge – could exist, and indeed does exist, viz. the divine intellect.  But there is in it neither gibberish nor indeterminacy.

Related reading:

Kripke, Ross, and the Immaterial Aspects of Thought

Revisiting Ross on the immateriality of thought

Indeterminacy and the comics

Kripke contra computationalism

Rucker’s Mindscape

The divine intellect

Augustine on semantic indeterminacy

Augustine on divine illumination


  1. In fact, every possible such book is there, so that the library contains all knowledge, every truth there is about everything.

    I'm sure that this has been said before, but it will also contain every falsehood there is about everything. And there is no way of knowing, if the books are your only source of information, if what you are reading is true or false. Thus this library is useless if you want to increase your knowledge, even leaving aside the questions of representation.

  2. Surely you are aware of Quine's essay, "Universal Library."

    1. Hmm, from Quiddities I see. I must have read that essay years ago, though I do not recall it. Going to pull it from the shelf.

  3. This reminds me of Hilberts Hotel

    1. I am convinced that the Library of Babel is in fact the reading room of Hilbert’s Hotel.

    2. Can we add an infinite number of Libraries of Babel, i.e. an infinite number of reading rooms of Hilbert's Hotel? Or is there something in set theory that rules out an infinity of infinities?

  4. Fascinating. Heard of the Library but never your well-argued idea before.

  5. There is a really cool (limited in scope, of course) simulation of this library online.

  6. If you're curious, there's a computerized simulation at https://libraryofbabel.info/ .

    'lo and behold, I stumbled across this wonderful book : https://libraryofbabel.info/bookmark.cgi?oj.lqsltcwb377

    It rings a bell... :D

  7. @Edward Feser This post raises a few big questions:

    1) The way semantic indeterminacy is described seems clearly to be neutral with respect to universality or particularity.

    And the specific types of determinacy - what words refer to or mean, such as Gavagai meaning rabbit or rabbit part or temporal part - seem to be clearly individualised and concrete.

    In other words, something which even animals have. For example, you can easily teach a dog the meaning of "ball" by association, as well as "throw" and he could then later know what those refer to, so the dog's knowledge has determinate meaning. You can even teach an unknown word to a dog in a context where one object is completely new, and the dog gets that the new word is likely a reference to the new object, and grabs it.

    So if this type of semantic determinacy, which isn't based on universals or forms per se, is immaterial...then shouldn't we also conclude that animal minds have an immaterial aspect to them as well?

    2) As for formal signs, the mentioning of such signs still being representations is interesting, and how they have to be immaterial due to not having any secondary nature that isn't intrinsically a sign.

    But isn't this still just a mediation, and not the thing known itself directly? It strikes me as possible to say that one could simply have the object itself, or an aspect of the object, directly in your mind, without this having to be mediated even by representations.

    In other words, even formal signs, as representations, are still in a sense mediators between the thing they represent - but if one could get rid of even those, and know a thing without any mediation, this would be even more, well...direct of a way of knowing.

    And it seems we already know of certain things this way - our own existence and self-awareness seems to be an example of knowing something directly and without mediation. The Beatific Vision seems to be yet another.

    What do you think?

    1. Having a dog, and having tried to "teach it some words" with varying success, I am far from clear on what is actually happening when a dog "learns" some word or other. So far, in fact, that I must lean on the brakes when you say "For example, you can easily teach a dog the meaning of "ball" by association, as well as "throw" and he could then later know what those refer to, so the dog's knowledge has determinate meaning." and all the following examples. I don't know what scientist THINK they have proven about animals learning words, but I am doubtful that they have actually proven them. And that's in spite of the fact that I tend to keep an open mind about the possibility that some creatures that we think are "animals" really might have rational souls, and the difficulty of proving definitively that they don't.

    2. @Tony

      Well here are some videos on dogs being taught to communicate using buttons which produce word sounds:



      From those videos it seems that some dogs can be taught to know the references of words sufficiently as to be able to use them in a way indirectly through buttons. What do you think?

    3. Joe, I love the fact that enterprising and intelligent people are actively pushing the boundaries of what we know in this area.

      However, I also think we need to be cautious about what things like this prove about animal communication, and (more specifically) about what is going on with "words" (i.e. signs) of interior "concepts" in these events. It has long been obvious that animals can learn words in some sense, because they are able to accurately respond to their own names, and they can (fairly reliably) pick up a sense of expressions like "food", "outside", etc. The question isn't whether they can "get" words in some sense, the question is what, precisely, is going on in their souls that enables them to "get" these words, and especially whether that activity is like what happens in us when we form concepts. And, to put that in its most critical context, whether what the animal is doing allows it to have universals in the relevant sense, and whether that would allow them to grasp a universal truth. That's what we really need to get to in talking about whether animals can learn words. And the first video is far, far from conclusive about that. (The second video isn't available any more.)

    4. @Tony

      Well, I wasn't wondering if animals therefore have universals, but whether they have basic semantic determinacy in such a way that they can know the intentional reference of words - so they have this sort of intentionality. Which doesn't require knowing universals or their form.

      Heck, even we can distinguish in our own minds the difference between universals and other forms of determinacy in meaning that isn't related to universals.

      So our own usage and understanding of words doesn't necessarily imply universals - so to say that animals can understand "words" in no way implies they must therefore also grasp universals.

      On a side note, Anselm Oelze has an interesting volume on medieval views on animal cognition, and the various layers in-between full-blown knowledge of pure immaterial universals fully abstracted from material conditions and cognition that is below that:


      The whole book is available for free to read there! I hope it's an interesting resource.

      More specifically, I recall him talking about how Pseudo-Peter of Spain, or Peter John Olivi, held that animals can have general intentions without this being the same as universals - desiring wine in general in comparison to wineness itself is one way of putting it. This implies there may be different kinds of degrees in between pure particularity and pure universality in terms of cognition.

      Another idea similar to this, but I think comes from Albert Magnus, is that there is a difference between knowing pure universals fully detached from material conditions, and knowing them only partially while still attached to matter, and how, if we assume no other animals have true intellect, we could also explain their abilities to generalise in this manner as well - and this does seem to be a genuinely real distinction in terms of cognition, regardless of whether or not some non-human animals have true intellect or not.

      What do you think?

    5. @Tony

      As for intellect in other animals, could you go into more detail about what you think of this issue?

      It's very interesting. Could we perhaps categorise things in such a way as to admit of different categories of intellect - maybe animals have intellect in the sense that they can grasp basic logic and basic universals, but it doesn't extend to certain other aspects of reality such as proper moral responsibility and awareness, whilst we humans do have higher intellects than those of other animals as we do have access to these and other higher truths?

      Or maybe some animals could have something that isn't intellect, but is still immaterial, or material but something like proto-intellect?

      Another issue is the difference being one of kind or degree - say animals have a kind of proto-moral awarenness (dogs feeling something like shame when caught or berated, whales saving humans and so having concern for others and/or compassion, elephants holding "funerals" for dead fellows and grieving, for example). Some could argue that this means morality, while still categorical, also comes in degrees and we're not different from other animals in kind. However, one could also easily say that moral responsibility is still categorical - maybe even that you either are a morally responsible agent or not, no matter what lies in-between - since even if one thinks animals have proto-moral awareness, this awareness is still not sufficient for proper moral theorising and awareness, and so what we have is still categorically distinct by definition.

      What do you think?

    6. JoeD, as I understand it, Western Civilization has been geared around an understanding of human thinking that it is essentially different from what happens in all other animals. What this difference is, is and has been under dispute for millennia, and in recent years the mere claim THAT it is essentially different is disputed as well. Aristotle's position reflects a belief that human kind of thinking implies grasps of non-concrete universals (like "justice" and "common goods") in addition to grasping the essential formal natures of concrete things like that tiger over there. And his teaching goes on to say that the human soul must have a kind of faculty that says of the soul that it is immaterial in a different way than the soul of another animal is the formal principle while matter is the substrate principle of the animal. That different way is, likewise, disputed, but has been claimed by the A-T tradition as representing an spiritual soul, which is capable of persisting even if the human being dies, because the soul has a beyond-matter principle.

      Because we are ourselves humans - i.e. a kind of animal - we rely on senses for primary input, and our faculty of intellect is DIFFICULT for us to examine closely - in particular, because being (we suppose) non-material, it is not easily subjected to empirical experimentation like we do in most sciences. Hence it should not be surprising that we can settle about the nature of that intellect only with difficulty as well, and (given fallen nature) with many disputes.

      As a student of the A-T schools, I incline heavily toward that understanding, but I respect that the view that ALL other animals have fundamentally lesser kinds of faculties has not been scientifically demonstrated. I remain willing to consider the possibility that A-T have the human intellect's difference wrong, but have not come across convincing evidence of it, only (like the video) suggestive evidence that the A-T bifurcation may be insufficient for (say) degrees, such as possibly degrees of what (in A-T thinking) involves grasping universals.

      I am sure that people much more capable than I as an A-T student have thought of how modern biology (and, specifically, animal behavior) does or does not bear out the A-T distinctions.

      To add fuel to the fire, I find it odd, even slightly suspicious (in a good way) that we keep coming across carnivorous animals which in the wild would seem to be wholly competitive with man, but (in individual cases) seem to come to men for help with some problem insoluble to them. What, I ask, is going on in their "minds" when they do that?

    7. @Tony

      Sounds fair. My own thinking on this is that A-T itself in no way entails that all other animals must be non-rational. That question is purely empirical - whether or not a given living being counts as rational (or can grasp universals fully divorced from matter) can't be judged by theory itself. So I'd disagree with connecting these two separate things such that A-T seems to necessarily imply it.

      The question of whether animals other than humans also have intellect / grasp universals fully is also distinct from the question of whether there are degrees of grasping universals fully / degrees of intellect. Which may also be distinct from the question of whether there are different categories or kinds of intellect, such that one could hold that some animals also truly have intellects so they can fully graps universals apart from matter, while still being categorically lesser than humans as our intellects can know categories other animals can't, and are thus made for things other animals aren't.

      I also wouldn't essentially identify A-T with the position that there aren't any degrees of intellection, or a hierarchy of different types of intellect. There doesn't seem to me anything incompatible with A-T in those positions, and nothing in A-T requires one to be opposed to those; I can easily imagine a basic general A-T metaphysics that accepts the two possibilities.

      Again, I'd also distinguish between semantic determinate meaning in the sense of knowing the referents of words (like the dog in the video), and semantic determinacy in the sense of knowing universals divorced from matter. Those are two very different things, and it's easily conceivable that animals could have the former but not the latter.

      As for your fuel to the fire...could you go into a bit more detail as to why you find animals seeking for help interesting? Sounds...interesting.

    8. For dogs, language is a bunch of random noises alphas generate for reasons best known to themselves. Dogs are capable, with sufficient conditioning, to associate specific alpha noises with specific objects or actions. So, for example, they might associate the alpha noise "ball" with this thing/i>. However, they have no concept of "ball" i.e. "ballness"that could be associated with more than one thing. Put 2 balls next to each other and tell Fido "ball" and he won't ask, "Which one?" He'll just get his ball because that's the thing he associates the alpha noise "ball" with. As Locke put it, beasts abstract not.

    9. Fred, I might have thought the same thing...until I actually observed my dog. He seems to have no trouble associating "ball" with a brand new ball brought into the house.

      could you go into a bit more detail as to why you find animals seeking for help interesting? Sounds...interesting.

      Joe, look for a video on, say, a shark asking for help from humans in getting a hook out of its body. What puzzles me is this: I imagined that a sharks (a top-level predator in its environment) would view (or "view") humans as either prey or competition, and nothing else. Not sure it even would have room for treating humans in any other way. Nor do sharks seem to exhibit the activity of "play" as we normally think of it, which many mammals do (especially the young). So, what, precisely, is a shark "thinking" when it "seeks help" from humans, and allows them to (temporarily) hurt it (like the dickens) to get the hook out? What mental processes allow it to do that? I am not highly confident that we can come up with an explanation of that sort of behavior that rests entirely on what would typically be ascribed to non-rational "minds".

    10. @Tony

      Interesting. What do you think would it mean for sharks in that case to be rational?

      If one grants rationality in this case, would we then have to subdivide different types of rationality, as though sharks may have some rationality they aren't capable of some of the things we are capable of?

      Would such a potential subdivision of different types of rationality, some being lower while others higher, explain how it's still morally okay to kill sharks or other fish that are rational for food? Meaning that there is a certain categorical cut-off where the rationality also includes proper full moral awareness like we have?

    11. @Tony

      Also, another example of animal intelligence I'd like to know your thoughts on are crows. Apparently, some say that they're as intelligent as 7-year-old children in some cognitive aspects.

      For example, when faced with a tube with water and a peanut floating on the surface along with objects that float and sink, they know to only put in heavier objects to get the water level to rise so they can eat the peanut. They even know to choose tubes filled with more water than less as that makes the job easier. Keep in mind this is a novel use of tools which the crows weren't taught beforehand, so they had to realise it themselves.

      Human children can't even do this until the age of 5.

      Even more amazingly, crows can delay gratification - in an experiment showing different tools for getting treats our of problem-solving-boxes and a small fruit among them, which was less tasty than the treat gained through tool-use, crows preferred to avoid the fruit and wait until they (and the tool they picked and held) were transported to the room where the boxes hiding the better rewarded were present - showing long-term thinking and expectations..

      Here's a 14 minute video on this:

      Why Crows Are as Smart as 7-year-olds: https://www.youtube.com/watch?v=7aWL2iEb6y4

      An article:


      A short article on analogical reasoning in crows - knowing "sameness" and "different-ness" in tasks where they have to recognise that two different pairs are the same because they contain two different letters, whilst two other pairs are the same because they contain two of the same letters (not literally the same like AA and AA, rather CC and DD): https://www.scientificamerican.com/article/crows-understand-analogies/?redirect=1&error=cookies_not_supported&code=21f3adb8-0fac-4272-b0dc-975621a4a263

      And a longer study on causal reasoning in crows: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0103049

      What do you think of the video and the shorter articles?

      Does this behaviour from crows require intellect proper?

    12. JoeD, I don't think that the videos or articles establish that crows (or other animals) are rational and have spiritual souls with intellects capable of knowing universals. But I do suspect that they indicate that we have not yet clearly explained what, precisely, is the "mental" activity in them that enables them to do these things, and how it differs (or doesn't differ) IN KIND from what humans are capable of by reason of their rational souls. I think there is still room for fleshing out the distinctions more clearly. I hope out more hope that we will scientifically discover the right explanations to make the differences more definitively known, that that we will discover that dolphins, sharks, crows, and primates are rational beings.

      St. Thomas argues (with older teachers) that angels come in many species - indeed, Thomas says that each angel is its own species. And the different species have different levels of knowledge that is natural to it. Thus there is nothing metaphysically impossible about there being also multiple intelligent races of animals (e.g. humans and those from Alpha Centauri), that have different modes of rational capacity, and that one could be higher than another. But I don't expect us to run into such races.

  8. "Since Quine thinks that is all we have to go on, he draws the radical conclusion that there is indeed no fact of the matter about what the speaker means. And since the scenario he describes differs only in degree from the situation we’re all in with respect to each other, he concludes that there is no fact of the matter about what any of us means either."

    This shows how bone-headed philosophers like Quine can be. Replace the "linguist" with a child, who is a de facto "linguist" and a well-studied one at that. The child who perfects his linguistic craft knows what other speakers of the language mean. Quine is simply wrong.

    Likewise Ross's is simply wrong, as I've pointed out at length many times. He uses indeterminacy to beg the question.

  9. A blog post without an appropriate comic panel *GASP*

  10. Robert SutherlandJune 1, 2022 at 5:52 PM

    Always thought Mortimer J. Adler nailed your point on "formal signs" in his book "Some Questions about Language: A Theory of Human Disclourse and its Objects" (Open Court, 1976)" and his further chapter 3 "Words and Meanings" in his book "Ten Philosophical Mistakes" (Simon and Schuster, 1985) and I concur with you and he.

  11. But because every possible combination is there, many intelligible books are there too. In fact, every possible such book is there, so that the library contains all knowledge, every truth there is about everything.

    Another aspect of the problem, which Feser alludes to but not fully, is that even if you have every possible letter combination of a given alphabet Alpha, the library still won't hold truths that haven't been correlated to that alphabet. That is, say a truth X has been stated in some other language that uses a different alphabet, Beta, and X is stated in terms of a concept which currently HAS NO WORD in the language(s) of Alpha. It is, in fact, a concept C that no user of all of the languages of Alpha have ever invented, so there is, in ALL of the combinations of Alpha, no word for C. Then the library will not contain the truth X.

    The infinity of the library distracts you from the fact that every word actually used anywhere in the world is a word concretely generated by a finite series of acts by a finite group of men acting over a finite time. There is, then, a finite number of formulated (by men) concepts. There will ALWAYS be a finite number of concepts formulated (by men). But there is no basis on which Borges can establish that there are a finite number of POSSIBLE concepts to be formulated. But until they HAVE BEEN formulated into words, they cannot be said to "be" in the library, because there is no word (no combination of letters) in the library that in fact represents them. Furthermore, there is no way to prove that every possible concept can definitely be represented by the letters of some word, in the relevant sense. While representation would seem to be open-ended (any word can represent any concept), that is more of an assumption than a provable fact. We don't know everything about representation - particularly about distinguishable representations (i.e. unique and different representations for each concept). What if there are an uncountable number of different concepts, but only a countable infinity of letter combinations? So there is even more room to doubt that the library "contains" every truth.

    A similar (but worse) set of problems attend the claims that in an infinity of universes, every possible event not only happens, it happens an infinite number of times.

  12. Seeing how the books are by themselves meaningless, supposing the library has no origin on a inteligent cause, but are not so when read, can't we say that the meaning of the books is given by their readers?

    It even gets on a funny situation if you have a certain book who has, say, exactly the content of The Last Superstition but them is read by a alien whose language, by sheer luck, is made in a way that the content of The Last Superstition is to him a totally diferent book like, say, The End of Faith.

    Now, which book would this book be? Would it be The Last Superstition in english? Would it be the End of Faith in the alien tongue? Would it be both? I can't think of a answer that do not generate more questions!

    1. If we know the efficient cause, doesn't that change things?

    2. Yep. But i imagine that the Library of Babel just exists eternally or something, never read the history. My bad there, i should had mentioned the library directly.

      If i and the alien enter the place and both open a book who looks like the Last Superstition to me but The End of Faith to him, what the book is?

  13. How are Thomistic formal signs different from Platonic Ideas?

  14. It occurs to me that the library wouldn't actually hold ANY truths. Why?

    Well, for example, let's say you wanted to find a how-to book on doing home electrical work. Even if you filtered out from Borges' library ONLY those books that consisted of coherent English paragraphs and had titles like "DIY Home Electrical Work," the vast majority of those books would consist of words that had nothing to do with electrical work.

    And even of those books whose contents actually consisted of how-to guides on electrical work, the vast majority would give advice that was completely wrong.

    The only way to know which books had good advice would be to have prior training on electrical work from a professional or from training materials intentionally written by actual people, so you could assess the books for accuracy.

    But in that case, there would be no reason to read a how-to book from the Borges library, because you would already have to know any information you might hope to get out of it.

    It follows, then, that none of the books in the infinite library contain any information. Since there is no intent behind any of it, readers must impose any meaning they get out of it.

    1. It occurs to me that the library wouldn't actually hold ANY truths...
      It follows, then, that none of the books in the infinite library contain any information.

      I would only point out that "truths" and "information" are not exactly univocal.

      If a book in the library held all of and only the same words as what is contained in some actual book actually written by an electrician for DIY work, then (arguably, at least) it would "contain" the same truths that the book written by intention. After after all, the premise of the Library is that it contains books with every pattern of letters, not HOW those books got written/prepared.

      I think that what you are pointing to is not about the content of the books, but our epistemic take on the content. Unlike a normal library, if we found a book titled "DIY Home Electrical Work", we would have fair confidence it was written by someone qualified to write it, because we know publishers would aim for that. In the Library of Babel, finding such a book would hold no indicators like that, we could have no pre-suppositions about how it got there, and could not reasonably think there was any expertise behind it. We could not read it assuming intention behind it, and we could not allocate to it any specific meaning that was "intended" to be conveyed. That's an epistemic problem, not an ontological problem.

      One of Feser's overall points, especially in prior posts, is that there could never have been ANY meaning to such physical phenomena as dark marks on light pages of paper, without some intention by intelligent agents somewhere in back of it. Thus if there had never been any intelligent agents in the universe, it would be difficult to say that any of the books in the Library would "contain" any truths at all, for there never would have been any specificity by which certain signs referred to certain things: you might as well claim that the leftmost line of the first "A" meant ALL of the truth of the universe, and to hell with the rest of the Library.

  15. I don't think that The indeterminacy of the physical is important with regard to the books Borges library. If the letters are of the modern alphabet, they will be in any modern language which uses this alphabet, and also in Latin. Just to select the grammatically correct Latin or English books, would provide you will all the information of the entire library, since every combination of letters or words (within a limited number of pages, let's say 500) is in it. And if you have 500 pages of English or Latin, the meaning of the terms will be determined enough. So the intederminacy of the material signs is not a big problem I guess. But there is a real problem, and that's the fact that within the category of the grammatically correct books there will be found future scientific discoveries and philosophical insights alongside the most crazy stuff. And no one can decide which books are to be categorized as fiction or non-fiction. So in the end this entire library is to no avail except for the fun of reading and perhaps as a source of inspiration for thinkers and poets.

    1. Ronald, I recommend reading through the entry again, respectfully

    2. I don't think that The indeterminacy of the physical is important with regard to the books Borges library.

      I don't think the books of the Borges library are important to the library - I think you missed the point. This is a thought experiment, not a quest to stock an actual library for people's reading pleasure and learning. The actual books are irrelevant.

  16. It is because material representations have this dual nature – of being representations and also, on top of that, material things of a certain kind – that material properties and meaning can “come apart” from one another in a way that entails either gibberish or ambiguity.

    I'm not sure this accounts for gibberish/ambiguity very well. Gibberish occurs on several levels. Alphabetic gibberish where the material presented cannot be broken unambiguously into a stream of recognised letters. Lexical gibberish where the letter steam cannot be broken into recognised words. Syntactic gibberish where the word stream is not grammatical or parses ambiguously. Semantic gibberish ('sleeping green ideas') where qualifying terms make no sense applied to a certain class of object term. Logical gibberish where a text contradicts itself. It's only at the alphabetic level that the material nature of the, ah, material makes a contribution. The higher levels are abstract, being relations between patterns or structures.

    But they [the readers] are not the ultimate source of the information said to be contained in the library, and could not be, since in none of their minds (considered either individually or collectively) is all of that information to be found....In some way, then, there must be something distinct not only from the library, but also from the minds of its inhabitants, that determines the meaning of the (subset of) representations contained in the books that count as all possible knowledge.

    How does it follow that 'there must be something distinct...'? Granted, only a trained mind can find a meaning in a text, and it's possible that two even well-trained minds will interpret a text differently, but then we would tend to conclude that the text really was ambiguous after all, given that we know that gibberish and ambiguity can exist, rather than of a single but humanly unknowable meaning.

    1. There had to be someone who invented (a) the language, and (b) the representations of the language, captured in the printed books of the library. Without the inventors, the physical realities of "marks on pages" would not REPRESENT letters, sounds, or words, they would merely be dark smudges.

      It is notionally possible that the inventors of the language and the printing are, also, denizens of the library (though you would have chicken-egg questions), but it is irrelevant to their being denizens as to whether they were also the inventors, and thus it would be a purely accidental happenstance as to whether they were or were not, and you can then assume the case where the inventors are not denizens. The point is, there has to BE inventors (intelligent agents) of the language and the letters, in order to have the library, and they are necessarily distinct from the library itself (which is not an intelligent agent).

    2. Tony, there are artificial languages invented by us individually or jointly---Esperanto, Elvish, Java, say---but a natural language such as English, which may be the only language the library's readers know, has no such inventor. So I can't think that Ed's 'something distinct' can be a language inventor. In any case, what justifies the claim that there must be something distinct, regardless of what it might be? There's a gap in the argument here, surely?

  17. How much of God's "infinite library" will I possess in Heaven?

  18. “Stan Lee’s sunglasses…”
    For reasons I don’t understand I thought of a scene from old movie where a man said, “Those were five hundred dollar glasses, [explitive]!”

    Anyways. Need to read and re-read this post, as per usual.