Relationship between AI/LLMs and prolepsis

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    Do you think there is something to learn about Epicurean prolepsis through the understanding how AI/LLMs (large language models) work?

    If my understanding of LLMs is correct, they form a "general notion" of all kinds of things through the processing of an extraordinary huge data base. Sounds familiar to the Human mind. Although some would say AI is just statistics at work, perhaps this is somehow our own minds function, too.

    There are further possible implications like: In which way does prolepsis form? How dependent/exposed is prolepsis on/to its database? How does LLMs relate to the debate on understanding prolepsis as (a) fixed innate ideas vs. (b) forming general notions out of impressions on our minds?

    I won't have time in the near future for discussion, but I just wanted to share my thoughts on a topic that has been on my mind for a long time.

  • Titus September 4, 2025 at 11:04 PM

    Changed the title of the thread from “Relationship between AI/LLM and prolepsis” to “Relationship between AI/LLMs and prolepsis”.

    I agree this could be a fruitful line to explore. It seems to be a key attribute of canonical faculties that they operate "mechanically" and without opinions of their own, and often here people have commented that there may be an aspect of "pattern matching" going on with prolepsis. (I started to say pattern "recognition" but that might not be the best word in this context.)

    At this point, I say no, it does not have something to teach us about preconceptions. I think it's like trying to learn about the physics of stars by observing Van Gogh's painting Starry Night. No matter how advanced or well-defined our models, they are still (for now) just models and analogies.

    Maybe it does, insofar as it can teach us what a preconception is not.

    As Diogénēs describes of a preconception, it is a "memory of the appearances from abroad", so being able to experience/process sensation, as I read it, is a necessary precursor to a preconception.

    In an Epicurean sense, I don't think it's accurate to say that LLM's can have "preconceptions" because they are prone to error. Rather, it looks to me like they are being programmed with "opinions", some of which are true ... but they are not, themselves, standards of truth. They lack the standard of sensation, so they're at the whim of their programmers' memories.

    We'll need to get to the point where an android organically dreams of sheep.

    If I were on Picard's Enterprise-D, I would, personally, trust Data, but not the ship's computer, even if 99% of their knowledge-base were shared. If I'm going to risk losing my arm, I'm not going to take advice from an armless thing. Give that thing an arm to lose, and then see how it thinks. Likewise, I'll trust Data's description of the texture of kitten fur before the computer's, or the flavor of Picard's tea (probably bitter Earl Grey), over anything else for which it lacks its own sensory organs.

    Quote from Titus

    I just wanted to share my thoughts on a topic that has been on my mind for a long time.

    Really cool thought, though! It's at least worth the thought experiment.

    Edited once, last by Eikadistes (September 5, 2025 at 12:46 PM).

    I understand the question from Titus and @Elkadites’ response as: currently, LLMs cannot have preconceptions if preconceptions mean an idea conceived before and independent of the question. Also, as I understand the LLMs, they function because of training that exposes them to data (everything on the internet and/or fed directly to them) plus additional training after data collection, on how to “talk” to the people asking questions. Then, the LLM matches the question to its data, based on how it is phrased, and answers in a polite colloquial manner. I’ve found sometimes it then summarizes the response it has given, once again based only on the data in its microchips.

    Dave Tamanini

    Harrisburg, PA, USA

    • New

    Today, I had a short but interesting talk with Chat GPT:

    Titus: Is there a connection between large language models and Epicurean prolepsis? Could Epicurean prolepsis be interpreted as what LLMs are processing?

    Yes, there is a surprisingly interesting analogy, although one should be careful not to identify the two completely.

    For Epicurus, prolepsis (πρόληψις, usually translated as "preconception" or "anticipation") is one of the fundamental criteria of truth, alongside sensations and feelings. A prolepsis is formed through repeated experiences: after encountering many individual humans, for example, the mind develops a general conception of "human." When we hear the word "human," this preconception is immediately activated and allows recognition and reasoning.

    An LLM works in a way that appears remarkably similar at first glance:

    • It is exposed to vast numbers of examples.
    • Statistical regularities are extracted.
    • It develops internal representations of concepts.
    • When prompted with a word such as "human," it activates patterns associated with countless previous examples.
    • It can then generate responses based on these learned patterns.

    An Epicurean might say that an LLM has something analogous to a prolepsis of "human," "justice," "friendship," or even "god," because it has formed generalized representations from repeated encounters.

    However, there are also important differences.

    1. Epicurean prolepsis originates in perception

    For Epicurus, prolepses ultimately derive from actual sensory contact with reality.

    A child sees many horses and develops the prolepsis "horse."

    The prolepsis therefore has an ontological grounding in the world itself.

    An LLM, by contrast, has no direct sensory encounter with horses. It processes symbols that humans have written about horses. Its "horse-concept" is second-hand and linguistic rather than perceptual.

    This is probably the biggest difference from an Epicurean standpoint.

    2. Epicurean prolepsis has evidential force

    Epicurus regarded prolepses as a criterion of truth because they are naturally formed by repeated encounters with real things.

    For example, all peoples possess some prolepsis of blessed and imperishable gods. Epicurus regarded this as evidence that the gods exist, even if many false opinions are attached to them.

    An LLM's internal representations do not have this status. They merely reflect statistical patterns in its training data. If a society collectively believed dragons existed, an LLM would develop a strong representation of dragons without dragons being real.

    Thus an Epicurean would likely deny that an LLM's "preconceptions" have the same epistemological authority as human prolepses.

    3. The strongest analogy: pattern abstraction

    The closest parallel is probably this:

    Epicurean prolepsis is the mind's natural abstraction of recurring features from experience.

    An LLM's embeddings and latent representations are statistical abstractions of recurring features from text.

    Both systems:

    • accumulate repeated inputs,
    • compress information,
    • form general categories,
    • enable recognition of new instances.

    In modern cognitive science, some scholars even describe human concepts as prototype-like statistical structures rather than fixed definitions. In that respect, Epicurus can seem surprisingly modern.

    A deeper Epicurean reflection

    There is an intriguing possibility that Epicurus would have found LLMs philosophically illuminating.

    The existence of LLMs demonstrates that sophisticated concepts can emerge from repeated exposure without requiring innate Platonic Forms, divine illumination, or Aristotelian essences. General notions arise naturally from accumulated experience.

    That is actually very close to the anti-Platonic spirit of Epicurean epistemology.

    An Epicurean might therefore say:

    Quote

    "The language model shows how a system can acquire general conceptions through repeated impressions alone, without any need for transcendent universals."

    That sounds remarkably Epicurean.

    Yet Epicurus would probably add an important caveat:

    Quote

    "The model possesses only something analogous to prolepsis. Genuine prolepsis arises from a living being's direct interaction with reality through sensation."

    So the connection is real and philosophically fruitful. LLMs can be viewed as a kind of artificial demonstration of how generalized concepts emerge from repeated inputs—a process that bears a strong family resemblance to Epicurean prolepsis, even though Epicurus would likely reserve the term prolepsis for conceptions ultimately grounded in actual sensory experience.

    Titus: Conversely, LLMs could be interpreted as proof of the validity of Epicurean prolepsis. Although they are not grounded in direct exposure to sensual stimulation, their pattern recognition seems to enhance Epicurus' idea of prolepsis.

    I think there is a strong argument in that direction, though perhaps not as a proof in the strict sense.

    The historical challenge to Epicurean prolepsis was always: How can mere repetition of impressions generate meaningful general concepts?

    Many philosophers after Epicurus doubted that this was sufficient:

    • Platonists argued that universals must somehow pre-exist experience.
    • Rationalists argued that important concepts require innate structures.
    • Some theologians argued that knowledge of certain truths requires divine illumination.

    An LLM demonstrates something remarkable: from exposure to enormous numbers of individual examples, a system can develop highly sophisticated conceptual structures without possessing explicit definitions or innate metaphysical forms.

    That is very much in the spirit of Epicurus.

    What LLMs seem to vindicate

    An Epicurean could point to LLMs and say:

    Quote

    "Look, a machine exposed to countless individual instances develops a functional understanding of categories, relationships, analogies, and even abstract reasoning. Why should we think the human mind requires Platonic Forms?"

    In that sense, LLMs strengthen the plausibility of the Epicurean claim that repeated impressions naturally generate general notions.

    Epicurus argued:

    1. Repeated encounters create memory.
    2. Memories accumulate.
    3. General conceptions emerge.
    4. These conceptions become tools for recognition and reasoning.

    Modern machine learning shows that a system can indeed move from countless particulars to surprisingly powerful generalizations.

    An especially interesting case: the gods

    Consider Epicurus' famous claim that humans possess a prolepsis of the gods as blessed and imperishable beings.

    Many modern readers wonder:

    Quote

    "How could such a concept emerge naturally?"

    An LLM offers a possible model.

    Humans repeatedly encounter:

    • excellence,
    • happiness,
    • power,
    • beauty,
    • wisdom,
    • longevity,

    and then mentally extrapolate toward an idealized limit.

    An LLM often does something similar. It learns patterns and can generate idealized or prototypical versions of categories that were never explicitly presented.

    This does not prove Epicurus was correct about the gods, but it makes the mechanism of concept formation seem less mysterious.

    Where the analogy becomes even stronger

    Some cognitive scientists today argue that human concepts are not definitions but statistical clusters.

    For example, most people cannot define "bird" precisely.

    Instead they possess a prototype:

    • sparrows are very bird-like,
    • penguins less so,
    • bats not at all.

    LLMs appear to represent concepts in a similarly graded way.

    This resembles prolepsis much more than it resembles Platonic essences.

    The Epicurean could therefore argue:

    Quote

    Prolepsis is not a dictionary definition stored in the mind. It is a stable pattern emerging from repeated encounters.

    That description sounds surprisingly close to modern representation learning.

    But there is one thing Epicurus might not have anticipated

    LLMs also reveal a weakness in prolepsis.

    An LLM can form strong representations of things that do not exist:

    • dragons,
    • Sherlock Holmes,
    • Middle-earth,
    • fictional gods.

    This raises a difficult question for Epicurean epistemology:

    Quote

    If a stable concept can emerge merely from repeated exposure, why should the existence of a prolepsis imply the existence of its object?

    This is precisely where an Epicurean would have to defend the difference between concepts grounded in reality and concepts grounded in cultural transmission.

    In other words, LLMs may strengthen Epicurus' account of how prolepses form while simultaneously weakening one of his arguments for what they guarantee.

    A possible modern Epicurean reformulation

    If Epicurus had known about machine learning, he might have reformulated prolepsis as:

    Quote

    "A prolepsis is a stable cognitive pattern produced by the accumulation of repeated impressions, enabling recognition, prediction, and reasoning about a class of objects."

    That would be remarkably compatible with contemporary ideas about learning systems.

    So I would say that LLMs do not prove Epicurean prolepsis, but they make one of Epicurus' central intuitions far more credible than it appeared to many philosophers in earlier centuries: namely, that sophisticated concepts can emerge naturally from repeated experience without requiring innate ideas, transcendent Forms, or supernatural intervention. The fact that a language model can do this from text alone makes Epicurus' epistemology look surprisingly prescient.

    Titus: I think you are on the right path, but I would argue that in the Epicurean sense this is where the senses become important. Because some people indeed believe in dragons and they believe in all kind of conceptions about the gods.

    I think that is exactly where an Epicurean would push back against an overly enthusiastic comparison between LLMs and human cognition.

    The crucial point is that prolepsis is only one criterion of truth. Epicurus never intended it to operate independently. The other criteria—sensations (aisthēseis) and feelings (pathē)—remain indispensable.

    An LLM has something analogous to prolepsis, but it lacks sensation. As a result, it has no way to distinguish between:

    • horses and unicorns,
    • Athens and Atlantis,
    • historical figures and fictional characters.

    All are merely patterns in text.

    An Epicurean human, however, can test conceptions against experience.

    Suppose a child develops a conception of dragons through stories. Epicurus would not deny that a conception exists. The question is whether it corresponds to reality. One then turns to the senses:

    Quote

    Have dragons ever been observed?

    If not, the conception remains a mental construction rather than a confirmed object.

    The same applies to many theological claims. Epicurus famously argued that people attach all sorts of opinions (doxai) to the gods:

    • that they become angry,
    • reward virtue,
    • punish sin,
    • intervene in history.

    The mere existence of these conceptions proves nothing. They must be examined.

    In this sense, the Epicurean method is actually more sophisticated than a simple theory of concept formation:

    1. Repeated impressions generate prolepses.
    2. We formulate opinions based on them.
    3. Those opinions are tested against sensory evidence.
    4. Unsupported additions are discarded.

    This is where your observation becomes interesting for the LLM analogy.

    An LLM is almost pure prolepsis without sensation.

    It possesses vast networks of generalized concepts, but no independent contact with reality to evaluate them. It cannot perform the Epicurean step of returning to the evidence of the senses.

    One might even say that an LLM resembles the state Epicurus warns humans against when they become detached from experience and live only among words and opinions.

    There is another subtle point here. Epicurus did not claim that every conception corresponds to a real thing. Rather, he claimed that conceptions arise from some basis in experience.

    Take dragons. An Epicurean could explain them as composites:

    • snakes,
    • lizards,
    • birds,
    • predators,
    • fire,

    combined and exaggerated by imagination.

    The conception is real as a mental phenomenon, even if the object is not real.

    Likewise, many anthropomorphic gods could be explained as idealizations of kings, parents, heroes, and natural forces.

    Thus the existence of a conception does not automatically establish the existence of its object.

    This is why, in Epicurean theology, the argument for the gods is not merely "people have a conception of gods." The stronger claim is that there is a universal and persistent prolepsis of blessed and imperishable beings that survives beneath all the false cultural additions. Whether that argument succeeds is another question, but it is more subtle than simply inferring existence from a concept.

    Viewed this way, LLMs may actually illuminate the Epicurean distinction between prolepsis and opinion.

    • The model's internal representations resemble prolepses.
    • Its generated outputs resemble opinions.
    • What it lacks is sensation, the corrective mechanism that Epicurus regarded as essential for separating true opinions from false ones.

    From an Epicurean perspective, that absence is not a small detail—it is the difference between a system that merely manipulates conceptions and a living being capable of knowledge.

    • New

    Titus I would say that that discussion of a working theory of what Epicurus mean by prolepsis is better than what 98% of us on the forum could do if we sat down and decided to devote 20 minutes to tackling it. I am sure that most of us would also find tweaks we would suggest but in general I think someone who followed this model would be in good shape. I think it does a pretty good job as well with what often seems to be the trickiest part - that anticipations are not in themselves opinions, but foundations on which opinions are generated.

    • New

    Also Titus this chat exchange has me thinking about something that I think needs to be a focus of the forum in the future - and it's an aspect of prolepsis.

    Taken separately, I think the data in the chat you presented is largely correct. As I said it's probably stated more clearly than many of us can do ourselves. That makes the information in the post a valuable data point.

    But the value of that data point is limited if we can't integrate it into a bigger picture of how and why it fits into the philosophy as a whole. I see this problem as analogous to what prolepsis itself does - it's a faculty that takes individual data points out of an otherwise overwhelming background noise, allows us to recognize patterns, and helps us apply those patterns to evaluate future experiences.

    Ultimately, the biggest pattern we need to be concerned about is the philosophy as a whole. Saying "I understand what Chatgpt just wrote about anticipations" accomplishes next to nothing if we have the ability to fit it into the big picture and then use that picture.

    I'll use another example I think is far more of a problem: Reading the letter to Meneoeceus and seeing "By pleasure we mean the absence of pain" means absolutely nothing unless we can intelligently fix that into the big picture. Failing to see that the letter is about happiness, and that happiness is about pleasure, but taking that part out of that context as if it can be taken alone converts the entire philosophy into the command "minimize pain." And that's a disaster.

    We've developed, and will continue to develop, lots of detailed information about individual letters and books and writers and summaries. Each of those detailed treatments gives us valuable data points. But if we don't integrate those points into the bigger picture they are useless and get us nowhere.

    Someone I follow on youtube had what I thought was a good video (below) about this issue of high level integrated thinking. He framed it in terms of how to stay ahead of AI, but the focus of his argument is that what makes humans smarter than AI is stronger ability to juggle lots of isolated facts and see their relationships and evaluate them by context.

    That's what I take away from your AI chat -- the facts stated seem to me to be generally correct. The issue is whether we ourselves can integrate that information into a big picture that allows us to see why it is important and what it means for daily life. The video makes the point that "low-level thinking" - the accumulation of isolated facts - does not necessarily lead to "higher-level thinking" where those facts are integrated into a working whole. I think he's right, and that's a big problem we face.

    I don't know what the best way to push that forward will be. The video makes a couple of suggestions. But I think "thematicallt" we need to move the forum forward needs to be in that direction. All of the detailed information we develop is useless or even potentially harmful if we don't see the relationships and integrate them into a working whole we can confidently apply.

    • New

    Dave Tamanini

    Harrisburg, PA, USA

    • New

    "At first I thought, well he never experienced a god, so how could he say he knows of them from prolepsis."

    This sounds to me as though you are not considering a prolepsis to be an experience. That's an issue we talk about regularly without much to work with, but at the very least: To the extent that prolepsis processes not only the five senses but also the feelings and also "images," I think some would maintain that Epicurus regarded "knowing them from prolepsis" as indeed "experiencing" them.

    Bryan would you say that differently?

    • New
    Quote from Cassius

    prolepsis to be an experience

    Yes, a prolepsis is an experience, but not a process of thought.

    The prolepseis are the direct experiences we have when we think of something.

    Anybody who uses the words “god” or “water” or “minotaur” has a sense of what they are talking about. That sense is always real, but we are left to determine what physical objects exist as the original source (the hypokeímenon).

    Hypokeimenon - Wikipedia

    If there is no correspondence (sympátheia) between an original source and the prolepsis, then it exists only as a mental impression and the word used for it is “empty."

    ----------------------

    Clement of Alexandria (fl. 190 CE), Miscellenies, 2.4

    "Epicurus... supposes an anticipation to be [our mental] perception's certainty: and he defines an anticipation [1] as attention directed toward something evident – and [2] [as attention] directed toward an evident concept of a thing {or "of a situation"}. And [Epicurus says] that it is not possible either to investigate, nor to be at a loss, nor indeed to judge -- but not even to refute -- without an anticipation."

    ----------------------------------

    Philodemus (fl.c. 70 BCE), On Piety, 1.66A.1882-1911
    "Time is distinguished as existing as an anticipation; and just as, in the Thirty-Second [book of On Nature], Epicurus says that the evident realities of the gods are thoroughly comprehended as existing, even though existing as a single [object of thought] among those [other objects of thought] in the original sources [of the films from their bodies], nevertheless [these detectable realities of the gods] have a nature less mentally perceptible than that of other existing things."

    --------------------------------------------

    Sextus Empiricus (fl.c. 200 CE), Against the Logicians, 1.203 - 216

    "[For Epicurus] the particularly of sensation is to receive only what is present and moving it: but not to thoroughly separate that [1] what is here is one thing -- but [2] what is underlying there is another thing."

    "so then, of the judgments, according to Epicurus, some are true, and others are false: true are those attested and not contested by evident reality -- false are those contested and not attested by evident reality"

    ---------------------------

    Edited 6 times, last by Bryan (June 12, 2026 at 11:57 PM).

    • New
    Quote from Bryan

    . And [Epicurus says] that it is not possible either to investigate, nor to be at a loss, nor indeed to judge -- but not even to refute -- without an anticipation."

    So Bryan correct me if I am wrong here but this is how the entire discussion of prolepsis refutes what Plato had taught about ideal forms/reincarnation.

    It is an obvious point that you can never investigate, refute, or judge whether you are correct about something unless you start with an understanding of what the "something" is. If you've never dealt with something before you cannot understand it unless you relate it to something you already understand.

    Plato and gang want to suggest that you must have been born with from another life, or have been given by a divine god, a set of understandings that you then take and apply to your experience after you are born. You recognize a horse because before you were born you were implanted with the "form" of a horse, and when you see a horse after you are born you know it's a horse becaues you're remembering your pre-birth knowledge (or what god told you).

    Epicurus says that 's nonsense. Like an LLM, your brain has evolved to be able to selectively pick out of the background noise the patterns that repeat within that noise. Sort of similar in a way that in the past when people looked at the noise on the screen of a black and white TV, you could begin to pick out the shapes of the objects on the screen even though they were covered in static.

    That ability to pick out repeated patterns comes from the fact that the repeated patterns are in fact there in the static and our minds get used over time to picking them out. We aren't born with the patterns and the patterns are not in fact arbitrary - they are there in the static of the picture if we apply our attention and pick them out. For those of us who tune our TVs to shows about horses, we begin to be able to pick out in the programming the shapes to to which we apply the word "horse" or "equus" or whatever language we use.

    This process is entirely natural and has no involvement with gods or pre-birth ideas or supernatural forms. But it is essential to human life and if this process did not exist, we would never be able to investige, judge, or refute anything. If provides the framework for understanding human knowledge that repudiates the supernaturalism of Plato and all those who claim that truth only exists in a "beyond-world" which is inaccessible to us as humans using our senses. No geometry or syllogistic logic or divine revelation is required.

    The disaster is that even today people continue to accept Plato's basic argument - that truth is impossible for humans to obtain through our natural faculties, and that we either (1) require supernatural assistance to find true knowledge or (2) should give up on the idea of true knowledge in the first place becaues it doesn't exist.

    • New

    Titus, @Brian, Cassius Thank you for the input to my question of whether or not Epicurus truly believed in the Greek gods' existence.

    I still don't understand how Epicurus actually believed there were Greek Gods from the Chat GPT dialogue, or the statements or citations you've provided above.

    If no one had ever actually seen the Greek Gods how could Epicurus have believed they actually existed? To rely on their existence because everyone believes in them doesn't seem consistent. Can this question be answered in two, or three or four sentences before being supported by authorities?

    Dave Tamanini

    Harrisburg, PA, USA

    • New
    Quote from DaveT

    I still don't understand how Epicurus actually believed there were Greek Gods

    At least as for me, I don't mean to say that Epicurus believed in the "Greek Gods." He may have spoken loosely at times about one or another of them, but I interpret him as never straying from the point that "gods as a class" exist - not that any individual Greek god has any individual characteristic attached to him or her.

    The images and prolepses we are talking about are generic perceptions of classes of things, as the chatgpt model referenced. As for the physical existece of such beings, you also have the conclusions that derive from how atoms work and lead to the formation of real entities over an eternal and boundless universe, such as those forces led to life here on Earth. And you have the "isonomia" in which we observe the spectrum of things from "lowest" to "highest," which means that what has happened here has happened a countless number of times elsewhere, and has led to the formation of beings much smarter and more successful and long-lasting than ourselves.

    I personally have no problem constructing from those various observations a firm belief that there is a class of being called gods. But anyone sassert to me that jehovah or Zeus or any other PARTICULAR god has done something or said something has an extremely high burden of proof which is going to be extremely difficult and likely impossible to meet given the observations that led me to conclude that they exist in the first place. Yes there will be aliens who are smarter and long-lived than we are, but even smart aliens doesn't get you to true "godhood" unless you're fully successful in those attributes.

    • New
    Quote

    To rely on their existence because everyone believes in them doesn't seem consistent.

    I have my own questions on this topic, DaveT , but I have come to an understanding that may be helpful on this one.

    Here is Bailey's translation of the text from the Letter to Menoikeus:

    Quote

    [123] The things which I used unceasingly to commend to you, these do and practice, considering them to be the first principles of the good life. First of all believe that god is a being immortal and blessed, even as the common idea of a god is engraved on men’s minds, and do not assign to him anything alien to his immortality or ill-suited to his blessedness: but believe about him everything that can uphold his blessedness and immortality. For gods there are, since the knowledge of them is by clear vision. But they are not such as the many believe them to be: for indeed they do not consistently represent them as they believe them to be. And the impious man is not he who popularly denies the gods of the many, but he who attaches to the gods the beliefs of the many.

    Regarding the sentence I've underlined, I no longer read this as Epicurus offering evidence of the existence of the gods. Rather, I think he is offering a definition of a god. This is in line with the pedagogy described in this passage in the Letter to Herodotus:

    Quote

    First of all, Herodotus, we must grasp the ideas attached to words, in order that we may be able to refer to them and so to judge the inferences of opinion or problems of investigation or reflection, so that we may not either leave everything uncertain and go on explaining to infinity or use words devoid of meaning.

    So when he says in Menoikeus that a god is 'a being blessed and incorruptible', he is saying that those are the ideas attached to the word god. It's not important or evidentiary that 'everyone believes in gods'. It is important (at least to Epicurus) that people commonly have an idea about the thing said to be represented by the word god.

    The actual evidence comes in the next sentence in Menoikeus: we know the gods exist because of 'clear vision', ἐναργὴς. They are manifest. The 'true impression', or preconception, that is, the prolepsis of the gods, seems to derive from this clear vision.

    TL:DR; From the point of view of the individual, other people are not involved in helping to determine the existence of the gods. They are only useful insofar as they ratify our grasp of the meaning of the word god.

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