Dinasra's Lecture on The Enumeration of Heritable Capital; and a proof of monotheism (conphilosophy/theology)

[Salmoneus]

I know, I have peculiar interests and a warped sense of fun. Which is why I sat down the other night and wrote up the following. It's perhaps the first stage in a broad outline of the course of the religious and philosophical history of the Gureha region of my conworld; although I recognise it's of interest to, most likely absolutely nobody but myself. But here it is anyway.

Do let me know if anything seems confusing! Or perhaps chime in with how your own concultures handle some of the issues raised. But please, don't just yell at me that modern Western mathematics/physics/philosophy/etc has disproven this. This isn't intended as a real-world physics lecture, it's a cultural feature. [and it's a way of, as it were, playing chess against myself]

I do hope that this comes across as reasonably realistic - and also as not being too immediately/obviously/implausibly imitative of the real-world parallels.

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

Background: Caria and Dinasra

The seven ancient city-states of Caria were small but highly organised polities, founded upon trade. Although their political structure was that of authoritarian, aristocratic republics, their oligarchs drew their wealth not from land but from international maritime trade, and they possessed vocal, powerful middle-classes of small landholders. As a result of this economic and political structure, institutions of law were central to their culture, and also allowed the cities to exist semi-co-operatively within a shared legal and economic system. Legal training was therefore a popular choice for second sons and daughters.

It is unclear exactly what role was played in the development of Carian culture by its most acclaimed juridical theorist, Dinasra the Great; although widely said by Carians to have founded the first sturna (university or academy – literally ‘row (of houses)’), it is likely that he was merely the first famous teacher at an institution that developed more gradually over time. Dinasra’s greatest role, however, was as the promulgator of a new metajuridical theory: a thoroughgoing and practical realism that opposed the sophistical, disreputable intellectual excesses of the preceding generation.
Metaphysics and abstract logic were regarded in Caria as methods of legal training: abstract and hypothetical scenarios with which to hone the reasoning of young lawyers. Dinasra, however, was critical of sophistry in metaphysical exercises, arguing that the public found it difficult to have faith in the rigour and probity of a lawyer litigating an inheritance dispute when they had heard the same lawyer embracing fantastical or incoherent reasoning on metaphysical questions the previous day. Dinasra instead believed in rigour and realism in all areas of thought. A particular target of Dinasra and the other reformers was the use of ‘expedient argumentation’ by lawyers: the practice of arguing passionately for one conclusion one day, and against it the next, purely because the interests of different clients would benefit from different conclusions. This, said the reformers, was disreputable, and brought the law into disrepute: lawyers should argue over which valid arguments applied, not contest the validity one day of an argument they will insist upon the next. Likewise, judges, and the state as a whole, should endeavour to be consistent in which arguments it accepts as true, not reasoning one way one day and the other the next without good cause.

The result of the widespread acceptance of these reforms was the concept of the qatm, the established foundational argument. Rather than arguing each case from first principles, lawyers came to argue by combining a series of elementary arguments, each of which had been established as binding precedent through the consensus of prior judges, and only overturned in extreme cases of obvious injustice. Once a given combination of qatmesh had been accepted as valid by a sufficient consensus of judges, it in turn became a valid qatm. The intellectual culture of Caria thus became highly conservative, as lawyers and philosophers obeyed precedent, maintained consistency, and attempted to demonstrate their points through the assembly of previously established arguments, which became extremely difficult to challenge. And one of the foundational texts of Carian metaphysics was Dinasra’s seminal lecture on the enumeration of heritable estate capital, which came to shape philosophy in Caria and beyond for millennia to come.

[Salmoneus]

The Enumeration of Heritable Estate Capital

Dinasra did not write any books – writing at that time being chiefly reserved for official documents. Instead, he became famous through his lecture series. Unfortunately, no original record of the content of these lectures survives, but the general structure of his Lecture on the Enumeration of Heritable Farmyard Capital, his most important work by far, can be pieced together from many later reports. What is not known is how much of the argument can truly be credited to Dinasra – given the credit given to him for the lecture, it is likely it contained key novel ideas, but it is also likely, given Dinasra’s approach, Carian intellectual culture, and the chief function of his lectures as education for young lawyers, that much of the lecture is a compilation and illustration of already-existing arguments. The concept of the qatmesh, their emphasis on unchanging inheritance of objective truth, tended to discourage such concepts as accurate citation. In addition, the paucity of Carian written records and the subsequent collapse of Palaeocarian culture mean that very little is known not only about Dinasra’s contemporaries and predecessors, but even about Dinasra himself. His background, personality, and even sex are unknowable.

The Farmyard Lecture is a foundational metaphysical argument, but it also, and primarily, an argument of legal theory, directed chiefly against the sophists and disreputable lawyers, but also with one eye always on practical matters of litigation and public policy. The issue Dinasra chose to address was simple: how to count possessions. This was a subject of vital importance in Caria, and could often be a central part of legal cases around inheritance and taxation. In his lecture, Dinasra addressed several urgent questions around this issue – some theoretical, others practical, as a chief part of his philosophy was the contention that theory and practice were, or should be, intimately entwined.

Valid and Invalid Catalogues, and the Particularity of Catalogues
In assessing the value of an estate – for example, a farm – the first step in Carian law was to enumerate a catalogue, a list of its parts or contents. Dinasra presumably covered in his lecture some technical questions of how to measure these parts and contents, and what should be included or excluded from such measurements, but these details are not recorded. His first recorded concern in the lecture is the problem of double-counting, arising accidentally or through disreputable practices by the conflation of items from different ‘genres’ of catalogues. In this way, a tax collector might value millstones, and then add them to the value of the working mill itself; or they might value hay, and then add to that the value of a fully-stocked haybarn; or they might value grain still in the field, and then add to that the value of the grain-field. These things are inappropriate, Dinasra said, because they confuse more and less ‘particular’ catalogues: they include an entry from a more ‘general’ catalogue, a catalogue at a higher level of abstraction, like a mill or a haybarn or a field, but they also include an entry from a more ‘particular’ catalogue, a catalogue less abstract, like a millstone or a bale of hay or an ear of grain on the stalk, that is already part of what has been counted in the more general catalogue. It is as though, Dinasra said, one were taxed for owning a sheep’s nose, taxed for owning a sheep’s ears, taxed for owning a sheep’s legs, and taxed for owning each other part of the sheep... and then taxed yet again for owning a sheep. Likewise these methods could be used to inflate or deflate the valuation of parts of an estate that is to be divided between heirs.

Single-Genre Catalogues and Absoluteness
Thus, Dinasra argued that any catalogue of estate contents was invalid if it described the same items under two different entries, and that this occured chiefly when the two entries operated at different levels of particularity (or ‘genre’). Further, he argued that any enumerated catalogue that combined different genres of catalogue, even if it did so without double-counting, could be regarded as identical to the compilation of fragments of complete catalogues of different genre. Thus, for example, a catalogue that enumerated cows one-by-one, yet had a single entry for a flock of sheep, was conceptually identical to combining one extract from an animal-by-animal catalogue with another extract from a flock-by-flock catalogue. No additional knowledge was gained by doing this that would not be present in the ‘pure’, single-genre catalogues. The purpose of this argument was to attempt to demonstrate commensurability: if one lawyer argued value from one mixed-genre catalogue, and a lawyer from a rival party argued value from another mixed-genre catalogue, these two catalogues were not incommensurable, but could each be reduced to pure catalogues and compared on those terms – so that, for example, an exhaustive third-party enumeration could compile a pure catalogue against which the two competing mixed catalogues could be checked, even though the third party had enumerated following a different method from either party to the suit. The sophist suggestion that multiple enumeration methods could produce multiple incommensurable catalogues of contents, none of which could be regarded as more basic than any other, was thus strenuously opposed. This approach was particularly significant due to the confusion of tax codes – a bale of hay, for example, might be ascribed one value, a haybarn another, and hence whether an estate contained ten bales of hay and a byre used to store hay, or one haybarn filled with hay, might have significant financial consequences.

Dinasra further pursued this line of argument by suggesting that for each estate, there could only be one pure catalogue of each genre: only one correct count of the number of animals, for example, or only one correct count of the number of flocks. This is because the catalogue depends on the contents of the estate forming natural wholes, which dictate a particular enumeration. For example, if sheep are lined from nose to tail in a circle, the only correct way to count them is one sheep at at time; it is not permissable to count ‘one’ for the back half of one sheep added to the front half of the next, ‘two’ from the back half of that second sheep added to the front half of the third, and so on. To do so is to implicitly move to a new, more particular genre of catalogue: if sheep are counted in this way, what the assessor is doing is not counting sheep but half-sheep. In this way, each genre of catalogue – each level of particularity/generality – contains only one correct catalogue for each given estate. These catalogues are thus absolute, not relative to who counted them. By contrast, methods of enumeration that mix entries from different genres of catalogues produce a sea of possible catalogues, all relative to the one who enumerated them, and rival parties can argue at great length, refusing to accept the rival catalogue. It is better if absolute catalogues are used – then, the enumeration may be judged clearly correct or incorrect by the standards appropriate to that genre of catalogue. Doing so also has the advantage of avoiding the possibility of double-counting errors.

[Salmoneus]

Comparing more particular and more general catalogues – the importance of distribution
Although Dinasra demonstrates that pure catalogues of a given genre were absolute, and that mixed-genre catalogues could conceptually be reduced to extracts from pure catalogues in combination, he was not able to deny that there could be multiple valid yet absolute catalogues of the same estate, provided they belonged to different genres – provided, that is, that one was more general and one more particular than the other. To count one flock of sheep and one flock of cows is just as correct as to count thirty sheep and six cows. Given this, the sophists contended that there was no one inherently superior genre of catalogue – that, where the two catalogues differed in their assessment of value, there was no objective way to determine which was ‘correct’.

Dinasra, however, disagreed. He argued that a more particular catalogue, enumerating the estate in more detail, would always provide greater knowledge than a more general catalogue of the same items. To know that there were thirty sheep would be to know that there was a flock of sheep; but knowing that there was a flock of sheep would say nothing about how many, exactly, there were; therefore the more particular catalogue provides greater knowledge, and hence is closer to the truth. Likewise, more is learnt by counting each spike of grain than by counting the number of fields, and more still is learnt by weighing the grain itself. As more is learnt by a more particular enumeration, it cannot be said that the particular and general enumerations are of equal value as evidence.

Against this, the sophists argued that the tax codes did in fact apply differently at different levels of enumeration: that the legal value of a field of grain may be more or less than the sum of the value of the grain grown from it, and that the legal value of a flock of sheep may be more or less than the sum of the value of each sheep in that specific flock. This, they argued, was not simply a mistake by the compilers of tax codes, but a reflection of the fact that, while, admittedly, a particular enumeration contained some information not present in a more general catalogue, at the same time the more general enumeration contained some other information not present in the more particular catalogue, and that this information related to things of value. In particular, a full field of grain might have more value than five small kitchen plots of grain, even if their yield were the same in a given year – the field might have more potential for yield growth, if it had been poorly planted, or could even be turned efficiently to another use in a way unfeasible for smaller plots. Likewise, when a farm was divided between a brother and a sister, it was not enough to count the number of rooms given to each, or even the number of floorboards – two rooms given to the brother in the form of a small, independent house might be more valuable than two rooms given to the sister in the form of two rooms within a larger house belonging to another. And again, the value of a suite of two adjacent rooms could be worth more than two rooms in different buildings on the same farm. It would hardly be appropriate to consider a millstone located in a mill to be of equal value to a millstone lying in a field. Thus, a more general catalogue of such things as houses, suites, fields, flocks and mills contains its own knowledge, distinct from that of the particular catalogue. Thus, the particular catalogue cannot be considered absolutely superior to the general one.

Yet Dinasra dissented. The question here, he said, was not the genre of the catalogue – its degree of generality – but its completeness. Specifically, the true complaint behind the sophist’s argument was simply that a poor enumeration could neglect to make note of important features of how the elements of the catalogue were distributed with regard to one another. Some of this knowledge was inherently included in a more general survey: to say that there is a field of grain of a certain size implies that the grain is all located together, just as to say that there is a working millhouse is to imply that the millstones are in place within it, not lying in the yard nearby. Indeed, Dinasra argued that this was the whole meaning of generality in enumeration: that whenever a more particular catalogue contained an enumeration of contents and, separately, a description of their distribution with regard to one another, a more general catalogue could contain much of the distributive information within the terms for the enumerated contents themselves, and that this, indeed, was the whole difference between the two catalogues, save that the more general catalogue inherently contained less information than the more particular. To say that there are a certain number of sheep at a farm, for example, is simply to say that there are a certain number of sheep heads, and a certain number of sheep bodies, and that the bodies and heads are distributed in a particular way with regard to one another, that is, one of each attached to one of each. And yet a full enumeration of the body parts of sheep, that, say, counts also the number of sheep’s legs, tells us more than the more general enumeration of the numbers of sheep, as the latter does not tell us whether any sheep are three-legged. The more particular catalogue, therefore, is always in theory superior to the more general, provided that, as is proper, it takes care to include also the appropriate information on the distribution of the particular parts.

Thus, Dinasra argues, when weighing two rival enumerations of the same estate, each a pure catalogue that does not mix genres, and where each surveyor is of the same reputation and skill, it is better to give more credence to the more particular – from this, all necessary knowledge may be gleaned, provided distributional information is properly included, whereas from the more general some knowledge cannot be obtained.

Comparing two mixed catalogues
Similarly, argues Dinasra, if two lawyers unwisely bring catalogues of an estate (or of two estates standing in comparison) that mix together entries of different genres, it may be hard to directly compare them as they are. But if each entry that properly belongs to a more general catalogue is translated into entries at the most particular level, direct comparisons may be made. For instance, if the brother has been given an estate his lawyer describes as containing four cows and a flock of sheep, and the sister has been given an estate her lawyer describes as containing fifteen sheep and a herd of cows, it may at first appear difficult for the judge to determine which party has gained the more. Yet this may be resolved with a pure catalogue at the most particular level – in this case, at the level of individual animals. So, by counting precisely how many cows and sheep each has, the estates can be compared directly at prevailing market prices (providing all salient information about the distribution of the animals is likewise included in the catalogue). This is particularly important when two catalogues may count the same particular under different general terms: as when, for example, one catalogue counts the cart-ox within the herd, a second counts the cart-ox as a part of the equipped cart, and the third counts the herd, the cart and the cart-ox all as separate entries. All three catalogues may describe the same estate, but it may be difficult for the judge to directly compare the value ascribed to each item; however, by conducting a pure enumeration at the most particular relevant level, the precise number of animals and carts may be unambiguously recorded (in this case, the tripartite catalogue was unwise, because it combined entries of different levels of particularity, while the entry counting the cart-ox in the herd and consequently giving the cart a lower value was simply incorrect, perhaps duplicitous, as the cart-ox is separate in function from the cows of the herd, and is an integral part of a functioning cart – the lawyer here was likely attempting to reduce the apparent value of the estate by hiding the cart-ox amid the herd and valuing the cart as defective for want of an ox).

Thus, in each case, the unambiguous truth is to be found by turning to the more particular enumeration, provided that appropriate distributional information is also included.

[Salmoneus]

The sophistical regress

Now, the sophist, frustrated to have their tricks stymied by this absolute standard, will reason as such: if the general catalogue contains no information that is not in the particular catalogue, and hence depends for its accuracy, its very being, on the more particular catalogue, does that particular catalogue not equally depend upon, and stand subordinate to, a more particular catalogue still? And does not that catalogue in turn depend upon another? As regards our knowledge, how could we ever then reach an acceptable confidence in our knowledge when it is always possible to refer to another catalogue of still greater detail, that might overturn our assessment? And as regards logical absurdity, how can we say that each catalogue depends upon another, and that there is no catalogue that stands independently – does this not form an infinite regress that shows that no catalogue could ever have a firm foundation? Thus, is Dinasra’s approach to estate valuation not nonsensical when carried on logically by its own path?
Dinasra accordingly takes some time to refute this attack, through three approaches. First, he says, it can again not be doubted that the more particular catalogue gives us a fuller knowledge of the estate than the more general. And indeed it is true that in practice an even more detailed survey could be undertaken. Instead of counting the number of sheep, the surveyor could weigh them shorn for their meat and weigh their fleeces too. And in turn, we could even imagine the truly pedantic assessor measuring and describing each hair of the fleece – as indeed, fleeces of the same weight but different quality may fetch different prices. But that does not mean that there is any conceptual regress. If such a regress were to occur, he points out, we would not be able to say that any knowledge were full, nor that any knowledge were empty – to talk of fuller knowledge presupposes a comparison to an at least theoretical, if practically unattainable, full knowledge, and equally to a state of full ignorance. But if each survey provides only incomplete information that could yet be supplemented by an even more detailed and particular enumeration, full knowledge would be an incoherent concept, that would attach to no possible catalogue, no matter how supernaturally fine. This is, indeed, the absurdity to which the sophists sought to press Dinasra. But the fact that it is clear that a more particular enumeration can in fact improve our state of knowledge irrefutably proves that knowledge is at least theoretically possible, which in turn demonstrates that there must come a time at which a further, more particular enumeration is not possible. There is, in other words, some maximally detailed catalogue all the contents of the estate – even if it is not one a surveyor would ever be able to compile in practice. Yet even if this catalogue is unobtainable, its existence is sufficient to ground the realism and utility of all more general catalogues that are built upon it. There is no regress, and knowledge is possible.

But if the sophists insist on pressing their absurd argument – by perhaps denying that we can ever have more or less knowledge, but asserting instead that we are in a state of perpetual and equivalent ignorance – Dinasra then suggests a more practical demonstration of how ridiculous this would be. He takes the example of a farm again. At one genre of catalogue, we may say there is a farm. A more particlar catalogue may say there are three buildings. A more particular catalogue still might say that there are seven rooms. But we cannot count the rooms with any more precision than that – once each entry in our catalogue has only one room, we can count them no more precisely, because we have run out of rooms to count. Now the sophist might say: but then we might count floorboards. And then we can conduct a more particular enumeration of the number of floorboards. But there are still only so many floorboards, and once our catalogue contains only one floorboard per entry, we have run out of floorboards and cannot be any more detailed in our enumeration of them. Maybe we should count nails? But there are only so many nails, and we cannot be more detailed than one nail per entry. Perhaps, Dinasra asks facetiously, we are to count the faces of the nails individually? But there are only four faces to each nail. Again, we can get no more detailed than that. There is a limit to how particular our enumeration can get.

Now the sophist becomes ridiculous again. Suppose, they argue, that each more particular catalogue continues to find more precise things to count, more precise than the faces on each nail, or the hairs on each sheep? It would be absurd in practice, but is it not conceptually possible? Well no, says Dinasra. Clearly, a large object contains more parts than a small one – that is what it is to be large. The sophist might go so far as to say that perhaps a small object and a large object contained just as many parts as one another, but that the parts of the small object were smaller – but that is absurd, for two reasons. For one thing, it is begging the question – since the ‘smaller part’ is smaller than the larger part because it, in turn, contains fewer parts. To argue for ‘smaller parts’, therefore, requires simply stating the absurd conclusion as a premise. But more importantly, it leads to paradoxes. If a metre-long rod contains ten parts (each a tenth of a metre), and a ten-metre rod contains ten parts (each a metre long), then the latter could be counted as ten of the former joined together, and then it would have both ten parts and ten times ten parts. And ten times ten times ten parts. And the sophist will object that this is exactly what Dinasra said about catalogues of different genres. In one catalogue, the rod may have ten parts, while in a more particular catalogue it has one hundred parts. But Dinasra has established that the most correct catalogue is the most particular, and that a more general catalogue contains no information that is not included in the more particular, and hence that the general catalogue can be reduced to the more particular without loss. So, it is more correct to say that the rod must have one hundred parts. Yet each of these parts is then equal in size to the parts of the shorter rod. Thus larger and smaller things have parts of the same size – the fallacy that they do not is simply caused by unjustly measuring one by a more particular standard of enumeration than the other. Thus, larger things have more parts than smaller things. In dividing the larger things, each component element has fewer parts than the whole. With successive divisions – increasingly pedantic surveys – the number of parts left in each component element decreases until it reaches one, and then no further meaningful division can be accomplished. And indeed, this theoretical conclusion, which reinforces the proof by progressive knowledge, is immediately demonstrated in practice: it can immediately seen that as a carved plank of wood is cut into smaller and smaller pieces, the level of detail in the pieces becomes less and less, until we are left with tiny fragments indiscernable and indivisible to the eye. And if we grind them further, into sawdust, and then into the finest powder, they lose indeed all divisibilty, and finally even discernability, to touch. And again: however many points of interest could be enumerated on an invisibly fine grain of sawdust must logically be lesser than the number of points of interest in an entire wooden ship, composed of such grains – because one number added to a second number, as one grain is added to the next, must yield a larger number than the first.

And finally, to those most extreme sophists who argue against all reason that the doctrine of the more particular enumeration entails an unending regress, Dinasra points out that this would in turn entail an unlimited number of parts to each whole. Each item in a catalogue must of course have some size – to have no size is to have no physical existence – which means that, as an estate is of a fixed size, it can contain only a limited number of contents. It may, in a sufficiently precise enumeration, be a vast number, but it must be a number with a limit. This, indeed, Dinasra suggests is what we mean when we say one estate is larger than another – they each contain a limited number of contents, and the limit for one is a larger number than the limit for the other. If everything contained an unlimited number of things, everything would be equal in size, and in particular would be equal in size to its own parts, which would be nonsensical, as a part is by definition smaller than the whole. And if, indeed, an estate contains only a limited number of contents, increasingly precise enumeration will eventually reach the point where there is only one item per entry on a catalogue.
Thus, by every direction of proof, it is demonstrably clear that the doctrine of recourse to a more particular enumeration does not entail conceptually an unending regress, but rather it is possible to conceive of a perfectly exact enumeration of all physical things; and the practical surveys it is possible to conduct can be regarded as increasingly correct approximations to this exact, maximally particular, enumeration.

[Salmoneus]

Practical considerations for estate catalogues

Now, while the theoretical aspect of the sophist attack has been rebutted, the practical complaint remains. Is Dinasra not continually going to call for increasingly more particular enumerations of contested estates? Well, no. Because here Dinasra introduces the concept of diminishing returns. Now, because Dinasra has demonstrated that each catalogue contains only a limited number of entries, and that the size of the things listed by these entries must diminish as the catalogue becomes more particular, and hence more particular catalogues detail items containing fewer distinguishing parts, it follows that the additional information gained from each increasingly particular enumeration becomes less and less. This is easy to see in practice. Counting buildings is important. Counting rooms instead gives substantially more information. Counting floorboards (and hence the size of rooms) is less important (rooms not varying much in size in general), but still useful. Counting the number of nails does give us a little more information, but very little – perhaps it tells us something about the quality of workmanship. But counting the sides on the nails tells us almost nothing – a farm whose floorboards use three-sided nails would not be worth less than one using four-sided nails. The more pedantic our surveys, the less new information they give us. The amount of new information never reaches exactly zero until we have reached the hypothetical full description of the estate... but it becomes smaller and smaller. There are therefore diminishing returns to increasingly particular enumerations of estates. The cost of increasingly particular enumerations, however, increases.

From this, we can conclude that although more particular enumerations of estate contents are superior, in practice we should not order a more detailed survey unless the sums at stake – the increase or decrease in valuation that can plausibly be expected from a more particular catalogue of contents – are greater than the cost of that survey. In practice, therefore, all parties to a dispute will face practical limits to their desire to appeal to a more particular enumeration, and there should be some particular degree of particularity that can be identified as, while not conceptually ideal, nonetheless pragmatically optimal. Thus in practice the adoption of the principle of the resort to a more particular catalogue should not lead to the paralysis or delay of continual regress.

The full metaphysical weight of these arguments, however, and in particular their implicit proof of the existence of a single all-powerful deity, were not immediately apparent, and would instead develop over the coming decades and centuries.

[akam chinjir]

Well I'm enjoying it. It's a really nice way to introduce and work through those metaphysical issues, imo, and sets up a believable dialectic.

A particularly nice moment for me was in the post on the sophistical regress---I'd been starting to wonder how close you might get to a Mādyamaka view, and right then you introduced the idea that all knowledge might be empty. Along no doubt with all catalogues, all inheritance, all ownership, and so on (And's a very powerful context into which to introduce ideas and arguments influenced by Buddhist philosophy, if that's one of the things on your mind.)

[Arzena]

Now this is content!

Great stuff always have wanted to see more conphilosophy on the Board

[Ares Land]

That's pretty great. And interestingly alien; I like the way atomism is logically derived from barnyard inventory. And I guess you really do have to demonstrate the existence of God now

One minor nitpick: I believe what your're discussing are inventories, not catalogues. (To me, if you have a quantity next to each item, it's an inventory. If you don't, it's a catalogue.)
Also, did Dinasra consider inventorying the inventory and stumble onto Russels' paradox?

[Salmoneus]

One minor nitpick: I believe what your're discussing are inventories, not catalogues. (To me, if you have a quantity next to each item, it's an inventory. If you don't, it's a catalogue.)

That's a fair distinction to make; I didn't think of it. To be honest, I think 'catalogue' sprange to mind as a sort of pun, because these catalogues are, as it were, break-downs (and down and down, either infinitely or until you reach the atoms), via logic, so kata (down, often in practice into parts) + logos...

But you're right than 'inventory' may be a less confusing word I may consider if I get around to editing/rewriting this...

Also, did Dinasra consider inventorying the inventory and stumble onto Russels' paradox?

Well, the question of the sophistical regress can effectively be seen as the question of whether the inventory of inventories in infinite in the downward direction (it can't be infinite in the upward direction because a sufficiently general inventory would just have one entry...)

That said, I think Dinasra would would distinguished strictly between things with physical existence, that can be inventoried, and things like inventories that are only concepts, and hence probably can't be inventoried. Dinasra's hypothetical complete, maximally-detail inventory of the world would not include any inventories per se (though it would include any actual physical documents detailing inventories). Dinasra was a practical guy not all that into abstract and metaphysical entities. He'd probably have viewed questions like "if there were an inventory of all inventories that did not list themselves, would it list itself?" as the symptom of somebody being a troublemaker.
But you're right that this sort of question will eventually have to arise in this philosophical structure.



akamchinjir: I'm not an expert on Buddhism, and I'm not aiming directly at a Buddhist end-point here. However, it's probably fair to say that there are going to be some concepts cropping up that might make more sense to a Buddhist than to, for instance, a Christian.

(the Gureha region where we'll be going shortly in in some ways a sort of 'India' of my conworld, though it's hard to pin down in what way exactly).




Thanks for the encouragement, people! I'm surprised so many people were interested, let alone so quickly...

[Salmoneus]

The Enumeration of Voids

A number of further key theoretical developments emerged among Dinasra’s followers.
First, the more speculative lawyers wondered, as a thought experiment, whether Dinasra’s conclusions could be extended to voids, areas of nothingness. It was concluded that they could. Since each void has a limited size, it may be regarded as being composed of parts of smaller size, just as physical objects can. By the same arguments, therefore, it must be possible to enumerate the contents of the void perfectly, without eternal regress. Furthermore, three paradoxes were seen to arise from the concept of the infinitely-divisble void: the paradox of capacity, the paradox of location, and the paradox of motion.

The paradox of capacity states that if a void can be continually subjected to more and more particular enumerations, without limit, each enumeration generating a catalogue of entries corresponding to empty spaces, either those empty spaces have the capacity to hold objects or they do not. If they do have the capacity to hold objects, it must be possible for there to be objects they can hold. But if we take the genre of enumeration that provides us with the theoretical exact description of objects and apply it to voids, and then attempt a finer survey of the void even than that, we are left with ‘spaces’ that are by definition smaller than the smallest objects that can exist. This is an evident paradox. Thus, the enumeration of void is limited in the same way as is the enumeration of filled space: there is a smallest unit of void, which is the size that would be filled by the smallest possible unit of matter. Otherwise knowledge is impossible.

The paradox of location considers a grain of matter within a void. It is evident that the grain occupies a particular place in the void – it is closer to one side than the other, or it has changed place over time. We may say, then, that a grain is six units of void from the left edge of the void, and eight units of void from the right edge of the void, and hence we have defined its location. But if a more particular survey is possible, we may survey the the left-hand void and find twenty-four units of void there, and still only eight on the right. Now of course, the sophist might say that this is only because the units on the left are smaller than the units on the right. And yet, unlike more particular surveys of objects, the two surveys are measuring exactly the same thing: void. How can we say that one void is larger than another without a fixed unit of distance? If both voids are divisible without limit, then both have an unlimited number of parts, so neither can be bigger than the other; nor can the smaller void be filled by less than the larger void, if the larger void is already filled by the smallest possible particle. And moreover: if both larger and smaller units of void contain nothing but void, then they contain nothing, so they contain exactly the same contents – one unit of absence, one unit of nothing that contains no characteristics or contents, cannot be said to be bigger than another. One zero is not larger than another zero. So unless we have recourse to small smallest possible unit of void, we cannot unambiguously state the position of a grain lost in a void – which would mean we could not fully describe the distribution of matter in the most particular catalogue, and hence all knowledge would be impossible.

Finally, the paradox of motion considers a grain thrown across a void. It is clear that it takes a limited time to travel all across the void. The void must therefore have a limited space, as otherwise the grain could not have a defined speed. Likewise, to cross half the void must take half the time, given a constant speed – half a limited time is a limited time, and given a defined speed that implies a limited distance. In the same way, no matter how far a grain travels through a void, it can never travel with an unlimited or zero speed. It must always therefore, if it takes a limited time, have crossed a limited distance of void. If a grain must cross an unlimited number of units of void to cross an entire void, at a limited speed, then it must take a limited time to cross each unit, and thus to cross the unlimited number of units would take an unlimited time. As the grain in fact travels the void in a limited time, either it has crossed only a limited number of units of void, or it has crossed some of then with an unlimited speed. To travel with an unlimited speed is to be in two places at once, which is to be two grains, not one. Hence only a limited number of units of void have been crossed. Hence, the void is not subject to unlimited particularity of enumeration but rather, like matter, is divisible into its smallest parts.

[Salmoneus]

Modus Tollens and Qualifiers

Meanwhile, lawyers of Dinasra’s school had also begun to classify the forms of argument – indeed, due to the qatmesh system, this classification was the foundation of law. One of the most important argument forms for the Carians was modus tollens: if A entails B, and B is not the case, then A is not the case. This was particularly often found in causal form: if A causes B (i.e. entails that B will immediately follow), and B has not occured, then A did not occur.

Alongside these developments in the form of arguments, the Carians also developed a limited logic of qualifiers, particularly ‘some’ and ‘all’. This allowed them to distinguish the true modus tollens, “ALL A entails B, and ALL B is not the case, therefore ALL A is not the case”, from the false modus tollens that begins with “SOME A entails B”.

Crucially, however, the Carians theorised that in the case of unity – the case where A referred only to one perfectly precise thing, then ‘some’ entailed ‘all’.

The proof of a deity that flowed from these conclusions was never ascribed to a single thinker (other than, in some ahistorical and hagiographic writings, to Dinasra himself), but appears to have emerged as perevident throughout the whole school of Dinasra’s followers, and was almost immediately accepted by the broader Carian intellectual community. Nonetheless, it may be worth outlining the general structure of the argument for the sake of completion, though it no doubt at this point has already become clear.


The Demonstration of Monotheism

The Carian argument for monotheism runs as follows:
1. it is granted as self-evident that the world is of a limited size;
2. it is granted as equally self-evident that the world has persisted, and will persist, without beginning or end for an unlimited time (to suggest otherwise invites obvious absurdities);
3. there is a limited number of particles in the universe (from Dinasra’s proofs of the maximally particular enumeration)
4. these particles are distributed in combination with a limited number of voids capable of receiving and containing a particle (from Dinasra’s school’s proof of the maximally particular enumeration of voids)
5. there are therefore only a limited number of possible distributions of particles within the world (from the previous two points)
6. the particles of the world cannot come to rest in any distribution for an unlimited time, as entering that state implies a limit to the time spent in that state (it does not extend without limit backward through time)
7. therefore, from the previous point, each distribution is maintained for a limited time only
8. thus, at least two distributions must each occur more than once in the course of time (from 2, 5 and 7)
9. a distribution is a single thing – as it is maximally exact and precise, there cannot be two forms of the same distribution; therefore, what is true of ‘some’ forms of the distribution is true of ‘all’ foms of the distribution (the coalescence of qualifiers in the special case of unity)
10. if distribution A is followed by distribution B, then it is true that “A is followed by B”; because there is only one unique distirbution A, “all A is followed by B” (from 9, and from elementary logic)
11. hence, by modus tollens, if a distribution X is not followed by distribution B, distribution X is not distribution A
12. or, to rephrase through modus ponens, if A occurs, B must follow
13. therefore, each time A occurs, B must follow
14. likewise, if B is followed by C, then each time B occurs, C must follow
15. and so on
16. therefore, if A occurs twice, it will each time be followed by B, and so on, through the following chain of distributions
17. if A has occured a second time, the chain of distributions that followed the first instance of A must have lead to A recurring; and so, when that chain recurs, so too will A occur for the third time
18. thus, if any distribution occurs twice, it must occur an unlimited number of times, and all distributions that occur must likewise occur an unlimited number of times, always in the same order
19. all events in the world, therefore, repeat without end in obedience to a fixed and unvarying design
20. there exists, therefore a design (pattern, rule, principle, logic, word) that imposes itself upon all things in existence, throughout all time, without exception, and that is the true cause of all events in the world, and that cannot be altered or challenged, but that is manifested in all things
21. this design that exists, which is constant, is not constructed of atoms, which are in constant motion, yet it controls all atoms
22. this invariant, all-controlling, omnipotent, omnipresent and implacable existing being, the Logos, is the supreme and singular deity of the world, having all the traits that are said to distinguish a deity, but to a greater extent than any other deity could possess; all other deities are only manifestations of its power.

Many of the premises and inferences of this argument have been challenged by various heretical groups in the intervening millennia, but none of these challenges has proven broadly successful, and consequently this general proof of the existence of a deity (and of eternal regression and determinism) has been held to be accurate ever since, and has dominated religion and philosophy from Seravos to Mirev – though often obscured beneath layers of syncretic theology.

The details of the religions founded upon this argument among the Carians and their successors vary; yet it is worth summarising some general conclusions of the worldview:
– the material world consists of nothing but material atoms
– there is a single power that transcends the material world and orders all things within the material world, with unlimited potency
– as all things in the material world are only assemblies of atoms, all material things, including people, arise and fall apart with the passage of time; they have no true essence and nothing of them is permanent
– naive perceptions of the world, insofar as they do not immediately recognise the above, are deceptive
– all events of the world are doomed to recur again and again, repeating infinitely
– the events of the world are beyond any human power, and cannot be altered

[akam chinjir]

Maybe a bit cheeky to derive monotheism from eternal return

One thing that strikes me about the argument is that, given the background, you might expect inferences from regularity to law to lawgiver to be foregrounded somehow; though those are a couple of the points at which the argument (or at least this sketch of the argument) seem especially vulnerable. (It's not explicit that the inferred deity is an agent, much less a lawgiver, but I'm assuming at least agency is implied by "all the traits that are said to distinguish a deity.")

The main thing I don't buy is that the argument could become the basis of or a dominating force in a whole religious tradition or society or whatever. It's just not that powerful an argument (logically or otherwise), and arguments of this sort aren't that important. (But maybe I'm reading too much into your comments about the argument's update.)

[mèþru]

I automatically think of ancient Anatolia as I read this

[Salmoneus]

Maybe a bit cheeky to derive monotheism from eternal return

One thing that strikes me about the argument is that, given the background, you might expect inferences from regularity to law to lawgiver to be foregrounded somehow; though those are a couple of the points at which the argument (or at least this sketch of the argument) seem especially vulnerable. (It's not explicit that the inferred deity is an agent, much less a lawgiver, but I'm assuming at least agency is implied by "all the traits that are said to distinguish a deity.")

You're right that 'law' would have been a good word to include there. 'Lawgiver' is not, though; that wouldn't make much sense for them. For one thing, they'd see human laws more as attempts to discern and spell out the natural law than as things 'given' or created.

But also, by deity I/they don't particularly mean an Abrahamic big-man-in-sky sort of deity. It's not some guy who hangs around giving commands: it's the absolute law that controls all things.

Does it have 'agency'? I'm not sure what you mean by 'agency' in this context, as that's sort of something we talk about with humans, rather than absolute principles. The Logos certainly has free will, in that its decisions are uncoerced - there is nothing that can coerce the Logos.

The main thing I don't buy is that the argument could become the basis of or a dominating force in a whole religious tradition or society or whatever. It's just not that powerful an argument (logically or otherwise), and arguments of this sort aren't that important. (But maybe I'm reading too much into your comments about the argument's update.)

I'm sorry you feel that way. Perhaps you could explain what flaws you can see in the argument, rather than just dismissing it out of hand? Because logically, it seems pretty robust, given its (all independently attractive) premises.

As for the latter point: history again and again shows that philosophical viewpoints do shape religion and culture - just look at how much of Catholicism can be traced directly to Aristotle and Plato. Look at Buddhism. Look at Kant, Hegel, Marx, Mill and so on in modern society.

Of course, i'm not suggesting that every agricultural peasant can recite the above argument by heart, or even that it's been preached to them - as I said, it emerges so naturally from the premises that there was not even one particular 'discoverer'. But the basic principles are taken as granted by most people.

After all, in essence, other than the loophole-closing bits, the basic thrust of the argument is simply a) radical atomism, causes b) eternal return and c) a single all-powerful deity. The fact that this was such a widespread view for so long in our own history should discourage 'but that's a terrible argument' arguments (as should the fact that, no, it isn't).

[akam chinjir]

Well, I didn't say the argument is terrible. I don't think it's plausible that this argument, or anything much like it, could convert an entire intellectual class or an entire tradition to monotheism, but that doesn't make it terrible. Anyway it doesn't make it more terrible than the cosmological argument or the argument from design, for example, neither of which has that kind of status.

Like I said, maybe I was reading too much into some of your comments. If the idea is just that in the course of working out the argument there arose a constellation of ideas---atomism, return, and monotheism---that became central to the ensuing tradition, then I've got no objection. I was commenting just about what role the argument might play in convincing large numbers of people of the truth of its conclusion.

After all, in essence, other than the loophole-closing bits, the basic thrust of the argument is simply a) radical atomism, causes b) eternal return and c) a single all-powerful deity. The fact that this was such a widespread view for so long in our own history should discourage 'but that's a terrible argument' arguments (as should the fact that, no, it isn't).

So a confession of ignorance: I don't know who you're talking about when you say this was a widespread view for a long time in our (I assume you mean European?) history. I don't have an encyclopedic knowledge of intellectual history and am probably missing something obvious, but I don't know of a single example of someone who's held all three of these views, much less someone who drew the inferences in the Carian argument. (Apparently the Stoics inferred eternal return in part from their beliefs about the deity, which is the opposite of the Carian argument, and anyway the Stoics weren't atomists. Nietzsche of course didn't infer monotheism at all.) That doesn't really speak to the strength of the argument, but you seem to be saying that the argument is not just strong but also sort of obvious, and if it were obvious I guess I'd expect it to be attested, given that atomism at least is hardly an obscure doctrine.

Besides which, there are steps in the argument that are obviously not obvious, even the ones that come labeled as self-evident. (How is it harder to conceive of an end to time than of an edge to space?) I daresay the spatial paradoxes and the appeals to quantifier logic and modus tollens (in the derivation of determinism) would strike many people as impenetrable hocus pocus. Again, that's more about the likely uptake of the argument than about its correctness, but that does seem important, probably more important for your purposes than any philosophical objection I might give.

But now you're inviting objections, so here are some thoughts along those lines.

Probably the most significant issue, for me anyway, is the inference in steps 19 to 22 from determinism to monotheism via an unchanging law or pattern that transcends particular matters of fact. I can see how someone who already basically agreed with the conclusion could think of these views as coming sort of together. But as an argument it's just a non sequitur. So, for example, I'm suspicious of words like "obedience," "design," and "imposes" in steps 19 and 20; what's supposed to justify interpreting causal regularities in such terms? Similarly with "controls" in step 21 and "all-controlling" and "omnipotent" in 22. Saying that for the law of gravity, for example, is omnipotent and controling just seems like a category mistake. Meanwhile it's easy to think of traits commonly taken to characterise deities that the argument doesn't purport to establish (benevolence, say, or creation, or concern with human beings).

Some of this language seems to attribute causal powers to the absolute law. That seems like it's got to be a mistake. Anyway it's hard to see how to square it with the idea (essential in the argument for determinism) that only atoms and their arrangements can affect what happens next. (Maybe that's just a terminological issue?) Similarly, it seems to be an upshot of the earlier arguments that all knowledge is knowledge of atoms and their arrangements, and also that the possibility of knowledge is a guide to what's real; the conclusion that there's also a transcendant causal law maybe calls for another look at those earlier arguments. I mean, it's not as bad as those versions of the cosmological argument that infer there is something uncaused from there is nothing uncaused. But it still seems a bit fishy.

Another sort of counterargument. Suppose at every moment, there come into existence both a new atom and a new location. Then even though at no time is there an infinity of atoms or locations, it's still impossible for any state ever to recur, and the argument for eternal return cannot get going. But nothing in the argument rules out this possibility. (Maybe this is a sort of argument your sophists could play with, and be ignored.) A bit more seriously, the argument assumes without argument that it's the same atoms and the same locations that exist at all times.

The identity of indiscernibles ends up playing an essential role in the argument for eternal return and determinism, but besides any issues one might have with that principle, it's not applied consistently. According to the argument, two states that involve the same atoms in the same arrangement are indiscernible and therefore numerically identical, so not really two states after all. But you could also argue that two times at which the same atoms exist in the same arrangement are also indiscernible, and therefore actually just one time after all. Is the first argument supposed to be more plausible than the second? Why? (Note that if you accept the conclusion of the second argument, the result is not eternal return but rather circular time.)

The reference to modus tollens is a red herring. At the relevant point of the argument, all you need is something like this:

• Some A state is followed by a B state.
• There is only one A state.
• So, all A states are followed by B states.

Modus tollens plays no role in this argument. I'm not really sure what role it's supposed to play. (My initial impression was that there was some sleight of hand involving three potential interpretations of "follow"---temporal sequence, causal result, and a conditional.)

Anyway, that argument is deductively valid. Obviously it doesn't get you very far without the conclusion that the A state returns at many different times (in fact at an infinity of times), but this isn't the part of the argument that's supposed to be establishing that conclusion, as far as I can tell.

(I hope that all makes sense and is helpful. Posting now even though it could probably use more thought because it's time for dinner here.)

[Salmoneus]

Well, I didn't say the argument is terrible. I don't think it's plausible that this argument, or anything much like it, could convert an entire intellectual class or an entire tradition to monotheism, but that doesn't make it terrible. Anyway it doesn't make it more terrible than the cosmological argument or the argument from design, for example, neither of which has that kind of status.

Again, i'm not suggesting every peasant memorises it. We're talking about a society with a very small intellectual class concentrated in (or at least having visited) a couple of university departments. Like the arguments of Aquinas, Aristotle, Plato, Nagarjuna or the like, the divine qatm is learned by those intellectuals. Their knowledge is the core of the belief system of the broader ruling and mercantile class who look up to and employ them. In the same way that it's fair to talk about how the summa was central to European culture for centuries, even though most people in society were not themselves Jesuits or Dominicans. It is true however that, just as many rural Europeans still believed all sorts of things, there will be many peasants in Gureha who still in practice adhere to shamanism.

So a confession of ignorance: I don't know who you're talking about when you say this was a widespread view for a long time in our (I assume you mean European?) history. I don't have an encyclopedic knowledge of intellectual history and am probably missing something obvious, but I don't know of a single example of someone who's held all three of these views, much less someone who drew the inferences in the Carian argument. (Apparently the Stoics inferred eternal return in part from their beliefs about the deity, which is the opposite of the Carian argument, and anyway the Stoics weren't atomists. Nietzsche of course didn't infer monotheism at all.) That doesn't really speak to the strength of the argument, but you seem to be saying that the argument is not just strong but also sort of obvious, and if it were obvious I guess I'd expect it to be attested, given that atomism at least is hardly an obscure doctrine.

I'm mostly thinking of the Stoics - who, it is true, did not believe in atoms per se, but believed in a pneumatically-structured plenum that fulfils a similar role (though later stages of this philosophical culture will become closer to that Stoic view). However, very similar views have also arisen in Hinduism.

Besides which, there are steps in the argument that are obviously not obvious, even the ones that come labeled as self-evident. (How is it harder to conceive of an end to time than of an edge to space?)

Well, historically this just is self-evident to most people: the finite world and the infinity of time are commonplace assumptions in ancient philosophy around the world, although I'm sure they're not universal. Obviously these people are not modern physicists - so the idea that time is in any qay equivalent to space has not at this point occured to them. The difference between a barrier in time and a barrier in space is that time has an inherent direction, that is inescapable, and space does not, which means that the end of time would mean the destruction of everything, whereas the end of space would not.

I daresay the spatial paradoxes and the appeals to quantifier logic and modus tollens (in the derivation of determinism) would strike many people as impenetrable hocus pocus. Again, that's more about the likely uptake of the argument than about its correctness, but that does seem important, probably more important for your purposes than any philosophical objection I might give.

Actually, I think both those points are very intuitively accessible, and were in fact widely if not universally adopted in European culture. You'd be hard pressed to find anyone (other than a philosopher) denying the validity of modus tollens today.

But now you're inviting objections, so here are some thoughts along those lines.

Probably the most significant issue, for me anyway, is the inference in steps 19 to 22 from determinism to monotheism via an unchanging law or pattern that transcends particular matters of fact. I can see how someone who already basically agreed with the conclusion could think of these views as coming sort of together. But as an argument it's just a non sequitur. So, for example, I'm suspicious of words like "obedience," "design," and "imposes" in steps 19 and 20; what's supposed to justify interpreting causal regularities in such terms? Similarly with "controls" in step 21 and "all-controlling" and "omnipotent" in 22.

OK, there's some qualitative language I put in there for effect. However, I'm not sure what you're really objecting to in terms of substance. Taking the words you highlight: something is obedient to a law when it follows it completely as a result of the law being as it is - so the atoms obey the Logos; when events occur according to a predetermined pattern laid down in advance, they follow a design (indeed, in the way I used the word, any series of thigns across time or space must follow a design, which is a synonym of 'pattern'; if you're worried that there must be a patterner or designer, that is of course not the intent); when the behaviour of things obeys a law, and would be different were the law different, then the law has been imposed upon them; a law controls an atom when the atom's behaviour is entirely in adherence with the law, and would be different were the law different; something is all-controlling when it controlls all things; something is omnipotent when it has power over all things. These are all common words used in commonplace ways - though I will concede that the 'omnipotence' spoken of here is a more limited, temporal omnipotence, and does extend into a broader logical omnipotence of the sort some Christians have believed in.

It is true that the concepts here are not particularly Christian, but that shouldn't be considered a fault. This view of the deity is similar to those found in, among other approaches, stoicism and several forms of hinduism (and I would imagine buddhism).

Saying that for the law of gravity, for example, is omnipotent and controling just seems like a category mistake.

It's certainly not omnipotent, because it can be counteracted by other laws. Certainly we do talk about gravity as a controlling force. The wikipedia article on gravity doesn't use the word 'control' specifically ('control' has taken on more specific meanings in empirical science that aren't relevant here), but it uses related language. In the first few paragraphs we hear of gravity "gives weight", "causes" things, we hear that it "is responsible" for things, we hear how it's so weak that it does not have much "influence" over small scales but "is dominant" at large scales. Later we hear Newton say that gravity "keeps" planets in their orbs, and throughout the article gravity is called "a force", which is only a fossilised syntactic variant of saying that it forces things.
I don't see why it's OK to talk of natural laws "forcing", "causing", "keeping", "being responsible for", "influencing" and "being dominant over", but inconceivable to use the closely-related word "controlling".
Of course, from a Christian perspective, "control" implies a sentient controller and "keeping" and "dominating" don't require a sentient keeper or a dominator, but I'm not writing about a Christian-dominated culture. Indeed, although I've not thought about this in detail, they're likely not even to share the modern SAE assumption that there's a difference between a principle and an actor (in the same way that, for example, the Greeks happily spoke of the same principle as a fact of nature and as a deity).

Meanwhile it's easy to think of traits commonly taken to characterise deities that the argument doesn't purport to establish (benevolence, say, or creation, or concern with human beings).
[/quote
Indeed, that was my own flourish. Although in the case of your examples - nobody in this culture would think of suggesting benevolence or (special) concern with human beings as particularly divine properties. Again, this isn't Christianity.

Some of this language seems to attribute causal powers to the absolute law. That seems like it's got to be a mistake.

Why? That seems pretty irrefutable, surely? The law is the efficient cause of all events: were that cause not as it was, the effect would be different. The law (in the sense of the predetermined pattern of events) is both a necessary cause and a sufficient cause of the effect. That doesn't of course necessarily rule out local causes too. We might reflect here on Chrysippus' argument on free will: if the soul is a cylinder, its motion is determined by the terrain it rolls over, which is God (/fate/the world/natural law/etc); but the fact it rolls and does not slide is due to the fact it is a cylinder, and therefore humans have free will (in that their actions, while wholly predetermined, nonetheless result from their own nature (which likewise predetermined)).
It's worth remembering here also that the notion of a 'cause' in the modern physics sense is something that took a lot of philosophical work to develop, and these cultures are rather more primitive.

Anyway it's hard to see how to square it with the idea (essential in the argument for determinism) that only atoms and their arrangements can affect what happens next. (Maybe that's just a terminological issue?)

Did I say that? I either misspoke or spoke loosely.

Indeed, the point of the modus tollens and the qualifiers is specifically that it does away with the need for the principle of sufficient reason (I've known the outline of this argument for many years, but I'd always struggled with the fact that an explicit PSR seemed inappropriate for this culture and context).

I suppose I did talk about one distribution causing the next, didn't I? Well, read 'causes' there as 'is followed by' or the like, with no imputation of efficient causal power. [In Aristotelian terms, they would probably say that the distribution of atoms was a formal cause, not an efficient one, but to be honest I don't know the details of how they would actually describe it in their own terminology].

Similarly, it seems to be an upshot of the earlier arguments that all knowledge is knowledge of atoms and their arrangements, and also that the possibility of knowledge is a guide to what's real; the conclusion that there's also a transcendant causal law maybe calls for another look at those earlier arguments.

Well, this is only the beginning of the culture, as it were, rather than the end, so many things may be reconsidered. However, I'd point out that at least for those who formulated these ideas, there is no contradiction here. The Logos is not an item in the world - no list of the world's contents would mention it. That doesn't mean it's not important. In the same way, when Dinasra was counting sheep at a farm, he wouldn't have denied that knowledge of the behaviour of sheep was important. He'd just have said that that knowledge could be gained through studying the location of sheep-parts at different times. Likewise his immediate followers at least thought the only way to learn of the Logos was through the study of the atomic world.

Another sort of counterargument. Suppose at every moment, there come into existence both a new atom and a new location. Then even though at no time is there an infinity of atoms or locations, it's still impossible for any state ever to recur, and the argument for eternal return cannot get going. But nothing in the argument rules out this possibility. (Maybe this is a sort of argument your sophists could play with, and be ignored.) A bit more seriously, the argument assumes without argument that it's the same atoms and the same locations that exist at all times.

That would be ruled out as an absurdity, as it involves things being created and things being destroyed, both of which everyone could agree to be obviously impossible. Where would a destroyed atom go - notexistingland!? (if you'll forgive me paraphrasing Parmenides). I suspect people would react to the thought much as Lucretius did on behalf of the Greeks:
For if things were created out of nothing, any breed
Could be born from any other; nothing would require a seed.
People could pop out of the sea, the scaly tribes arise
Out of the earth, and winged birds could hatch right from the skies.

That said, it may indeed be something sophists might have suggested.

The identity of indiscernibles ends up playing an essential role in the argument for eternal return and determinism, but besides any issues one might have with that principle, it's not applied consistently. According to the argument, two states that involve the same atoms in the same arrangement are indiscernible and therefore numerically identical, so not really two states after all. But you could also argue that two times at which the same atoms exist in the same arrangement are also indiscernible, and therefore actually just one time after all. Is the first argument supposed to be more plausible than the second? Why? (Note that if you accept the conclusion of the second argument, the result is not eternal return but rather circular time.)

How time is dealt with will indeed be an issue for later generations, and you've almost hit upon one rival school of thought here. However, the question you end with is not important - you assume that circular time and eternal return in linear time are different, but they're really just two ways of saying the same thing. Note, for instance, that nobody's been able to work out whether the stoics believed in return, circularity, or both.

The reference to modus tollens is a red herring. At the relevant point of the argument, all you need is something like this:

• Some A state is followed by a B state.
• There is only one A state.
• So, all A states are followed by B states.

Modus tollens plays no role in this argument. I'm not really sure what role it's supposed to play.

Well, they couldn't actually phrase it like that, because your second line is way too conceptually difficult. But sure, you could rephrase it as 'the A distribution is unique'.
OK, I guess I can't explain why I needed modus tollens/modus ponens - I guess the qualifiers do the work. Maybe it's just that I was working it out through modus tollens, and then realised i'd need the qualifiers as well. Although I think you might need modus tollens to prove the fact that 'some' entails 'all' in the case of singularity. But anyway.

[akam chinjir]

Cool!

Doesn't sound like we disagree about anything that matters in this context, so I'll just add some minor and probably tangential comments.

Well, historically this just is self-evident to most people: the finite world and the infinity of time are commonplace assumptions in ancient philosophy around the world, although I'm sure they're not universal.

Interesting. I'd have guessed that it was fairly common to think that the past has a limit (or at least that the cosmos has a beginning, which I guess doesn't have to be the same thing). Ancient Chinese common sense didn't obviously involve finite space, for what it's worth, or a spatially finite cosmos, if that's different; the most obviously relevant text that comes to mind treats it as an open question whether the south has a limit, for example. (Maybe I'd also expect lots of people to think that down has a limit.)

The bit about the past matters a bit, because without an infinite past your argument leaves open a peculiar loophole (where there's a loop, but we haven't gotten to it yet).

Actually, I think both those points are very intuitively accessible, and were in fact widely if not universally adopted in European culture. You'd be hard pressed to find anyone (other than a philosopher) denying the validity of modus tollens today.

Oh, I didn't mean people would deny the validity of modus tollens, just that the use you put it to in that particular argument would confuse them and they'd conclude it was nonsense. (It confused me.)

Indeed, the point of the modus tollens and the qualifiers is specifically that it does away with the need for the principle of sufficient reason (I've known the outline of this argument for many years, but I'd always struggled with the fact that an explicit PSR seemed inappropriate for this culture and context).

Interesting---I'd wondered about the PSR, both because I wasn't sure you could get away with it in the argument for determinism, and because the obvious lines of argument against the expanding-inventory cosmos I suggested appeal to something like a PSR.

Another sort of counterargument. Suppose at every moment, there come into existence both a new atom and a new location.

That would be ruled out as an absurdity, as it involves things being created and things being destroyed, both of which everyone could agree to be obviously impossible. Where would a destroyed atom go - notexistingland!? (if you'll forgive me paraphrasing Parmenides).

Well, the idea didn't involve anything getting destroyed; and anyway, Parmenides needs to learn what "destroyed" means. (Where does a fire go when it's extinguished?---A nice Buddhist example of an absurd question.)

For if things were created out of nothing, any breed
Could be born from any other; nothing would require a seed.
People could pop out of the sea, the scaly tribes arise
Out of the earth, and winged birds could hatch right from the skies.

You get analogous arguments in India, fwiw. But nothing says the new atoms/locations would have to be uncaused.

Although I think you might need modus tollens to prove the fact that 'some' entails 'all' in the case of singularity. But anyway.

You could do it with a reductio, anyway.