SNAP / SPAN IN BASIC FORMAL ONTOLOGY : AN ARISTOTELIAN SUGGESTION

Abstrakt: Basic Formal Ontology (Základní formální ontologie, zkr. BFO) vyvíjená Barry Smithem a jeho spolupracovníky je fundamentální ontologie užívaná v informační vědě k popisu entit na nejvyšší úrovni obecnosti. Jedním z nápadných rysů BFO je rozdělení entit na ty, které trvají (continuants) a jsou součástí ontologie SNAP (snap = snímek), a na ty, které se dějí (occurents) a jsou součástí ontologie SPAN (span = rozpětí). Toto dělení je motivováno kontroverzí mezi endurantismem a perdurantismem v současné analytické metafyzice. V tomto článku, v návaznosti na Aristotela, navrhuji v zájmu realismu určitou modifikaci Smithova přístupu.


Introduction
Basic Formal Ontology (BFO), developed by Barry Smith and his colleagues since 2002, is a foundational or upper-level ontology used in information science for the description of entities at the highest level of generality. 1 Though BFO is geared towards use in practical application rather than in philosophical speculation, due to its explicit realist orientation it directly concerns philosophy too. 2 Moreover, one of the salient features of BFO is the division of entities into continuants of so-called SNAP (or snapshot) ontology and occurents of so-called SPAN (or spanning-time) ontology and this division is at least partially motivated by an apparent impasse in the endurantist/perdurantist controversy in recent analytical metaphysics.The controversy has to do with the traditional philosophical problem of identity of material entities across time.BFO attempts to bypass the controversy by taking endurantism and perdurantism to be two distinct and irreducible, nevertheless true and transparent ontological perspectives of one reality (= realist perspectivalism).The former (SNAP) is intended to capture static aspects of reality, while the latter (SPAN) dynamic ones. 3I briefly describe the controversy and BFO's attempt to evade it in section 1 of this paper.
In section 2 I turn my attention to focus on the Ancient Greek philosopher Aristotle who seems to me to have anticipated BFO's approach.Aristotle contended that 'being' is non-univocal and that there are two fundamental modes of being, namely categorial (static) and potential/actual (dynamic).I further discuss the extent to which Aristotle's approach resembles BFO: I argue that Aristotle's doctrine of the non-univocity of being amounts to BFO's realist perspectivalism and that Aristole's categorial and potential/actual distinction resembles SNAP and SPAN ontology.Among other things, however, I point out that by acknowledging other "modes" of being besides the actual one, Aristotle's dynamic ontology (i.e.potential/actual being) is more transparent to reality than Smith's SPAN.In the conclusion I make a suggestion, inspired by Aristotle and Ingarden, as to how to make BFO a more robust form of common sense realism.

Diachronic Identity and SNAP/SPAN 4
It is an undisputable part of our common sense view of the world that material things, with which we are all well acquainted, preserve their identity or sameness through various changes in time. 5ince this "sort" of identity has to do with what is going on in or through or across time, it has been called 'dia-chronic' (henceforth DI).6 Thus, for instance, Daniel Novotny ten years ago is believed to be diachronically identical with Daniel Novotny today.But how is this possible?Ten years ago he was much different from what he is today -he was younger, smaller, less educated, lived in a different place, etc. Biochemists will also tell us that there is likely not a single atom of him that he would have both then and today.Now, an easy way out of this problem is to give up our common sense belief and to accept that material entities (persons) do not preserve DI.So, at best, Daniel Novotny is "identical" throughout all those years just in a loose sense -he thinks that way, there is still some resemblance between how he is now and how he was ten years ago,7 etc. Strictly speaking, however, Novotny during all those years is not identical.
Still, there are philosophers who do not want to give up our belief in DI so easily.These philosophers have to account for how there can be entities which apparently both change and remain identical.Two basic strategies seem to be available.The first originates in Aristotle and recently has been called 'endurantism '. 8 According to this view, material things have two types of properties: essential and non-essential.As long as a thing preserves its essential properties it remains DI, i.e. change concerns only non-essential properties.The second strategy is propounded especially to David Lewis and has been called 'perdurantism'.According to this view, material things have only essential properties.So if a thing is to remain DI, it may not change at all.As we proceed, this audacious claim will become clearer.
The two accounts presuppose different ontological "pictures" of what a material individual is.In the first account a material individual is a familiar object of our experience, extended in space but not in time.So Novotny's parts include legs, trunk, hands, head, etc., each occupying the appropriate spatial region.The sum of all these (non-overlapping) regions is the region that Novotny occupies as a whole.In the second account a material individual is extended not only in space but in time as well.Novotny's parts include all his spatial parts at all times at which they existed (or will exist), i.e. during his pre-natal life, childhood, young age, adulthood, etc.Each of these parts occupies a spacio-temporal "region", which is a sub-region of Novotny as a whole.In short, endurantist account takes entities to be three-dimensional whereas perdurantist account takes them to be four-dimensional.9For endurantists any material individual persists through time by existing as a complete whole at any given time at which it exists, whereas for perdurantists any material individual persists through time by existing as a temporal part at any given time at which it exists. 10w it has become clearer why the proponents of the second approach deny the existence of such an all-pervasive phenomenon as change: change is mere appearance due to our minds' transition from observing reality at a time t1 to observing reality at a time t2; reality in itself, however, at any given time, remains unchanged.Novotny at tx is just a part of Novotny as a whole, which is the (mereological) sum of all Novotnys-at-a-time.The illusion that Novotny is changing is just due to the contingent human epistemic condition: we always "see" just a part of Novotny, namely Novotny-at-a-time.
Let us turn now to one of the major arguments that perdurantists advance against endurantism.11Suppose that, P1 Novotny-at-the-age-of-six is non-wrinkled.P2 Novotny-at-the-age-of-sixty-six is wrinkled.

Further, endurantists would hold P3 Novotny-at-the-age-of-six is identical to Novotny-at-the-age-of-sixty-six. P4 Given any two entities, if one is identical to the other, then they have all properties the same.
C There is an entity which is non-wrinkled and wrinkled.Now, P1-P4 obviously imply C. C, however, is false, since it asserts the existence of an entity with materially incompatible properties.So, at least one of the premises must be false.Since for the sake of argument we have assumed that P1 and P2 are true, it is P3 or P4 that must be false.P3 amounts to the endurantist view, P4 to (Leibniz's Principle of) Indiscernibility of Identicals.The latter only few people will be willing to give up and so it is P3 that has to be abandoned.QED.
Following the dictum 'Whenever stuck in contradiction, thou shalt make a new distinction', the endurantists may say, however, that properties are time-indexed.So, the modified argument is: P1' Novotny-at-t1 is non-wrinkled-at-t1 .P2' Novotny-at-t2 is wrinkled-at-t2 .P3' Novotny-at-t1 is identical to Novotny-at-t2 .P4 Given any two entities, if one is identical to the other, then they have all properties the same.C There is an entity which is non-wrinkled-at-t1 and wrinkled-at-t2 .
C is true and so P1', P2', P3', P4 may be true as well and there is no need to give up endurantism.
Unfortunately for endurantists, the costs of this move are high: introducing time-indexed properties entails a very strange and revisionistic ontology -there is no gray or white color as such anymore but only grays-at-tx and whites-at-ty. 12us, it appears that neither endurantism nor perdurantism is very successful in squaring well with all our basic common sense intuitions about material entities, their properties and identity.Aware of the apparent impasse in the discussion between endurantists and perdurantists, Barry Smith in designing BFO attempts to resolve the problem by invoking realist perspectivalism (RP), 13 which may be roughly characterized as follows: Realist moment of RP: There is a reality to which true ontologies correspond independently of actual or possible capabilities of cognitive agents.

Perspectivalist moment of RP:
There is more than one true and irreducible ontology, i.e., more than one irreducible perspective of reality.
A (true) ontology is what we "see" from a perspective: reality as partitioned at its natural joints.A perspective is through which we see reality: a grid or "glasses" which gives us to see some but not all aspects of reality.Perspectives are epistemic correlates of ontologies, which are, of course, ontic. 14Irreducibility of perspectives means that there is no perspective (at least within human reach) from which one could "see" comprehensively all of reality.How does Smith apply RP to the problem of DI? First, he distinguishes between SNAP and SPAN ontology, which corresponds to endurantism and perdurantism respectively. 15Second, appealing to his RP, he asserts the truth of both and the irreducibility of one to the other.SNAP ontology is to be an inventory of entities viewed from the snapshot, i.e. statically; in fact, it is rather a series of ontologies "indexed" at successive instances of time.SPAN ontology is to be "an inventory (processory) of all processes unfolding through time". 16The former is to truthfully capture static aspects of reality whereas the latter dynamic ones.

SNAP/SPAN and Aristotle
In this section I would first like to highlight two Aristotelian insights which are relevant for our current concerns.Then I shall compare these insights with BFO's SNAP/SPAN division.

Aristotle's Insight no. 1: Non-univocity (ambiguity) of 'being'
As Aristotle on several occasions points out, "being is said in many ways".Leaving aside various sophisticated interpretations of this claim, let me present my understanding of it.
The opposite of 'ambiguous' is 'univocal'.Every meaningful word is either one or the other. 17In order for a word to be ambiguous it is necessary and sufficient for it to have more than one normal meaning.In order for a word to be univocal it is necessary and sufficient for it to have only one normal meaning. 18Given the definitions, 'being' is obviously an ambiguous word and this implicates some serious troubles.First, an epistemic trouble: if 'being' is used ambiguously across various domains, these domains should be the subject-matter of various disciplines.Consequently, there would seem to be no "first" philosophy.Second, an ontic trouble: if 'being' is used ambiguously and 'being' is the most general term referring to everything, to the whole of reality, then there would seem to be more than one reality, more than one world! 15BFO is inspired here by ZEMACH, Edward.Four Ontologies.The Journal of Philosophy, 1970, vol.23, pp.231-247.ISSN 0022-362X. 16Strictly speaking, however, this is not true: in SPAN nothing can "unfold", rather, it is "given".This, by the way, explains a fundamental difference between perdurantism (four-dimensionalism) and process philosophy.Process philosophers insist on something like "essential Heraclitean changeability" of processes, whereas for perdurantists processes are simply things with temporal parts.See e.g.SEIBT, Johanna.Process Philosophy.In The Stanford Encyclopedia of Philosophy (Winter 2012 Edition).Ed.E. Zalta, URL = <http://plato.stanford.edu/archives/win2012/entries/process-philosophy/>;RESCHER, Nicholas.Process Philosophy.The Stanford Encyclopedia of Philosophy (Summer 2012 Edition).Ed.E. Zalta.URL = <http://plato.stanford.edu/archives/sum2012/entries/process-philosophy/>. 17The views of the historical Aristotle on ambiguity are more complex since besides "pure" ambiguity (which he calls 'homonymy'), he admits "pros hen" ambiguity.For a detailed exegesis of this point, see HINTIKKA, Jaakko.Aristotle and the Ambiguity of Ambiguity.In Time and Necessity.Ed.J. Hintikka, Oxford: Clarendon Press, 1973, pp. 1−26. ISBN 0-1982-43650. 18 Apparently, in natural languages it is very difficult to find a word that would not be ambiguous.In this sense it is not surprising that the word 'being' is ambiguous.What is usually at stake, however, is not whether a given word is ambiguous but whether it is used ambiguously when applied in two or more given contexts.For instance, the word 'model' is used univocally within fashion industry and within semantics, i.e., taken separately, but ambiguously across these two fields, i.e., taken jointly.
For Aristotle, of course, neither of the consequences is acceptable, the latter perhaps even unthinkable.The solution that Aristotle offers goes along the following lines: The word 'being' is used ambiguously and thus refers to more than one "reality".One of these "realities", however, is primary (namely, the substances) and the others are derivative (e.g.potentiality/actuality).The derivative reality is related to the primary one in that if the primary one did not exist, the secondary one would not exist either.In other words, the latter is existentially dependent upon the former. 19otice, however, that in spite of this dependence the derivative reality is distinct from the primary one (I shall come to this point briefly in the next section).

Aristotle's Insight no. 2: The distinction between essential and potential/actual being
What are the basic domains across which the word 'being' is used?In Aristotle's view there are four: (1) accidental, ( 2) essential (=categorial), (3) true and false, (4) potential and actual (Met V, 7).Aristotle does not elaborate much on ( 1) and ( 3) and these are irrelevant for our concerns anyway.So we are left with the "division" of being into (2) essential and (4) potential/actual.Aristotle's fourfold distinction is, of course, well known.However, it seems that little work has been done in addressing its nature and importance.A notable exception is Jiyuan Yu who has recently argued that the distinction between essential and potential/actual being is the key to understanding Aristotle's Metaphysics VII, VIII, IX, especially for understanding his theory of mater and form (hylomorphism).Leaving aside the technicalities of Aristotle's hylomorphism, it is instructive to quote Yu's characterization of this distinction: The distinction of categorial being and potential-actual being cannot be merely verbal.When Aristotle sets out to distinguish them, I believe that what he means is that they are distinct perspectives or enquiries into reality.Since potentiality and actuality are associated with the analysis of process and function, while categorial being is fundamentally a classification of language and thought which bears on the structure of reality, we may say that the former is a dynamic and the latter a static approach. 20

Aristotle and BFO
Now, let us draw comparisons between Aristotle's views and Smith's views as expressed in BFO.At first sight there are some striking similarities: (A) Smith's RP appears to amount to Aristotle's non-univocity of being doctrine: Smith's 'reality' applies to everything but in each of the (fundamental) perspectives some aspects of the reality are "visible" while others are not -these in turn being visible in other perspectives.So, epistemically speaking, these perspectives are distinct, in fact, they have nothing in common.Ontically, however, they target and are transparent to the same real world.Similarly, Aristotle's 'being' applies to everything but in different senses, i.e., within distinct perspectives.Again, epistemically speaking, categorial and potential/actual being have nothing in common, though ontically speaking they target the same real world (of being). 21(B) Both in Aristotle and in Smith two of the most fundamental perspectives have to do with a static and a dynamic view of reality.
Concerning the last point, however, there is also some dissimilarity.SPAN ontology, following the lead of perdurantism, presents entities (processes) as existing at any moment in time as actual.In fact, within SPAN entities cannot "unfold" in time, they simply are in a timeless manner.In contrast, Aristotle's potential/actual being is intended to capture precisely the changing aspect of reality.
Unfortunately, Aristotle's considerations about potential/actual being involve some conceptual confusion.Aristotle is aware that the being of the future is different from that of the present -the former being 'potential', whereas the latter 'actual'.An entity E is green actually and red potentially if and only if it will (or at least may) become red in the future.As for the being of the past, however, it appears to be neither actual nor potential, whereas in my view it should be classified as 'potential' as well.The reason why Aristotle does not apply potentiality to the past is that he confounds modality 22 and temporality.Potentiality is not distinguished from possibility and since in a sense the past cannot be changed, it is necessary and therefore not potential. 23aving aside the temporality/modality issue, Aristotle is right, I think, in accepting into his potential/actual being the moment of change (i.e., the transition from non-actual to actual) and therefore the fact that the dynamic perspective on reality contains at least two modes of beingactual and non-actual (perhaps even three in order to distinguish the past from the future). 24In this respect, Smith's SPAN ontology fails to be transparent to reality, since all being in it is considered to be actual.It is true that, within SPAN, entities have temporal parts but at most one of these parts is actual.
In my view (pace Aristotle), Roman Ingarden's description of processes is to be taken seriously by any SPAN ontology, which aims to be truly transparent to reality: 21 Moreover, as I have said, Aristotle holds that reality in its categorial being is ontically more fundamental than reality in other senses of 'being' (notably, potential/actual).This seems to be supported by Smith as well.

22
That is, logical modality, where something is logically possible if and only if it does not involve a contradiction.

23
For more elaborate discussion of this point see HINTIKKA, Jaako.Aristotle on the Realization of Possibilities in Time.In Reforging the Great Chain of Being.Ed. S. Knuuttila, Dortrecht: D. Reidel, 1980, pp.57−72.ISBN 9-0277-11259.24   The concept of modes of being is highly suspicious to contemporary analytical metaphysicians.[C]ontinuous transience of the phases constitutes their particular mode of being [of every determinate process].This [mode] is essentially connected with temporality of a process, and is characterized by the following moments: (1) One and only phase is […] actual [during the entire development of the process]; (2) one new phase after another is always becoming actual; (3) an actual phase is continually losing its actuality and a new phase, just then oncoming, is becoming actual; (4) in the instant that the then actual phase occurs, the phases antecedent to it are […] no longer actual […] but have existed previously, while the phases subsequent to it are not yet in existence, but are going to exist (will be actual); (5) in that instant when the last phase attains actuality, the process has already passed. 25 I have indicated, the reason why perdurantist account of processes fails to be transparent to reality is the assumption that 'being' is univocal (that there is only one true perspective on reality).Endurantists correctly hold that (in SNAP view) things do not exist at other time(s) than the present.Perdurantism correctly hold that (in SPAN view) entities exist as extended along temporal line.The mistake, however, on both sides is to suppose that the notion of 'being' involved in both SNAP and SPAN is univocal.

Conclusion
Given my preceding considerations and the difficulties discovered both in the (original) Aristotelian and BFO's view of persistence, let me propose the following hypothesis: SNAP/SPAN Enperdurantism: Any material individual persists through time (1) in SNAP view by existing as a complete whole at any given time at which it exists; (2) in SPAN view by non-actually existing (being) at past and future times.The existence transparent in SNAP view is primary whereas in SPAN derivative.
Enperdurantism, I would claim, has several advantages, integrating the insights of both Aristotle (Ingarden) and Smith.First, it can deal well with the problem I have mentioned at the end of the section on endurantism/perdurantism: In SNAP there are gray or white colors as such -no time index is needed, since SNAP being per se is actual -right now.In SPAN view the colors are time indexed; their being, however, is different (potential, non-actual) from the being to which SNAP is transparent.Second, enperdurantism does justice both to the irreducibility of ontologies (stressed by Smith) and to the unity of reality (stressed by Aristotle).Third, SPAN of enperdurantism fits Ingarden's common sense phenomenological description, which does not seem to be the case with BFO's perdurantist SPAN.
There are, of course, some difficulties as well, such as, for instance, whether the actuality of SPAN is distinct from the actuality of SNAP or whether the past as non-actual is necessary or not.It would further be important to translate the modified SNAP/SPAN into a formal language and test its consistency and adequacy.These are issues for other occasions.The aim of this paper was modest: to suggest a modification in the philosophical underpinning of BFO.The modification, I argued, would make BFO more realistic, i.e., it would help it to "cut reality better at its natural joints".However, to what degree does such modification affect the usability of BFO in practical applications?How necessary is it to deal with it?This is another and much larger issue of how much (philosophical) realism we need in information science. 26 For a recent defense, see McDANIEL, Kris.Ways of Being.In Metametaphysics: New Essays on the Foundations of Ontology.Ed.D. Chalmers, D. Manley, R. Wasserman, Oxford: Oxford University Press, 2009.ISBN 0-1995-46002.