Julie Etienne

Armelle Penhoat

Marie-Caroline Michalski

Carole Knibbe

Uptake of fatty acids by the enterocyte: New insights gained from mathematical modeling

Introduction

Are the observed dose-response curves of apical enterocyte FA uptake compatible with the pathways suggested by the literature? Uptake of fatty acids by enterocytes is debated in the literature and usually reviewed as a dual mechanism . 20, 349-356. Goré, J., andHoinard, C. (1993) J. Nutr. 123, 66-73. Murota, K., andStorch, J. (2005). J. Nutr. 135, 1626-1630. Stremmel, W. (1988). J. Clin. Invest. 82, 2001-2010.

Conclusion Take-home messages Perspectives

• New experimental uptake data to improve our understanding

• Gaining insights on sensitive topics using quantitative and mechanistic modeling

• pH enhances uptake

• Passive diffusion alone (M0) is not sufficient to provide realistic uptake responses

••

  For intermediate parameter values Dose-responses : collection time set to 10min .pH enable greater uptake responses and slope discontinuities Further study of dose-responses at different collection times For parameter maximizing the uptake 7 Experimental data • 7 datasets • Digitized from research papers using WebPlotDigitizer 1 Expressed in the same units of measure (µmol/mg protein/min) using conversion factors found in the literature Data fitting • MCMC algorithm (FME package, R) (Bayesian methods) • Parameter a posteriori distributions -We have >1,000 values for each parameter for each model and each dataset GERLI 16 th Lipidomics Meeting 26 -29 th September 2021 Material and Methods 10 GERLI 16 th Lipidomics Meeting 26 -29 th September 2021 Result 3 M2 and M2.pH show better quality of fits (The lower the normalized RMSE, the better the fit) Quality of fits 11 GERLI 16 th Lipidomics Meeting 26 -29 th September 2021 Result 4 Responses of M0 and M1 are far from data (even with pH) • Responses of M2 and M2.pH are close to data Only M2 and M2.pH show slope discontinuities 10 Data fitting Chow, S.L., and Hollander, D. (1979a) J. Lipid Res

•

  Adding an intracellular enzymatic transformation of FA (M2) is more efficient for the enterocyte than adding a membrane protein (M1) On-going submission of a research paper 11 Open to discussion! Images: https://www.pinclipart.com/

pH variation of each model: pKa = 7.5

Rohatgi, A. (2020). WebPlotDigitizer (Pacifica, California, USA) https://automeris.io/WebPlotDigitizer/

Thank you to the GERLI committee We thank the lipid team at CarMeN laboratory and the Beagle team at Inria We are also grateful to Samuel Bernard, Fabien Crauste, Sylvie Demignot, Frédéric Carrière, and Hugues Berry for fruitful discussions Special thanks to Paul Banse who helped improving this presentation GERLI 16 th Lipidomics Meeting 26 -29 th September 2021 Acknowledgments


Georges Mrlina

Guy Lemperiere

Jean P Calmon

Determination and Uptake of Carbosulfan and Carbofuran in Young Douglas Firs (Pseudotsuga menziesii Mirb.)

Keywords: Insecticide, carbofuran, carbosulfan, Hylobius weevil, Douglas fir, uptake, formulation

Protection of young Douglas firs and other conifers from attacks by the large pine weevil, Hylobius abietis L. (Col. Curculionidae), consisted of repeated insecticide treatments by dipping or spraying with organochlorine or py rethroid insecticides. The use of a controlled-release formulation as Marshall SuSCon containing the systemic carbamate insecticide carbosulfan in nurseries or on reforestation sites as a single treatment at planting time ensures a good level of protection. Using gas chromatography as a standard analytical method, carbofuran, a byproduct of carbosulfan, was detected and admitted to be the effective product. Its penetration in young plants is quick, and high leve::..•of this product are observed 24 months after treatment. Comparisons between nursery and field trials show good protection of young Douglas firs over the critical period of establishment of the plantation with this formulation.

INTRODUCTION

To limit this damage, a controlled-release formulation of the carbamate insecticide carbosulfan (100 g/kg) was tested with a single application at planting time. The dry, dust-free granular formulation Marshal/SuSCon provided superior protection from attack by H. abietis when compared to the less environmentally benign standard practice of repeated spraying/dipping with synthetic pyrethroids or organochlorine insecticides [START_REF] Julien | Estimation of the long-term effectiveneaa of a system ic insecticide sgainst the Large Pine Weevil, Hilobius abietis L. (coL Curculionidae)[END_REF]. Marshal is the trade name from FMC Corp.

for the active ingredient carbosulfan, and SuSCon is the trademark oflncitecLtd. for the controlled-release granule formulation of carbosulfan. Protection of young Douglas fü,Pseudotsuga men8iezii (Mirb.), was demonstrated with the Marshal/SuSCon formulation through a set of 22 field trials (Lemperiere and Julien, 1989). The mode of action of the systemic insecticide and its uptake into the plant have been characterized using analytical methods.

This study was designed to determine the rate and pathways of penetration of both carbosulfan and its main byproduct, carbofuran, in Douglas fir (Figure 1). 1. Standard deviation of the whole-stem samples is lower than that of the pa:rtitioned stems, since they have approximatelythesame growth stage (weight and spread).

MATERIALS AND METHODS

Nursery

According to the rootspread and to the spatial distribution of granules around the root system, standard deviation in carbofu:ran uptake will be large. Levels for 28 days have the same range as for 150 days for both upper and lower parts (Table 1). For the whole stem, the increase rate of carbofu:ran over time is related to plant growth.

Field Study. The controlled release of carbosulfan from

Marshal/SuSCon granules occurs over a 2-year period (Cooper et al., 1986). The level of carbofuran in plant tissue was thus determined over time (Table 2). The observed concentration of carbofuran in the stem decreased with time. This may in part be due to the growth of the plant since the granules deliver the same quantity of insecticide. Despite this, field trial results after 18 months show that some damage by the insect was tolerated by the plant in :relation to the increased size of the plant (Lemperiere et al., 1989).

Table 3 gives the quantity of carbofuran per plant according to the weight of each plant. The results are similar for the 5and 18-month samples and show a slow decrease after 24 months. For the 30-month samples, the fall in carbofuran content (LP, 7 .91,ig; UP, 8.91,ig; WS, 16.5 1&g) could be attributed to the exhaustion of the active ingredient in the matrix. The progressive exhaustion of carbosulfan in the granules could be reflected by a decreasing intake of carbofuran in the plant and a possible decreasing concentration of carbosulfan in the soil.

Dose Effect.

The dose effect is dependent on the standard deviation of the samples in relation with the inhomogeneity of distribution of the granules in the soil. After 28 days, the higher treatment rate (100 g of ai/m 2 led to a significant difference in the level of carbofuran in the plant when compared with the low treatment rates (Table 4). This difference was also reflected in results from the field study, where the treatment at 0.8 g of ai/ plant provided good protection when compared with treatments at 0.2 and 0.4 g of ai/plant.

DI SCUSSION AND CONCLUSION

ln this study, plants treated with Marshal/SuSCon granules were protected from 3 weeks after treatment up to 24 months and carbofu:ran level was estimated to be stable during this period, in relation with a continuous absorption of the active ingredient present in the soil, the growth of the plant, and its potential metabolizing activity. The effective concentration in Douglas firs seems to be dependent on the available concentration of active in gredient {carbosulfan or carbofuran) in the soil and is obtained for rates as 100 g of ai/m 2 or 0.8 g of ai/plant. Due to the mode of action of the granules, there is a need for the root system to forage through the whole treated area for a full efficacy of uptake of carbofuran, and a high coefficient of variance can result in the observed residue levels in both nursery and field plots.

Nursery. The plant carbofuran uptake rate is quite fast, and effective concentrations are reached within 3 weeks (Table 1). The high levels observed in Douglas fus are consistent with those observed in Mugho pine by Pree andSaunders (1973, 1974), where a high concentration was noted in the 24-day needle samples and where metabolism of carbofuranseems to be slowerthan in other plants. An analytical study done in the same conditions on the roots showed that a typical :r.ylemic translocation pathway of carbofuran may be suspected si nce the concentration is decreasing from the roots to the upper part {roots, 30-40 ppm; LP, 20 ppm; UP, 14 ppm for 28 day samples).

Field. The observed levels of carbofuran in the young Douglas firs are corroborated by the field results dem onstrating an efficient protection of the young trees 24 months after treatment (Lemperiere and Julien, 1989). The decrease in carbofuran concentration may be due a metabolic pathway of carbofuran, which cannot be the same as for a "one-dose" application since the plant is in constant contact with the carbosulf a n-<: a rbofuran com plex. The age of the plant may also affect the• way the plant responds to the presence of these insecticides and changes the metabolic pathways propoeed by Umetsu et

al. (1980) and by Pree and Saunders (1973).

Investigation of 3-hydro:r.ycarbofuran, wbich could be considered another insecticidally active molecule and a major metabolite of carbofuran, was undertaken using the 18-month samples and the analytical method of Nelsen and Cook (1983). This metabolite could not be detected at a significant level, suggesting that the metabolism of carbofuran in Douglas fir could be different from that occurring in other plants as mentioned by [START_REF] Pree | Metabolism of carbofuran in M ui ho pine[END_REF]. These authors proposed N-(hydro:r.y methyl)carbofuran {2,3-dihydro-2,2-dimethyl-1, 7-benzo furanyl N-{hydro:r.yethyl)carbamate), which can be me tabolized into carbofuran phenol, as the major metabolite. However, carbofuran phenol could not be detected under our chromatographie conditions .since our gas cbromato graph was not set up to detect it. Although we could not confirm theN-(hydrox.ymethyl)carbofuran pathwayin this study, it is postulated as the major breakdown product of the carbofuran residues in these plant samples.

As residue levels are constant 5-18 months after treatment, showing a slow decrease after 24 months and ensuring good protection of the young trees over the critical period of establish ment of the plantation, it is of major environmental interest to use this long-term controlled release formulation in forestry.

  The large pine weevil, Hylobius abietis L. (Coleoptera: Curculionidae), is one of the most serious pests of young conifer plantations throughout Europe, generally. after Scotch pine or Norway spruce mature forests have been clear-cut. The insectdevelops in the roots of fresh stumps, and adult weevils emerge in March-April and feed on the• bark of newly planted trees, causing damage and death of the. plants by ring-bar king. Young conifers are most susceptible during the füst 2 years after planting.

  Plots. The field trials were conducted at Saint Junien-la-Brégère (Creuse, France), in a forest nursery, and at Perols-sur-Vezere (Correze, France), on a reforestation site, both on brown acid soil, pH 5.5. In the nUISery, Marshal/SuSCon granules were applied at the rates of 25, 50, and 100 g of ai/m 2 incorporated into the soil, near the root system of 3-year-old t Ecole Nationale Supérieure A gr onomique de Toulouse. * Université Paris VII. ? Figure 1. Studied structures: carbosulf a n (1) and carbofuran (2). Douglas füs. On the basis of our calculation, an appromnate level of 0.2 g .of ai per plant could be found with the higher rate. Field Plots. On the reforestation site, Marahal/SuSCon granules were applied at a rate 0.8 g of ai/plant at planting time in April 1987, in the planting hole before the 3-year-old Douglas firs were placed. Asse1sment1 and Sampling. Nursery. Each plotoontained 100 trees, and samples of 5trees per dose were randomly collected 7, 14, 21, 28, and 150 days after treatment. Semples were stored in plastic b ags at -20 °C until analyzed. Fi.eld Site. Samples of 5 trees were randomly collected on a subplot of 50 trees treated at 0.8 g of ai/plant 18, 24, and 30 months after treatment. $amples were stored in plastic bags at -20 °C for transport. Residue Analysis. Sample Preparation. In the laboratory, roots and branches were discarded and the remaining stems were frozen (-20 °C). • For each sample of five young Douglas firs, stems were weighed. The stems of two medium-weight plants were directly analyzed, and the stems of the three remaining plants were separated into a lower part (LP), where mostHylobius damages occur, and an upper part (UP) including the terminal bud. ExtractionProcedure. The extraction procedure is similarto the one used by Leppert et al. (1983) for low-moisture crops and takes into account their modification for acidic crops (Leppert et al., 1984). Subsamples (3-20 g) were eut in emall pieces and blended with a Waring Blendor for 3 min in 100 mL of a 9:1 (v/v) mixture ofmethanol/pH 8 phosphate buffer. The ground stem was macerated for 10 min and then ftltered through Büchner funnels lined with ashless paper. The filter cake and the filter paper were again blended for 3 min with a second portion of the extraction mixture. The blending jars and the filter cakes were rinsed with 50 mL ofblendingsolvent. The volume of eachsample was adjusted to 300 mL with the blending solvent. Aliquote of 100 mL were transferred in a 250-mL separatory funnel and diluted with 100 mL of borax buffer (0.0052 M) containing 15 g of sodium chloride. The sample was extracted three times with

  A Hewlett-Packard 5890 gas chromatograph equipped with a nitrogen-selective detector was used in a splitless mode of injection (Ripley and Braun, 1983). The operating parameters were as follows: carrier gas, nitrogen (1 mL/min); column, 25 m X 0.32 mm fused silice. column with HP-1 flhn (0.17 µm); injector temperature, 250 °C; initial oven temperature program, � °C for 1 min, raised 200 °C at a rate of 35 °C/min, and maintained at this temperature for 4 min; second plateau at 240 °C reached at 20 °C/min and maintained for 5 min. Chromatograms and quantification were performed using a Spectra-Physics Chromjet integrator. Peak areas of responses in samples were compared to external standards of carbosulfan and carbofuran. The standard molecules were provided by Dr. Ehrenstorffer GmbH Co. and 3-hydroxycarbo furan by FMC Corp., Brussels, Belgium. RESULTS Carbosulfan was not detected in the different parts of the stem, except in some low-weight Douglas fin. As U metsu et al. (1980) reported high :rates of decomposition of carbosulfan into carbofuran under acidic conditions, a study was conducted on the :root system of plants sampled on the field site (pH of the soi l, 5.5). Roots were washed with water, prepared,and analyzed as previously desc:ribed for the stems. After 28 days, the carbosulfan level ranged between 3.70 and 5.22 ppm for an 8.0-g treatment of Marshal/SuSCon per plant. The corresponding levels of carbofu:ran were 27.0 and 42 ppm. After a flash washing of the roots with methanol, only carbofuran was found at a level of 34 ppm. Carbosulfan did not seem to penetrate into the roots. This fact confümed the results of analysis of the aerial parts of young Douglas firs. Traces of carbosulfan may then be due to a contamination at sampling time, and protection of the plants against Hylobius may then be attributed to carbofu:ran. Partition of Carbofuran in Douglas Firs vs Tim.e . of Contact with Marshal/SuSCon Granules. Nursery Study. Observed levels of carbofuran are shown in Table

Table 1 . Residues of Carbofuran in Douglas Fin Treated iD the Nursery at 100 g of ai/m 2 residue level, ppm part Of plantG

 1

		7days	14days	21days	28days	150 days
	LP UP WS	0.40 (0.11) 0.57 (0.09) 0.63 (0.06)	5.15 (0.55) 2.64 (0.78) 3.23 (0.04)	16.24 (3.44) 11.86 (3.78) 7.20 (0.40)	20.71 (0.36)� 14.34 (3.15) 7.73 (0.20)	17.90 (7.50) 14.15 (2.27) 18.61 (1.04)

4 LP,

lower part or attackabluone; UP, upper part; WS, whole stem. � Mean value for two plants;for tbree plants the values are 14.97 (9.94). 50 mL of methylene chloride; each portion of methylene chloride was filtered through anhydrous sodium sulfate, and the total volume per aliquot was noted. This extract could be partially ooncentrated or directly used for chromatographie injection. No cleanup was necessery. Under these conditions carbosulfan and carbofuran were coemacted. Gas Chromatography Analysis.

Table 2 . Residues of Carbofuran iD Douglas Fin in the Field witb a Manhal/SuSCon Formulation (10% ai

 2

	)
	residue level, ppm

.04) Quantitiet of Carbofuran Becovered per Plant at Different Times alter Tnatment Aecording to the Weïtht of Each SamplP. time treatment part of plant range,pg median,pg 5months 100 g of aî/m 2

	18months 8 g/plant 24months 8g/plant	LP UP ws LP UP ws LP UP ws	93.1-181.9 33.5-61.3 141.&-236.3 113.2-173.9 32.5-74.0 134.4-267.2 72.5-98.7 32.2-52.0 121.&-152.8	124.7 42.8 179.5 143.6 53.3 200. 8 85.6 42.1 129.4

Table 4 , Residues of Carbofuran in Douclas Fin of the Nursery 28 Days alter Treatment at Different Dates part of plant LP UP ws residue level, ppm, at application rate of 25 g of aî/m 2 50 g of aî/m 1 100 g of ajjm 2 7.18 (4.55

 4

	) 6.04 (2.64) 9.89 (3.18)	7.69 (4.13) 4.58 (2.32) 9.21 (8.03)	14.97 (9.94) 14.34 (3.15) 7. 73 (0.20)

ACKNOWLEDGMENT

We are very grateful to Incitec Ltd., Brisbane, Australia, for financial support and to FMC Corp., Brussels, Belgium. W e are thankful to Dr. D. Bevan, who initiated the project, P. D. May and M. Valvasori, Incitec Ltd., and M. Hullebroeck, FMC Europe, for reviewing the manuscript.


Baptiste Le Bihan

Adrien Barton

Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology

Keywords: analytic metaphysics, naturalized metaphysics, applied ontology, philosophy of physics, biomedical ontology

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French &

McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field.

Introduction

According to Ladyman & Ross (2007) ("L&R" hereafter) analytic metaphysics should be discontinued because of its lack of emphasis on scientific knowledge that makes it a waste of intellectual resources. Although most analytic metaphysicians 1 would 1 Here, we do not take stock on the nature of the relation between analytic metaphysics and naturalized metaphysics (e.g. the question of whether the latter is actually a part of the former according to some definitions of the fields), although we will argue at the end that analytic metaphysics should not be discontinued and can evolve largely independently from metaphysics of science.

presumably believe that their discipline has intrinsic value insofar as it describes the actual world or the field of possibilities, L&R deny this. They focus especially on the appeal of intuitions, and argue that intuitions are the "product of cultural learning" and that many philosophers "do not share as many intuitions with the folk as they usually suppose" (Ross, Ladyman & Spurret, 2007, 12). But they do not condemn only the kind of analytic metaphysics based on intuitions (cf. ibid. 17-27). The scope of their criticism is broader, and they seem to despise any form of metaphysics which is not firmly empirically grounded -as when they ask: "Metaphysicians seek to understand the general composition relation itself. But why suppose that there is any such thing?" (ibid., 21).

Asking when such a thing obtains or not, and whether it is restricted or universal, would then be a waste of time. In short, according to them "Mathematics and science have undoubtedly borne fruits of great value; a priori metaphysics has achieved nothing remotely comparable, if it has achieved anything at all" (ibid., 16). From this, they conclude that: "No scientist has any reason to be interested in most of the conversation that now goes on under the rubric of metaphysics" (ibid., 26).

A popular answer to this charge is the heuristic approach to metaphysics offered by [START_REF] French | Rethinking Outside the Toolbox: Reflecting Again on the Relationship Between Philosophy of Science and Metaphysics[END_REF] ("F&M" hereafter). According to them, analytic metaphysics develops many methods and tools that already turned out to be useful for philosophy of physics. Independently of whether Ladyman & Ross (2007) are right that analytic metaphysics lacks any intrinsic value when it comes to the truth 2 , analytic metaphysics thereby remains a fruitful enterprise 3 . Therefore, because of its heuristic value for philosophy of physics, analytic metaphysics should not be discontinued. For instance, philosophers of physics working on loop quantum gravity or string theory (e.g. [START_REF] Huggett | Emergent Spacetime and Empirical (In)Coherence[END_REF], trying to explain what it could mean that space and time, or 2 One could argue that metaphysics has intrinsic value, but that this intrinsic value has nothing to do with truth -see for instance [START_REF] Benovsky | Meta-metaphysics: On Metaphysical Equivalence, Primitiveness, and Theory Choice[END_REF] who defends the claim that metaphysical views do have values grounded in their beauty. But we will not consider these forms of value not grounded in truth within the scope of this paper.

3

Our only disagreement with Ladyman & Ross in this article is about their claim that analytic metaphysics should be discontinued. We are otherwise sympathetic to their claim that special sciences must be taken into account in order to address metaphysical questions. They raise in particular another interesting issue, that we do not address here, about the status of folk metaphysics and what they call "notional worlds". relativistic spacetime, are not fundamentally real, will build on theories about emergence, fundamentality, or metaphysical views on space or time.

The heuristic approach strikes us as a good motivation to accept that we should not discontinue analytic metaphysics. In this article, we do not defend, or argue against, the intrinsic value of analytic metaphysics; we only discuss the extent of the value of metaphysics for other domains, and whether constraining research in metaphysics could maximize this heuristic value. In particular, we complement French's and McKenzie's argument by showing why the heuristic value of metaphysics depends not only on the way it is presently used, or could be used in the future by philosophers of contemporary physics 4 , but also on the way it is or could be used in applied ontology. Therefore, our first goal -in section 2 -is to offer new examples of the utility of analytic metaphysics for other fields. Our second goal -in section 3 -is, taking the first conclusion into account, to elaborate on a parallel between the heuristic justification of analytic metaphysics and the instrumental justification of mathematics, in order to argue that analytic metaphysics could continue to exist as a largely autonomous field.

A Toolbox for Applied Ontology

Applied Ontology

In this section, we argue that we may extend the heuristic justification of analytic metaphysics beyond philosophy of physics 5 . We agree with French and McKenzie that ana-4 "Philosophy of contemporary physics" will denote here the set of philosophical investigations on our most fundamental empirically confirmed physical theories since the quantum and relativistic revolutions (general relativity, quantum field theory) and all the philosophical investigations on the research programs aiming at making at least a step towards a theory of quantum gravity (string theory, loop quantum gravity, non-commutative geometries, causal set theory, etc.). 5 Special sciences played a crucial role in this debate since Ladyman & Ross (2007) includes a chapter devoted to special sciences (see Ross,Ladyman & Collier,chapter 4). The crux of its content is that special science ontologies always have, in fine, to be consistent with the ontology of physics. As they write (Ross, Ladyman & Collier, 2007, 190): "failure of an interpretation of special science generalizations to respect negative implications of physical theory is grounds for rejecting such generalizations". In this perspective, the role of metaphysics, according to them, is to offer a general unification of sciences, being granted that physics rules out some otherwise possible ontological interpretations of special sciences. lytic metaphysics is an important toolbox for the philosophy of physics. But, as we shall see, analytic metaphysics has other applications in a field of information science named "applied ontology". The point is important as it shows that analytic metaphysics has many possible applications, and that the methodological constraints that some philosophers of physics may be eager to put on metaphysics are related to physics, and do not take into account other scientific practices. As we shall see, analytic metaphysics can be at the same time at odds with physics and extremely useful for applied ontology.

Applied ontologies are structured terminological frameworks that can be represented as computer files or more generally in a logical format. One of their aims is to enable semantic interoperability between data concerning the same domain: indeed, various information systems use different terminologies and vocabularies, which make their data often difficult to gather, share or re-use; ontologies aim at providing a unified, structured terminology that can serve as common language between those information systems. Applied ontologies are formal representations of the various categories of entities in a domain, and the relations that hold between them. For example, FMA (Foundational Model of Anatomy; cf. [START_REF] Rosse | A Reference Ontology for Biomedical Informatics: the Foundational Model of Anatomy[END_REF] is an ontology of human anatomical entities and their relations; it contains a variety of terms among which Organ, Mitral_valve and Peri-cardial_sac. Those terms are organized along a taxonomic structure, with formal statements (commonly called "axioms" in the field) involving the is_a relation such as Heart is_a Organ, which means that every instance of heart is also an instance of organ. But the ontology also encompasses mereological relations such as constitutional_part_of or at-tached_to, that enable to formalize axioms such as Mitral_valve constitutional_part_of Heart. Moreover, the logical properties of these relations, such as transitivity or reflexivity of the relation part_of, are also specified.

Applied ontologies are nowadays developed and used in a large variety of domains such as education [START_REF] Mitrovic | A Model of Multitutor Ontology-based Learning Environments[END_REF] or geography [START_REF] Mark | A Research Agenda for Geographic Information Science[END_REF]. In particular, they are becoming more and more important in biomedical sciences, with a notable large initiative of building ontologies on common, rigorous metaphysical principles named the "OBO Foundry" [START_REF] Smith | The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration[END_REF]. Such ontologies should enable the re-usability of biomedical information contained in journals, clinical trials and electronic health records by the clinicians and researchers of the domain. But they must be built on solid bases to enable interoperability, and philosophical ontology has an important role to play here. As a matter of fact, developing rigorous and exhaustive applied ontologies raises issues very similar to those that are classically raised by philosophical ontology, and it has become clear that the success of the former will depend on building upon the theories and methods of the latter. In many respects, building a coherent and solid applied ontology of biomedicine amounts to building a formalized, philosophical ontology of biomedicine.

We will now present two arguments with a focus on the OBO Foundry biomedical applied ontologies as a case study. First, we will argue that metaphysical principles that are not particularly associated with contemporary physics, but rather grounded in the work of analytic metaphysicians, can be helpful for building biomedical applied ontologies. Second, we will argue that it might be too difficult or even counter-productive to try to build an applied ontology of biomedicine on the basis of contemporary physics.

As we will see, taken together, those arguments show that analytic metaphysics can have a high heuristic value for building an applied ontology, even if it was developed without taking into account the lessons of contemporary physics.

From analytic metaphysics to applied ontology

Applied ontologies are often based on metaphysical principles that are not inspired by contemporary physics. These principles are sometimes closer to common sense (and the naïve physics coming with it) or classical physics. This is especially obvious in the applied ontologies that explicitly claim to capture the ontological categories underlying human common sense and natural language, such as DOLCE (Descriptive Ontology for Linguistic and Cognitive Engineering; [START_REF] Gangemi | Sweetening ontologies with DOLCE[END_REF], which is developed to ease interactions with human agents by "making already formed conceptualizations explicit" [START_REF] Masolo | Wonderweb deliverable d18, ontology library (final)[END_REF].

Other applied ontologies do not rely as explicitly on human common sense but aim at providing an ontology compatible with some special sciences such as biomedicine, where the first aim is not to develop metaphysical principles inspired by contemporary physics. This is due to the fact that for their largest part, many special sciences such as biomedicine do not require the use of physical models more elaborate than naïve or classical physics (with a few possible exceptions such as quantum biology -cf. [START_REF] Lambert | Quantum Biology[END_REF].

Consider the example of the Basic Formal Ontology (BFO; cf. [START_REF] Arp | Building Ontologies with Basic Formal ontology[END_REF], which is used in particular in the context of the above-mentioned OBO Foundry project that aims at devising a set of interoperable biomedical ontologies. BFO introduces high-level categories 6 such as "occurrent" and "continuant". Occurrents are entities that persist through time by having temporal parts, such as the process of the life of a specific tree. Continuants are entities that persist through time by being wholly present at each time at which they exist. They are divided between independent continuants, namely entities whose existence does not depend on the existence of another entity (such as material objects, e.g. a leaf) and dependent continuants, namely entities whose existence depends on the existence of another entity (such as qualities -e.g. the green color of a leaf -or dispositions -e.g. the fragility of a twig). This distinction between occurrents and endurants can be traced back to William Johnson, the teacher of Bertrand Russell [START_REF] Jansen | Categories: The top-level ontology[END_REF], and has benefited in contemporary philosophy from [START_REF] Lewis | On the Plurality of Worlds[END_REF] analysis of "endurance" and "perdurance".

BFO also rests on a distinction between universals and particulars -e.g. the universal of a tree versus this particular tree. Arguably, those distinctions are closer to the constructs that may be found in analytic metaphysics than to many forms of naturalized metaphysics; indeed, the broadly Aristotelian inspiration of such an ontology has been emphasized regularly [START_REF] Jansen | Categories: The top-level ontology[END_REF]Smith & Ceusters, 2010). Grenon (2003) speaks of Smith (1997) as a "neo-Aristotelian metaphysics of substances". Furthermore, definitions in the OBO Foundry are expected to take the "genus-species" form of so-called 6

In this text, we use "category" and "class of entities" as synonymous, with a broad understanding of the term "entities" that covers structures. "Aristotelian definition", where an A is defined as a B that C's, where B is a parent class of A, and C is the difference characterizing the instances of B which are also instances of A [START_REF] Smith | The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration[END_REF] -on the model of Aristotle definition of "human" as an animal that is rational. Note however that the structured taxonomies developed in the OBO Foundry far exceed in terms of sophistication and complexity what Aristotle could have produced -as they capitalize on thousands of years of biomedical sciences.

Note that other ontologies -such as the ones developed in the DOLCE galaxy -do not endorse explicitly the same Aristotelian inspiration, but acknowledge their debt to philosophers such as Strawson, Searle, Simons, Varzi and Casati [START_REF] Gangemi | Sweetening ontologies with DOLCE[END_REF] or Quine, Goodman, Sider and Kit Fine [START_REF] Bottazzi | The Mysterious Appearance of Objects[END_REF]) -many of which are also cited in the BFO-inspired literature. Finally, relations that are classically studied in analytic metaphysics have attracted considerable attention from the applied ontology community -such as mereology, sometimes combined with topology [START_REF] Masolo | Atomicity vs. infinite divisibility of space[END_REF][START_REF] Smith | Ontology and Geographic Kinds[END_REF].

Such ontologies are then used for various scientific projects of data structuring and exchange. For example, the ontology CDIM (Clinical Data Integration Model) [START_REF] Ethier | Clinical Data Integration Model: Core interoperability ontology for research using primary care data[END_REF], which is based on BFO and other OBO Foundry ontologies, has been used in the context of the TRANSFoRm project [START_REF] Ethier | The TRANSFoRm project: Experience and lessons learned regarding functional and interoperability requirements to support primary care[END_REF], a proof of concept of a learning health system used to exchange data from five different clinical and genomical databases across four different countries, to support retrospective data analysis, prospective recruitment of patients for clinical data trials, and decision aid. This ontology avoided classical mistakes in classification by being based on BFO, which relies on sophisticated theories concerning e.g. persistence across time, inherence of properties and the ontological nature of information. Such uses also exist in other domains -for example, mereotopological theories have been used to support geographical information systems.

Interestingly for our purpose, the BFO ontology does not aim (yet) at addressing metaphysical issues raised by our most fundamental theories in contemporary physics.

According to quantum field theory, the basic units seem to be excitations of fields, and several problems appear for an ontology of particles in this context. For instance, the number of field excitations seems not to be constant through time and, therefore, if we want to identify particles with excitations of fields, we must accept that the number of particles within a physical system is not constant through time 7 . It shows that it is difficult to view particles as continuants that would endure across time for long periods (for a more general discussion of the issues raised by the category of object/particle in physics, see [START_REF] French | The Structure of the World: Metaphysics and Representation[END_REF]. However, an ontology of material objects persisting for a long time is consistent with the claim that these objects are composed of an always shifting number of particles. This shows that it could make sense in the macroscopic domain to conceive of material objects and their properties as enduring across time, as proposed by BFO.

Leaving QFT aside, BFO allows objects to have both well-defined positions and velocities8 at a single time, which is at odds with quantum mechanics. However, the absence of mutual constraints between positions and velocities is an excellent approximation in the macroscopic realm. Furthermore, BFO endorses a "container view" of space, which holds that "spatial regions are entities in their own right" [START_REF] Grenon | SNAP and SPAN: Towards Dynamic Spatial Ontology[END_REF]) -a view related to the "substantivalist" view (cf. for instance Le Poidevin 2004, Benovsky 2011 in the metaphysical literature and for instance Earman & Norton 1987, Pooley 2013 in the philosophy of general relativity literature). According to this container view, endurants "can be located at or in them" [START_REF] Grenon | SNAP and SPAN: Towards Dynamic Spatial Ontology[END_REF]. BFO considers that a reference frame is implicitly defined out of the formal apparatus of the ontology (typically, the reference frame of the Earth), and that spatial and temporal regions are defined relatively to this reference frame [START_REF] Arp | Building Ontologies with Basic Formal ontology[END_REF]. BFO's apparatus that includes such spatial and temporal regions (on top of spatiotemporal 7

The compatibility of an ontology of particles with QFT is still debated -cf. for instance [START_REF] Halvorson | No Place for Particles in Relativistic Quantum Theories?[END_REF] and [START_REF] Baker | Against Field Interpretations of Quantum Field Theory[END_REF]. Also, Le Bihan (2015) argued that if we accept the reality of dispositions, then a description in terms of particles seem to be redundant with a description in terms of dispositions. In this section, we do not take stance on the reality of particles.

regions, which are more in line with general relativity) has proven to be highly efficient for formalizing special sciences like biomedicine.

Note also that the classical debate between substantivalism (the view that spacetime is a substance that can exist independently of its material content) and relationism (the view that spacetime is the name of the collection of material relations obtaining between objects or events) has taken a new direction with general relativity. Whatever the best ontological interpretation of general relativity and of any forthcoming theory of quantum gravity turns out to be, it will likely need to account for three kinds of entities: spacetime points, the metric field and matter fields 9 . However, such considerations are not useful for dealing with some special sciences such as biomedicine, and therefore are currently not yet integrated in BFO's ontological framework.

It is worthy of attention that applied ontologists engaged in the BFO project take those inputs from physics seriously, and BFO is engaged in a continuous process of modification to account for a larger portion of contemporary science. Thus, although BFO's ontological framework is based on principles drawn from analytic metaphysics, it aims at integrating progressively inputs from advanced science. But our point here is the following. Although some current features of BFO's formal framework (classical time and space, construal of material objects as independent continuants) may be classified as belonging to analytic metaphysics and are not yet fully aligned with contemporary physics, they are adequate for most of biomedical science -and, arguably, several other special sciences. Therefore, metaphysical principles found in analytic metaphysics have proven to have a high heuristic value not only for philosophy of physics but also for 9 Any solution to Einstein's equations of general relativity is a triple <M, g, T>, M being a manifold of points with coordinates and some weak topological structure, g being the metric field (which carries the information about the metric, i.e. the spatial, temporal and spatio-temporal relations between spacetime points, and the local curvature of spacetime) and T the stress-energy tensor that relates in particular the metric field g to the matter field Φ (the distribution of matter, from which we may derivate the gravitational field). In this framework, it is not clear whether spacetime should be identified with the manifold, with the metric field, or with the conjunction of the manifold and the metric field. In fact, there are two distinct debates, one about the relationship between the manifold M and the metric field g or, moving from the mathematical level of description to the physical level, between spacetime points and the physical metric field described by g (cf. for instance [START_REF] Esfeld | Moderate Structural Realism about Spacetime[END_REF], the other one about the relationship between the manifold M and the metric field g on the one hand, and the matter field Φ on the other hand (see [START_REF] Pooley | Substantivalist and Relationist Approaches to Spacetime[END_REF]. applied ontologies, even though these principles were developed to describe the natural world without engaging with contemporary physics.

Finally, note that some metaphysical theories have been used in both philosophy of physics and applied ontology. Consider for example the metaphysical theory of disposition, on which there has been a long string of investigations in analytic metaphysics, including milestones such as the influential work of [START_REF] Mumford | Dispositions[END_REF]. Dispositions have been invoked for interpreting quantum mechanics (see e.g. [START_REF] Dorato | GRW as an Ontology of Dispositions[END_REF]. They also have been adapted in applied ontology to the framework of BFO by [START_REF] Röhl | Representing Dispositions[END_REF], who endorse Mumford's 10 realism about dispositions and retain his distinction between a disposition and its categorical base -a framework that has been refined by an analysis of the mereological structure of dispositions [START_REF] Barton | A taxonomy of dispositionparthood. FOUST II: 2nd Workshop on Foundational Ontology[END_REF].

This theory was then used to formalize various kinds of entities, such as diseases [START_REF] Scheuermann | Toward an Ontological Treatment of Disease and Diagnosis[END_REF], functions [START_REF] Spear | Functions in Basic Formal Ontology[END_REF] or probabilities in medicine [START_REF] Barton | An Ontological Analysis of Medical Bayesian Indicators of Performance[END_REF]. Thus, a theory that was developed out of the field of naturalized metaphysics later found its way in both philosophy of physics and biomedical applied ontology.

Applied Ontology Sans Contemporary Physics

We now argue that views found in analytic metaphysics may have a higher heuristic value for biomedical applied ontology than views that would be founded on metaphysical principles related to contemporary physics, for two reasons.

First, an ontology built upon a non-physicalist methodology might facilitate computations. Automatic reasoners such as Hermit [START_REF] Shearer | HermiT: A Highly-efficient OWL Reasoner[END_REF] or Pellet [START_REF] Sirin | Pellet: A Practical OWL-DL Reasoner[END_REF] are used to test the coherence of an ontology and its logical consequences, but the computation times quickly become too 10 Note however that contrarily to Mumford who sees a disposition and its categorical base as identical at the token-level, Röhl & Jansen would see them as different entities that belong to two different categories, namely (set of) qualities vs. realizable entities.

long for any practical purpose if the ontology is too convoluted; using somewhat simpler metaphysical principles from analytic metaphysics (rather than a description based on contemporary physics) might be a way to ensure that the logical consequences remain computable in a reasonable time for practical purposes. Additionally, these principles enable human users to browse and use the ontology more easily than if it was based on e.g. quantum mechanical or relativistic principles. It is surely easier to use a description in terms of independent entities localized in spatial regions, bearers of properties, and that participate in processes spanning temporal regions, than a description in terms of excitation of a quantum field in a set of spacetime points accompanied by a metric field and a matter field -or any other descriptions more in line with our current knowledge in quantum gravity. Analytic metaphysics can provide the tools to articulate a description of the former kind, and has been largely used in this respect, as reminded above.

Second, we note that the task of reducing special sciences such as biology or even classical physics on the basis of contemporary physics is not fully articulated, and highly tentative since there are several physical views explaining different aspects of the world and taken to be fundamental, in the sense that we do not have a unique most fundamental description of the world; actually, Ross, [START_REF] Ross | Rainforest Realism and the Unity of Science[END_REF] -among other philosophers of science -even think that there is no basis for supposing that such a reduction is possible. For instance, quantum field theory and general relativity are our most fundamental theories in this sense, and there is no reason to take one as being more fundamental than the other. The goal of finding one unified fundamental theory of physics might still be far away, and we cannot put in standby all the rest of science, waiting for this hypothetical next step in the history of theoretical physics to happen. It would thus be illusionary to pretend basing an ontology of biomedicine on the ontology of contemporary physics, as no such unique ontology has been found yet. As long as there is no reduction all the way down of all special science to fundamental physics, we must build applied ontologies of special sciences that stand independently of ontologies of fundamental physics, if we want to use them for practical purposes. Here again, analytic metaphysics can (and does) provide some tools for completing this goal, even if they were developed independently of considerations of contemporary physics.

Therefore, the heuristic justification of analytic metaphysics advocated by F&M does not hold only in reference to philosophy of physics: applied ontology offers a relevant use of analytic metaphysics not modeled on contemporary physics 11 .

Sealing the Fate of Analytic Metaphysics

In this section, we review F&M's heuristic approach to metaphysics to alleviate some tension in their account. In sub-section 3.1, we expose their heuristic justification and their somewhat ambivalent attitude towards it, and extend it by taking into account the results of section 2. In sub-section 3.2, we propose an amendment to their distinction between "type I" and "type II" metaphysics. In sub-section 3.3, we examine what kind of value the heuristic approach might provide to analytic metaphysics. In sub-section 3.4, elaborating on an analogy provided by F&M between analytic metaphysics and mathematics, we argue that one does not need to be more ambivalent about the heuristic justification of analytic metaphysics than about the instrumental justification of mathematics, and that F&M's discomfort with the heuristic justification of metaphysics may thereby be eased to some extent.

French & McKenzie's heuristic justification

French & McKenzie's heuristic justification of analytic metaphysics runs as follows.

First, some metaphysical tools have been used in philosophy of physics, such as Parfit's theory of personal identity in the Everett interpretation of quantum mechanics [START_REF] Wallace | Epistemology Quantized: Circumstances in which We Should Come to Believe in the Everett Interpretation[END_REF]) -although they have not been developed with this target discipline in mind. Second, the development of physics cannot be predicted: therefore, any metaphysical work might eventually be applicable to philosophy of physics in the future.

Similarly, as we argued, many theories that are now used in applied ontology were not developed with this objective in mind -consider e.g. endurantist and perdurantist theories 11 We are thereby complementing French & McKenzie's work, who seem to be sympathetic to the idea of justifying the toolbox approach with applied ontology (private correspondence).

of trans-temporal identity (used in [START_REF] Grenon | SNAP and SPAN: Towards Dynamic Spatial Ontology[END_REF]. Thus, metaphysical tools can be helpful not only for philosophy (namely philosophy of physics), but also for science (namely applied ontology; for other examples, see [START_REF] Bryant | Keep the chickens cooped: the epistemic inadequacy of free range metaphysics[END_REF]. By a direct adaptation of F&M's reasoning, since we do not know in which direction applied ontology will unfold in the future and what conceptual tools it will need, metaphysical works that presently find no application, or that may appear irrelevant to it, might eventually find such an application in applied ontology in the future. This is especially obvious for the kind of applied ontology that is the closest to empirical sciences: since the progress of science cannot be predicted, the development of applied ontology that aims at fostering data exchange in those sciences may not be fully anticipated. Therefore, any metaphysical work might eventually be applicable to it in the future. F&M (49) express some ambivalence towards their conclusion though, emphasizing "how precarious [their] heuristic justification of metaphysics is", as it is conditionalized on its use in other disciplines: this support "will depend on the extent to which utilizing extant packages instead of making everything to order is not a grossly inefficient way to go about things". They also mention the possible objection that the heuristic justification of analytic metaphysical practice might make it similar to "monkeys at typewriters", in which only a vanishingly small part of the work in metaphysics might turn out to be useful. Right after this statement, though, they point out that "this is the case, at least to some extent, for science as well". And they conclude that the prospects on the efficiency of such practice are "not something that [they] feel anyone is in much a position to place bets on" 12 . 12 Another statement reflecting the somewhat ambivalent attitude of F&M towards the heuristic justification of analytic metaphysical practice is that "analytic metaphysics should not take place in a disciplinary vacuum". Prima facie, this appears to suggest that a change in methodology is required, namely that metaphysical practice should be constrained by other disciplines. However, the rest of F&M's article suggests instead that this statement should be interpreted as concerning the justification of analytic metaphysics, which lies in other disciplines, such as philosophy of physics (as emphasized by F&M) or applied ontology (as emphasized by us). Indeed, they say elsewhere that "all that metaphysicians have to accept is the occasional raiding party from philosophers of science, keen (we hope) to see what they're up to and what they can use for their own purposes" -suggesting that no methodological change is required for metaphysicians. Finally, they explicitly state their ambivalence when they recognize that "the picture [they] have painted is a complicated one, and that there are considerations pulling from both sides", and call for "more nuanced positions on the basis of which more productive engagement between the two factions might be achieved".

We will now clarify several points to reach the conclusion that the heuristic justification of analytic metaphysics is qualitatively similar to the instrumental justification of mathematics, and that one does not need to be ambivalent about the former if one is not ambivalent about the latter. As a first step, we need to analyze F&M's distinction between two types of metaphysics.

The normative definition of type II metaphysics

F&M distinguish two kinds of analytic metaphysics that they call "type I" and "type II": Definition 1: "Type I metaphysics is the metaphysics that is scientifically disinterested and that, at least prima facie, doesn't need to be so interested, or even that might have to be so disinterested." Definition 2: "Type II metaphysics is the metaphysics that is scientifically disinterested but that should not be so." Note that definition 2 is "normatively charged" (using this term as Grill 2013): it defines type II metaphysics as being overall normatively defective, since it is scientifically disinterested when it should not be. But if type II metaphysics is defined as being overall normatively defective, then no argument could show it to be overall normatively acceptable. However, this possibility is left open by F&M, since they point out that support could "[…] be given to either Type I or Type II metaphysics via the heuristic approach […]" 13 . The fact that type II metaphysics is both normatively defective and (possibly) supported by the heuristic approach appears as a tension.

We see two possible strategies to address this tension. The first one is to leave untouched definition 2 of type II metaphysics. But then, the heuristics approach does not bring 13 Note that they remain very careful about the kind of support that the heuristic approach does indeed provide to the type I and type II metaphysics (and specify that this support is significantly conditionalized). But the mere consideration that type II metaphysics could be given some support is problematic, given the fact that type II metaphysics is defined as being normatively defective. support to type II metaphysics; rather, it entails that there is no type II metaphysics: indeed, any scientifically disinterested metaphysics might turn out, eventually, to be useful for other disciplines. Therefore, it is never the case that it should be (although it certainly could be) scientifically concerned. In this case, the metaphysical tools (theories, arguments, concepts) that were taken to belong to type II metaphysics actually belong to type I metaphysics. However, we then lose what seems to be a bona fide distinction between two kinds of analytic metaphysics, type I metaphysics being intuitively more justified than type II metaphysics because it does not directly contradict any scientific claim. The second possibility, which we favor, is to change the definition of type II metaphysics by adding a proviso as follows:

Definition 2*: Type II metaphysics is the metaphysics that is scientifically disinterested but that should not be so if it is aimed at describing reality adequately.

Then, type II metaphysics is not normatively defective per se: it is only so when it claims to describe reality adequately. But it may be effective if it is regarded as fulfilling other tasks. If we replace definition 2 by definition 2* -as we will do in the remainder of the article -the heuristic argument does indeed provide support to type II metaphysics, which is allowed to remain scientifically disinterested when it only aims at fulfilling a heuristic purpose for other disciplines 14 .

The value of analytic metaphysics

We return now to the question of whether analytic metaphysics, including type II metaphysics, is valuable, in the framework of the toolbox approach15 . Note that, operating 14 Note that by ful#lling this heuristic purpose, type II metaphysics can help other disciplines (such as philosophy of physics, or applied ontologies of special sciences) to describe reality adequately once its tools are appropriately contextualized by those disciplines. Therefore, in de#nition 2*, "if it is aimed at describing reality adequately" should be understood as "if it is directly aimed at describing reality adequately".

under the assumption of the toolbox approach, it is clear that analytic metaphysics sometimes turns out to be valuable for other fields. But does it mean, as a consequence, that metaphysics is always valuable simpliciter? In this section, we clarify this point and show that the two possible answers to this question lead to the same practical consequences.

Ladyman & Ross and F&M provide many examples of analytic metaphysical theories that discount scientific knowledge although they intend to describe entities about which we have contradictory scientific knowledge; in these cases, analytic metaphysics fails to describe reality and as a consequence, is not valuable, at least when it comes to the value related to adequate descriptions of the world. However, the heuristic justification by F&M suggests that analytic metaphysics has, or may have in the future a different kind of value, namely heuristic value. At this point, one may ask whether a potential future heuristic value of analytic metaphysics grants it actual present value simpliciter. There are two possible answers to this question but, as we shall see, the two answers lead to the same practical consequences: analytic metaphysics should not be discontinued.

The first answer is not committed towards the existence of a current value of analytic metaphysics, grounded in a potential future heuristic value. Insofar as a metaphysical view, principle, concept, or argument has or could come to have a heuristic value in the future, this justifies the development of this artifact. According to the second, stronger, interpretation, any metaphysical view, concept, principle or argument has value now because it has or could have heuristic value in the future 16 . We do not need to commit here on whether we should accept this stronger statement: it is enough to accept the weaker statement that analytic metaphysics may turn out to have heuristic value in the future and that this sole fact justifies developing analytic metaphysics.

Building on the parallel with mathematics 16

In this approach, this actual value is arguably intrinsic, since it holds even though it might never be used by another field. This actual present intrinsic value thereby depends on a potential future extrinsic value.

We are now in a better position to (hopefully) ease F&M's discomfort about the heuristic justification of analytic metaphysics. A comparison with mathematics will clarify this issue, elaborating on an analogy proposed by F&M themselves. Mathematics may have (at least) two kinds of value. First, it might be the case that mathematics describes a part of reality, as Platonists would claim -namely, mathematical reality -and therefore has value (and alternative frameworks in philosophy of mathematics, such as intuitionism or nominalism, may assign alternative kinds of value to mathematical practice). We will not take a position here on whether mathematics has such value. Second, mathematics is sometimes used as a tool in other sciences -physics being an obvious example -in which case it has some actual instrumental value; and because it might serve as a tool in the future, any mathematical construct has some potential instrumental future value.

Similarly, as the heuristic justification goes, analytic metaphysics has some potential instrumental future value because of its potential use not only in philosophy of physicsas emphasized by F&M -but also in the scientific domain of applied ontology -as we emphasized in section 2. There is thus a strong parallel between the heuristic justification of both mathematics and analytic metaphysics.

Maybe it would be more psychologically reassuring to claim that both analytic metaphysics and mathematics, because they have potential future instrumental value, actually have value now -as we considered in subsection 3.3. However, this psychological reassurance has no normative bearing, and what matters is that this potential future instrumental value provides an instrumental justification for the development of mathematical or analytic metaphysical theories, whether or not we consider that this provide to them actual, present value. This parallel between mathematics and analytic metaphysics implies that it is not at all obvious that analytic metaphysics should be constrained by the needs of other disciplines (such as philosophy of science or applied ontology). An external observer of mathematics a few centuries ago might have thought that in order to maximize the instrumental value of mathematics, it should evolve in a constrained -rather than free -manner. For example, one might have suggested that mathematical progress should answer to specific needs from other sciences. Some mathematical tools have indeed been developed to solve specific issues in physics, such as Fourier series to solve the heat equation. However, on other occasions, physics or other disciplines find already pre-existing tools in mathematics that were not developed to answer such issues. As mentioned by F&M (34), Riemannian geometry may have originally seemed to be empty of any instrumental value, but it later found an application with General Relativity. Similarly, some investigations in number theory may have seemed useless at first, but were later used in cryptography. It is not obvious that mathematics would have presently more instrumental value if it had been constrained by its applications rather than let free to evolve in a freerange manner. By analogy, it is not obvious that constrained metaphysics would have more instrumental value than unconstrained metaphysics.

We might add here some argument to make our case. If all metaphysics would become constrained, can we be sure that it would not dry the pool of ideas and tools in such a way as reducing the overall richness of the discipline and, thereby, its usefulness for target fields? To strengthen this idea, note that the two disciplinary fields of analytic metaphysics and philosophy of science rest on largely different (although partly overlapping) intellectual traditions. The organization of metaphysics as a mostly unconstrained field might thus enable the development and expression of specific skills in its practitioners -such as creativity in building new metaphysical tools, or familiarity in using them -the same way that the organization of mathematics as a dedicated field did.

Unless more evidence is given to the opposite thesis, it is not obvious that a constrained metaphysics would have more future heuristic value than unconstrained metaphysics.

Another argument suggests ensuring the continuous existence of unconstrained analytic metaphysics, namely the impossibility to predict new -scientific, philosophical or otherfields that might emerge in the future. When metaphysics started to be largely applied to applied ontology, this came as a surprise: "We find it remarkable that an activity that traces its origins to the work of philosophers who lived more than two millennia ago has become central to the development of modern information technology" [START_REF] Guarino | Applied Ontology: Focusing on Content[END_REF]. Who knows which other future fields might benefit from the progress of analytic metaphysics? Putting analytic metaphysics to order might skew it towards the needs of present customers (such as philosophy of physics and applied ontology) and restrict its potential applications to other as-yet-unforeseen fields 17 . Thus, we may summarize the lessons learned in section 3 as follows: the heuristic approach justifies the practice of both type I and type II metaphysics (as redefined with definition 2*), in the same way that the practice of mathematics is justified instrumentally. This is true independently of whether the potential use of any metaphysical tool or mathematical construct grants it some actual value. There are four caveats to this argument though. First, one could argue that although the heuristic/instrumental justification is qualitatively similar for both analytic metaphysics and mathematics, some quantitative differences may be relevant. For example, mathematics has been applied to a larger range of disciplines, and for a longer time, than analytic metaphysics. Second, the methodology of metaphysics might be more precarious than the methodology of mathematics: whereas the methods of mathematics are largely settled and well accepted, there is more disagreement about the methods of metaphysics.

Maybe, for example, the appeal to intuitions or thought experiments makes metaphysics methodologically more fragile. And certainly, some metaphysical theories go wrong when they pretend to describe a portion of reality about which we do have relevant scientific knowledge, while not taking this knowledge adequately into account -as argued convincingly by L&R and F&M. Third, the structure of the academic field of mathematics has arguably evolved because of its applications; indeed, a whole field of "applied mathematics" has been developed next to "pure mathematics". Similarly, 17 A reviewer objected that this argument could be "used to defend the allocation of academic resources to any fanciful speculation at all", such as "formal semantics for Klingon and Romulan. (After all, someone might someday decide to use Klingon for some currently unimagined purpose)". We have two replies to this argument. First, Klingon (to take one of these two fictional languages drawn from Star Trek) might indeed have some applications someday; for example, it might provide some insights in linguistics. If the study of Klingon would start to bring such insights (the same way that analytic metaphysics has brought important insights to philosophy of physics and applied ontology), then it might be justified, indeed, to allocate some academic resources to its study (in proportion to the magnitude of its expected results). Second, it seems to us intuitively more likely that the purported study of the general structures of reality (which is the object of analytic metaphysics), because of its highly general scope of inquiry, would bring more insights to other fields than the study of the structure of an imaginary language (such as Klingon) would. However, and as noted by the reviewer, a specific account of the circumstances in which a high degree of generality would maximize utility for other fields is still lacking, and could be investigated in future works. analytic metaphysics might be divided into two fields: "pure" analytic metaphysics, and "applied" analytic metaphysics. But one might argue that this is already what has happened with the emergence of the field of applied ontology; and that for the same kind of reasons that motivate the continued existence of pure mathematics, "pure" analytic metaphysics deserves to continue an autonomous existence next to applied ontology.

Fourth, pure mathematicians may be encouraged to periodically step down from their mathematical heavens and visit other scientific fields, to consider whether some of their tools could bring some worthy insight; similarly, analytic metaphysicians could be encouraged to wander out at times to consider whether some of their tools could bring valuable contributions to other philosophical or scientific fields.

But in a nutshell, as far as the instrumental justification goes, metaphysics and mathematics appear to be in qualitatively similar situations, and one therefore does not need to be ambivalent about the heuristic justification of the former if one does accept the instrumental justification of the latter. Thus, it might be a justification for those who think that metaphysics does not have satisfactory epistemic credentials (although we remain neutral here on this question) and that the metaphysician should stop its "bad faith" [START_REF] Bryant | Keep the chickens cooped: the epistemic inadequacy of free range metaphysics[END_REF]. And it could be the case that analytic metaphysics makes possible the existence of some of the best naturalized metaphysics and applied ontologies, just like freely developed mathematics entitles the construction of some of the best scientific theories.

Conclusion

We have argued for two points in this article. First, French & McKenzie's heuristic defense of analytic metaphysics can be extended to its utility for applied ontology.

Second, a comparison with mathematics shows that the toolbox approach suggests not interfering with the whole field of analytic metaphysics even when it is inconsistent with what we know about the world, according to our best current science.

As a disclaimer, we do not claim that applied ontologies should remain based on analytic metaphysics foundations only. It may become useful, when dealing with data systems in the field of e.g. structural engineering, to develop ontologies based on metaphysical principles based on classical physics. It might even become useful to build them on metaphysical principles based on advanced physics principles if one wants to deal with e.g. particle physics or cosmological data. As mentioned earlier, ontologies such as BFO progressively incorporate such inputs from science. But given constraints of usability (as explained in 2.3) by domain experts such as medical doctors or biologists, we will anyway need ontologies using a level of description in terms of domain categoriesalthough those categories could be connected with categories more in line with contemporary physics. Well-chosen principles inspired by both analytic and naturalized metaphysics could serve as common foundations for those categories.

At the end of the day, we share the main ideas of Steven French and Kerry McKenzie and want to warn against the temptation of scientific triage, namely that the intellectual resources should be distributed differently, according to expected usefulness, to help philosophy of physics to make its way. Philosophy of physics is not the only player in town, and we do not see any convincing reason to believe that an active redistribution of intellectual resources would be overall useful, either for the philosophy of physics, applied ontology or possible other yet-unexpected-fields.

In the sense that the process to which an object participates can have a well-defined instant velocity process profile[START_REF] Smith | Classifying Processes: an Essay in Applied Ontology[END_REF]. Note however that BFO does not require positions and velocities to be well-defined -so quantum mechanical constraints could be integrated in the future.

Again, we do not take stock here on whether analytic metaphysics is valuable for other reasons, unrelated to the toolbox approach.

Acknowledgments

The authors would like to thank two anonymous reviewers for their helpful and detailed comments, as well as Jiri Benovsky, Michael Esfeld, Steven French, Kerry McKenzie, Barry Smith, Fumiaki Toyoshima and Christian Wüthrich for valuable comments on an earlier draft. The work of B.L.B was performed under a collaborative agreement between the University of Illinois at Chicago and the University of Geneva and made possible by grant number 56314 from the John Templeton Foundation; its contents are solely the responsibility of the authors and do not necessarily represent the official views of the