Alessandro Longo
email: alessandro.longo@esrf.fr

Romain Wernert

Antonella Iadecola

Christoph J Sahle

∥, §,⊥ Lorenzo Stievano

¶, §,⊥ Dany Carlier, ¶, §,⊥ Laurence Croguennec

Dany Carlier

Alessandro Mirone
email: alessandro.mirone@esrf.fr

An Original Empirical Method for Simulating V L 2,3 Edges: The Example of KVPO4F and KVOPO4 Cathode Materials

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Introduction

Vanadium is a versatile transition metal element, exhibiting a large variety of oxidation states ranging from +2 to +5 and very different coordination polyhedra including regular octahedra, strongly distorted octahedra, square based pyramids, as well as tetrahedra. [START_REF] Boudin | Review on vanadium phosphates with mono and divalent metallic cations: syntheses, structural relationships and classification, properties[END_REF][START_REF] Schindler | Crystal chemical aspects of vanadium: polyhedral geometries, characteristic bond valences, and polymerization of (VO n ) Polyhedra[END_REF] Such properties provide a rich crystal chemistry for V based compounds, especially phosphates. For this reason, many studies have been conducted in the field of battery electrode materials based on V, such as LiV 2 O 5 , 3 LiVPO 4 F, [START_REF] Barker | Structural and electrochemical properties of lithium vanadium fluorophosphate, LiVPO 4[END_REF][START_REF] Gover | LiVPO 4 F: A new active material for safe lithium-ion batteries[END_REF] Na 3 V 2 (PO 4 ) 3 , Na 3 V 2 (PO 4 ) 2 F 3 [START_REF] Serras | High voltage cathode materials for Na-ion batteries of general formula Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF][START_REF] Serras | Electrochemical Na extraction/insertion of Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF][START_REF] Masquelier | Polyanionic (phosphates, silicates, sulfates) frameworks as electrode materials for rechargeable Li (or Na) batteries[END_REF] and many more. Indeed, electrochemical properties such as the potential window, the shape of the electrochemical curve or the capacity can be tailored by crystal structure and composition engineering. [START_REF] Masquelier | Polyanionic (phosphates, silicates, sulfates) frameworks as electrode materials for rechargeable Li (or Na) batteries[END_REF] For example, the preparation of mixed anion phosphates containing O and/or F allows triggering the V 5+/4+ or V 4+/3+ redox couples. Such materials were investigated for Li-ion batteries, Na-ion batteries and even K-ion batteries using, among others, LiVPO 4 F 1-y O y , Na 3 V 2 (PO 4 ) 2 F 3-2y O 2y and KVPO 4 F 1-y O y (0 ≤ y ≤ 1). [START_REF] Nguyen | Stability in water and electrochemical properties of the Na 3 V 2 (PO 4 ) 2 F 3 -Na 3[END_REF][START_REF] Broux | Strong impact of the oxygen content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0 ≤y≤ 0.5) on its structural and electrochemical properties[END_REF][START_REF] Boivin | LiVPO 4 F 1-y O y tavorite-type compositions: influence of the concentration of vanadyl-type defects on the structure and electrochemical performance[END_REF][START_REF] Wernert | Controlling the cathodic potential of KVPO 4 F through oxygen substitution[END_REF] In these compounds, for the case of oxygen-rich compositions containing only V 4+ , a very short bond of 1.65 Å is formed between V and one of its surrounding oxygen atoms. Such a short bond distance is analogous to the vanadyl VO 2+ ion and is referred to as a "vanadyl bond" depicted as V=O. Vanadyl bonding is a typical oxo-metal bond where the geometrical distortion lifts the t 2g degeneracy so that the d xy orbital is solely occupied by the unpaired d 1 electron. [START_REF] Ballhausen | The electronic structure of the vanadyl ion[END_REF] It also features strong π-bonding interactions between V d xz , d yz and the filled O 2p x , 2p y .

Interestingly, some vanadium compounds exhibit multi-electron transfer properties such as tavorite LiVOPO 4 , where Li + can be either deintercalated or intercalated from LiVOPO 4

to yield VOPO 4 or Li 2 VOPO 4 , by triggering the V 5+/4+ or V 4+/3+ redox couples respectively. [START_REF] Bianchini | Multiple phases in the ϵ-VPO 4 O -LiVPO 4 O -Li 2 VPO 4 O system: a combined solid state electrochemistry and diffraction structural study[END_REF][START_REF] Wangoh | Uniform second Li ion intercalation in solid state ϵ-LiVOPO 4[END_REF] It was reported that VO 6 octahedra are distorted with a V=O bonding scheme in tavorite-type VOPO 4 and LiVOPO 4 , whereas V lies in a symmetric octahedral coordination site in Li 2 VOPO 4 . [START_REF] Bianchini | Multiple phases in the ϵ-VPO 4 O -LiVPO 4 O -Li 2 VPO 4 O system: a combined solid state electrochemistry and diffraction structural study[END_REF] In addition, some unusual redox mechanisms were uncovered in Na 3 V 2 (PO 4 ) 2 F 3 . Upon charging, it was shown that the final composition Na 1 V 2 (PO 4 ) 2 F 3 contained equal amounts of V 5+ and V 3+ , whereas only V 4+ was expected. [START_REF] Bianchini | Comprehensive Investigation of the Na 3 V 2 (PO 4 ) 2 F 3 -NaV 2[END_REF][START_REF] Broux | V IV Disproportionation upon sodium extraction from Na 3 V 2 (PO 4 ) 2 F 3 observed by operando x-ray absorption spectroscopy and solid-state NMR[END_REF][START_REF] Nguyen | A combined operando synchrotron x-ray absorption spectroscopy and first-principles density functional theory study to unravel the vanadium redox paradox in the Na 3 V 2 (PO 4 ) 2 F 3 -Na 3 V 2 (PO 4 ) 2 FO 2 compositions[END_REF] Recent studies have also shown the formation of a short V-O bond upon charge of Na 4 FeV(PO 4 ) 3 . [START_REF] Park | An asymmetric sodium extraction/insertion mechanism for the Fe/V-mixed NASICON Na 4 FeV(PO 4 ) 3[END_REF] Overall, vanadium battery materials show a wide variety of possible redox mechanisms and local environments, which are difficult to disentangle.

X-ray spectroscopy is the technique of choice especially at the V L 2,3 edges, which correspond to electronic transitions from occupied V 2p 1/2 and 2p 3/2 core levels to unoccupied V 3d states (2p 6 3d n -→ 2p 5 3d n+1 ). Such spectra are expected to carry information on oxidation state, local geometry and bonding. Probing these edges could help confirming both redox and structural mechanisms, as well as understanding unusual charge compensation processes. In spite of these promising features, the investigation of early 3d transition metal L-edges is sometimes hindered by both the spectral distortion and the surface sensitivity of total electron yield (≈ 10 nm) and total fluorescence yield (≈ 50 nm) soft X-ray absorption spectroscopy (soft-XAS) techniques. [START_REF] Frati | Oxygen K-edge x-ray absorption spectra[END_REF][START_REF] Fehse | The rise of x-ray spectroscopies for unveiling the functional mechanisms in batteries[END_REF] X-ray Raman scattering (XRS) spectroscopy can overcome such issues since it relies on highly penetrating hard X-rays and an inelastic excitation process, thus providing bulk sensitivity. When the energy loss is close to the V L 2,3

edges excitation energies, the resulting XRS spectra contain information similar to the conventional soft-XAS ones. However, there are currently only few studies addressing properly the interpretation of V L 2,3 edge spectra by a calculation approach, limiting the thorough understanding of the carried information, especially about the electrochemical properties. [START_REF] Hébert | Oxygen K-edge in vanadium oxides: simulations and experiments[END_REF][START_REF] Willinger | Electronic structure of β-VOPO 4[END_REF][START_REF] Firet | Chemisorption of anionic species from the electrolyte alters the surface electronic structure and composition of photocharged BiVO 4[END_REF] In the literature, two approaches tackling these problems are available. First, a rigorous ab initio quantum chemistry configuration interaction formalism is applied, [START_REF] Brik | Fully relativistic calculations of the L-2,L-3-edge XANES spectra for vanadium oxides[END_REF][START_REF] Hoeche | Vanadium L-2,L-3 XANES experiments and first-principles multielectron calculations: impact of second-nearest neighboring cations on vanadium-bearing fresnoites[END_REF][START_REF] Aquilante | Modern quantum chemistry with [Open]Molcas[END_REF] for a given crystallographic structure, and, importantly is parameterless. Such method has the advantage that molecular orbitals are optimised for each calculated excited state. However, these calculations are very demanding in terms of computing time, and this makes the comparison with experimental data a cumbersome procedure. In the second approach, a more straightforward formalism is implemented, [START_REF] Abbate | Soft-X-ray absorption-spectroscopy of vanadiumoxides[END_REF][START_REF] Gloter | Vanadium valency and hybridization in V-doped hafnia investigated by electron energy loss spectroscopy[END_REF][START_REF] Herrera | Excited states in yttrium orthovanadate YVO4 measured by soft X-ray absorption spectroscopy[END_REF][START_REF] Jimenez-Mier | X-Ray absorption to determine the metal oxidation state of transition metal compounds[END_REF][START_REF] Hopkins | Ba3V2S4O3: a Mott insulating frustrated quasi-one-dimensional S=1 magnet[END_REF][START_REF] Matsuura | X-ray magnetic circular dichroism study of an orbital ordered state in the spinel-type vanadium oxide AV(2)O(4) (A = Mn, Fe)[END_REF][START_REF] Herrera-Perez | The influence of charge transfers effects in monazite-type LaVO4 and perovskite-type LaVO3 prepared by sol-gel acrylamide polymerization[END_REF][START_REF] Kowalska | Iron L-2,L-3-edge x-ray absorption and x-ray magnetic circular dichroism studies of molecular iron complexes with relevance to the FeMoCo and FeVCo active sites of nitrogenase[END_REF][START_REF] Wu | Investigation of the vanadium L-23-edge x-ray absorption spectrum of SrVO3 using configuration interaction calculations: multiplet, valence, and crystal-field effects[END_REF][START_REF] Schmitz | Soft x-ray magnetic circular dichroism of vanadium in the metal-insulator two-phase region of paramagnetic V2O3 doped with 1.1% chromium[END_REF][START_REF] Murota | Vanadium 3d charge and orbital states in V2OPO4 probed by x-ray absorption spectroscopy[END_REF] where a small cluster is considered but the orbitals are not optimised for the excited states. Instead a model Hamiltonian, with fixed empirical parameters, and modelled as a sparse matrix, acts on the second-quantisation vectorial space spanned by the cluster states. Then the spectra are efficiently calculated in the Krylov sub-space generated by recursive linear-algebra applications of the Hamiltonian. The inconvenience of the latter approach lies in the relatively high number of parameters to be tuned to calculate the crystal field. Moreover, two extra parameters are needed if hybridisation has to be considered. The total number of parameters, by neglecting the hybridisation, can be reduced for high symmetry sites. Nevertheless, this is also multiplied by the number of non-equivalent sites. Since a direct link between the crystallographic structure and the used parameters is missing, data interpretation is not trivial. Even though some ab initio methods have been already proposed to control the free parameters, significant discrepancies between the calculated and the best fit crystal field parameters are still observed, which weaken the overall results. [START_REF] Haverkort | Multiplet ligand-field theory using Wannier orbitals[END_REF][START_REF] Wang | Analyzing the local electronic structure of Co3O4 using 2p3d resonant inelastic x-ray scattering[END_REF] In the methodology reported here, all the weaknesses are overcome by the novel approach implemented in Hilbert++ and reported below. Two different possible approaches within the code are here explored. The first case shows an improved Wannier approach, applied in a relaxed crystal structure, which overcomes the use of crystal field and hybridization parameters. In the second case, a semi-empirical method is adopted which involves the use of free parameters directly linked to the physics used to describe the system, such as hybridisation energy, crystal field and spatial position of the ligands around the transition metal. To highlight the elements of novelty a summary of the salient aspects of Hilbert++ code is reported in the next section. We apply our approach to experimental V L 2,3 -and O K-edges XRS data of KVPO 4 F and KVOPO 4 cathode materials, which were used as references for V 3+ and V 4+ =O containing compounds. Accordingly, multiplet calculations of the V L 2,3 edges were conducted using the Hilbert++ code with the above introduced different approaches: i) the conventional one using the ab initio Hamiltonian obtained with localised Wannier orbitals from a full density functional theory (DFT) simulation; ii) an original and user-friendly method based on empirical parameters. In order to prove the complementarity of the two methodologies, a multi techniques approach is applied.

More precisely, ab initio relaxed crystal structures resulting from GGA+U calculations with VASP were used to validate the experimental X-ray diffraction (XRD) crystal structures.

Moreover, the relaxed structures were used as input for a DFT calculation, post-processed then with the Wannier90 code which sets the crystal field and hybridisation part of the Hamiltonian implemented in Hilbert++. The results are finally corroborated by spectral calculations at the O K-edge (see SI).

Remarkably, the combination of all such different theoretical approaches provides a complete picture of the electronic structure of the V atoms, which is directly linked to the distorted coordination geometry and electronic structure of the vanadium cations. Such distortion is hardly detected by Extended X-ray Absorption Fine Structure (EXAFS) analysis as the information contained in the spectra is averaged between the different oxygens and the features are less distinct. [START_REF] Wernert | Controlling the cathodic potential of KVPO 4 F through oxygen substitution[END_REF] The approach implemented in Hilbert++, instead, provides a full treatment of the correlation effects. These effects induce spectral features which are sufficiently resolved to be studied with our approach and, importantly, have different orbital characters with a rich dependence on the ligand environment, in particular for their relative variations.. Hilbert++ can also be applied using empirical parameters with a direct physical meaning such as ligand coordinates and Slater-Koster tight-binding parameters, thus allowing the qualitative recovery of structural information directly from the data without depending on expensive ab initio calculations. In conclusion, we show how such an empirical approach is a reliable and easy-to-use tool to correctly interpret XRS and XAS data. The pellet was calcined at 750°C under argon atmosphere. The samples studied are the same as those used in an earlier work where the precise control of anionic composition was demonstrated. 12 X-ray Raman Scattering (XRS) Spectroscopy measurement XRS data were collected at beamline ID20 of the ESRF (Grenoble, France). [START_REF] Huotari | A large-solid-angle X-ray Raman scattering spectrometer at ID20 of the European Synchrotron Radiation Facility[END_REF] The pink beam from three U26 undulators was monochromatized at an incident energy of 9.6837 keV, using a cryogenically cooled Si(111) monochromator and a subsequent Si(311) channel-cut post-monochromator. The final beam was focused to a spot size of approximately 30 µm × 30 µm (V × H) at the sample position using a mirror system in Kirkpatrick-Baez geometry.

Methods and experiments

XRS is an inelastic X-ray scattering process, in which a high energy X-ray photon excites a core electron into an unoccupied state. At low transferred momenta, the process is, in principle, analogous to X-ray absorption spectroscopy (XAS), but the energy transfer to the outgoing photon plays the role of the X-ray photon energy absorbed in XAS. At high transferred momenta instead, compared to XAS, the spectra is enriched by the higher multipole contributions coming from the expansion of Eq. 4 in powers of Q. The large solid angle spectrometer at ID20 was used to collect XRS data with 36 spherically bent Si(660) crystal analysers. The data were extracted with the XRStools program package as described in detail elsewhere. [START_REF] Sahle | Planning, performing and analyzing X-ray Raman scattering experiments[END_REF] The sample was placed into the beam at 10°grazing incidence. All XRS measurements were carried out at room temperature. Full range scans were measured from 505 to 565 eV energy loss with a 1 eV step size. After acquisition of the survey scan, several detailed scans of specific edges were collected with a 0.2 eV step by scanning the incident beam energy to record energy losses in the vicinity of the V L 2,3 -edge and O K-edge (505-565 eV). Acquisition scans lasted approximately 6 hours per sample. In order to be sure to hit always a fresh part of sample and to avoid radiation damage, the X-ray beam was moved on the sample during the measurement. Each XRS spectrum was recorded for about 10 minutes at a different spot of the sample, and no structural modification of the sample was observed during this time. All scans were checked for consistency before averaging over them. The overall energy resolution of the XRS spectra was 0.7 eV as estimated from the FWHM of elastic scattering from a piece of adhesive tape.

Calculation scheme

Ab initio structural relaxation DFT relaxed crystal structures of KVPO 4 F and KVOPO 4 were computed using the projectoraugmented wave (PAW) method with the Vienna ab initio simulation package (VASP) code. [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF][START_REF] Blöchl | Projector augmented-wave method[END_REF][START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Ab initio molecular-dynamics simulation of the liquidmetal-amorphous-semiconductor transition in germanium[END_REF] The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was used for all calculations. [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] A Hubbard correction (U ef f = U-J = 5 eV) was applied to take into account the self-interaction error of the strongly correlated 3d electrons. [START_REF] Dudarev | Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study[END_REF] U ef f = 5 eV was already used in previous studies of these compounds and provided a good agreement with experimental structure, voltage curve, and electronic structure. [START_REF] Wernert | Controlling the cathodic potential of KVPO 4 F through oxygen substitution[END_REF][START_REF] Kim | A new strategy for high-voltage cathodes for K-ion batteries: stoichiometric KVPO 4 F[END_REF] All calculations were spin-polarized with ferromagnetic ordering. [START_REF] Carlier | Understanding the NMR shifts in paramagnetic transition metal oxides using density functional theory calculations[END_REF] The plane-wave cutoff energy was set to 600 eV and a 4×4×4 k-mesh was used. The octahedral distortion was calculated according to Equation 1 where d is a given bond distance among the first coordination shell and d is the average bond distance:

dist = 1 6 6 i=1 (d i -d) 2 d2 (1)

Hilbert++ and Wannier localized orbital

Multiplet calculations of the dynamic structure factor were performed with the Hilbert++ code. [START_REF] Mirone | Ligand-field atomic-multiplet calculations for arbitrary symmetry[END_REF] Compared to other existing multiplet codes, [START_REF] De Groot | 2p x-ray absorption spectroscopy of 3d transition metal systems[END_REF][START_REF] De Groot | Multiplet effects in X-ray spectroscopy[END_REF] Hilbert++ allows to simulate local environments (i.e. first coordination sphere) of arbitrary symmetry 53 using few empirical Slater-Koster parameters, here detailed, and can simulate the XRS spectra and their momentum transfer (q) dependence. Moreover, alternatively to using empirical parameters, the code can extract the crystal field and hybridization Hamiltonian directly from modern ab initio codes, like Quantum Espresso (QE) 56,57 or the Vienna ab initio simulation package (VASP), through the Wannier90 code. [START_REF] Mostofi | A tool for obtaining maximally-localised Wannier functions[END_REF][START_REF] Mostofi | An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions[END_REF] For a simple cluster composed of a central ion and its surrounding coordinated , we calculate the photon scattering cross section due to the excitation of an initial cluster state |i⟩, and an incoming photon at energy hω with polarisation ϵ, into one of the excited cluster states |f ⟩ and a scattered photon hω ′ , as the dynamic structure factor obtained by this formula:

d 2 σ dΩdE loss ∝ ω ′ ω (ϵ ′ .ϵ) n |⟨f |T b←a (Q)| i⟩| 2 δ(E f + h(ω ′ -ω) -E i ) (2)
where T b←a expresses the action of the A 2 -term of the photon-electron Hamiltonian between two one-particle atomic spin-orbitals, with the annihilation â of an electron in (n a , l a , m a , s) and the creation b † in (n b , l b , m b , s):

T b←a = m b ,ma,s t m b ,ma b † m b ,s âma,s (3)
where the t coefficients are calculated, writing the atomic spin-orbitals as the product of a radial part,φ n,l (r) , and angular part Y l m (r/r), [START_REF] Edmonds | Angular momentum in quantum mechanics[END_REF] as :

t m b ,ma = φ n b ,l b (r)φ na,la (r)/r 2 Y l b m b ⋆ (r/r)Y la ma (r/r)exp(-iQ.r)dr 3 (4)
The cluster wave-functions |f ⟩ and |i⟩ are many-electrons eigen-functions of our cluster, the Hamiltonian can be written as:

H = H atomic + H dd + H dv + H vv . (5)
The four contributing terms are, from left to right: the atomic Hamiltonian H atomic of the central atom, the crystal field acting on the d electrons of vanadium H dd , the hopping between the d orbitals and the 2p orbitals at the sites around the central vanadium atom H dv (latter orbitals are represented by v † , v), and finally H vv , the Hamiltonian governing the electron propagation over the neighbouring orbitals. The three latter contributions describe the crystal field and the hybridisation:

H dd + H dv + H vv = m ′ ms c m ′ m d † m ′ ,s dm,s + ims t i,m v † i,s dm,s + c.c. + i,j,s (t ′ i,j + δ ij ∆)v † i,s vj,s , (6)
where the 3d orbitals are indexed by m, m ′ , while i, j index the v orbitals and s is the spin.

The coefficients c, t and t ′ are determined, based on the atomic positions, by two alternative methods: using maximally localized Wannier orbitals as calculated by the Wannier90 code, or empirical parameters. In the first approach, a self consistent field (SCF)ab initio calculation, using QE, is first performed using a local density approximation (LDA) functional. Then the Wannier90 code is used to form the maximally localised 3d wavefunctions of the selected vanadium site and, at the neighbouring oxygen and fluorine sites, the ligand 2p orbitals, which are possibly hybridised with the vanadium 3d electrons. Non equivalent vanadium sites are calculated independently and their spectra are averaged. The orbital synthesis is performed using an energy window, which encompasses both bonding and anti-bonding molecular orbitals.

The Wannier90 code outputs the tight-binding Hamiltonian matrix containing a first estimation of the c, t, and t ′ coefficients. A further refinement is made on the c factors to avoid double counting of the electron-electron interaction, which is already accounted for in H atomic . This is realised by rotating the density matrix, given by the DFT code, obtaining its representation in the Wannier basis, and using it to extract the mean field approximation of electron-electron Coulomb operators of H atomic . The result is subtracted from the matrix of c coefficients. This is at variance with what is described in [START_REF] Haverkort | Multiplet ligand-field theory using Wannier orbitals[END_REF] where the LDA potential is altered by removing the non-muffin-tin terms.

We have verified that the estimated crystal field without this correction shows a poor agreement with the experimental one.

Recently, a local electronic study on CO 3 O 4 has been reported on the 2p -3d transition where a clear discrepancy was observed between the best-fit 10Dq value, for the Co 3+ site, and the value obtained by the Wannier method. [START_REF] Wang | Analyzing the local electronic structure of Co3O4 using 2p3d resonant inelastic x-ray scattering[END_REF] Our proposed procedure, tested on this structure, produces 10Dq = 1.2eV which is close to their best-fit 10Dq up to 5%, while by removing the correction terms we obtain 10Dq = 0.66eV which is very close to their Wannier approximated value.

Another refinement is done introducing ∆ as a free parameter of the model in equation 6.

This parameter tunes the energy difference between the vanadium 3d and ligand 2p orbitals and it compensates for our ignorance about the very complex mechanism of screening, which occurs in particular for the 3d shell.

The H atomic Hamiltonian is composed, in Hilbert++, by writing in second quantisation the Coulomb operators with their coefficients given by products of Slater integrals and angular moment coupling factors. The Slater integrals are reduced, following the standard procedure for multiplet calculations in the literature, [START_REF] De Groot | Multiplet effects in X-ray spectroscopy[END_REF] by a factor between 0.7 and 0.9 for multipoles of order L > 0; the monopole terms corresponding to L = 0 and strongly screened by the surrounding charge, are taken equal to 5.0 eV, which is in line with the U adopted in the literature for LDA+U calculation of vanadium phosphates. [START_REF] Wernert | Controlling the cathodic potential of KVPO 4 F through oxygen substitution[END_REF][START_REF] Kim | A new strategy for high-voltage cathodes for K-ion batteries: stoichiometric KVPO 4 F[END_REF] Alternatively to the ab initio calculation needed for the Wannier Hamiltonian, the crystal field and hybridisation contributions can be determined from empirical parameters. In this case the t ′ i,j matrix is diagonal, and is given by a free parameter (∆), which tunes the energy difference between the vanadium 3d orbitals and the 2p orbitals of the ligands. Further, H dv and H dd are determined by two parameters each, one for σ-and the other for π-symmetry orbitals and by summing the contributions for each bonding vector r b , and re-scaling for each bond the interaction strength according to a power of the ratio <r> r b , with the average bond length.

In particular, introducing a Cartesian reference system (x b , y b , z b ) for each bond, aligned with r b along the z b axis, allow us to rewrite the H dv and H dd as follows:

H dv = b,s < r > r b
and

H dd = b,s < r > r b 3 c σ d † z 2 b ,s dz 2 b ,s + c π ( d † x b z b ,s dx b z b ,s + d † y b z b ,s dy b z b ,s ) . (8)
Finite Difference Method Near-Edge Structure (FDMNES) approach

To validate the electronic structure of the materials, O K-edge ab initio simulations were performed using FDMNES software package. [START_REF] Joly | Full-potential simulation of x-ray Raman scattering spectroscopy[END_REF] This code is particularly suited for X-ray absorption near-edge structure (XANES) simulations within the one-particle potential approximation. Therefore it is not appropriated for multiplet calculations but can treat large systems where correlation weakly affect the spectra. The atomic positions were generated from the crystallographic data reported in a previous work. [START_REF] Wernert | Controlling the cathodic potential of KVPO 4 F through oxygen substitution[END_REF] Moreover, the simulations were also performed on the two different KVOPO 4 and KVPO 4 F structures previously relaxed by DFT calculation with VASP and using GGA+U with U ef f = 5 eV. The simulations of the O K-edge spectra were performed by using multiple scattering theory based on the muffin-tin (MT) approximation for the potential shape of the Green scheme, non-relativistic calculations and the Hedin-Lundqvist exchange. [START_REF] Joly | Full-potential simulation of x-ray Raman scattering spectroscopy[END_REF] The MT radii were tuned to have a proper overlap between the different spherical potentials. The approximation of non-excited scatterers was used. Finally, an arc-tangent convolution to account for the core-hole lifetime and photoelectron state width was performed, followed by a Gaussian convolution. This last step is necessary to consider the experimental resolution. The obtained spectra were then normalized to the same integrated intensity of the experimental data in the suitable energy loss range. To take into account the ionic character of the oxygen atom, the dilatorb parameter m, available in the FDMNES code, was considered. This parameter modifies the spatial extent of the valence orbitals, hence allowing one to alter the degree of covalency.

Moreover, it also takes into account the actual charge of the oxygen species at the O K-edge.

Dilatorb can be adopted for each ionic species in the material, depending on the investigated edge, but it was mainly applied on the O 2-anion, the atomic basis of which is generally taken from the neutral atom to simulate the O K-edge data.

Results and discussion

Homeotypic KVOPO 4 and KVPO 4 F crystallize in the KTiOPO 4 (KTP) type structure (P na2 1 ). [START_REF] Benhamada | KVPO 5 , an intersecting tunnel structure closely related to the hexagonal tungsten bronze[END_REF][START_REF] Fedotov | A 4 V cathode material for high-power rechargeable batteries[END_REF] For KVPO 4 F, the framework can be described by infinite corner-sharing VO 4 The very slight variation of the oxygen K-edge features are localised in the pre-edge region between 530 and 535 eV. To directly correlate the electronic structure modifications with the changes occurring at the vanadium edge, multiplet calculations were performed using Hilbert++. A preliminary simulation of the L 2,3 edges for different vanadium isolated ions V n+ (n=3,4,5) is reported in Figure 3. From these curves one can evaluate, in the absence of any ligand field and orbital hybridisation effect, the impact of solely varying the 3d occupancy from n 3d = 0 for V 5+ to n 3d = 2 for V 3+ on the spectra. In agreement with the literature, ( 64 section VI.B) these simulations show that the L 3 /L 2 peak ratio increases when the occupancy increases from V 5+ to V 3+ . This results is expected as the L 3 /L 2 ratio depends on the interplay between the vanadium 2p spin-orbit coupling and the action of direct and exchange Coulomb interaction between vanadium 2p and 3d orbitals. The multiplet simulations of KVPO 4 F and KVOPO 4 (containing V 3+ and V 4+ , respectively) are shown in Figure 4. These simulations are obtained on the basis of the Wannier Hamiltonian for the ab initio optimised structures (left panels) and for the experimental structure (right panels), with the V 3+ system in the upper row and V 4+ in the lower one.

The Slater integrals reduction factor that were applied are 0.8 for V 3+ and 0.7 for V 4+ .

It should be pointed out that once the Slater integral reduction factor is fixed, only one free parameter ∆ (see equation 6) is needed for the simulation employing the localized Wannier orbitals as input. We recall that ∆ tunes the energy difference between 3d-and neighbouring ligand 2p-orbitals and thus the value of such free parameter has been fixed by considering that the oxidation process tends to re-equilibrate the electron affinity of the different ionic species. Therefore, ∆ is calculated such that the HOMO is evenly shared between the vanadium 3d and the ligand 2p orbitals when, to disentangle the ∆ parameter from the value of the hopping terms, the hopping term is strongly reduced. This is simply obtained by scaling down the t factors to below 10 -2 eV. When the code is used with a realistic hopping strength the HOMO-LUMO gap is increased and the HOMO character is clearly V-3d like.

The resulting approximated crystal field 10Dq parameter, 55 defined here as 10Dq, and the electron π-bonding charge δq are displayed in Table 1. The π-bonding charge, δq, is the difference between the average occupancy of the 3d shell in the ground state and the nominal occupancy. The parameter 10Dq, instead, is deduced from the H dd term, which can always be written as a cubic (local) symmetry term plus a perturbation term with possibly no symmetry, i.e. the difference between the average energy of the perturbed e g levels and the average of the perturbed t 2g levels (see Figure 1 S1 in SI). In practice, to monitor the strength of the H dd term, the matrix is diagonalized and 5 levels are obtained. Then, the 10Dq monitor is provided as the difference between the center of gravity, by considering separately the average energy of the upper two levels (perturbed e g 's) and of the the lower three ones (perturbed t 2g 's). As an additional monitor value, ∆ CF , defined as the maximum absolute distance between a crystal field split level and the center of gravity of its perturbed group (perturbed e g 's or t 2g 's ) is also introduced. In O h symmetry 10Dq is equal to 10Dq, with ∆ CF = 0 (Figure S1 in SI), while it would be equal to 5/(3 √ 30)X 400 in a regular T d symmetry. A high value of ∆ CF indicates the necessary condition of strong departure from octahedral symmetry, which still is not a sufficient condition for detecting an high ∆ CF . In fact, the departure can be realised also in the eigenvector space. symmetry, with an increased ∆ CF for the trans configuration, which aligns two fluorine ions on the same axis. We notice a discrepancy for 10Dq between the V 4+ trans experimental and ab initio cases. This discrepancy is found also in the geometrical distortion: in the experimental structure, the very short vanadyl bond is mirrored on the opposite side by an elongated bond (see Figure 1). This elongation probably plays a compensation role for the stabilisation of the crystal structure, even though in the ab initio calculated structure it is less pronounced. Besides depending on the crystal field, the local environment also depends on the neighbouring orbitals and their hybridisation with the vanadium 3d ones. By inspection of the t ′ term of Eq. 6 it can be observed that the 2p orbitals of fluorine, in the V 3+ system, have an average energy of about 1.5 eV lower than those of the oxygen ligands. Concerning V 4+ instead, the oxygen-vanadium hopping t ′ terms are 57% stronger for the short vanadyl bond than for the other longer bonds, while the 2p average energy on the oxygen V-V bridge sites are 0.8 eV higher than that of the other oxygen sites. The agreement with the experiment is quite satisfactory, especially considering that all parameters are determined from the ab initio electronic structure. In particular, apart from a rigid shift in energy and an overall intensity rescaling, no fitting procedure was applied. The rigid shift is necessary because, at variance with the ab initio quantum chemistry configuration interaction codes, the relaxation processes occurring in the final state atomic orbitals are not described in our model Hamiltonian. This results in over-estimated transition energies. The scaling is also needed as the experimental protocol does not contemplate the absolute calibration of the signal, which would require a laborious procedure to acquire a full characterisation of the beam shape, the exact density distribution of the sample, and the calculation of the scattering paths through the sample. The same rescaling factor is applied to the pairs of trans and cis sites.

Such results were obtained for an a a priori known stable structure, used here as a reference system. For measurements carried out in operando conditions, it may happen that the system far from equilibrium and its configuration is difficult to catch by ab initio calculations, which may converge to a different stable structure.

In order to understand which structural information can be obtained from multiplet simulation, the calculation was repeated, matching the experimental data by using the empirical parameters instead of the Wannier Hamiltonian. Accordingly, the complementary nature of the two approaches can be proved.

Figure 5: Simulation of V 3+ and V 4+ XRS spectra with Hilbert++ and optimal empirical parameters considering a distorted octahedron given by ab initio optimisation (blue line), an ideal octahedron (green line), and finally a distorted octahedron whose coordinates have been manually optimised (red line). 2. The same set of crystal field and hybridisation parameters was used for the two systems, as they are transferable parameters, which are rescaled according to the geometry in Eq. 20 (7,8). Tables 3 and4 display the ligand positions for the V sites in (0,0,0) position, which are drawn in Figure 6: 3 and4.

The resulting approximated crystal field 10Dq, and electron π-bonding charge δq are displayed in Table 5. Figure 5 shows that the simulations for the V 3+ system are in good agreement for all three considered structures, of which the VASP optimized and manually optimised structure show slightly better agreement with experiment than the simulation based on an ideal octahedron.

For this system, Figure 5 only shows the trans structure as it is clear based on the ab initio simulations that the differences between the spectra of the cis and trans forms are negligible. Starting from the octahedron and manually setting the ionic positions along the trans axis(red curve), a slight improvement of the simulation of the ratio of the two edges could be obtained. Along this axis, in fact, the hybridisation of the fluorine atoms depends, in a real system, not only on the V-F distance but also on the fluorine energy, which is different than the oxygen one (see the above discussion on the Wannier90 derived Hamiltonian). As the actual version of Hilbert++ considers, in the empirical model, all ligand orbitals as degenerate, the extra distortion along the fluorine axis mimics, by using positional parameters, the effect of such degeneracy removal on the spectra. It can be noted that the best simulations of experimental spectra was achieved with longer V-F distances (2.28 Å) than V-O (2 Å). Even though different from what is experimentally observed, it can be explained by considering that F -2p orbitals are more contracted than O 2-such that, in an empirical simulation, this effect is accounted by longer V-F distances. This observation opens the door to future developments of the empirical model of the Hilbert++ code, where the parameters will be adapted to the nature of the different ligands.

For the V 4+ system, we found that the distortion plays a significant role by improving the ratio of the L 3 and L 2 edges. The contraction describing the vanadyl bond in the manuallymodified positions from the regular octahedron, is sufficient to improve the agreement with the experimental data, and a similar results is obtained with the structure derived from DFT relaxation.

Conclusion

In this work, experimental XRS spectra at the V L 2,3 -and O K-edges of KVPO 4 F and KVOPO 4 are interpreted based on the results of full charge transfer multiplet simulations with different approaches to approximate the Hamiltonian of the site environment. In particular, it is shown how spectra simulated either using empirical parameters or by a full ab initio treatment of the problem confirm the presence of a distorted local environment of the V 4+ ions, whereas only subtle differences exist between the heteroanionic cis or trans arrangements. Simulations of the oxygen K-edge using a multiple scattering approach corroborates these results (see SI).

The perspective of using inexpensive empirical calculations arises as a very powerful tool for the analysis, the understanding, and the prediction of transition metal L-edges X-ray spectroscopy. Such calculations can be easily carried out on the fly by material science researchers, and can be of particular help when investigating the redox mechanisms at the atomic scale in transition metals compounds as electrode materials for M-ion batteries.

F 2 chains

 2 linked by F atoms. Phosphate groups hold the chains together and large channels can accommodate K + ions. Two symmetrically nonequivalent vanadium sites exist, with either a cis or trans arrangement of the F -ligands. In KVOPO 4 , fluorides are substituted by O 2-, which implies an oxidation state of +4 for the vanadium and consequently the V 4+ O 6 octahedra are strongly distorted in order to stabilise the d 1 electron configuration. The experimental crystal structure and V-O/F bond lengths of each V site in KVPO 4 F and KVOPO 4 are presented in Figure 1.

Figure 1 :

 1 Figure 1: a) Crystal structure of KVPO 4 F. The F sites can be completely or partially substituted by oxygen, up to the composition KVOPO 4 . b) Detailed experimental bond length of the first coordination shell in KVPO 4 F (top) and KVOPO 4 (bottom) for both vanadium sites.

Figure 2

 2 Figure2shows the experimental XRS spectra for the vanadium fluoride phosphate KVPO 4 F and vanadium oxide phosphate KVOPO 4 . VL 2,3 edges correspond to excitations from the 2p 6 3d n V ground state towards the 2p 5 3d n+1 V states. The two major features of these edges are the strong white-lines L 3 and L 2 due to the spin orbit splitting of the vana-

Figure 2 :

 2 Figure 2: Experimental XRS spectra at the L 2,3 and O K edges of KVPO 4 F and KVOPO 4 . The arrows point out the pre-peaks of the L 3 and L 2 white lines.

Figure 3 :

 3 Figure 3: Simulation of different nominal vanadium ions, without any crystal field nor hybridisation, obtained with Hilbert++ code.

Figure 4 :

 4 Figure 4: Energy loss spectra for KVPO 4 F and KVOPO 4 systems. The corresponding V 3+ and V 4+ spectra are calculated on the basis of the Wannier Hamiltonian for the ab initio structures (left panel) and experimental structures (right panel).

Figure 5

 5 Figure 5 shows the simulations obtained by varying the empirical parameters, first by fixing the geometry and letting only the hybridisation and crystal field parameters to vary (green curve), then by manually distorting the octahedra (red curve). During the manual optimisation of the structure the hybridisation parameters are kept constant because they are transferable. The spectra obtained fixing the ionic positions to the DFT optimised structure are shown for comparison (blue curve). The empirical parameters are reported in Table2.

Figure 6 :

 6 Figure 6: Local environments of V 3+ and V 4+ sites corresponding to Tables3 and 4.

  atmosphere to obtain VPO 4 , which was oxidized in air at 750 °C for 5 hours to form VOPO 4 . KVPO 4 F was then synthetized by mixing KF (Alfa Aesar) with VPO 4 in stoichiometric ratio. A pellet was placed in a sealed gold tube under argon ( < 0.1 ppm H 2 O/O 2 ) and calcination was performed at 650 °C for 6 hours. For KVOPO 4 , the precursor mixture consisted in K 2 CO 3 (Sigma-Aldrich, 99%), VPO 4 and VOPO 4 in a molar ratio.

	Sample preparation
	VPO 4 and VOPO 4 precursors were synthesized from NH 4 H 2 PO 4 (98 % Sigma-Aldrich) and
	V 2 O 5 (99.6 %, Sigma-Aldrich). The powder mixture was heated to 800 °C for 10 hours
	under Ar/H 2

Table 1 :

 1 Local environment effect on the V ions in the calculations with Wannier Hamiltonian.The analysis of the values summarized in Table1, shows that the crystal field monitor values 10Dq and ∆ CF are compatible with a slight deviation of the crystal field from O h

			vasp struct.			exp. struct.
		10Dq (eV) ∆ CF (eV) δq 10Dq (eV) ∆ CF (eV) δq
	V 3+ cis	1.33	0.13	0.39	1.44	0.1	0.39
	V 3+ trans	1.24	0.27	0.40	1.37	0.24	0.40
	V 4+ cis	1.37	0.47	0.43	1.25		0.44
	V 4+ trans	1.34	0.39	0.43	1.07	0.1	0.44

Table 2 :

 2 Empirical crystal field and hopping parameters used for V 3+ and V 4+ .

	Empirical parameter Value(eV)
	c σ	0.6
	c π	0.0
	t σ	1.0
	t π	0.5

Table 3 :

 3 Local structure of VO 6 octahedron in KVOPO 4 . Distances are reported in Å.

			V 4+ vasp		V 4+ manually opt.
	Ligand	x	y	z	x	y	z
	O 1	0	0	2.06	0	0	2.0
	O 2	-0.23 0.005 -2.02 0	0.0	-2.0
	O 3	1.73	0	-0.1 1.6	0	0
	O 4	-2.05 -0.23 -0.17 2.0	0	0
	O 5	-0.144 1.98 -0.14 0	2.0	0
	O 6	-0.195 -1.98 -0.05 0 -2.0	-0

Table 4 :

 4 Local structure of VO 4 F 2 octahedron in KVPO 4 F

			V 3+ vasp		V 3+ manually opt.
	Ligand	x	y	z	x y	z
	F 1	0	0	2.04 0 0	2.28
	F 2	0.08 -0.1 -2.02 0 0	-2.28
	O 1	2.02	0	0.07 2 0	0
	O 2	-2.01 -0.1	0.2 -2 0	0
	O 3	-0.01 2.02 -0.2 0 2	0
	O 4	0.01 -2.06 0.2	0 -2	0

Table 5 :

 5 Local environment indicators in the non distorted case.

		10Dq (eV) ∆ CF (eV) δq
	V 3+ vasp	1.8	0.03	0.38
	V 4+ vasp	1.81	0.15	0.42
	V 3+ manually set	1.85	0.22	0.39
	V 4+ manually set	1.9	0.26	0.43
	V 3+ octahedra	1.8	0.0	0.38
	V 4+ octahedra	1.8	0.0	0.42

t σ v † z b ,s dz 2 b ,s + t π (v † x b ,s dx b z b ,s + v † y b ,s dy b z b ,s ) + c.c.(7)

Acknowledgement

We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities. The authors gratefully acknowledge financial support from the French National Research Agency (projects Labex STORE-EX, grant no. ANR-10-LABX-76-01 and TROPIC, grant no. ANR-19-CE05-0026). F. Gerbon is acknowledged for technical support before and during the experiment at ID20.

Supporting Information Available

Additional experimental results of O K edge are here fully described. This material is available free of charge via the Internet at http://pubs.acs.org.

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Cindy François

Arthur Bonafé

Camille Roubille

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Patients with Obstructive Sleep Apnea and Cardiovascular Diseases: What, When, and Why Is Mandibular Advancement Device Treatment Required? A Short Review

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


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Thomas Sfara

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Molyneux Epicureanism : Locke

Why

EPICUREANISM AND MOLYNEUX'S QUESTION

When scholars attempt to fi nd ancient traces of the Molyneux problem, and of the Lockean epistemological perspective in which the problem is inscribed, they almost always refer to Aristotle 1 and, less frequently, to Cicero and the Stoics. 2 The reference to Aristotle is easy to explain because the problem of Molyneux originates from the problem of common sensibles, originally an Aristotelian concept, later adopted by Locke:

The ideas we get by more than one sense are of space, or extension, fi gure, rest, and motion; for these make perceivable impressions, both on the eyes and touch: and we can receive and convey into our minds the ideas of the extension, fi gure, motion, and rest of bodies, both by seeing and feeling.

Locke 1975 : II, ch. 5

According to Aristotle, 3 there are sensible objects that belong exclusively to one organ of sense (such as color for the eyes and sound for the ears) and common sensibles, perceptible by more than one sense (such as movement, fi gure, number). Locke, as we'll see later, inherits this theory.

The second reference to Cicero and the Stoics concerns the philosophical conception that constitutes the critical target of Locke's empiricism, "the problem of innate ideas," of which Cicero and the Stoics would, for some, be "the founding fathers." 4 This 5 is the background to the Molyneux question and is, in a way, its presupposition. If Locke had not been a strong critic of innate ideas, if he had not conceived the mind before experience as a tabula rasa , the problem of Molyneux would not arise. Despite the relatively obvious conceptual legacies from which it derives, the problem of Molyneux is and remains a modern problem which, as many scholars have shown, 6 fi nds its sources in the philosophical and scientifi c context of the time in which it was born. The aim of this study does not lie, therefore, in the search for new infl uences or fi liations between the philosophical-cultural context in which the problem was conceived and ancient philosophical theories. Rather, it compares the theories that constitute the conceptual basis of the problem, those of Locke's epistemology shared by Molyneux, with the theories of another older epistemology, that of Epicurus and Lucretius.

Why Epicurus and Lucretius? Certainly, there are similarities between Locke's and their conception of cognitive processes, in particular, because of the central role that experience plays in both systems. The two philosophers share the idea that all knowledge comes from the senses and the processing of perceptual material. This is particularly interesting with regard to the problem of Molyneux, where it is precisely experience or rather diff erent forms of experience, tactile and visual, that are the heart of the problem. Such issues are also examined and discussed by the Epicureans, as this passage from Lucretius' poem On Nature shows:

Here is a further point: when we handle an object of a particular shape in the dark, we recognise it as having the same shape that we see in the brilliant light of day. Therefore, touch and sight must be eff ected by the same cause. Now then, if we feel a square object in the dark and receive the impression of a square, what in the light will be able to give us the visual impression of a square, except the image of the object? It is evident therefore that images are the cause of vision, and that without them nothing could be seen. DRN III vv. 230-239. Tr. Smith 2001 Despite the obvious diff erences due to the diff erent historical-philosophical contexts to which they belong, it is useful to compare the "empiricisms" of the two philosophers to better understand the specifi city of Locke's empiricism and the theories that constitute it and that eventually diff erentiate it from Epicurus'. I chiefl y aim to answer two questions: (a) how would Epicurus have responded, based on his epistemological theories, to Molyneux's question: in the same way as Locke and Molyneux or diff erently? (b) And in the fi rst case: for the same reasons or diff erent reasons?

To do this, I will attempt to analyze Locke's response to the Molyneux problem in the light of the theories that the two thinkers shared by comparing them with the "corresponding" Epicurean doctrines. In the fi rst part, I examine the Lockean theory of common sensibles concerning the quality of form and the Epicurean theory of the senses. In the second part, I analyze the theories of the two philosophers which explain the perception of three-dimensionality.

Th e problem of form

Molyneux presents the problem to Locke in two diff erent versions. In the second version, 7 shorter, the author writes: Suppose a man born blind, and now adult, and taught by his touch to distinguish between a Cube, and a Sphere of the same metal, and nightly of the same bigness, so as to tell, when he felt one and t'other, which is the Cube, which the Sphere. Suppose then the Cube and Sphere placed on a Table, and the Blind Man to be made to see. Quaere, Whether by his sight, before he touch'd them, he could now distinguish, and tell, which is the Globe, which the Cube.

Locke 1975 : II, ch. IX, §8

As we know, Molyneux's response was negative:

Not. For, though he has obtained the experience of how a globe, how a cube aff ects his touch, yet he has not yet obtained the experience, that what aff ects his touch so or 9780367030926_pi-344.indd 37 9780367030926_pi-344.indd 37 22-Jun-20 7:39:02 PM 22-Jun-20 7:39:02 PM so, must aff ect his sight so or so; or that a protuberant angle in the cube, that pressed his hand unequally, shall appear to his eye as it does in the cube. Ibid.

Locke's was equally negative but more nuanced:

A person born blind would not be able to say immediately with any certainty which was the sphere and which the cube.

Ibid.

Now, to understand this answer, it is necessary to analyze the main parts that constitute the problem: the problem of form and the problem of three-dimensionality. As we have seen, the problem mainly concerns the ability of a blind born person to recognize the shape of an object by sight, an object previously known only by touch. The fi rst element to consider is, therefore, the perception of form and the explanation that Locke gives of it. According to the English philosopher, who follows in the footsteps of Aristotle, there are simple ideas 8 that can only be grasped by a sense such as color for the eyes and sound for the ears. This means that for a person born blind or deaf the idea of color or sound will be totally inaccessible. There are also simple ideas that can be grasped by several senses, as In the case of colors and sounds, the problem of people born blind or deaf who subsequently gain their abilities does not arise: having never had access to color and sound, these experiences will be totally new once hearing and sight are gained. But in the case of form? Since form is a simple idea, passively perceived through experience alone, and since both sight and touch are ways of accessing its perception, is it possible that the fi rst visual perception of a form, previously known through touch, allows the sentient subject to recognize it? Is the intermodality of this sensitive quality suffi cient for its recognition? This seems to be the fi rst diffi culty from which the problem of Molyneux arises. If the shape of an object is accessible to sight and touch, since the shape is common to both senses, it should be possible to switch from one sensory mode to another without there having been a simultaneous experience of the two sensations previously. But as we've seen, that is not the case according to Molyneux or according to Locke. Before investigating the other parts of the problem that explain Locke's negative answer, let me compare this theory of common sensibles with the Epicurean theory of sensation.

The fi rst element to take into account is that there is no Epicurean theory of common sensibles. The Epicurean theory of the senses is based mainly on the theory of eidola / simulacra and pores 10 and the theory of the fourth nameless nature ( quarta natura vacans nomine ). 11 The fi rst theory explains the functioning of sight, smell, hearing and, in part, taste. The second theory explains the functioning of all senses, including touch. About the simulacra or eidola 12 of sight, Epicurus 13 writes: Moreover, there are delineations which represent the shapes of solid bodies and which in their fi neness of texture are far diff erent from things evident. For it is not impossible that such emanations should arise in the space around us, or appropriate conditions for the production of their concavity and fi neness of texture, or effl uences preserving the same sequential arrangement and the same pattern of motion as they had in the solid bodies. Hrdt §46. Tr. Long and Sedley 1987 : 72 14 Sight is the result of the detachment from solid bodies of simulacra or eidola , that is, of very thin and very fast atomic fi lms that enter the eyes through pores suitable for their shape and size. The fact that the pores are suitable for simulacra / eidola of sight is a fundamental element of the theory. This is what allows the senses to access only their own sensibles and not to grasp other forms of emanation. In fact, Epicurus explains the senses of smell and hearing in the same way: there are atomic emanations of diff erent shapes, compositions, and sizes coming from solid bodies. 15 In the case of taste, 16 the explanation is slightly diff erent because, unlike what happens in the case of sight, smell and hearing, the perception takes place in the mouth, in direct contact with (the pores of) the organ of sense. This external stage, so to speak, is followed by un internal one. Once the emanations have penetrated the body through the pores, the simulacra / eidola touch and set the soul in motion. That's where the fourth nature theory comes in:

At death a sort of light breath impregnated with heat leaves the body, and heat draws air with it; indeed, there is no heat that is not impregnated with air, because the rarity of its substance means that it must be interpenetrated by many primary particles of air. Already, then, the substance of the soul has been found to consist of three elements. But a combination of these three is not suffi cient to produce sensibility, since the mind refuses to accept that any one of them is capable of producing sensory motions and the thoughts that it itself revolves. Therefore, a fourth element must be added to their number. This is entirely nameless. DRN III vv. 234-242. Tr. Smith 2001 According to Epicurus 17 and Lucretius, the soul 18 would be composed of four diff erent elements: heat, breath, air, and a fourth nature without a name. This unknown nature, more subtle and mobile than any other existing nature, explains the existence of thought and sensation, which are phenomena that could not be produced by the other three elements. 19 The fourth nature set in motion by the simulacra / eidola touches and sets in motion the heat, the breath, and the air and then all the materials that make up the body or a part of it, 20 in a sort of chain reaction. In this way, Epicurus and Lucretius also account for the touch which occurs through external and direct contact (and not through emanation and penetration) between a solid body and a sentient body and does not need to be explained as sight, smell, hearing, and taste. Now, as we have seen, every sense has its structure (i.e. the conformation and position of its pores) to which corresponds a specifi c sensible and which does not allow it to grasp the other sensibles. Nevertheless, there is consistency between perceptions:

Here is a further point: when we handle an object of a particular shape in the dark, we recognize it as having the same shape that we see in the brilliant light of day. Therefore, touch and sight must be eff ected by the same cause. Now then, if we feel a square object in the dark and receive the impression of a square, what in the light will be able to give us the visual impression of a square, except the image of the object? It is evident therefore that images are the cause of vision, and that without them nothing could be seen. DRN III vv. 230-239. Tr. Smith 2001 9780367030926_pi-344.indd 39 9780367030926_pi-344.indd 39 22-Jun-20 7:39:02 PM 22-Jun-20 7:39:02 PM Lucretius' objective in these verses is clear: to defend the idea that sight is produced by the penetration in the sensory organ of a part of the perceived object. In other words, we can perceive the shape and the color of the object because it is the object itself or at least a part of it, its surface, that "meets" us. The poet demonstrates this by using an example: we can recognize in the form of a solid body perceived in the dark by touch the same shape that we perceive with our eyes in sunlight. This is possible because, in reality, the perceived object, that is the surface composed of atoms positioned in such a way as to create a certain shape, is the same.

The only diff erence is that touch perceives it by direct contact, with the hands for example, and sight perceives it because this surface detaches itself from the body and penetrates the eyes. This aspect is fundamental for the epistemology of Epicurus, which is based on the absolute reliability of the senses, whose product is always true. 21 To avoid any risk that the truthfulness of the senses be questioned, the perceptive representation produced by each sense must derive, without medium, 22 from the contact between the organ of sense and the perceived object, 23 in this case the emanation of its surface. 24 In the problem of Molyneux, we fi nd a situation very similar to that presented in Lucretius' problem. The diff erence lies in the fact that his verses do not clearly say, as Molyneux does, whether the experience described is preceded by a simultaneous tactile and visual experience of the object. In other words, Lucretius does not say if this recognition is possible because the sentient subject already possesses a multisensory knowledge of the object. 25 The aim of these verses is to demonstrate that sight is a kind of "remote touch," but there is another interesting element of the theory in this example. According to Lucretius, the quality of form is inherent in the object. But, as I mentioned earlier, there is no Epicurean theory of common sensibles. This same quality is perceived in diff erent ways by diff erent structures. The perceptive representation is, therefore, specifi c and proper to the organ that produced it, even though the quality is inherent to the object and apprehended by more than one sense. 26 The question is: since the quality of form is inherent to the object, is visual recognition of the object, based on previous tactile experience, possible in Epicurus? I will return to this question but fi rst I must analyze the second part of the problem.

Th e problem of three-dimensionality

As aforementioned, form as a simple and common idea between sight and touch does not seem to be a suffi ciently valid reason to justify Locke and Molyneux's negative response to the problem; on the contrary, it justifi es a positive response. As has been recognized by more than one scholar, 27 the problem seems to concern not so much the perception of the form itself, but the nature of the form perceived by sight and touch.

In the following paragraph, in the Essay , Locke explains how simple ideas from experience can often be confused in the intellect by judgment. The example chosen by the English philosopher is sight, about which he writes:

From that which is truly variety of shadow or colour, collecting the fi gure, it makes it pass for a mark of fi gure, and frames to itself the perception of a convex fi gure and an uniform colour; when the idea we receive from thence is only a plane variously coloured, as is evident in painting.

Locke 1975 : II, ch. IX, §8

According to Locke, sight has access to the form but only to the two-dimensional form of a body. This means that the blind born man, once his sight is restored, would not see a sphere and 9780367030926_pi-344.indd 40 9780367030926_pi-344.indd 40 22-Jun-20 7:39:02 PM 22-Jun-20 7:39:02 PM a cube on the table but a circle and a square. 28 The passage from two-dimensionality to threedimensionality would occur thanks to habit, that is, thanks to the repeated and simultaneous experience of sight and touch. This habit would allow the individual to "learn" the correspondence between the two-dimensional fi gures perceived by sight and the three-dimensional forms perceived by touch. This explains why a man born blind who gained his sight, would not immediately be able to associate the visible form, circle and square, to the touched form, cube, and sphere. 29 I now move to Epicurus. Is the three-dimensionality of solid bodies, as in the case of Locke, the fruit of habit or is it a datum immediately provided by the senses?

On this point, as explained above, Epicurus already stated that eidola reproduce the concavity of solid bodies, but Lucretius gives us more information in three related passages:

Images are sort of membranes stripped from the surfaces of objects and fl oat this way and that through the air. DRN IV vv. 31-32. Tr. Smith 2001 […] I contend, then, that things emit fi lmy forms and images from their surfaces; and the proofs that follow wilI enable even the dulIest wit to understand that I am right. DRN IV vv. 41-44. Tr. Smith 2001 […] In the fi rst place, many things visibly discharge matter. Some of these discharges are rare and diff used, like the smoke emitted by wood or the heat by fi re; others are of a closer and denser texture, like the sleek coats that cicadas periodically shed in summer, or the superfi cial membranes of which newborn calves divest themselves, or again the vesture that the slippery serpent works off on the thorns as is evidenced by the familiar sight of brambles decorated with its nuttering slough. DRN IV vv. 56-62. Tr. Smith 2001 In these verses, Lucretius' objective is to defend the theory of simulacra . In line with the Epicurean strategy, 30 he invites his reader to observe nature: all bodies produce matter, fi re emanates smoke and heat, cicadas abandon their "tunics," and snakes, their old skin. In the same way, materials continuously fl ow out of solid bodies. The examples provided by Lucretius, especially those of the cicada and the snake, evoke the idea of three-dimensional membranes, i.e. fi lms that come from the whole body and that reproduce their shape while retaining their depth. Confi rmation of this can be found in paragraph 48 of the Letter to Herodotus , where Epicurus writes, to explain the rapidity in the formation of eidola , "they do not need to be fi lled out in depth." 31 , 32 The eidolon has a depth, the same as the solid body to which it belongs, but being only its outer membrane, once detached it remains empty inside. This is one of the reasons, according to Epicurus, for the rapidity of its formation. Unlike Locke, according to Epicurus the threedimensionality of bodies is a datum provided immediately by visual perception and not the product of a habit. As we have seen, the "formation" of visual three-dimensionality seems to be the main reason for Locke's negative answer to Molyneux's question. Does this mean that Epicurus would have answered Molyneux's question "Yes?"? I don't think so.

Epicurus and Molyneux

As I showed in the second part of this article, Epicurus conceives a theory of the senses that harnesses, so to speak, the senses to their sensibles and guarantees their exclusive relationship. Each sensory organ has its own structure suitable for the reception of a given type of sensible. Although many qualities are inherent to a body, each sense receives only one "aspect" of this body. Now, the question is: does the fact that the diff erent aspects of the body are inherent to the same object (as is the case with the shape of an object for sight and touch) mean that a quality perceived by one sense can automatically evoke to the soul the same quality perceived by another sense? The texts rule out this possibility for two reasons. The fi rst is related to the non-"communication" between the senses. 33 As Lucretius clearly states:

Or can sight be corrected by hearing, or hearing by touch? Can the evidence of touch be challenged by taste, refuted by hearing, or invalidated by sight? Not so, in my opinion. The fact is that each sense has its own special sphere, its own separate function. Thus, the discernment of softness, cold, and heat must be the province of one particular sense, while the perception of the various colours and everything connected with colours must be the business of another. Taste too has its own distinct function; smell is produced separately, and so is sound. It necessarily follows therefore that one sense cannot refute another. DRN IV vv. 486-497. Tr. Smith 2001 Since the structure of the senses is suitable for only one specifi c type of sensitive quality, one sense cannot confi rm or correct the perceptual material captured by another sense. This means that the senses cannot contradict each other. This is a fundamental element of Epicurus' epistemological theory because it constitutes his main weapon against sceptical challenges. The multiplicity of the senses and their ability to describe diff erent aspects of a body is often the fi rst step in questioning the truthfulness of the senses. It is no coincidence that this type of approach can be found in the Pyrrhonist Sextus Empiricus in the famous example of the apple:

Each of the objects of perception which appears to us seems to impress us in a variety of ways -for example, an apple is smooth, fragrant, sweet, and yellow. It is unclear, then, whether in reality it has these qualities alone, or has only one quality but appears diff erent depending on the diff erent constitution of the sense-organs, or actually has more qualities than those which are apparent, some of them not making an impression on us. Sext. Emp. HP I, 94. Tr. Annas & Barnes 1994 : 26 The argument of the sceptical philosopher continues with the example of a deaf and blind man for whom solid bodies have only three "types" of quality, the only ones he can perceive. The objective is clear: the true scope of the senses is doubtful since their access to reality could be partial and "deformed" by the structure that constitutes each of them.

Although Sextus wrote this a long time after Epicurus' death, this type of argument was very common at the time of the birth of the Garden. Epicurus opposed to it total confi dence in the senses as the only access to reality: since the activity of the intellect is based on the material provided by the senses, if this is considered fallacious, the mind will not be able to defend itself or correct senses and the subject would, therefore, remain in a situation of impasse. 34 It is therefore not possible to doubt the senses since there is no other cognitive criterion that could replace them. Nevertheless, to strengthen this trust, the master of the Garden eliminates or attempts to eliminate all the factors that could weaken their eff ectiveness. An example of this is the aforementioned theory of emanations that involves the elimination of any possible medium between the sense and the sensible, which would only threaten the truth of the senses 9780367030926_pi-344.indd 42 9780367030926_pi-344.indd 42 22-Jun-20 7:39:02 PM 22-Jun-20 7:39:02 PM by distancing them from the objects they perceive. Another strategic move of Epicurus is to exclude any possibility of contradiction or correction between the senses. As Lucretius adds at the end of the verses cited, not only can the senses not correct each other, but in addition "it is also impossible for any sense to correct itself." As he had previously specifi ed about the example of the moving shadow we see behind a body and which might be taken to be an illusion:

However, in this connection we do not allow that the eyes are in any way deceived.

Their business is to observe the areas of light and shadow. But the question of whether the light is the same or not, and whether it is the same shadow passing from place to place, or whether the position is rather as I have stated it above this can be decided only by the reasoning of the mind. DRN IV vv. 379-387. Tr. Smith 2001 According to Lucretius, the sensations, even those that derive from the same sense, do not have the ability to confront, correct or contradict themselves. This happens for two reasons. The fi rst is that the sensations are equivalent: there is no reason why one sensation should have more value than another. The other reason is that the sensations have immediate validity and no memory. This is well described by Diogenes Laertius who, in the tenth book of the Lives of the Philosophers , devoted to Epicurus, writes:

All sensation, he [Epicurus] says, is irrational and does not accommodate memory, for neither is it moved by itself, nor when moved by something else is it able to add or subtract anything. Nor does there exist that which can refute sensations: neither can like sense refute like, because of their equal validity. Diogenes Laertius X, 31. Long & Sedley 1987 : 79 The feeling is without memory and irrational, or rather a-rational. This means that, as Long and Sedley point out, "unlike the Stoics, Epicurus is insistent that sensations are entirely irrational events, involving no interpretation at all." 35 Sensation consists in setting in motion, by the sensible through the sense organs, a part of the soul that Epicurus considered alogon 36 and Lucretius called anima . 37 This part, which is widely distributed throughout the body, is clearly separated from the mind, located in the chest, where thought and judgment take place. This means that sensation is only the product of the temporary action of reality on the subject who passively receives it. 38 The sensations are not subjected at the perceptual level, that is, at the level of the a-rational soul, to any operation of comparison, synthesis or judgment.

To return to Molyneux's problem, these aspects of Epicurean epistemological theory exclude the idea that the mere visual perception of the sphere evokes its previous tactile perception. For this to be possible, the sensation should draw on a perceptual (intersensory) memory that, as we have seen, Epicurus does not admit at the level of the sensation alone. So recognition is not possible at the level of sensations. If the sensation is not enough, what would be enough for the "intermodal" recognition of the shape of the sphere and the cube to take place? Probably, according to an Epicurean, the anticipation or the prolepsis. 39 What is this about? Preconception, they [the Epicureans] say, is as it were a perception, or correct opinion, or conception, or universal "stored notion" (i.e. memory) of that which has frequently become evident externally: e.g. "Such and such a kind of thing is a man". For as soon as the word "man" is uttered, immediately its delineation also comes to mind by means of preconception, since the senses give the lead. Thus, what primarily underlies each name 9780367030926_pi-344.indd 43 9780367030926_pi-344.indd 43 22-Jun-20 7:39:02 PM 22-Jun-20 7:39:02 PM is something self-evident. And what we inquire about we would not have inquired about if we had not had prior knowledge of it. For example: "Is what's standing over there a horse or a cow?". For one must at some time have come to know the form of a horse and that of a cow by means of preconception, Nor would we have named something if we had not previously learnt its delineation by means of preconception.

Diogenes Laertium X, 33-34. Long & Sedley 1987 : 87-88 Anticipation, or prolepsis, is, after sensation, the second most important cognitive criterion according to the Epicureans. If the feeling is endowed with what Pierre-Marie Morel calls " principe d'actualité, " 40 or a validity that is contemporary to the action of the sensible object on the sensory organ, the anticipation is a "prolongation" and takes place when this object is no longer present. It is, therefore, a notion built on the basis of the repeated perception of a body.

Using the example of Molyneux, it would be the multisensory perception of a sphere or a cube that allows a person to put together the perceptual material provided by the diff erent senses and to form an idea, a "composite" concept of a "cube" or of a "sphere". The formation of this composite idea or concept allows not only the "possession" of the notion of a universal object (formed by the reiteration of the perception of many particular examples) in the absence of the corresponding object, but also its recognition once present. In other words, if sensations are the way to the knowledge of an object, anticipations allow its acknowledgment.

Returning to Epicurus' hypothetical response to Molyneux, I think that the intermodal recognition of a shape could only take place under one condition: that a general notion has previously been constituted in which all the qualities of the object are synthesized. In the case of the Molyneux problem, the person born blind has a general notion of the sphere and the cube, but in this notion, the qualities provided by sight are not synthesized. This means that once sight has been acquired, the person observing the sphere and the cube without being able to touch them will not be able to appeal to the general concept 41 of the cube or sphere that they possess to implement the recognition.

It is interesting to note that both in the case of Locke and Molyneux, and in the case of Epicurus, the answer to the question is negative and, despite some theoretical diff erences, for the same reason. In fact, according to our philosophers, for intermodal recognition to be possible, it would be necessary for the person born blind to have already experienced their visual and tactile sensations simultaneously. In other words, the individual would need to have learnt the perception of form (perceptual learning) by passing through the diff erent senses. In the case of Locke and Molyneux, this step, as we have seen, is necessary for the subject to get used to moving from the perception of two-dimensional visual forms to the perception of threedimensional tactile forms. Learning of this correspondence between the perceived qualities, possible thanks to the reiteration of the tactile and visual experience of the sphere and the cube, is the necessary condition for intermodal recognition to take place. As Molyneux explains well, the person must understand that what is visually perceived as a corner, from a tactile point of view produces a sensation of angularity and that a form of correspondence is created between these two sensations. In the case of Epicurus, recognition is not possible at the level of sensations. In fact, because the sensations are a-rational and without memory they have an immediate validity and cannot compare to, evoke or correct each other. The visual sensation cannot, therefore, recall a previous tactile sensation. For this to be possible, it is necessary to appeal to the anticipations that preserve the perceptive material and that, through the comparison and synthesis of this material, allow the formation of a general and composite notion. Even for Epicurus, a composite notion formed by habit, i.e. the reiteration of the intermodal perception of the sphere and the cube, is necessary. Despite the theoretical diff erences between the two systems, on the matter of common sensibles and three-dimensionality, the answer is the same: the person born blind who has subsequently acquired sight will not be able to immediately recognize 42 the sphere and the cube.

The diff erent Epicurean texts that I analyze in this study and which allowed me to provide an Epicurean answer to the Molyneux problem are proof of the fact that, beyond the diff erences between two distant versions of empiricism, due to the diff erent systems and contexts to which they belong and to the diff erent objectives they pursue, the problem of the limits and potentialities of experience alone remains common. On the one hand, there are the limits of visual experience: the perception of form without depth, in Locke's conception, and the limits of perception that we could defi ne as "temporal", because it is valid only and exclusively hic et nunc , in the Epicurean doctrine. On the other hand, we cannot deny the potential of experience and, in particular, of repeated (habitual) experience, which in both systems provides the perceptual material for the constitution of more complex knowledge. The Molyneux problem fi nds the right perspective to challenge Lockean empiricism on this central issue. The proof of this is its success at the time. However, the analysis of this problem in the light of Epicurean epistemology has demonstrated the relevance of this type of problem even in a context as distant philosophically and historically as the Ancient one. This shows how these kinds of questions constitute the heart of empiricism itself, both Lockean and Epicurean.

N o t e s

1 Mackie 1976 : 28-32;[START_REF] Degenaar | Molyneux's Problem. Three Centuries of Discussion on the Perception of Forms[END_REF]: 19. 2 McRae 1972 : 31. 3 DA II, 6. 4 This interpretation could be explained in the light of some studies such as that of [START_REF] Brochard | Descartes Stoïcien[END_REF] on "Descartes Stoïcien". According to the scholar, some Cartesian theories, including those of innate ideas, derive from a Stoic infl uence on the French philosopher. McRae seems to accept the interpretative proposal, citing Cicero and the Stoics among the fathers of innatism, although he would like to point out that in his opinion Locke's critical objective was Lord Herbert of Cherbury and not Descartes (McRae 1972 : 31). The attribution of the theory of innate ideas to Stoicism is a very controversial issue. On the one hand, this attribution may seem paradoxical since the theory of tabula rasa belongs to the Stoic milieu (Aet. IV, 11, 1-4). On the other hand, because of the few sources, specialists

do not yet agree on the presence or absence of a certain form of innatism in stoicism, i.e. dispositional innatism. To examine the question in depth, see [START_REF] Sandbach | Ennoia and prolepsis in the Stoic theory of knowledge[END_REF][START_REF] Scott | Innatism and the Stoa[END_REF]et Dyson 2009 . 19 In fact, if it were, any body equipped with these elements would be sentient. For Epicurus, this is a way of safeguarding the diff erence between living and non-living beings (i.e. sentient and non-sentient), as witnessed by experience, while remaining consistent with his materialistic psychology. 20 In the case of sight, the eyes, in the case of smell, the nose, in the case of hearing, the ears, in the case of taste, the tongue, and the palate and in the case of touch, the region of the body concerned. This is an important aspect of the Epicurean theory according to which the soul does not perceive through t he body but together with the body ( DRN III vv. 359-369). 21 Errors do not belong to the senses but to judgment. According to Epicurus, saying that a sensation is true means that the sensation is real (Sextus Empiricus, M VII = Us. 244 9) and could not be otherwise since it is the action (direct or remote) of bodies on the subject. 22 This is the main diff erence between the Epicurean theory of eidola and the Democritean theory of eidola (Theophr. Sens. §50) See [START_REF] Baldes | Democritus on visual perception: two theories or one?[END_REF][START_REF] Bukert | Air-imprints or eidola: Democritus' aetiology of vision[END_REF], Rudolph 2011 . 23 Hrdt §53. 24 For an interpretation of Epicurus as an exponent of direct realism see: Ehli 2017 . 25 These verses aim to demonstrate the validity of the theory of the simulacra of sight and not to question, as Molyneux does with his question, the relationship between the senses. 26 In this sense, Epicurus appears to anticipate Berkeley's theories (Berkeley 1732 : § 109). As Mackie rightly underscores: On Berkeley's view there is, at least primitively, no one common sensible shape […] the name of any particular shape, say 'square', stands for a pair of correlated ideas, one visual and one tactual, and what Aristotle takes as the perceiving of some one object through two senses is really the separate perceiving, by each of the two senses, of an idea special to that sense, accompanied by an inference to or expectation of the correlated idea which is peculiar to the other sense.

Mackie 1976 : 30 27 See Degenaar 1996 : 28-9;[START_REF] Parmentier | Le proble ̀ me de Molyneux de Locke a ̀ Diderot[END_REF]Chottin 2014 : 121. 28 Or a hexagon, this depends on the position, as Degenaar 1996 rightly writes: 28. See also [START_REF] Park | Locke and Berkeley on the Molyneux problem[END_REF][START_REF] Vienne | Locke et l'intentionnalité: le problème de Molyneux[END_REF][START_REF] Parmentier | Le proble ̀ me de Molyneux de Locke a ̀ Diderot[END_REF][START_REF] Berchielli | Color, space, and fi gure in Locke: An interpretation of the Molyneux Problem[END_REF], Bruno and Meldembaum 2010. 29 Mackie 1976: 30. 30 Asmis 1984and Morel 2015 . 31 Where "depth" indicates here the unfi lled (three-dimensional) space of the eidolon body. 32 Hrdt §48. Tr. Long and Sedley 1987 : 73. 33 Since, according to Epicurus, there are no common sensibles, knowledge is sensory-specifi c: each sense accounts for a specifi c aspect of reality. As we have seen, this aspect recalls Berkeley's theories. The diff erence between Epicurus and Berkeley lies in the fact that, according to the latter, no material reality exists: the essence of a being resides in being perceived. Therefore, according to Berkeley, not only the cognitive access to reality is sensory specifi c, but reality itself (Berkley 1734: §9). 34 DRN IV vv. 479-486. 35 Long & Sedley 1987: 85. 36 Hrdt. §66. 37 DRN III vv. 136-142. 38 Sext. Emp. M VII, 210. 39 See Goldschmidt 1978 ;[START_REF] Glidden | Epicurean prolepsis[END_REF][START_REF] Hammerstaed | Il ruolo della Prolepsis epicurea nell'interpretazione di Epicuro, Epistula ad Herodotum 37 SG[END_REF][START_REF] Morel | Method and evidence: On Epicurean preconception[END_REF]Konstan 2008b. 40 Morel 2009 : 141. 41 This "general concept" must be distinguished from the common sensible. The general concept is produced by the sum of the specifi c data each sensory organ provides about the object. Accordingly, it is not a single datum shared by several senses. 42 Where "immediately" refers in both cases to the need for a previous multisensory experience of the object.

9780367030926_pi-344.indd 44 9780367030926_pi-344.indd 44 22-Jun-20 7:39:02 PM 22-Jun-20 7:39:02 PM

See Adams 1975 ; Vienne 1991 : pp. 18-46.

Degenaar 1996 : 13-24; Paris 1990 : 171-173;[START_REF] Parmentier | Le proble ̀ me de Molyneux de Locke a ̀ Diderot[END_REF] Chottin 2014 : 9-25.

I analyze this version and not the fi rst one, although it is more detailed, since this second one was published by Locke followed by his answer.