Paula L Silva

Reinoud J Bootsma

Priscilla Rezende

Pereira Figueiredo

Bruna Silva Avelar

Gustavo André

Sérgio T Pereira De Andrade

Marisa Cotta Fonseca

Mancini

Priscilla Rezende Pereira

Pereira De Andrade

Sérgio T Fonseca

Marisa Cotta Mancini

Task difficulty and inertial properties of hand-held tools: An assessment of their concurrent effects on precision aiming

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

Introduction

Numerous daily and sports activities involve aiming the distal end of a hand-held tool or implement to targets in space. Driving a nail into the wall with a hammer or placing a screwdriver onto a screw head are but two representative examples. When performing any of these activities, a skillful actor patterns his or her muscular forces to control the motions of the end-effector (here the hand-held object) so as to achieve the intended targetobject relation. Task-specific use of hand-held tools and implements therefore requires sensitivity to constraints at the level of the task (e.g., accuracy requirements) and constraints at the level of the end-effector (e.g., mechanical properties of the tool or implement being used). In the present contribution, we examined the concurrent influences of both types of constraints on the performance and kinematics of precision aiming, which is a fundamental component of the functional use of hand-held objects. Inspired by the seminal work of [START_REF] Woodworth | Accuracy of voluntary movement[END_REF] and [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF], [START_REF] Fitts | Information capacity of discrete motor responses[END_REF], the effects of task constraints have been extensively explored in goal-directed aiming (see [START_REF] Plamondon | Speed/accuracy trade-offs in target-directed movements[END_REF][START_REF] Plamondon | Speed/accuracy trade-offs in target-directed movements[END_REF]Elliot, Helsen, &[START_REF] Elliott | A century later: Woodworth's (1899) two-component model of goal-directed aiming[END_REF] for reviews). Both the duration and the kinematic pattern of a successful aiming movement have been demonstrated to vary as a function of a task index of difficulty (ID) combining the distance D to be covered and the tolerance for terminal spatial variability delimited by target width W. The relation between task difficulty -with ID = log2(2D/W) being the most commonly used form -and movement time (MT) is in fact so robust, in both the discrete and reciprocal versions of Fitts' paradigmatic aiming task, that it has come to be known as Fitts' law. The lengthening of MT observed when the aiming task becomes more difficult has been related to systematic changes in the kinematic pattern of aiming movements, in both the discrete (e.g., [START_REF] Beggs | Movement control in man in a repetitive motor task[END_REF][START_REF] Elliott | A century later: Woodworth's (1899) two-component model of goal-directed aiming[END_REF][START_REF] Mackenzie | Three-dimensional movement trajectories in Fitts' task: Implications for control[END_REF] and reciprocal (e.g., [START_REF] Guiard | On Fitts's and Hooke's laws: Simple harmonic movement in upper-limb cyclical aiming[END_REF][START_REF] Huys | Fitts' law is not continuous in reciprocal aiming[END_REF][START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF] versions of the task. When task difficulty is low (i.e., when aiming for relatively large targets) movement patterns demonstrate symmetrically-shaped velocity profiles. Movements performed under higher levels of task difficulty are characterized by a progressive asymmetry in the velocity profile, mainly due to a lengthening (both in absolute and relative terms) of the duration of the deceleration phase. The window into the perceptual-motor processes underlying task execution offered by analysis of the characteristics of the kinematic patterns is perhaps richest for [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF] reciprocal version of the aiming task, as portraying the to-and-fro movements into phase and Hooke spaces provides insight into the underlying dynamics [START_REF] Bongers | Linear and logarithmic speed-accuracy trade-offs in reciprocal aiming result from task-specific parameterization of an invariant underlying dynamics[END_REF][START_REF] Bootsma | Behind Fitts' law: Kinematic patterns in goal-directed movements[END_REF]Bootsma & Mottet, 2004;[START_REF] Bootsma | Trajectory formation and speed-accuracy trade-off in aiming movements[END_REF][START_REF] Buchanan | Systematic scaling of target width: dynamics, planning, and feedback[END_REF][START_REF] Buchanan | Target width scaling in a repetitive aiming task: Switching between cyclical and discrete units of action[END_REF]Fernandez & Bootsma, 2004;[START_REF] Fernandez | Non-linear gaining in precision aiming: Making Fitts' task a bit easier[END_REF][START_REF] Guiard | On Fitts's and Hooke's laws: Simple harmonic movement in upper-limb cyclical aiming[END_REF][START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF][START_REF] Mottet | Two-handed performance of a rhythmical fitts task by individuals and dyads[END_REF]. Geometrical and mechanical characteristics of the end-effector have also been demonstrated to affect the time requiredto perform an aiming movement. For a given level of task difficulty, increasing the length of a hand-held probe [START_REF] Baird | The effects of probe length on Fitts' law[END_REF] and increasing the mass transported (Fernandez& Bootsma, 2004;[START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF][START_REF] Hoffmann | Effect of transported mass and constant force on times for ballistic and visuallycontrolled movements[END_REF][START_REF] Hoffmann | Movement times of different arm components[END_REF][START_REF] Konz | The control effect of small weights on hand-arm movements in the horizontal plane[END_REF][START_REF] Langolf | An investigation of Fitts' law using a wide range of movement amplitudes[END_REF] both give rise to a lengthening of MT. Most of these studies focused exclusively on MT and did not address the kinematic patterning of the aiming movements. One exception is the study performed by [START_REF] Fernandez | Effects of biomechanical and task constraints on the organization of movement in precision aiming[END_REF]. These authors exploited the anisotropy of the arm's workspace to investigate the effect of total transported mass through manipulations of the direction of end-effector motion during a reciprocal aiming task. Results showed that, at each level of task difficulty (IDs of 3, 4, and 5), the duration of movement increased when participants moved in directions associated with higher magnitudes of transported mass. For example, movement time was longer when transport of the entire upper limb was required to move between targets than when only transport of the less massive forearm was required. Importantly, manipulations of total transported mass did not provoke changes in the movement's kinematic patterns. In particular, no changes in the harmonicity of aiming patterns or in the underlying dynamical organization were observed. From these results they concluded that while (informational) constraints at the level of the task affected the processes underlying movement organization, (biomechanical) constraints at the level of the effector did not.

In the present study, we explored the effects of mass distribution along a long-shafted probe on the duration and organization of reciprocal aiming movements. The mass distribution of a hand-held object can, in principle, affect its appropriateness for performing manual tasks, and hence, influence the organization of aiming movements. For example, by the laws of mechanics, a hammer (whose mass is concentrated far from the point of grasp) is effective for transferring momentum to an external target, minimizing the need for generating muscular torque. However, maneuvering the hammer to adjust the position of its weighted end is relatively hard, particularly when the task involves high accelerations. Designing hammers with large heads is a strategy to compensate for the low maneuverability of the hammer's end position when hitting the typically very small nail heads. In contrast, by virtue of its mass being concentrated closer to the point of grasp, a screwdriver is comparatively ineffective for transferring momentum, but less difficult to maneuver. Maneuverability would be particularly beneficial for precision tasks requiring high speeds and rapid adjustments in end-effector's acceleration pattern. Here we arrive at the main hypothesis of the present experiment: tools with their mass concentrated close to point of grasp are expected to allow adjustments in the underlying perceptual-motor organization that minimize declines in performance (speed) as precision demands increase. We therefore expect that, differently from manipulation of transported mass, manipulation of a probe's mass distribution will affect not only the duration of aiming movements but also their kinematic pattern, particularly when accuracy demands are more stringent. Confirmation of this hypothesis would push a reassessment of the current view that task level constraints are informational while biomechanical constraints are not. Recently, [START_REF] Lin | Modeling movements of a long hand-held tool with effects of moments of inertia[END_REF] have studied the effect of mass distribution of long-shafted probes on the duration of aiming movements. No difference in movement time was observed when proximal and distal loading conditions were compared though middle loading was associated with faster performance). The authors suggested that distal and proximal loading benefit different aspects of aiming movements, leading to a similar effects on global performance. However, these authors did not address the kinematic patterning of the aiming movements and, therefore, the effect of end-effector's mass distribution on the perceptual-motor processes supporting aiming tasks remains unknown. Accordingly, in the present contribution we evaluated the concurrent effects of task difficulty and asymmetric loading of a hand-held probe on (a) performance of a reciprocal aiming task (in terms of MT), and (b) kinematic patterns of end-effector movements supporting such performance.

Method

Participants

Twelve right-handed volunteers (2 male and 10 female), ranging in age from 19.9 to 26.9 years (M ± SD = 23.5 ± 2.5 years) participated in the study. All participants reported normal or corrected to normal vision and had no neuro-musculoskeletal conditions that could interfere with their performance of the experimental task. Participants provided their informed consent prior to inclusion in the study, which was approved by the local ethics committee.

Task and materials

Participants were asked to tap the distal point of a long-shafted probe between two targets as fast and as accurately as possible. The probe's shaft consisted of a cylindrical wooden rod (length = 50 cm; diameter = 1 cm; mass = 50 g). The mass distribution of the rod (and, hence, the probe's appropriateness for the experimental task) was manipulated using a steel cylinder (length = 7 cm; mass = 140 g) that was firmly attached to the rod at either 10 or 40 cm from its point of grasp. This manipulation effectively created two different probes (PWprox and PWdist) of equal length, diameter and mass, but with different maximal principal moments of inertia (PWprox = 63.1 g cm2; PWdist = 273.1 g cm2). PWdist is more difficult to maneuver by virtue of its higher concentration of mass far from the hand, which is most simply reflected in a higher magnitude of I (see [START_REF] Hove | Perceiving affordances of hockey sticks by dynamic touch[END_REF]. Following the same line of reasoning, PWprox is less difficult to maneuver. Three equally-sized (50 by 15 cm) target boards were constructed from ethylene-vinyl acetate. In each board, two circular targets were positioned at a center-to-center distance D of 35 cm. The three boards differed with respect to the diameter representing width W of the targets (W = 1, 3 and 10 cm), which were selected to obtain three levels of task difficulty. Combinations of W and D gave rise to task ID's of 6.1, 4.5, 2.8 (hereafter referred to as ID6.1, ID4.5, ID2.8). A passive marker attached to the probe's distal end allowed sampling of the probe's position at a rate of 200 Hz using a three-camera ProReflex video-based motion analysis system (Qualisys Medical AB, Gothenburg, Sweden). The system was calibrated before each session, with maximal accepted residual error of 0.5 mm.

Procedure

For performance of the reciprocal aiming task, participants stood facing a table of adjustable height. For each trial one of the three target boards was firmly attached to the table top. The boards were positioned according to pre-set markers to guarantee that the location of the centers of the targets remained the same for all task IDs. The height of the table was adjusted such that participants would be able to maintain their upper arm along the side of the body and the forearm at about 90° at the elbow joint during performance of the task that required mediallateral movements. Prior to the experiment proper, participants had approximately 10 min of practice in order to ensure understanding of task requirements. They practiced with the three ID's, starting with the lowest, followed by the intermediate and the highest. For the practice trials participants used the wooden probe designed for the experiment with no load attached to it. During the familiarization phase, participants selected a comfortable base of support for task performance and an experimenter marked the position of their feet. This procedure assured the same position of the participant with respect to the targets for all experimental conditions. Before each experimental trial, participants were properly positioned and handed one of the two probes. They grasped the probe so that its proximal end was flush with the bottom of the hand. Participants then performed the reciprocal aiming task after the experimenter had started data collection by the motion analysis system. Each valid trial consisted of a sequence of 25 successful aiming movements. If participants missed a target, they were asked to repeat the trial and the previous was discarded. Four participants had to repeat trials. Each of these participants repeated 3 to 4 trials for the highest ID condition. There were six task conditions (two probe types crossed with three task ID's). The participants performed each condition twice, totaling 12 fully randomized trials. Participants were allowed to rest between trials as needed.

Data reduction and analysis

Guided by the task dynamic approach, we assume that the action system exploits limit cycle dynamics to produce self-sustained, rhythmic precision aiming motions with frequency and stability adapted according to extant task constraints [START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF][START_REF] Saltzman | Skilled actions: A task-dynamic approach[END_REF]. We were interested in understanding whether biomechanical constraints (in particular end-effector mass distribution) affect the period of oscillations and most importantly whether such effects are related to changes in the dynamical regime producing the oscillations. Movement time (i.e., half-cycle duration) was used as an index of global performance of the aiming task while

x the kinematics of aiming movements were used as a window into the underlying dynamical regime. According to the task dynamic approach, the underlying dynamical organization of goal-directed rhythmic movements (the focus of the present contribution) can be appropriately captured in a one-dimensional task space-in this case the task's main axis, linking one target center to the other [START_REF] Saltzman | Skilled actions: A task-dynamic approach[END_REF]. Therefore, for all analyses described below, we have used position time series of the probe, in the latero-lateral axis1 . All position time series were filtered using a dual-pass second-order Butterworth filter with a cut-off frequency of 5 Hz. Velocity and acceleration time series were subsequently derived using a 3-point central difference technique. Each trial was segmented into individual (half-cycle) aiming movements based on peaks and valleys in the position signal corresponding to zero-crossings in the velocity signal. In order to minimize the chances of including transient performance the first three and last two aiming movements were discarded. For each trial, analysis thus concerned 20 aiming movements.

Movement time

MT was defined as the mean half-cycle time, that is, the mean time it took participants to move from one target to the other [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF]. MT was calculated (for each condition performed by each participant) as the average time between two consecutive reversals of movement direction.

Kinematic patterns

The movement of the probe between targets in each trial was summarized in an average normalized cycle (Fernandez & Bootsma, 2004;[START_REF] Fernandez | Non-linear gaining in precision aiming: Making Fitts' task a bit easier[END_REF][START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF]. To this end, the 10 leftto-right and the 10 right-toleft movements were first averaged at constant phases of the movement (21 points, using steps of 5% MT) for position, velocity, and acceleration. The resulting time-series were then normalized to render their scales comparable over conditions. This was achieved by dividing the position, velocity and acceleration time-series, respectively, by A, Ax and Ax2, with A defined as mean maximal deviation from the center of oscillation and x as the mean frequency of motion (defined by 2p over mean trial period or 2 MT). The average normalized cycle was obtained by combining the back-and-forth average normalized half-cycles. To characterize the patterns of motion produced in each experimental condition, we portrayed the betweenparticipant average normalized cycles in phase space (velocity as a function of position; cf [START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF] and Hooke space (acceleration as a function of position; cf [START_REF] Guiard | On Fitts's and Hooke's laws: Simple harmonic movement in upper-limb cyclical aiming[END_REF][START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF]. The degree of asymmetry in acceleration and deceleration phases of aiming movements is reflected in the (a) offcenter location of the peak velocities in the phase portrait; and (b) the off-center location of the zero crossings in acceleration in the Hooke portrait (Mottet & Bootsma, 2001). Inspection of phase and Hooke's portraits also allowed an evaluation of the dynamical organization of the perceptualmotor system supporting task performance. As previously noted, we assumed that the action system exploits limit cycle oscillation dynamics to produce selfsustained rhythmic movements in an abstract task space [START_REF] Saltzman | Skilled actions: A task-dynamic approach[END_REF]. We further assume that analysis of aiming trajectories on phase and Hooke's portraits can reveal the underlying processes, both dissipative (energy-related) and conservative (stiffness-related), supporting production of aiming movements [START_REF] Beek | Tools for constructing dynamical models of rhythmic movement[END_REF][START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF]. The type of non-linearity characterizing the operative dissipative and conservative processes and the magnitude of their contribution to task performance are revealed respectively in the deviations from a perfect circle in phase space and in the deviations from a straight line in Hooke space. The particular types of nonlinearities and their contribution to task dynamics depends on the desired end-product: here a reciprocal aiming movement satisfying task and biomechanical constraints. To quantify the qualitative changes in the movement patterns associated with changes in the underlying dynamical organization, we calculated for each aiming movement the normalized peak acceleration (NPA, Fernandez & Bootsma, 2004), by dividing the observed peak acceleration by Ax2, where A corresponds to half the distance between movement extremes andx to p over the aiming movement's (half-cycle) duration. NPA for each trial was then obtained by averaging the individual values for the 20 aiming movements (half-cycles). With Ax2 corresponding the peak acceleration of a sinusoidal movement of amplitude A and frequency x, a movement governed by a linear dynamics gives rise to a NPA value of 1. Progressive deviations of NPA from 1 index progressive deviations from a sinusoidal movement pattern, signaling the progressively stronger contributions of non-linear processes to the performance of aiming movements.

Statistical analysis

For each dependent measure (MT and NPA), the results were averaged across the two trials of each condition and 2 x 3 repeated-measures analysis of variance (ANOVA) was conducted. The independent variables were the probe's functional appropriateness operationalized by the mass distribution of each probe type (PWprox and PWdist) and the accuracy demands of the task operationalized by task ID (2.8, 4.5 and 6.1).

Results

Movement time

The 2 x 3 ANOVA performed on MT demonstrated significant main effects of Task ID [F(2, 22) = 82.49; p < 0.001, hp 2 = 0.88] and Probe Type [F(1, 11) = 37.59; p < 0.001, hp 2 = 0.77]. The analysis also showed a significant Task ID x Probe Type interaction [F(2, 22) = 6.87; p < 0.01, hp 2 = 0.39 ]. As can be seen from Fig. 1 and confirmed by contrast analyses, for each type of probe MT increased with task ID (p's < 0.001). Moreover, probe type affected MT at each level of ID (p's < 0.001), with PWprox (easier to maneuver) associated with shorter MTs than PWdis. While MT was thus shorter when the task was performed with PWprox across all levels of difficulty, the interaction indicated that the difference between probe types increased with increasing task ID (see Fig. 1).

Kinematic patterns

The 2 x 3 ANOVA performed on NPA demonstrated significant main effects of Task ID [F(2, 22) = 39.09; p < 0.001,hp 2 = 0.78] and Probe Type [F(2, 22) = 15.34; p < 0.001, hp 2 = 0.58], as well as a significant Task ID x Probe Type interaction [F(2, 22) = 18.03; p < 0.001, hp 2 = 0.62]. As can be seen from Fig. 2 and confirmed by contrast analysis, for each type of probe NPA increased with task ID (all ps < 0.001), indicating an increasing deviation of aiming movements from a perfectly sinusoidal pattern as the level of task difficulty increased. Contrast analysis also demonstrated that probe type only affected NPA at the highest ID (p < 0.001), with PWdist (more difficult to maneuver) showing a smaller NPA than PWprox. Thus, under the most challenging condition, PWdist gave rise to less pronounced deviations from a sinusoidal pattern (values of NPA closer to 1) than PWprox (see Fig. 2). The above analysis of the effects of task difficulty and probe type on NPA provides grounding for the visual inspection of the (between-participant averaged) phase (Fig. 3) and Hooke (Fig. 4) portraits obtained under each condition. Variations in task difficulty (that is, variations in ID) gave rise to the same phenomena described for end-effector movement in earlier studies. For the lowest level of task difficulty phase portraits were close to circular and Hooke portraits close to linear, indicating that probe movement was quasi-sinusoidal. Within each half cycle the acceleration and deceleration phases were symmetrical, while the deceleration phase of half-cycle n (bringing the probe to stop within the target area) was fully merged with the re-acceleration phase of half-cycle n + 1 (driving the probe towards the other target). As ID increased, movement patterns lost their symmetrical character, due to the disproportionate increase in the duration of the deceleration phase with respect to the acceleration phase, as can be seen in phase space (Fig. 3) from the displacement of the peak velocities from the midpoint between the targets. At the same time, the deceleration of half-cycle n and the subsequent reacceleration of half-cycle n + 1 began to separate, as evidenced by the displacement of the point of peak acceleration from the point of movement reversal (Fig. 4). Of particular interest for the present purposes was the influence of probe type on the movement patterns that appeared at the higher levels of task difficulty. In particular, the progressive deviations of trajectories from a perfect circle in phase space (Fig. 3) and from a straight line in Hook space (Fig. 4) were less pronounced for PWdist than for PWprox. At the lowest level of task difficulty movement was quasi-sinusoidal for both probes, but at the highest level of task difficulty PWprox gave rise to stronger non-linearities (a larger degree of asymmetry between acceleration and deceleration phases and a larger separation between deceleration and subsequent reacceleration) than PWdist. These observations correspond to the finding that NPA was statistically different between probes only at the highest level of difficulty (ID6.1).

Discussion

The present experiment examined the effect of end-effector mass distribution on task performance and underlying movement organization in the framework of reciprocal precision aiming. We hypothesized that tools with mass concentrated close to point of grasp would optimize performance of aiming tasks by allowing adjustments in the underlying perceptual-motor organization that minimize performance decrements as precision demands increase. To test this hypothesis, we crossed three levels of task difficulty with two types of probe varying in their maneuverability: one with mass concentrated close to the point of grasp (arguably more appropriate for fast precision aiming tasks) and one with mass concentrated far from the point of grasp (arguably less appropriate for such tasks). We evaluated the effect of task difficulty and probe type on (a) movement duration, a measure of task performance, and (b) the kinematic pattern of aiming movements, a window into the dynamics of underlying perceptual-motor organization supporting performance. Movement duration was longer for smaller targets as predicted by Fitts' Law. Lengthening of movement duration as a function of task difficulty was mediated by changes in the kinematics of aiming patterns, as expected from the existing literature on precision aiming, whether the task is discrete (e.g., [START_REF] Beggs | Movement control in man in a repetitive motor task[END_REF][START_REF] Elliott | A century later: Woodworth's (1899) two-component model of goal-directed aiming[END_REF][START_REF] Mackenzie | Three-dimensional movement trajectories in Fitts' task: Implications for control[END_REF] or reciprocal (e.g., [START_REF] Guiard | On Fitts's and Hooke's laws: Simple harmonic movement in upper-limb cyclical aiming[END_REF][START_REF] Huys | Fitts' law is not continuous in reciprocal aiming[END_REF][START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF]. For the lowest task ID, movement patterns were quasi-sinusoidal, as indicated by NPA values close to 1. Indeed, the shape of trajectories in Hook space suggests a linear dynamical organization supporting task performance. Put differently, the end-effector behaved as though governed by a linear stiffness function [START_REF] Bongers | Linear and logarithmic speed-accuracy trade-offs in reciprocal aiming result from task-specific parameterization of an invariant underlying dynamics[END_REF][START_REF] Guiard | On Fitts's and Hooke's laws: Simple harmonic movement in upper-limb cyclical aiming[END_REF][START_REF] Guiard | Fitts' law in the discrete vs. cyclical paradigm[END_REF][START_REF] Kelso | Theoretical concepts and strategies for understanding perceptual-motor skill: From information capacity in closed systems to selforganization in open, non equilibrium systems[END_REF][START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF]. The quasi-circular trajectories in phase space for the lowest ID suggest a mode of behavior with minimal interference with limb motion through non-linear dissipative mechanisms [START_REF] Guiard | On Fitts's and Hooke's laws: Simple harmonic movement in upper-limb cyclical aiming[END_REF][START_REF] Guiard | Fitts' law in the discrete vs. cyclical paradigm[END_REF]. As tolerance for spatial variability at the end-point decreased (i.e. as target width was reduced), movement patterns became less sinusoidal, as indicated by the progressive deviation of NPA values from 1. The related changes in phase portraits index the increasingly prominent operation of non-linear dissipative processes (in particular Rayleigh damping 2 ) in the underlying dynamic, which enhances end-effector stability to cope with the higher precision requirements. To allow time for the operation of dissipative processes, the movement system was constrained to slow down, particularly at the vicinity of the targets. Therefore, when faced with higher accuracy demands, the preferred strategy seems to be a local (rather than global) slowing down. Such strategy is revealed in the N-shaped form of the Hooke portrait at higher levels of difficulty. The implication is that at higher levels of difficulty the neuromuscular system behaved as though governed by a nonlinear softening (Duffing 3 ) stiffness function. Probe type also affected both duration and kinematics of aiming movements, though effects were increasingly more pronounced as task ID increased. As expected, the proximally-loaded probe gave rise to significantly shorter MTs than the distally-loaded probe, an effect that increased in magnitude as the width of the target decreased. This result confirms that proximal loading yields a probe that optimizes performance of rapid aiming tasks. Regardless of probe type, the non-linear organizational process referred to earlier (notably Rayleigh damping and Duffing softening spring stiffness, cf. [START_REF] Mottet | The dynamics of goal-directed rhythmical aiming[END_REF] came to the fore as task difficulty increased. However, at the highest level of task difficulty the contribution of non-linearities in these dissipative and conservative mechanisms was more pronounced (larger NPA) when participants used the proximally-loaded probe. This result is consistent with our hypothesis: proximal loading seems to allow adjustments in the dynamical organization of aiming patterns that minimize reduction in performance (here reduction in movement speed) as a function of increased task demands. To reiterate, the particular Rayleigh-Duffing dynamical organization revealed here produces a local slowing down of the end-effector in the vicinity of the targets, which allows the stabilizing (dissipative) processes to reduce variability where it is needed. The higher stiffness around the center of oscillation produces faster movement (with less spatial control) when the end-effector is away from the target and spatial precision is not required. Therefore, Rayleigh-Duffing dynamics results in a reduction in spatial variability where it counts while minimizing movement time as much as possible (which is the task goal). Notably, the contribution of Rayleigh damping to the stability of aiming patterns is moderated by the inertial properties of the end-effector. For a given velocity, the distally-loaded probe will be less influenced by dissipative processes due to its higher inertia (or lesser maneuverability) than the proximally-loaded probe. The implication is that to achieve a similar level of end-point stability, participants would need to either increase the contribution of Rayleigh damping or scale down aiming speed. Results related to the kinematics of aiming patterns suggest the latter strategy was at play. The greater degree of global slowing down with the distally loaded probe is particularly visible in Hooke portraits (smaller deviations from a straight line) and confirmed by the lower magnitude of NPA. Perhaps increasing the contribution of Rayleigh damping would be too energy consuming or too inefficient when resistance to changes in rotational acceleration of the end-effector is high. In any case, the lesser maneuverability 2 The operation of a Rayleigh function in an oscillatory regime yields an asymmetric velocity profile, with peak velocity occurring during the first half of a movement. Hence, the contribution of a Rayleigh type function to aiming dynamics is revealed by a skewing of the trajectories with peak velocities moving into the 2nd and 4th quadrants of the phase plane. Such deviations were especially prominent in the present experiment for higher ID's and PWprox. 3 The operation of a Duffing function yields a non-linear relation between end-effector acceleration and position. When instantiating a softening-spring, stiffness is highest around the center of oscillation and progressively decreases outward. The contribution of this type of Duffing function to aiming dynamics is revealed by an N-shaped profile in Hooke's plane. Such deviations were especially prominent in the present experiment for higher ID's and PWprox.

of the distally-loaded probe seemingly prevented full exploitation of RayleighDuffing dynamic, which explains the longer movement times observed particularly at the highest level of difficulty. The discussion above suggests that the proximally-loaded probe is more responsive to task sensitive adjustments in its pattern of motion. The flip side is that it must be controlled with less noise (or more precision). [START_REF] Bongers | Variations of tool and task characteristics reveal that tool-use postures are anticipated[END_REF] tested this assertion by observing the control strategy used when displacing an object with a longshafted rod varying in mass distribution. When the rod was loaded proximally, postures were selected to increase control of the rod (e.g. participants used a less extended arm synergy). Given this finding, it is possible that the greater nonlinearity associated with proximal probe loading might not simply reflect the preferred dynamical strategy for reaching small targets. It might also reflect the use of additional dissipative processes to comply with the greater stability requirements related to the probe's lower inertia. In that case, improvements in performance associated with proximal probe loading might be contingent on individual's capability to efficiently implement a more non-linear aiming dynamic that allows faster performance while maintaining the required level of accuracy. The greater inter-individual variability in kinematic patterns observed for the smallest target provides initial support to this possibility. The implication is that the benefit of proximal probe loading might disappear the presence of motor disabilities associated with noisier movement patterns (e.g. Parkinson's disease). In that case, distal loading might be more beneficial to task performance given its greater resistance to perturbation. This hypothesis can be tested in future experiments and if confirmed would contribute to theory development in tool use. In particular, it would suggest that the properties of a tool are insufficient to determine its potential to support performance of particular tasks; these properties would have to be considered with respect to the action capabilities of the tool user.

In contrast with the present study, [START_REF] Lin | Modeling movements of a long hand-held tool with effects of moments of inertia[END_REF] did not report significant differences in MT between conditions in which the probe was loaded proximally and distally to the handgrip. To explain this finding, the authors compared the load distribution of the probe with the gain setting in control-displays [START_REF] Accot | Scale effects in steering law tasks[END_REF][START_REF] Jellinek | Powermice and user performance[END_REF]. When choosing the optimal gain setting, designers of control displays have to deal with a trade-off between gross-positioning time (acceleration time to get to the vicinity of a target) and finepositioning time (deceleration time for final acquisition of the target). The authors assumed that with distal probe loading (analogous to a high gain setting), participants could quickly maneuver the instrument tip to the vicinity of the target but final acquisition time was longer due to difficulty in precisely controlling its position. With proximal probe loading (considered analogous to low gain setting) fine positioning was facilitated but there was a loss in terms of gross-positioning time. Accordingly, the authors argued that proximal and distal loading lead to different adjustments in movement pattern that are nonetheless related to similar increases in MTs. Analysis of aiming pattern and dynamics in the present experiment does not support this interpretation: proximal loading yielded faster performance with higher degree of non-linearity when targets were smaller. This pattern of results suggests that proximal loading actually facilitates maneuvering towards the target (relatively lower grosspositioning time) but is actually more demanding in terms of fine-positioning (greater degree of non-linearity in damping and stiffness functions). Therefore, the lack of difference between proximal and distal loading reported by Lin and Chen (2014) might be related to the magnitude of the loading. While the added mass represented 10% of the total weight of the probe in their study, it represented 70% in the present study. To our knowledge, this is the first study showing that biomechanical constraints at the level of end-effector can affect the higher order organization of aiming movements and not simply its execution. Pointedly, changes in the mass distribution of the probe generated more than a global change in movement duration; it affected the dynamics of precision aiming. Importantly, the effect of biomechanical constraints on the dynamics of precision aiming seems to be task dependent. Arguably, such effect might only show up when the particular biomechanical manipulation affects compliance with task requirements. For example, increases in the magnitude of transported mass (with no associated changes in mass distribution) require scaling of forces to produce the same end-effector trajectory during aiming tasks, but the manner in which torque should be directed is unchanged. As a result, manipulation of this particular biomechanical parameter generates a global slowing down of aiming movements without affecting its underlying dynamics (Fernandez & Bootsma, 2004). In contrast, changes in mass distribution of a hand-held tool modify the relative efficiency of strategies used to stabilize it when the task demands reaching at high speed. This might explain why adjustments in aiming pattern were only observed in the present study for the highest ID (smallest target). The effect of probe's mass distribution on performance and underlying dynamics of aiming movements for the lower IDs was not qualitatively different from the effect of transported mass observed by [START_REF] Fernandez | Effects of biomechanical and task constraints on the organization of movement in precision aiming[END_REF]. The task specific effect of biomechanical constraints is consistent with minimal interference models of motor control (or models of motor abundance). These models would predict no changes in the perceptual-motor organization of movement patterns when variations in extant dynamical constraints do not affect task performance [START_REF] Latash | Motor control strategies revealed in the structure of motor variability[END_REF][START_REF] Todorov | Optimal feedback control as a theory of motor control[END_REF].

There is evidence that adjustments in the kinematics of aiming patterns as a function of task level constraints (e.g. target size) are directed by ongoing visual information about geometric relations between target and endeffector in the context of task performance [START_REF] Bootsma | Informational constraints in human precision aiming[END_REF]Fernandez & Bootsma, 2004;[START_REF] Fernandez | Non-linear gaining in precision aiming: Making Fitts' task a bit easier[END_REF][START_REF] Fernandez | Kinematic adaptation to sudden changes in visual task constraints during reciprocal aiming[END_REF]Mottet et al., 2001). Arguably, the observed effects of probe type on movement patterns would be primarily driven by the haptic perceptual system, most particularly the haptic subsystem of dynamic touch. The demonstrated sensitivity of dynamic touch to mass-based properties of hand-held objects -lawfully related to the functions they can promote -provides support to this assertion [START_REF] Hove | Perceiving affordances of hockey sticks by dynamic touch[END_REF][START_REF] Wagman | Affordances and inertial constraints on tool use[END_REF][START_REF] Wagman | Haptically creating affordances: The tool user interface[END_REF][START_REF] Wagman | Metamers for hammer-with-ability are not metamers for poke-with-ability[END_REF]. The role of dynamic touch would be to register the end-effector's mass moments in a form and manner that specify the patterning of muscular forces required for achieving the kinematic patterns appropriate for task performance. The mass distribution of the end-effector (here the probe) determines the possibilities for patterning forces by a particular individual. The possibilities for patterning forces in turn affect what patterns (or group of patterns) can be achieved. The haptic perceptual system might, therefore, co-direct adjustments in pattern to get the task done through detection of end-effector's mass distribution. Hence, the inertial properties of the probe seem to provide informational constraints for the organization of aiming patterns beyond those provided by task level demands. Therefore, perceptual-motor processes responding to task level constraints are likely sensitive to, and not independent from, processes organized in response to biomechanical, end-effector constraints as previously argued (Fernandez & Bootsma, 2004).

Conclusions

The performance of precision aiming tasks and the perceptual-motor organization of aiming movements are codetermined by the accuracy demands of the task and the inertial properties of the probe. Tools with mass concentrated close to the point of grasp allows achievement of the dynamical organization that produces an aiming strategy that produces the required level of stability while optimizing movement speed. Results suggest that task and biomechanical constraints influence precision aiming through interactive perceptual processes.

Fig. 1 .

 1 Fig. 1. Mean movement time (MT) as a function of task ID and probe type. (*) identifies significant differences between probe types

Fig. 3 .Fig. 4 .Fig. 3 .Fig. 4 .Fig. 4 .

 34344 Fig. 3. Average phase portraits for each experimental condition. The area defined by gray curves indicates the 95% probability intervals around chance levels.

Fig. 3 .

 3 Fig. 3. Average Phase portraits for each experimental condition. The area defined by gray curves indicates the 95% probability intervals around chance levels.

It is conceivable that physical contact of the pointer with the target could affect the pointer's motion in the horizontal plane close to the target. There is, however, no evidence of such effects in the data, which reinforces the pertinence of our choice of restricting analysis to the one-dimensional task space.

Acknowledgements

Financial support for this study was granted by Brazilian government agencies National Council for Scientific and Technological Development (CNPq), Coordination for the Improvement of Higher Level Education Personnel (CAPES), and by the Research Support Foundation from the State of Minas Gerais (FAPEMIG). Funding sources had no involvement in study design, data collection, data analysis, interpretation of data, manuscript writing, nor in the decision to submit the article for publication.


D R Livingstone

I Presume?

Pascal Engel
email: pascal.engel@ehess.fr

Keywords: abduction, doxastic attitudes, practical reasoning, inquiry, Edna

Presumption is often discussed in law, less often in epistemology. Is it an attitude? If so where can we locate it within the taxonomy of epistemic attitudes? Is it a kind of belief, a judgment, an assumption or a supposition? Or is it a species of inference? There are two basic models of presumption: judgmental, as a kind of judgment, and legal, taken from the use of presumptions in law. The legal model suggests that presumption is a practical inference, whereas the judgmental model suggests that presumption is an epistemic attitude. I argue that presumption is neither a practical inference nor a merely epistemic attitude: it involves both, within the category of what we may call the inquiring attitudes Key words: presumption, assumption,

Introduction

On November 10th 1871, after a long journey of 700 miles in the tropical forest in the Great Lakes region in Tangakyka, the journalist Harry Morton Stanley reached the village of Ujiji. He was in search of David Livingstone, who had not been seen since 1866. Stanley entered the market-place, and saw among the chiefs "the prominent figure of an elderly white man clad in a red flannel blouse, grey trousers, and a blue cloth, gold-banded cap". He narrates the episode: "Up to this moment my mind had verged upon non-belief in his existence, and now a nagging doubt intruded itself into my mind that this white man could not be the object of my quest, or if he were, he would somehow contrive to disappear before my eyes would be satisfied with a view of him. Consequently, though the expedition was organized for this supreme moment, and every movement of it had been confidently ordered with the view of discovering him, yet when the moment of discovery came, and the man himself stood revealed before me, this constantly recurring doubt contributed not a little to make me unprepared for it. 'It may not be Livingstone after all,' doubt suggested. If this is he, what shall I say to him? My imagination had not taken this question into consideration before. All around me was the immense crowd, hushed and expectant, and wondering how the scene Not all presumptions are legal ones, but these can serve as a model for a conception of presumption as a piece of practical reasoning, or as an argument, produced in the course of a deliberation with the aim of reaching effects in a dialogue. So the question arises whether presumption is predominantly a kind of epistemic, or a kind of practical attitude and inference.

In what follows, I shall try to evaluate these competing conceptions of presumption. After having first examined whether presumption is an attitude or an inference, I shall consider two main epistemic models of presumption, the traditional one according to which it is an abductive inference made on the basis of perception, and the belief model of presumption according to which it is a judgment based on belief. I shall then evaluate the legal notion of presumption, which takes presumption as a practical inference and discuss whether it can serve as a general model for presumption. I shall argue that it cannot. The view of presumption that I put forward is that it is neither a purely epistemic nor a purely practical kind of attitude or inference, but a form of what we may call an inquiring attitude, which has both an epistemic and a practical import.

Presumption : attitude or inference?

The Stanley-Livingstone example is perhaps not typical. Let us consider a few others.

(a) Perception. I see a man in the distance, but do not fully recognize him. He looks like my friend Theaetetus. I presume that it is he. But I was wrong. The man was Theodorus. (b) Memory. I seem to remember that I last met Paul at a conference in Venice. I presume it was in Venice. I check and it turns out that this was indeed in Venice. (c) Testimony. I am lost in Klagenfurt. I see a woman in Tyrolian dress, and, presuming that she knows, ask her my way around. (d) Best explanation. At the beginning of the nineteenth century, it was discovered that the orbit of Uranus departed from the trajectory predicted by Newton's theory of universal gravitation. Leverrier presumed that there was an eighth, as yet undiscovered, planet in the solar system; that, they thought, provided the best explanation of Uranus' deviating orbit. Not much later, this planet, now known as "Neptune," was discovered. (e) Legal. This child was born during lawful wedlock, hence he is presumed to be legitimate. No one has heard of this person since seven years, hence she is presumed dead.

These cases are diverse, but all are usually called presumptions. Most of them involve inferences. They also all involve searching for a certain kind of information, where one has already some conception of what one is looking for. But there are important differences. The perceptual and the memory cases involve seemings: it seems to you that this is Theaetetus, and that you met Paul in Venice. But in both cases, it is not clear that an inference from propositions in made. The presumed fact is reached directly. By contrast, the testimony and the inference to the best explanation rest on inferences, as well as the legal case. In all these examples the propositions which are the outputs are only plausible, and defeasible. But can we say that these are suppositions or hypotheses? Only the scientific case is a form of hypothesizing: faced with an alternative hypothesis -the falsity of Newton's laws of motion-Le Verrier chooses the hypothesis that there is another planet. The other cases cannot be so described, and are not suppositions either. When I presume that I met Paul in Venice, I do not suppose that I met him there, I take it to be the case that it was him, although I do not fully affirm it. In the other cases there is a forward looking attitude: I anticipate that this is Theaetetus, that this woman is from Klagenfurt, and Le Verrier anticipates that there is another planet. In Rescher's (2009) terminology a presumption is a kind of "tentative cognition", which one puts forward as plausible in the absence of further information, and which one is prepared to withdraw in case one gets more information. But it is not a mere conjecture or supposition. Stanley is not saying: "Perhaps this is Livingstone". One assumes that such and such is the case. Let us call these two conditions those of potential defeat and of assumption. They seem to conflict: how can one assume something that one considers as potentially defeasible? They do not conflict if presumption is a kind of decision whereby one takes oneself to be entitled to a proposition on the basis of uncertain evidence, or on the basis of no evidence at all, as in the legal case: the presumption of innocence holds whatever further information we have. But it would be incorrect to say that presumptions have no connection at all with evidence, for even when a potential defeat is envisaged, a further justification is expected. Let us call this, after [START_REF] Pryor | Tucker 2013: 90-132 2018[END_REF], a condition of prospective justification. It is a matter of degree, and it has a certain strength which allows one to produce the presumption. Let us call it the presumptive link.

All the uses of "presumption" considered so far are inferences: a proposition is put forward, as presumably true, on the basis of some doxastic state, belief or judgment. But what is the force of the adverb presumably? Does it apply to the inference itself under the form:

(i)
Q, hence presumably P or only to the attitude, leading to a judgement of the form:

(ii) Presumably P, or: I presume that P

The inference (i) is a relation between two propositions. This applies to the scientific and the legal cases, but it is not clear that it applies to the other cases, those of perception, memory and testimony. In the latter, if there is an inference, it is direct and immediate. When the inferential relation is between propositions, as in (i), it is not a deductive one: hence presumably does not have the force of therefore. The inference is an ampliative one, where the information reached in the conclusion is not already contained in the premise and expands it. Neither is (i) a conditional of the form

(iii) If P, presumably Q or (iv) What if P? presumably Q
The antecedents in a conditional like (iii) or a supposition like (iv) may be part of the information leading to the presupposition, but the presumption itself is not the assertion of a conditional. Stanley is not saying "If this man is a white among the blacks, he is Livingstone": he is asserting the consequent in the presumptive mode. Neither is he supposing, or suspecting, or conjecturing, that this man is Livingstone: he makes a speech act which has the force of a tentative assertion. He is actually assuming that his man is Livingstone. The difference between a supposition and a presumption is that the latter involves a mental act of positing or taking as true a given proposition2 . Stanley neither simply believes nor suspends his judgment. He has the belief, but makes a mental move which goes beyond his belief. This move is inferential, but it is also the expression of an attitude. Someone who presumes that P, or who accepts P presumably is in a particular state of mind, which is an attitude. What kind of attitude? It belongs to the same family as suppositions, hypotheses, conjectures, imaginings and assumptions, but is not identical to any of these. All these attitudes are called by [START_REF] Meinong | Engl On Assumptions[END_REF] under the generic name of "assumptions" (Annahmen), which he characterizes as "judgments without belief". Calling it an attitude is not in opposition with its being a form of (ampliative) inference, because the inference is the expression of the attitude and presupposes it, either as its input or as its output. As we shall see, some views take it to be essentially as inferences, whereas others take it mostly as attitude.

Whether presumption is an inference or an attitude, it is a complex one, for the presumer not only makes an assumption which is the product of a tentative cognition, and which is also based on an antecedent cognition. Stanley has a previous description of Livingstone, in advance of being visually acquainted with a man fitting this description. He not only infers that this man must be Livingstone from his seeing a man with that appearance but also judges that he is entitles to infer this. So presuming involves an attitude about an attitude, a secondorder attitude. It also involves a meta-inference, whereby the presumer evaluates the strength of the evidence which allows him to draw the inference and moreover is prepared to withdraw it:

(i)

There is evidence for me that P [ first order attitude : belief, judgment] (ii)

This evidence allows me to presume that P [second-order attitude] (iii) This presumption may be defeated [second-order attitude] (ii) and (iii) are actually the same: my judging that I am allowed to infer that P comes with my judging that I might be wrong. These conditions are usually those of default reasoning, where a tentative conclusion is reached through premises which can be retracted: one presumes for a reason, which one weights as being sufficient in the circumstance, but which one may retract later3 . But two problems arise: if presumption involves this second-order inference, how can it have an immediate and direct character? And if the presumer both takes himself to have grounds to assert that P and to retract it, isn't he incoherent? Before answering these questions, we can try to give a preliminary definition:

A presumption is a kind of doxastic attitude, a species of assumption, associated with an inference, which a subject makes on the basis of evidence, which he evaluates as susceptible of a prospective justification and as potentially defeasible.

The perceptual-abductive model

The first model of presumption is perceptual. When Stanley meets the man whom he presumes to be Livingstone, when one identifies an approaching silhouette as that of Theaetetus, or when one seems to remember something, one forms judgments from perception. I seems to one that such and such is the case, and one presumes from perceptual appearances and looks. But that can mean two different things: either that the seeming itself is the presumption because it involves some recognitional judgment, or that the presumption is inferred from the seeming. On the latter view, although presumption is based on a perception or a memory, it is not an actual perception, but a judgment inferred from an experience with a given content. This ambiguity is present from the very origins of the problem of the nature of presumption. The Epicureans and the Stoics called it prolepsis. The usual translation is anticipations, prenotions or preconceptions, and sometimes also presumptions. 4 On the Epicurean view prolepseis are cognitions based on some preconceptions stored in the mind. They are images or concepts, empirically formed through habits, stored in memory with the type of object under which they fall, which give rise to beliefs. Epistemologically they are self-evident, as the beliefs arising from them. They come, according to the empiricist view defended by the Epicureans, from sensations, and are in this sense passive. But in various texts, Epicureans say that the mind also projects itself onto the object thus recognised and focuses on it. So they give rise to judgments.

The case (a) of my seeing the silhouette of Theaetetus, is a clear case of prolepsis. I have the image of Theaetetus stored in my mind, and when the figure appears, I recognize him at once. Stanley's judgment that this man must be Livingstone is close, except that he has never seen Livingstone. He has only a description or a prenotion of him, which matches the individual he becomes acquainted with visually.

The Epicurean view of presumption as prolepsis takes it as an anticipative perception, not as an actual perception giving rise to a categorical judgment of the form "I judge that p", but the seeming that one can believe or judge on the basis of an experience. On this view a presumption is not a seeming, but the inclination to judge on the basis of that experience. On the prolepsis view of presumption, one both anticipates a judgment and does not endorse it. But the usual concept of presumption differs from the Epicurean one, for prolepseis are supposed to be self-evident, whereas ordinary presumptions are essentially defeasible.

What is the exact nature of this inclination, if it is not an actual belief? On one view it is not an attitude at all, but a feeling, similar to epistemic feelings, such as the feeling of knowing (such as having a word on the tip of the tongue) or the feeling of familiarity (such as having seen this face before), which are neither beliefs nor judgments, and whose phenomenology is closer to affective states. These record, most of the time on the basis of a previous experience stored in memory, the presence of a content which is felt to be retrievable but not easily accessible [START_REF] Dokic | Seeds of self-knowledge: noetic feelings and metacognition[END_REF]). On such a view, they are hardly perceptions at all, being mostly qualitative and associated to certain emotions. It is hard to understand how they can be inclinations to believe, given that their content is so indeterminate. But a presumption, even based on perception, is not a feeling.

On another view of presumptions as perceptions, these are unconscious inferences or hypotheses within the perceptual process. They are abductions, but in a special sense of this term. In the ordinary sense "abduction" is an "inference to the best explanation" whereby a fact is observed, and a hypothesis is formed which would explain it (Douven 2017):

(AI) A surprising fact, C, is observed. But if A were true, C would be a matter of course. Hence, there is reason to suspect that A is true This fits the ordinary concept of presumption as an inference between propositions or beliefs, as in the Leverrier case. However, the view that a presumption is an abductive perception is not that it is an explicit inference between propositions. It is the idea that perception is itself a judgment, whereby a hypothesis is implicitly or unconsciously formed. This was Helmholtz's view, taken up by Peirce:

'Abductive inference shades into perceptual judgments without any sharp line of demarcation between them, so that 'our first premises, the perceptual judgments are to be regarded as an extreme case of abductive inferences . . .' 'the abductive faculty, by which we divine the secrets of nature, is, as we may say, a shading of, a gradation of that which in its highest perfection we call perception' [START_REF] Peirce | Essential Peirce: Selected Philosophical Writings[END_REF]2: 224, see Tiercelin 2004).

The ambiguity between presumption as an attitude and presumption as an inference, which is present on the Epicurean model, is here most explicit. On Peirce's view of abduction, perceptual beliefs or judgments are inferences. In the Stanley case, the inference is of the form (AI) above, but on Peirce's early view, this inference is not an actual inference, but the content of a perceptual judgment: it seems to Stanley that this man is Livingstone, but this seeming already involves an inference. This double status is potentially incoherent. If , on the one hand, presuming is a seeming, in the sense of an experience, how can it present directly its content, with the kind of transparency characteristic of perception, and at the same time anticipate this content through some sort of hypothetical inference? On a plausible view of perception, perception is supposed to trade with non -inferential contents. Now if perception is in some sense inferential, it hard to avoid the idea that it has a propositional content which can be belieflike. If, on the other hand, it is not a belief, but only an inclination to believe, how can it be based on evidence? Moreover, how, on the perceptual view, can we account for the fact that presumptions have a second-order component? If there is a seeming and its potentially defeat, there is not only a first-order attitude of perceiving, but also a second-order attitude of judging this first-order content defeasible. How can this first-order content be fully endorsed? Whatever can be the relationship between the first-order content and the second order content, both have to be in some sense belief contents, in order to be appraisable as worthy of judgment. This feature clashes with the idea that presumptions are perceptual seemings. It clashes even more with the view that they could be epistemic feelings.

The belief model

Whatever presumptive seemings can be, it is hard to understand how they cannot involve beliefs. And if presumptions are inferences, they have to involve beliefs and judgments. But here too there two models. On the one hand we can take presumptions to be beliefs, in the sense of full beliefs, or as dispositions to judge, associated with degrees of belief. Let us take each hypothesis in turn.

A presumption may be a belief, but is not a full belief or a judgment. A full or categorical belief is the holding true of a proposition, either consciously or not, whereas presumptions are assumptions, the contents of which are consciously taken to be true. The difference is that, in Rescher's phrase (2012:23) presumptions are "candidates for truth", which might turn out false, whereas beliefs or judgments are held true, period. Indeed one may believe or judge presumptively that P, but when one believes one does not take one's belief as potentially defeasible. Nevertheless, it is odd to say:"I presume that P, but I do not believe it" because presuming in some sense presupposes believing. Presumption, however, is quite compatible with believing that P to a certain degree. A presumption has a certain strength, which is in part determined by the degree of evidence one has for its truth and the stronger the degree of belief the more successful the presumption. In this sense presumptions may be identified, or partly identified with degrees of beliefs, or credences. If we understand this on the Lockean model [START_REF] Foley | Working Without a Net[END_REF]), a presumed belief would be one with a sufficiently high degree of evidential support. Stanley might be not fully certain that this man he Livingstone, but almost sure that it is him. On the alternative Bayesian model for degrees of belief, presuming that P would be to give a prior degree of belief or subjective probability to P, which on the observation of a given fact, would be updated by conditionalization upon the prior belief, to yield a new degree of belief. In the terms of our Stanley-Livingstone example, Stanley thinks that it is likely, on the basis of the fact that the villagers have brought with them a foreigner, that this foreigner is Livingstone. He might actually be prepared to bet on the proposition that this man is Livingstone. Alternatively (although this is not the actual story that he tells) he might be surprised to find this man, given that he did not expect to meet him in this village, but could revise his initial low probability. This seems to be a straightforward case of expectation, in the Bayesian sense: given initial or prior probabilities a given proposition is unexpected, but the observation of the fact raises the probability, which leads to a higher degree of belief once revised. So we can conceive of presumption as a form of Bayesian inference, based on a conditional probability leading from an antecedent degree of belief to a posterior one. But neither the Lockean nor the Bayesian models of presumption are convincing, for at least two reasons.

First consider the defeater condition on presumptions. On the degree of belief or credence view, Stanley has a higher degree of belief in the proposition that this man is Livingstone than on the proposition that he is not Livingstone, but he is open to the potential discovery of evidence which would reverse his credence function, which would make him acquire a degree of belief in the proposition that this is not Livingstone. But if he has actually a high credence in the proposition that this man is Livingstone, he cannot reverse his credence function. 5 The Bayesian model does not easily account for the defeater condition of presumptions, unless it postulates that presumptions cannot have defeaters. But it is part of the attitude of presuming that the proposition under consideration might well be false. In the usual taxonomy of defeater conditions [START_REF] Pollock | Defeasible reasons[END_REF] it might be defeated in a rebutting wayby discovering that this white man is not Livingstoneor in the undermining wayby discovering a fact which would imply that he is not Livingstone.

There is a second reason why the Bayesian reading does not fit the attitude of presuming. Presumption is not, in the intuitive sense, a graded notion: one either presumes that P or that not P. The judgment expressing the presumption might well be perfectly categorical, without any hint of certainty or strong degree of belief on the part of the presumer. In this sense, the presumer is ready to assume, without strong evidence, or without evidence at all that p. This seems to fit the scientific case (d) and most cases of abduction. Le Verrier has no evidence for a eighth planet perturbing the orbits of Uranus, but he assumes that there is on, for the sake of explaining this anomaly. He is not simply having a high degree of belief in this hypothesis. He takes it for granted that it is the case, and on the basis of an abduction leading to his accepting that hypothesis, he proceeds to making observations which would confirm this fact. Whatever vocabulary we adoptassumption, abduction or acceptance,the attitude at stake is a full one. It is not, as we saw above, full belief, but it is not a kind of credence either. It has to be a kind of judgment, although not an assertoric one. Whether one takes high credibility, or knowledge, as the norm of assertion, presuming is not asserting, but assuming. One cannot criticize someone who presumes that P by saying: "But you did not have the best reasons to presume that P ", even less "But you did not know that P". In order to presume one needs to have good enough reasons, to which the agent gives proper weight. The agent could have a relatively low credence in P, and nevertheless be perfectly apt to presume that P.

So presumption is a doxastic attitude which is closer to what philosophers have called acceptance that to belief or judgment. If we understand acceptance along the lines of [START_REF] Cohen | An essay on belief and acceptance[END_REF] 6 , it differs from belief or judgment in being not necessarily based on evidence, not necessarily integrated rationally with other beliefs, contextual, voluntary, and not necessarily aimed at truth. Acceptance is a practical attitude, governed by intentions, and used in the course of a practical reasoning directed towards certain end. The end may be some good or practical goal, as when one accepts a given proposition as a means towards that end. It can be an epistemic end or goal, such as looking after truth in a domain and when one takes a proposition as true, say for the purposes of a demonstration. In both cases one need not believe the proposition, and one may even believing that it is false or based on no evidence at all. Acceptance is a kind of assumption that P, or premising that P, or taking it as true for the sake of a further end. A least some presumptions, the legal ones, are acceptances in this practical sense. Can they provide a general model for presumption?

The legal and dialogical models

The term "presumption" has long been used in law 7 : people are presumed innocent until proven guilty, presumed dead if not seen for more than seven years, children under a certain age have no criminal intentions, a marriage regularly celebrated is valid, etc. On the usual sense of the term in law, "A presumption means a rule of law that courts and judges shall draw a particular inference from a particular fact, or from particular evidence, unless and until the truth of such inference is disproved" (Stephen, quoted by Ullman-Margalit 1983 :145) This means that a presumption is a particular kind of inference. A standard example is the following:

(1) There is a presumption that a child born in wedlock is legitimate.

(2) Adam (a particular child) was born in wedlock.

(3) Adam is legitimate The conclusion does not follow deductively from the premises, and it can hardly be categorical like (3). It is rather (4) There is a presumption that Adam is legitimate which is concluded from (1) and (2) modulo the premise expressing the presumption. This is clearly not an inference based on evidence, apart from the fact reported in (2). The presumption (1) is itself based on a specific legal decision, so it cannot be an ampliative inference at all. On the classical conception of this legal inference, however, evidence can be adduced, but it has to be adduced by a distinct party from the one who puts forward the presumption. The burden of proof lies "on the side of him who would dispute it" [START_REF] Whately | Elements of Rhetoric[END_REF] Edna Ullman-Margalit (1983), in her important work on presumption, proposes the following form for a presumptive inference: Pres (P,Q) there is a presumption of Q from P The presumption itself is made according to a presumptive rule which says 7 On the history of the notion , see Hansen 2019 (R) Given that P is the case, you (= the rule subject) shall proceed as if Q were true, unless or until you have (sufficient) reason to believe that Q is not the case.

The rule (R) allows to conclude: Presumably (or presumptively) P Two features are important on this model. The first is that presumptive rules are practical rather than theoretical, and are "concerned not so much with ascertaining the facts as with proceeding on them" (Ulmann-Margalit 1983: 147). Thus, the conclusion of a presumptive inference is "to the effect that a certain fact is presumed … [rather than] to the presumed fact" (ibid). The second is that the force of the presumption operator is to shift the burden of proof to anyone who would reject the claim being presumed as fact. On this model presumptions serve as guides for practical deliberation in cases where an absence of information, or conflicting information, impedes the formation of a rational judgement, and where nevertheless some determination of a matter of fact must be found in order that matters proceed (Ulmann-Margalit 1983: 152). Other reasoners, not faced with the practical need of reaching a judgment, have the option of reserving their judgment, and thereby may not be bound by the presumptive rule. In this respect, presumptions are quite different from other sorts of defeasible reasoning, such as making a prima facie case for a claim. Because presumption rules apply in cases where there is practical need to proceed, it might seem that they can be grounded in purely prudential considerations.

The main characteristic of the legal model of presumption is that presumptions are purely stipulative. The presumption of innocence is laid down by judicial fiat in Anglo-American law, and other systems of jurisprudence may allocate the presumption differently. One may object that a number of legal presumptions are in agreement with the normal balance of probability and such that the chance of error is small. These epistemic considerations are indeed present, and they play a central role when a presumption is rebutted. If a defendant is to be proved guilty when he was presumed innocent, it is for evidential reasons. For instance it is highly probable that a man who has not been seen for seven years is dead. But on Ulmann-Margalit's view, these considerations "are neither necessary nor sufficient to justify the presumption rules relating to them" (1983: 158-15). They are not sufficient when there are equal grounds for a claim, for instance that the accused is innocent or guilty. They are not necessary because the presumption of innocence is granted whatever evidence one has. Ullmann-Margalit also argues the second-order element that is present in presumption is a second-order decision (Ulmann-Margalit and Sunstein 1999). But her view that legal presumptions cannot be justified in any epistemic way is too strong, if this means that no epistemic consideration is in place. 8 If presumption is to be the hallmark of acceptability and acceptability is to be normative, presumption must not be a matter of fiat. We cannot simply stipulate what premises are to be acceptable. Are there other senses of "presumption," which can be applied in situations outside formal legal proceedings, where "natural" or "rational", as opposed to arbitrary or stipulative, presumptions may be identified? There are indeed. There is a presumption of equality which enjoins that individuals be treated equally in the absence of discriminating information, in order to satisfy some practical goal, such as justice or fairness [START_REF] Rabinowicz | Presumption of Equality as a Requirement of Fairness[END_REF]. But if we try to apply this model to other examples apart from the legal one, there is indeed no practical presumption at hand. Stanley wants to know whether this man is Livingstone.

Other writers following this practical reasoning model have proposed dialogical rules which are supposed to allow the epistemic evaluation of presumptions. Thus according to the dialectical theory of presumption presented by Walton (1992, pp. 56-61), presumption is a kind of speech act in a dialogue. When a proponent in a dialogue asserts a proposition, if the respondent asks for justification, the proponent must either give an argument to justify the proposition, or she must retract the proposition. The requirement of the burden of proof here means that if you assert something, you are committed to the truth or acceptability of what you asserted. You are obliged to back it up if you are challenged. This requirement is a kind of rationality assumption that defines the nature of assertion as a speech act in dialogue. Assumption may be contrasted with assertion. You are free to assume any proposition you like in a dialogue. There is no burden of proof attached. You can assume that the moon is made of green cheese, for purposes of a discussion. Presumption, on the dialogic view, is a dialectical notion that fits in between assertion and assumption. If you presume that something is true, you don't have to prove that it is true, or offer evidence to prove it. But you do have to give it up if the other party can prove it is false. The dialectical function of a presumption is to reverse a burden of proof. This reversal is indeed epistemic in nature. On Freeman' s (2005) model, the epistemic standards are set up by a dialectical exchange, where the epistemic point of view is that of a rational adjudicator presenting a challenge. There is a presumption if the proponent has answered all the dialectical exchanges. But from a dialogical point of view, are there objective standards independent of the point of view of proponents and challengers? When is a presumption acceptable rationally? The dialogical model as such is silent. If we try to apply this to our examples, it is not clear that there is any such dialogical situation. Indeed Stanley addresses Livingstone, and he is entitled to expect the answer that he actually receives: "Yes". Indeed no one has better authority than Livingstone to assert that Stanley's presumption is correct. There could have been a dialogical situation: for instance Livingstone might have become amnesic and forgotten his name, or under the influence of a drug. Then Stanley's presumption would have had to be checked against other participants in the dialogue. But this is not the normal situation.

The notion of burden of proof used by these legal ad dialogical models seems to introduce an evidential element in the justification of presumptions. But this is merely apparent. For the burden of proof is intimately tied to the notion of a measure or standard of proof that needs to be met by the proponent of a claim. In law, this standard tends to be set by legal areas, with one standard for private and one for criminal law. In the context of argumentation, it has sometimes been set to the conviction of the opponent. But as [START_REF] Hahn | The Burden of Proof and Its Role in Argumentation Argumentation[END_REF] remark, this standard is too restrictive and too lenient: the mere conviction of the opponent fails to set an objective and reasonable standard to the burden of proof.

One might think that the legal and dialogical models of presumption conveniently make it a public speech act within a social context, and that the kind of epistemic episode that presumption involve is itself social. If this is so, presumptions resemble rules more than facts, even though the reasons one can give for presumptions in particular circumstances are factual (Petrowski 2008: 398). The problem is not only that this model makes the justification of presumptions rest upon rules which are social in nature, but also which have no epistemic basis. The epistemic base of presumptions is dependent upon the rules. This may be fit or legal contexts, but it cannot account for the other contexts, in particular the scientific and the perceptual ones. A presumption, even if it is not an inference or an attitude based on facts or justified by some epistemic ground, must at least certain epistemic correctness conditions. The legal and dialogical model conflate the correctness of a presumption with the correctness of the activity of presuming. Not only it puts all the explanatory weight on the activity of inferring, but it also conflates the justification of presumptions with their agreement to social rules.

Presumption as an inquiring attitude

Let us take stock. None of the models examined so far is satisfactory. Presumptions, on the most intuitive sense of the term, have certain conditions of correctness, and they at least must be susceptible of being said to be epistemically justified or not. The legal model or the dialogue model of presumption trivializes this feature, in making presuppositions depend upon rules and on agreement in dialogue. Moreover these models classify presumptions as practical attitudes and inferences. But whether or not one accepts that there can be genuine epistemic agency in general and in this particular case, it is certainly a defect of these models that they are not able to account for the epistemic nature of the activity of presuming and for the fact that presumptions can be normatively and objectively correct.

So we have to turn back to the initial intuition from which we started. Presuming, as in Stanley's example and in our other examples, is an attitude of asking a question -"Dr Livingstone I presume? -Theaetetus I presume? -Where did I last met Paul? -Is there another planet in the solar system?" It belongs to a specific class of what we might call question-raising attitudes, or, to use Jane [START_REF] Friedman | Inquiry and Belief[END_REF] apt term, of "question-directed" and "inquiring" attitudes, attitudes which one is disposed to have in the course of inquiry. Among these are attitudes are doxastic ones such as: asking, wondering whether, being curious, doubting, suspending judgment, conjecturing and assuming. To doubt whether P is to raise a question about whether one ought to believe that P or disbelieve it; to suspend judgment about P is to neither believe nor disbelieve P. To conjecture that P, to suppose that p, to deliberate about P and to assume that P, to wonder that P are inquiring attitudes which raise, and tentatively answer whether P. I propose to say that presumption belongs to his family of attitudes, and his distinctive.

Although presuming is one of these inquiring attitudes, it is not reducible to any one of these. I have argued that it is not a certain kind of belief, or degree of belief. Neither is it a kind of supposition. One may suppose what is false, and also presume something false, but supposing is free in a sense in which presuming is not. One may suppose, in the imaginative sense, whatever one wants tosay that the moon is made of green cheese. But one cannot presume whatever passes through one's mind. Presumption has to beat least regulated by some connection to evidence. Presuming, however, has this in common with supposing that it puts forward a hypothesis, in the counterfactual mode: If P were true, it would explain the observed fact Q as an answer to the question : "Why is there the surprising fact Q ?" This is what we may call, with Ullman-Margalit, the presumption raising fact. It raises a question, to which the presumptive judgment is an attempted answer This is actually exactly the formula of abduction. So we come back, in this sense, to the very notion which was present in the perceptual model and in the notion of abductive inference presented above. There is, however, no reason to limit this model to the perceptual case. A presumption is any kind of assumption which can play an explanatory role. It has to rest on some evidence, but it is not an inference from evidence only. As most writers on inference to the best explanation insist, abduction and inference to the best explanation have to move beyond evidence.

In classifying presumption under the kind of inquiring attitudes, I consider it as a form of active cognition: asking questions, making assumptions, and putting forward presumptions are kinds of mental actions, and not epistemically passive states, such as perceivings or rememberings. They are distinctively cognitive. But perhaps the most distinctive feature of presumptions is that they are not only first-order attitudes, but that they involve a secondorder stance. When one presumes that P, one makes an assumption, which one tentatively accepts as true and as potentially explaining a given fact, but one is also ready to withdraw this assumption. Indeed the legal and dialogical models make room for this defeasibility feature, but they take it to be involved in the dialogical situation, where an opponent may rebut one's presumption. But there is no reason to consider that this feature is present only in dialogical contexts, for it can occur in personal doxastic deliberation, when one asks oneself whether one ought to believe that P. Typically in this kind of deliberation one asks a secondorder question: Am I entitled to believe that P? 9 Presuming is also a second-order attitude in this sense: one has evidence that P, and on that basis one assumes that P. But one does so only if one has a second-order evidence that one first order evidence justifies, prospectively, this assertion. And one does not rule out that can have higher-order evidence to the effect that one's first order evidence is undermined. Does this make the attitude of presuming while at the same time accepting a potential defeat incoherent? The threat of incoherence is actually only apparent. It would arise if presuming were a belief or a judgment, as in the Preface paradox, where one judges that one has written a book in which figure only true beliefs, but also judges that one belief at least must be false. But presumption does not imply that one is at the same time in the attitude of judging and in the attitude of withdrawing this judgement. Nor is it a kind of suspension of judgement, where one hesitates between believing that P and disbelieving it. The presumer does not hesitate. He is in the attitude of inquiring whether P might be true for good epistemic reasons, and on the basis of this attitude he makes the assumption that P, while having also the second-order judgement that his evidence might not be sufficient to assert that P. There is no incoherence here because the discovery that one might be wrong will by definition come later. One nevertheless goes ahead and asserts "P, I presume?" This is what is involved in prospective cognition.10

Conclusion : correctness conditions for presumptions

We may now try to refine the definition proposed above. I hope to have made a case for singling out presumption as a sui generis doxastic attitude. It is doxastic because it involves beliefs. In order to presume that P one must have a belief about some presumption raising fact, which prompts a question, as well as a second-order belief about the strength of what I have called the presumptive link and the prospect of issuing a presumption. But the presumption does not consist in these beliefs and is not a special kind of belief. It is a further mental move, which involves an assumption and an inference. A presumption is made on the basis of the evidence that one has, but it may be made irrespective of it, for the sake of a practical or of an epistemic end. So presumption turns out to be a rather complex attitude, which differs from suppositions and from acceptances. It involves a kind of cognitive action, directed at an epistemic goal: discovering and coming to know.

Although I cannot argue for this here, doxastic attitudes have specific correctness conditions, which are normative and which determine the status of the epistemic reasons. These conditions are themselves those which make an attitude "fitting" or appropriate 11 . This view which was defended by Brentano and his followers, can be applied to presumption. As I noted above, the class of assumptions for Meinong is wider than the attitude of assuming itself . It includes conjectures, suppositions, imaginings, fictions. Presumptions could be included in the class, as assumptions in the sense of positing or taking for granted certain propositions for some further end.

The correctness condition of belief is truth (or knowledge according to some views), the correctness condition of conjectures is that it be probable that P, the correctness condition of questions is that it be questionable whether P. What is the correctness condition of a presumption? Its independence from belief makes it close to supposing and forming hypotheses, which need not be conformed to the evidence that one has. Its assumptive character makes it different from a judgment. But its correctness condition is the same: a presumption is correct or fitting if it is true or knowledge conducive. But that does not mean that there are not many ways of presuming, some of which are bold and risky, others more reasonable, some successful, others not. A presumption is essentially defeasible. This defeasibility is not a condition of correctness, since a presumption is withdrawn when it is false or unsupported, but it is often a condition of success of a presumption that one can be aware of its defeasibility. Otherwise one would merely affirm a conviction. So there are, in addition to correctness, conditions of success of presumptions, which are the conditions under which one is prima facie entitled to assuming that they are true and ready to revise them. But these conditions are not only backwards looking, so to say; they are also forwards looking, and directed towards further inquiry. Specifying these conditions is a matter of epistemological argument, and one can adopt various kinds of epistemologies on the basis of presumptions. 12 My concern here was not to formulate the epistemological consequences of the use of the notion of presumption. It was just to argue that it a distinctive epistemic attitude. 13

The example is also used byWalton 1992,

2019, and[START_REF] Rescher | Presumption and the Practices of Tentative Cognition[END_REF]

Suppositions can be conceived as kinds of believings, or as kinds of imagings (see[START_REF] Arcangeli | Supposition and the imaginative Realm[END_REF]. If supposition is a component of presumption it is more plausibly belief-like.

See e.g.[START_REF] Pollock | Defeasible reasons[END_REF],Horty 2012

See Diogenes Laertius, X, 33, in[START_REF] Long | The Hellenistic Philosophers[END_REF], and , Tsouna 2006, Dyson 2009.

See e.g Pryor 2013 : 98, and for reasons to doubt that the Bayesian framework works here. In particular it is interesting that Pryor actually uses the notion presumption in this case: "It is debatable what effect such evidence should have, but there is a presumptive case that it would put some kind of pressure on you to raise your credence"(ibid p. 98)

See alsoBratman 1997[START_REF] Engel | Believing and accepting, and holding true", Philosophical Explorations I, 2018 "The doxastic zoo[END_REF]

This was pointed to me by Alex Guererro and by Giovanni Tuzet. Tuzet 2015 argues that even the absence of evidence is not legally inert in a juridical deliberation.

This differs from wondering whether P which is answered in the first-order mode: P . In this sense deliberating and inquiring attitudes like presuming are not "transparent" in the sense of doxastic deliberation about whether P[START_REF] Shah | Doxastic Deliberation[END_REF].

[START_REF] Pryor | Tucker 2013: 90-132 2018[END_REF] discusses this incoherence threat, although he does not consider presumptions

See Textor 2019, On Meinong Mc Hugh 2014[START_REF] Engel | Believing and accepting, and holding true", Philosophical Explorations I, 2018 "The doxastic zoo[END_REF]