Jeremy Guillaume
email: jeremy.guillaume@centralesupelec.fr

Maxime Pelcat
email: maxime.pelcat@insa-rennes.fr

Rubén Salvador
email: ruben.salvador@centralesupelec.fr

Virtual Triggering: a Technique to Segment Cryptographic Processes in Side-Channel Traces 1 st

Keywords: Cybersecurity, side-channel attacks, screaming channels, electromagnetic side-channels, trace collection

, which initially used a Frequency Component (FC) known to appear at a single time in leaked signals, as a trigger to segment traces. We demonstrate that VT not only performs equivalently to FC on a standard attack scenario, but we also show how using VT with the automatic pullout technique improves the attack efficiency and enables more realistic attack scenarios. Thanks to VT, screaming channel attacks can now:

(1) succeed with only half of the segments collected compared to the FC trigger from the original attack; and (2) absorb time variations between CPs.

I. INTRODUCTION

Side-Channel Attacks (SCAs) [START_REF] Standaert | Introduction to Side-Channel Attacks[END_REF] exploit data-correlated leakages that arise when a device operates on data. The term side-channel is used to denote physical leakage signals carrying confidential information. Side-channels are inherent to CMOS computing devices and can take many forms, from timing to power consumption to Electromagnetic (EM) emanations. We call traces to the sampled measurements of a side-channel during the execution of one or multiple targeted operations. The most common scenario in SCAs targets a cryptographic key manipulated by Cryptographic Processes (CPs), as eavesdropping such a key can jeopardize system confidentiality. We refer to these attacks as Side-Channel Cryptographic Attacks (SCCAs) [START_REF] Choi | TEMPEST Comeback: A Realistic Audio Eavesdropping Threat on Mixed-signal SoCs[END_REF]. A trace can contain leakage from multiple CPs. Trace segmentation separates the different segments from the leakage, each corresponding to the side-channel measurement of one CP execution. During the attacking phase, a hypothesis ŷ ∈ Y on the data y is made (Y = all possible data values). Techniques like Differential Power Analysis (DPA) [START_REF] Kocher | Differential Power Analysis[END_REF], Correlation Power Analysis (CPA) [START_REF] Brier | Correlation Power Analysis with a Leakage Model[END_REF], Mutual Information Analysis (MIA) [START_REF] Gierlichs | Mutual Information Analysis[END_REF], template attacks [START_REF] Chari | Template Attacks[END_REF] and more recently Deep Learning (DL) [START_REF] Masure | A Comprehensive Study of Deep Learning for Side-Channel Analysis[END_REF], evaluate the relationship between ŷ and the segment leakage values. Each hypothesis Y is tested, and a probability is returned for all of them. The ŷ having the highest probability is expected to correspond to the data y. For these attacks to work, it is important to know, for each segment point, to which CP operations they belong. It makes it possible to find a relation between y and leak values of the same CP data-correlated operations present in all segments. To respect this requirement, segment synchronization is done during the collecting and preprocessing phases of the attack.

Focused on screaming channel attacks, we look into its collecting and pre-preprocessing phases, which aim at obtaining synchronized and denoised segments from the victim's leakage traces using techniques like time diversity (average multiple CPs computing the same data to reduce the noise). To relax the triggering requirements for trace capturing and synchronization, our contributions include:

• Virtual Triggering (VT), a method to segment traces from side-channels of an embedded device executing a cryptographic software implementation. VT requires neither external synchronization nor tampered victim software. Fclock FRadio Fclock Fclock Digital Fig. 1. Screaming channel attacks: Conventional side-channels leak to the RF module in the analog part, present on the same die. This one transmits side-channels at a larger distance (until some meters). dard (AES) on an embedded device.

• a discussion on the method limitations and solutions.

• experimental results demonstrating the gains obtained with these solutions. VT does not require any specific setup on the victim side, like a trigger signal to indicate the start of a CP. It consists in finding a precise enough time duration of the targeted process executed periodically. This makes it possible to act as if a trigger would indicate a common location in all the process segments. This virtual trigger can then be used to segment CPs from a trace. The method aims at helping researchers to reduce the effort in target preparation and in the collecting phase of the attack, while also giving a small step toward a more realistic attack scenario.

The paper is organized as follows. Section II provides the context of this work and Section III discusses related works. Then, Section V details the proposed virtual trigger segmentation method, and Section VI evaluates it experimentally on a screaming channel setup. Section VII discusses the limitation of the method and proposes a solution to overcome it. Finally, Section VIII concludes the paper.

II. SCREAMING CHANNEL ATTACKS

Experimental results build on the attack scenario called screaming channels introduced by Camurati, et al. [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF]. As illustrated in Fig. 1, screaming channels occur on mixed-signal devices where digital processing is collocated with analog Radio Frequency (RF) electronics over a single die. Sidechannels originated from digital processing mix with RF signal and get amplified, modulated, and broadcast. The primary threat posed by screaming channels is the risk of transmitting secrets over long distances, i.e., scream them.

The screaming channel signals are very noisy. Plus, to collect them, it is necessary that the RF module transmits a legitimate signal. In the context of this paper, it is a Bluetooth signal. Between two Bluetooth transmissions, the collected signal contains holes. As in regular screaming channel analysis, to counterbalance these constraints, time diversity is used during the collection phase. The principle is to force the device to compute multiple encryptions with the same plaintext and key. Since the same data has been computed, their segment values should be the same, except for the noise. Averaging the segments returns a CP segment with reduced noise.

III. RELATED WORKS ON SEGMENT SYNCHRONIZATION

Synchronization is used to know to which CP operations each segment point belongs to. Otherwise, segment points corresponding to operations whose leakage values are datacorrelated would be compared with other unrelated points. Therefore, it would be harder to distinguish a relationship between leakage values and data. We name these data-correlated points as Points of Interest (POIs). To synchronize segments, an alignment between them can be done using techniques like static alignment [START_REF] Mangard | Attacks on Hiding[END_REF], longest common sequence [START_REF] Jia | Side Channel Leakage Alignment Based on Longest Common Subsequence[END_REF], elastic alignment [START_REF] Abdellatif | Towards Efficient Alignment for Electromagnetic Side Channel Attacks[END_REF] and synchronous real-time sampling [START_REF] Yang | Synchronous Real-Time Sampling Technique for Side-Channel Analysis Against Randomly Varying Clock-Based Countermeasures[END_REF]. Before aligning segments, it is first necessary to locate these segments of interest in the traces. The most common technique in SCA research consists of inserting a trigger signal to start the trace measurement synchronized with the beginning of the CP. Attack setups are prepared to either have (1) the victim to create the trigger signal to inform the attacker when encryption starts, or (2) the attacker sending a trigger signal to the victim to make it start at a precise moment. This is an accepted scenario in the community to enable SCA research. But it assumes attackers have access to the victim to generate or listen to a trigger synchronization signal. SAKURA and NewAE's Chipwhisperer are widely used platforms in the community that follow this approach.

However, in many cases, using a trigger signal is impossible. For example, when a given firmware cannot be modified to add instructions that control the trigger signal. Or simply because the device used to collect traces is not capable of capturing two signals, the side-channel signal and the trigger signal, concurrently. Locating CPs in traces without using trigger signals can be done with pattern recognition techniques. For this purpose, Beckers, et al. [START_REF] Beckers | Design and Implementation of a Waveform-Matching Based Triggering System[END_REF] compare methods that calculate the correspondence between trace and pattern values. When this match score is over a pre-defined threshold, the corresponding part of the leakage is considered as being the location in the trace of a targeted segment. IcWaves1 implements such pattern recognition methods.

Nevertheless, to use these methods, the attacker is supposed to already have a pattern or characterized segments having the same statistical properties as the researched segments, representative of the triggering moment. Therefore, the question of how to find this pattern remains open. To that end, Trautmann et al. [START_REF] Trautmann | Semi-Automatic Locating of Cryptographic Operations in Side-Channel Traces[END_REF] proposed a technique to locate AES CPs in leakage signals by searching for parts of the leakage having consecutive similar patterns corresponding to the 10 AES rounds. This method can find AES CPs in long traces also containing other CP operation leakages. Souissi et al. [START_REF] Souissi | Novel Applications of Wavelet Transforms based Side-Channel Analysis[END_REF] used wavelet transforms to detect the limit of AES segments in traces and then used these segments to do pattern recognition.

In the screaming channels context, in order to locate CPs from leakage signals, the only technique reported so far in the literature, by Camurati et al. [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF] and Wang et al. [START_REF] Wang | Far Field EM Side-Channel Attack on AES Using Deep Learning[END_REF], used a frequency component trigger mechanism 2 Segsin ← Shif tV alues(Segsin, shif t)

8: template ← average(Segsin[: index], axis = 0) 9:
end if 10: end for 11: Segout ← average(Segsin, axis = 0) Fig. 2. Algorithm: Fine alignment between segments continuously monitors a frequency band at which a given signal is present only at a unique instant of the targeted CPs. Segment locations should then correspond to trace locations where this signal is found.

In contrast with the proposed VT, all these methods require specific equipment other than the ones needed for the SCA itself, like a spectrum analyzer [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF], [START_REF] Wang | Far Field EM Side-Channel Attack on AES Using Deep Learning[END_REF] or a powerful GPU [START_REF] Trautmann | Semi-Automatic Locating of Cryptographic Operations in Side-Channel Traces[END_REF]. Therefore, before using more complex, expensive, or time-consuming solutions, VT is a trace segmentation method that can be used when the targeted device runs CPs without interruptions, in order to reduce the collecting phase complexity.

IV. CONSIDERED ATTACK SCENARIO

We consider a passive attack on system confidentiality exploiting power or EM side-channels from a CP manipulating AES keys. This causes leakage propagation through sidechannels with very low Signal to Noise Ratio (SNR). The attacker capabilities include: they (1) know the precise CP duration (or can use the method presented later in the paper to find it) and ( 2) have access to a copy of the victim device used to build a profiled attack.

When collecting segments of interest, during the profiling or the attacking phase, the following steps retrieve N segments from a collected trace and average them to generate a final segment with reduced noise:

1) The victim starts running a series of encryptions using the same plaintext and key.

2) The attacker, using a Software Defined Radio (SDR), starts collecting the trace after a certain delay to make sure CP executions have begun.

3) The collected trace is cut into N segments. To make sure segmentation happens only while CPs are present, N is chosen in a way that N ×CP duration is inferior to the CPs series execution duration. Except for the noise, these segments carry the same information, as each CP computed the same data. 4) A fine alignment is done between these segments, and the N aligned segments are averaged together, yielding a single representative CP segment with reduced noise (see Algorithm in Fig. 2).

V. PROPOSED VIRTUAL TRIGGERING METHOD

Virtual Triggering (VT) aims at cutting each captured trace in segments (step 3 of trace collection, Section IV), with a distance between cuts being closely enough to the CP length L cp to correctly segment CPs in the trace. If L cp is not known very precisely, as illustrated in Fig. 3, an offset appears in the VT position. Consequently, segment starting points would be triggered at different instants in the CPs, making the final segments too different from each other to be aligned. This would deteriorate the denoised CP segment, as averaged samples would not correspond to the same instructions.

A. Find accurate CP length L cp

We propose a two-step method to find the accurate CP length. This step can be performed only one time as L cp is the same for all CP segments. First, an approximate value Lcp is found, reducing the effort to find the accurate length L cp in the second step.

The first step consists in exploiting one trace containing multiple CPs. Auto-correlating such a trace, a peak is obtained each time CPs are aligned together. Therefore, Lcp can be approximated by manually measuring the average distance between two peaks.

The second step aims at finding the precise length L cp of one CP, which is equal to the approximate length plus one δ. The method used to find the value of this δ is presented in Algorithm in Fig. 4. It consists of testing a range ∆ of δ candidates. It segments the trace with the corresponding length: Lcp + δ (line 5), separates these segments into two equal groups, to distribute at best one group contains the even segments, the other the odd segments, averages each group SegmentA ← average(pair Segs)

7:
SegmentB ← average(odd Segs) [START_REF] Chari | Template Attacks[END_REF]. Then, the L1 distance (line 8) between the two reference segments should be at its minimum when the most accurate δ value is used. This distance is computed using equation [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF].

L1 Distance = abs(Segment A -Segment B) NB samples in one segment ( 1
)
where abs is the absolute value, and NB samples in one segment is the number of samples in one segment.

B. Align the segments together

After having found the accurate length L cp of a single CP execution, it is possible to segment correctly any trace containing the same CPs executed recursively. All the obtained denoised segments contain leakage samples from the same instructions but are not aligned together since segmentation begins at a random point in each trace. To have aligned segments, it is important to make them begin at a common point in the CP. For that, it is possible to take one of the segments as a reference and shift the values of the others until they reach the position where they best correspond to the reference segment. Afterward, a fine alignment can get them perfectly aligned to each other.

VI. EXPERIMENTS

A. Experimental setup

Fig. 5 shows the setup. It comprises a victim board, a mixedsignal Nordic Semiconductor chip as in the seminal screaming channels work [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF] (PCA100403 ), processing software-based AES encryptions. On the attacker side, an SDR captures the victim RF emissions: a USRP N210 4 with an SBX daughterboard covering a frequency band from 400MHz to 4.4GHz. Instructions are sent to the victim to initialize the new plaintext value and launch a series of N = 500 encryptions. The signal captured by the SDR is received by the attacker's computer, which runs the pre-processing and decoding process.

B. Finding the accurate CP length L cp

The auto-correlation results after applying the first step to find the approximate CP segment length are shown in Fig. 6 a). The average distance between two correlation peaks gives an approximate length of 4350 samples, which considering a sample rate of 5MHz, gives an approximate CP length of 870us.

The second step is performed to find a more accurate CP length. The algorithm in Fig. 4 runs on a range of 1000 ns (from -500 ns to 500 ns) with a step of 1ns. When the difference between the two CP appears to be at its minimum, this means δ is close to the real δ value. As shown on Fig. 6 b), the best value is found at 18ns. Automating this step is kept for future work. It would consist in automatically detecting the δ value having the lowest result. For that, it would be possible first to detect the range containing the lower minima.

C. Segmentation and alignment

Knowing the precise CP length, the trace is segmented (first row of Fig. 7 shows one segment), and the segments are finely aligned together and averaged (second row of Fig. 7). In the denoised segment, a specific instant of CPs is localized, and the segment values are shifted to make the segment begin at this instant (third row of Fig. 7). In this case, the time between two encryptions is easily recognizable as it does not vary. By computing the variance with a window of its size (230 samples), we can detect it as this variance has its lowest result at the same CP location in all segments. If the segment starting point is placed in the middle of this instant, it is then undetectable since the 230 samples are cut into two parts, one at the beginning of the segment, and the second at the end.

To anticipate these cases, the operation is performed on the denoised segment concatenated with its own 230 first samples. Therefore, this instant can be reconstituted at the end of the segment and be detectable. With this final step, a coarse-grained alignment is done between all denoised segments. A fine alignment (Algorithm in Fig. 2) can be necessary to have them even better aligned.

D. Comparison with original screaming channel attack

To evaluate VT, different experiments are run to compare against the original method [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF]. Denoised CP segments are extracted from the same collected traces using both the VT and the frequency component triggers. 5000 segments are used to build a profile, and 200 for the attack phase. We evaluate attack efficiency with the Partial Guessing Entropy (PGE) of each AES key byte. The PGE corresponds to the rank of the correct key byte value in a list of the possible hypothesis on data from the decoding process. Fig. 8 plots the average PGE over 30 attacks of each of the 16 key bytes sorted from best to worst, versus the number of traces used in the attack phase. The darker the blue, the lower the PGE is, i.e., the closer the attack is to guess the correct key byte. If PGE is equal to 0, the hypothesis made on the key byte is correct; if it is equal to n, then n hypothesis have a higher probability than the correct one. The red color corresponds to a PGE higher or equal to 4, which is the PGE value that no more than one key byte should reach for the key being easily recoverable in a few seconds using brute force. We can see that the PGEs are equivalent for both methods: 100 traces are enough in most cases to have only one byte with a PGE superior or equal to 4. These results show that VT, a simpler and less expensive method, achieves an equivalent efficiency to the original attack [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF].

We also evaluate VT according to the CP length precision. The top left result in Fig. 9 shows the attack result after a segmentation with the most precise length we were able to determine (precision: 1ps). The attack was repeated forcing an offset of respectively 500ns, 1µs, and 2.5µs. It can be seen that an offset of 500ns does not deteriorate segment information, but from 1µs the attack efficiency decreases.

E. Generalization of the method

To test the generalization of VT beyond the screaming channels context, hence on regular power/EM traces, we apply it to a signal collected by other authors [START_REF] Trautmann | Semi-Automatic Locating of Cryptographic Operations in Side-Channel Traces[END_REF], using leakage from a MCU device (STM32F303) executing a secure boot process containing 500 AES encryptions. As one of the requirements of our method is to have a signal containing only a series of CPs, we kept only the part of their signal containing AES segments. Using VT, the denoised segment in Fig. 10 is obtained.

VII. IMPROVING VT WITH PATTERN RECOGNITION

VT enables pinpointing reliable points from CPs by precisely computing segments length, hence acting as if a trigger signal was used. In turn, this makes it possible to segment traces in a way that all final segments are aligned with each other. However, when delays vary between the starting instants of segments, or if the attacker targets a device executing CPs asynchronously, the method does not hold.

In these contexts, VT can still be used during a profiling phase to build a template of the CP segments for later use during an attack. Next, we propose a simple technique that builds on VT to: (1) locate and extract a denoised CP segment from a profiling device (a copy of the victim), and learn a segment template; (2) automatically locate and pullout CP segments from traces collected on a victim instance of the device. We also demonstrate how, interestingly, this technique can absorb arbitrary time variations between CPs and improve the efficiency of existing attack methods.

During profiling, the attacker can force the device, e.g., with resets, to repeatedly execute a program containing CPs without time variations. Afterward, during the attack phase, the learned segment template (or only a subpart of it corresponding to a CP) can be used to locate CP segments in the traces using pattern recognition techniques. For pattern recognition, we cross-correlate traces with the learned pattern and detect peak positions indicating CP locations.

We compare our results with the efficiency of the FC trigger. The experiment has been performed in two scenarios: one using periodic encryptions and another with a variable delay between them. Fig. 11 shows how using pattern recognition significantly increases the attack efficiency. As previously with FC trigger, around 100 segments are needed. Using pattern recognition with the VT extracted pattern, less than 50 segments are enough.

An obvious advantage of VT compared to the pattern pullout technique with pattern recognition is that VT needs less computation effort, hence the collection phase is faster. In our case, collecting 10K denoised segments took 20 hours using pattern recognition, when only 5 hours were needed with VT. However, using the pattern pullout technique enables attacks in scenarios with time variations between CPs, which can come from system interrupts or simple countermeasures using time randomization. Nonetheless, we have not verified the method in these conditions, this is left for future work.

VIII. CONCLUSION

This paper has proposed VT, a simple-to-implement method to collect denoised CP segments, exploiting time diversity in the context of screaming channels. The efficiency of VT is demonstrated with respect to the state-of-the-art screaming channel trace collection method [START_REF] Camurati | Understanding Screaming Channels: From a Detailed Analysis to Improved Attacks[END_REF]. Compared to more complex and recent methods to find CPs in traces containing other operations than those exploited by the attack [START_REF] Trautmann | Semi-Automatic Locating of Cryptographic Operations in Side-Channel Traces[END_REF], VT is much simpler. While our experimental results concentrate on screaming channels, VT and the pattern pullout technique are generic and can be used for other forms of physical leakages.

Fig. 3 .

 3 Fig.3. Segment CPs using the virtual trigger: 1st row: the beginning of the collected trace and the VT positions determined according to the known CP length. 2nd row: a segment aligned to segment start time. 3rd/4th rows: if the length is not precise enough, a drift appears in start times, and hence VT indicates a very different point in CPs at the end of the trace.

Input:repeat 5 :

 5 Approximate CP length: Lcp Input: Range of δ candidate values : I nterval Output: Accurate CP length: Lcp 1: δ ← -I nterval /2 ▷ Delta 2: S ← I nterval /2 ▷ Stop 3: δstep ← I nterval /number of steps ▷ Delta step 4:Segs ← Cut the trace in N segments of length = Lcp + δ 6:

8 :Fig. 4 .

 84 Fig. 4. Algorithm: How to find accurate CP length Lcp

Fig. 5 .Fig. 6 .

 56 Fig. 5. The setup: 1) The victim PCA10040 device running AES encoding and transmitting a Bluetooth signal at 2.4GHz. 2) The SDR device collects the victim's data-correlated leakage at 2.528GHz.

Fig. 7 .

 7 Fig. 7. Obtain denoised and align CP segments: 1st row: shows a segment in the initial collected trace. 2nd row: corresponds to averaged segments from trace cut with a precise length. 3rd row: is the average segment aligned to a recognizable point, to be aligned with all other denoised segments. The ten rounds of AES are visible.

Fig. 8 .Fig. 9 .

 89 Fig.8. Comparison between FC and VT triggers as PGE per key byte (the higher the blue array, the better, 16 is a maximum): the proposed method does not decrease the attack efficiency for screaming channel attacks while reducing the segmentation complexity.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Virual trigger applied for segmentation of 500 AES of a secure boot process:. First row: initial trace. Second row: Denoised Segment.

  Segments misaligned Output: Aligned CP segment: Segout ▷ Segment aligned 1: template ← None 2: for index IN len(Segsin) do

	3:	if template == None then
	4:	template ← Segsin[index]
	5:	else
	6:	shif t ← max(corr(Segsin[index], template))

. The method Input: Misaligned CP segments: Segsin ▷ 7:

https://www.riscure.com/security-tools/hardware/icwaves.

https://github.com/bolek42/rsa-sdr.

https://www.nordicsemi.com/Software-and-tools/Development-Kits/ nRF52-DK.

https://www.ettus.com/all-products/un210-kit/


Dr João Pedro Ferreira
email: jpferreira@med.up.pt

John G F Cleland

Nicolas Girerd

Pierpaolo Pellicori

Mark R Hazebroek

Job Verdonschot

Timothy J Collier

Johannes Petutschnigg

Andrew L Clark

Jan A Staessen

Stephane Heymans

; Faiez Zannad

Patrick Rossignol

Early and late renal function changes with spironolactone in patients at risk of developing heart failure: findings from the HOMAGE trial

Keywords: estimated glomerular filtration rate, tubular injury, spironolactone, heart failure risk

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

Background

Mineralocorticoid receptor antagonists (MRA) induce hemodynamic changes that reduce estimated glomerular filtration rate (eGFR), which usually occurs early after treatment initiation and then stabilises and is generally of small magnitude, and not associated with a decrease of clinical benefit from MRA therapy. [START_REF] Rossignol | Incidence, determinants, and prognostic significance of hyperkalemia and worsening renal function in patients with heart failure receiving the mineralocorticoid receptor antagonist eplerenone or placebo in addition to optimal medical therapy: results from the Eplerenone in Mild Patients Hospitalization and Survival Study in Heart Failure (EMPHASIS-HF)[END_REF][START_REF] Vardeny | Influence of baseline and worsening renal function on efficacy of spironolactone in patients With severe heart failure: insights from RALES (Randomized Aldactone Evaluation Study)[END_REF][START_REF] Beldhuis | Spironolactone in Patients With Heart Failure, Preserved Ejection Fraction, and Worsening Renal Function[END_REF] However, clinicians may withhold or stop spironolactone (and other RAAS inhibitors) when eGFR decreases (even if transient), which may increase the risk of subsequent events. [START_REF] Rossignol | Heart failure drug treatment[END_REF] In the HOMAGE (Heart OMics in AGEing; NCT02556450) trial enrolling patients with risk factors for developing heart failure (HF), spironolactone (compared to usual care) reduced markers of collagen synthesis, blood pressure, natriuretic peptides, and improved cardiac structure and function, while decreasing eGFR by ~5 ml/min/1.73m 2 from baseline to month 9. [START_REF] Cleland | The effect of spironolactone on cardiovascular function and markers of fibrosis in people at increased risk of developing heart failure: the heart 'OMics' in AGEing (HOMAGE) randomized clinical trial[END_REF] The factors associated with early and late eGFR decrease and respective biomarker correlations have not been studied in this population.

Methods

The HOMAGE clinical trial was a prospective, randomized, open-label, blindedendpoint (PROBE) study comparing spironolactone vs. usual care in people at increased risk of developing HF. The protocol and design of HOMAGE have been previously described. [START_REF] Pellicori | Effects of spironolactone on serum markers of fibrosis in people at high risk of developing heart failure: rationale, design and baseline characteristics of a proof-of-concept, randomised, precision-medicine, prevention trial. The Heart OMics in AGing (HOMAGE) trial[END_REF] In short, the main inclusion criteria were age greater than 60 years, plasma concentrations of natriuretic peptides above the normal range, coronary artery disease or at least two of the following: diabetes mellitus, hypertension, microalbuminuria, or abnormal ECG. The key exclusion criteria were an eGFR <30 ml/min/1.73 m 2 , serum potassium >5.0 mmol/L, left ventricular ejection fraction <45%, atrial fibrillation, a prior diagnosis of HF, or treatment with loop diuretics. After randomization, eGFR was assessed at one and nine months.

Spironolactone was initiated at a dose of 25 mg/day. Doses could be increased up to 50 mg/day or reduced to 25 mg every other day or stopped with or without reinitiation according to serum potassium. [START_REF] Pellicori | Effects of spironolactone on serum markers of fibrosis in people at high risk of developing heart failure: rationale, design and baseline characteristics of a proof-of-concept, randomised, precision-medicine, prevention trial. The Heart OMics in AGing (HOMAGE) trial[END_REF][START_REF] Monzo | Dyskalemia in people at increased risk for heart failure: findings from the heart 'OMics' in AGEing (HOMAGE) trial[END_REF] Furthermore, spironolactone had to be discontinued if eGFR fell to or below 30ml/min/1.73m 2 . Treatment could be restarted at the investigator's discretion if eGFR rose above 30ml/min/1.73m 2 .

Worsening renal function (WRF) >20% from baseline was a prespecified secondary outcome.

In this analysis, eGFR was determined using the CKD-EPI 2009

Results

Spironolactone effect on early and late eGFR changes

A total of 527 participants (265 spironolactone and 262 usual care) were included in the analysis. Supplementary Table 1. Compared to usual care, spironolactone decreased eGFR from baseline to month one: -3 (-4 to -2) ml/min/1.73m 2 , P <0.001 (corresponding to a -4% change on average). This effect was similar in patients with baseline eGFR above or below 60 ml/min/1.73m 2 , interactionP =0.63. On the other hand, spironolactone did not decrease eGFR between months one and nine: -1 (-3 to 0) ml/min/1.73m 2 , P =0.085. No significant interaction was found by eGFR above or below 60 ml/min/1.73m 2 measured at one month, interactionP =0.11. Figure 1.

The proportion of patients with eGFR decrease ≥20% from baseline was small and not significantly different between spironolactone and usual care: any timepoint: spironolactone =36 (14.0%) vs. usual care =25 (9.9%), P =0.15; baseline to month one spironolactone =14 (5.5%) vs. usual care =6 (2.4%), P =0.074; month one to month nine, spironolactone =22 (8.9%) vs. usual care =19 (7.6%), P =0.60. The proportion of patients with eGFR drop ≥30% from baseline was also small and not significantly different between spironolactone and usual care: any timepoint: spironolactone =16 (6.2%) vs. usual care =8 (3.2%), P =0.10; baseline to month 1, spironolactone =5 (1.9%) vs. usual care =1 (0.4%), P =0.11; month 1 to month 9, spironolactone =11 (4.5%) vs. usual care =7 (2.8%), P =0.32.

Patient's characteristics across tertiles of eGFR change

Compared to patients in whom eGFR increased from baseline to month one, those in whom eGFR decreased had higher eGFR at baseline and were more often randomized to spironolactone (P <0.01 for both). Supplementary Tables 2 &3.

Association between eGFR and circulating biomarker changes

eGFR decrease from baseline to month one was caused by spironolactone initiation (without differences in the usual care group) and these were negatively correlated (i.e., eGFR decrease/biomarker increase) with renin, and positively correlated (i.e., eGFR decrease/biomarker decrease) with BNP, KIM-1, and SBP (P<0.01 for all). No biomarker predicted the occurrence of WRF >20%.

Conclusion

This analysis shows that spironolactone exerted a small decrease in eGFR from baseline to month one, without a significant difference thereafter compared to a control group, suggesting that the eGFR decrease associated with spironolactone is caused by early hemodynamic changes without renal injury; findings that are furtherly supported by a positive correlation with BNP, KIM-1 and SBP decrease.

Graphical abstract.

These findings expand those from RALES, EMPHASIS-HF and TOPCAT in patients with chronic HF with reduced or preserved ejection fraction, where steroid-based MRAs induced a mild eGFR decrease (from -2 to -4 ml/min/1.73m 2 ) that was apparent within weeks of treatment initiation, but thereafter participants assigned to MRA experienced eGFR trajectories similar to those observed with placebo in the following years. Together these data suggest that steroid-based MRAs cause an early eGFR decrease but do not accelerate long-term, age-related decline in renal function in patients at risk for or with chronic HF.

In HOMAGE the early eGFR decrease was negatively correlated with the increase in plasma renin concentration, which is occurs as a feedback mechanism to the blockade of the mineralocorticoid receptor by spironolactone. [START_REF] Ferreira | Proteomic and Mechanistic Analysis of Spironolactone in Patients at Risk for HF[END_REF] The positive correlation between eGFR decrease and BNP, KIM-1, and SBP supports the hypothesis that the early eGFR decrease after initiating spironolactone is hemodynamic in origin rather than reflecting structural renal damage or tubular injury. [START_REF] Ferreira | Blood and Urine Biomarkers Predicting Worsening Kidney Function in Patients with Type 2 Diabetes Post-Acute Coronary Syndrome: An Analysis from the EXAMINE Trial[END_REF][START_REF] Ahmad | Worsening Renal Function in Patients With Acute Heart Failure Undergoing Aggressive Diuresis Is Not Associated With Tubular Injury[END_REF] In summary, among patients at risk of developing heart failure enrolled in HOMAGE, spironolactone induced an early and mild eGFR decrease due to hemodynamic changes in the kidney, without evidence of tubular injury. After 1 month, changes in eGFR were similar between spironolactone and usual care.

  creatinine-based formula. The effect of spironolactone on early and late eGFR changes was assessed by analysis of covariance. Patients' characteristics were compared across tertiles of early and late eGFR changes. Associations between eGFR changes and changes in biomarkers of cardiac stretch (BNP, brain natriuretic peptide), tubular kidney injury (KIM1, kidney injury molecule-1), mineralocorticoid receptor blockade feedback (renin), and systolic blood pressure (SBP) were assessed with linear regression models. Analyses were performed using Stata® version 17.1 (StataCorp. 2021. Stata Statistical Software: Release 17. College Station, TX: StataCorp LLC).

Figure 1 .

 1 Figure 1. eGFR change from baseline to month 1 and month 1 to month 9 in spironolactone and usual care ("control") groups

Ethics approval and consent to participate

The study was approved by all relevant ethics committees and regulatory bodies. All participants provided written informed consent prior to study specific procedures.

Consent for publication

There is no data of individual persons included in the manuscript.

Competing interests

The authors have no relevant conflicts of interest to disclose regarding the content of this manuscript.


Claudia Serban

Internal and External Experience: From Husserl to Kant

Keywords: Husserl, Kant, internal experience, external experience, idealism, psychology

If Kant and Husserl both elaborate a form of transcendental idealism, they undoubtedly assign a quite different function and consistency to internal experience in relationship to external experience. The paper analyzes the consequences of this remarkable discrepancy and shows that bringing together the two forms of idealism could imply a significant risk of confusion. Kant and Husserl's relationship to Descartes is invoked and examined as an illustration of this claim. While stating that the nature and conditions of internal experience decide of the meaning of transcendental idealism, the paper also discusses the positions of the two German philosophers towards psychology.

Kant and Husserl both elaborate a form of transcendental idealism. Nevertheless, they assign quite a different function and consistency to internal experience in relationship to external experience. I aim to analyze here the consequences of this remarkable discrepancy and to show that bringing together the two forms of idealism could imply a significant risk of confusion. Kant and Husserl's relationship to Descartes will be invoked and analyzed as an illustration of this claim.

In order to examine the manner in which the nature and consistency of internal experience decides of the meaning of transcendental idealism, I will adopt a somewhat particular perspective: that of Husserl and Kant's position towards psychology. The objections that Husserl opposed to Kant in a quite large number of important texts are well known: the author of the three Critiques is considered not to have thoroughly and entirely completed his transcendental project insofar as -in spite of his resistance and opposition to 1 5 dogmatism -he remained imprisoned by some undoubtedly dogmatic (either rationalist or empiricist) presuppositions. Such presuppositions are exhibited by Kant's decision to restrain the validity of the pure concepts of our intellect that are the categories and of our knowledge in general, both by limiting their application field to phenomena and by attributing them only to "finite reasonable beings", that is, in particular, to us humans. But there is another, much more discrete and yet powerful critique that Husserl addressed to Kant, for instance in § 57 of his Crisis of European Sciences: that of establishing a "fatal separation (verhängnisvolle Trennung)" between transcendental philosophy and psychology. Against such a separation, Husserl manifests the ambition of "transforming psychology in a universal transcendental philosophy" (Hua VI,201,207), and finds it quite surprising that "since Kant, transcendental philosophy never really profited from psychology" (Hua VI, 211). Furthermore, in what concerns Kant himself, Husserl also expresses his astonishment regarding the fact that critical philosophy "did not edify a better psychology." (Hua VI, 205) For Husserl, indeed, as the last sequence of the Krisis shows it by attempting to consolidate (according to § 72) the "relationship of transcendental psychology to transcendental phenomenology as a genuine access to pure self-cognition", not only is a pure selfcognition, and consequently, a pure, aprioric psychology, possible, but one can even legitimately envisage a "transcendental psychology", related to transcendental philosophy like a "twin sister (Verschwisterung)", through the "the identity and the difference […] of the transcendental and the psychological I." (Hua VI,209) By aiming to renew in this fashion the connection between transcendental philosophy and psychology, Husserl is obviously conscious of transgressing a Kantian prohibition; but he considers that his project of an eidetic psychology as ultimately leading to a transcendental science of consciousness is not affected by this prohibition, which is only active when the dogmatic, rational psychology is concerned. The Introduction of his 1925 lecture on Phenomenological Psychology puts it quite clearly:

1 6 "Long ago, in the Leibniz and Wolff school of the 18 th century, the apriorical psychology was much debated, but Kant's Critique has put an end to it. Yet this psychology was an ontological, metaphysical one. It was not an intuitive, descriptive and at the same time apriorical one, like this new psychology..." (Hua IX 39) -this new psychology, that is, phenomenological psychology.

All the objections raised by Husserl against the destiny that Kant had reserved to psychology (by limiting it to be only empirical and never to be pure without relapsing into transcendental dialectics) not only suggest that the author of the Krisis might not have fully grasped and assimilated the meaning of Kant's critique of rational psychology, but also that, for this very reason, he is perhaps himself not entirely immune to some of the specific arguments at work in this critique. Doesn't Husserl succumb to a certain extent to what Antoine Grandjean has called "the reflexive illusion of the transcendental" (Grandjean 2009, 107), that is, the illusion that reflection grants an access to an egological sphere conceived as an absolute? Is he completely preserved from the temptation of reviving the 4 th Paralogism of pure reason, and doesn't this potential risk express the sheer Cartesianism of the author of the Cartesian Meditations? For indeed, while criticizing Kant's psychologisation of the faculties of the mind, Husserl maintains the very alliance between transcendental philosophy and psychology that Kant had ruined. For this reason, the status and place of psychology in respect to transcendental philosophy could decide of the meaning of transcendental idealism and, at the same time, the relationship of transcendental philosophy towards Descartes could appear in a quite radically different light.

In order to explore the paths that I have just sketched, I will start by examining Kant's critique of the 4 th Paralogism (the Paralogism of ideality); I will then analyze the motor and the implications of the 1787 Refutation of idealism, and my final objective will be to measure the consequences of Kant's radically new manner of articulating internal and external experience.

A last introductory remark before engaging the analysis: in the Amphiboly of the concepts of reflection, Kant makes the following crucial statement: "I [...] have nothing absolutely but only comparatively internal, which itself in turn consists of outer relations." (Kant 1998, 375;AA, A 277/B 333) The context of this assertion is provided by the discussion of the couple form-matter -more precisely, by the question of knowing if something like a substantia noumenon does intrinsically belong to matter. This discussion will lead to denying any substantiality (or absolute interiority) to matter, and the fashion in which the demonstration progresses is remarkable in itself insofar as its terms are very close to those that the Refutation of idealism will use while questioning and criticizing the supposed primacy of internal experience on external experience. The destitution of this primacy not only determines the peculiar nature of critical idealism, but, as it is at the same time present at the very heart of the deconstruction of the 4 th Paralogism, is also crucial for clarifying Kant's relationship to psychology.

The Paralogism of ideality and the problem of exteriority

To begin with, it might be useful to recall the fact that by rewriting the Paralogisms for the second edition of the Critique of pure reason, Kant makes a significant architectonic change in the structure of his work: the refutation of idealism, entrusted in 1781 to the discussion of the 4 th Paralogism, is now transferred from the Transcendental Dialectics to the Analytics, where it will occupy a particular place right after the exposition of the Postulate of actuality. This modification accomplished by the 1787 edition clearly suggests that Kant might not have been quite pleased with the manner in which he had solved, in 1781, the problem of idealism. His dissatisfaction must also have been increased by a tendency present within the very first reception of the Critique: that of reading this work as a mere savant and more elaborated renewal of idealism and skepticism. The most eloquent illustration of this early interpretative trend is provided by the famous Garve-Feder review of the first Critique, published in January 1782 by the Göttinger Gelehrte Anzeiger. This review is important in spite of its undeniable philosophical shallowness, insofar as it clearly touches a weakness present in the 1781 edition, namely, the 1 8 fact that the first version of the Critique eventually made a too significant concession to idealism. This explains the need that Kant felt to propose, in 1787, a genuine refutation of idealism, whose mechanisms and implications I will attempt to evaluate.

But let us start by examining the shape taken by the 4 th Paralogism in 1781, and Kant's solution to it. This Paralogism is presented as follows: "all outer appearances (Erscheinungen) are of this kind: their existence cannot be immediately perceived, but can be inferred only as the cause of given perceptions"; consequently, "the existence of all objects of outer sense is doubtful". In spite of his critical intentions, Kant is relatively clement here towards the idealist position, by admitting that "one can rightly assert that only what is in ourselves can be immediately perceived." (Kant 1998, 425;AA, A 367) From this point of view, the idealist is "not someone who denies the existence of external objects of sense, but rather someone who only does not admit that it is cognized through immediate perception." (426; A 368) Therefore, the idealist claim is not that of the non-existence of the outer world, but that of its inescapably mediate experience or perception; idealism does not necessarily rhyme with acosmism, but is rather to be understood as a potential and always imminent skepticism. The reasoning of the idealist is indeed the following: I cannot really perceive external things, but only infer their existence from my inner perception, insofar as I regard this as the effect of which something external is the proximate cause. But now the inference from a given effect to its determinate cause is always uncertain, since the effect can have arisen from more than one cause." (425; A 368) After the formulation of the Paralogism, which insists on the indirect and inferential character of our experience of the outer world and deduces from this the uncertainty of its existence, comes Kant's solution, which deserves to be extensively quoted:

[…] external objects (bodies) are merely appearances, hence also nothing other than a species of my representations, whose objects are something only through these representations, but are nothing separated from them. Thus external things exist as well as my self, and indeed both exist on the immediate testimony of my selfconsciousness, only with this difference: the representation of my 1 9

Self, as the thinking subject, is related merely to inner sense, but the representations that designate extended beings are also related to outer sense. I am no more necessitated to draw inferences in respect of the reality of external objects than I am in regard to the reality of the objects of my inner sense (my thoughts), for in both cases they are nothing but representations, the immediate perception (consciousness) of which is at the same time a sufficient proof of their actuality (Wirklichkeit)." (427; A 370-371) One can clearly see here that, in order to deactivate the idealist affirmation of our mediate and always indirect access to exteriority, Kant insists on the fact that the objects of our external sense are mere appearances, and eventually, mere representations: for this reason, external experience is not more indirect or more mediate than internal experience, insofar as in both cases we have to do with representations which are just as immediately present in me.

Thus, the 1781 resolution of the 4 th Paralogism establishes an equivalency between internal and external experience by asserting that they are equally immediate and certain. But quite visibly, this equivalency can only be instituted by dissolving exterior objects within the immanent sphere of representation. Through the external sense, I represent myself objects that are outside me, but their representation is in me. We are confronted here, as Christophe Bouton has shown it in two enlightening papers (Bouton 2002, 77-88;Bouton 2004, 15-41), with a genuine aporia of representation which seems to sign the failure of any attempt to leave the sphere of interiority: as long as the object of the external sense is only considered as my representation, the reality of the outer world taken as existing outside me will always ineluctably escape me. Otherwise said, the aporia of representation, present in the first Critique -and not only within the resolution of the 4 th Paralogism, but also within the first draft of the transcendental Deduction -goes together with an irreducible ambiguity of exteriority. Kant is undoubtedly conscious of this difficulty when he admits that "the expression outside us carries with it an unavoidable ambiguity, since it sometimes signifies something that, as a thing in itself, exists distinct from us and sometimes merely something that belongs to outer appearance." (Kant 1998, 428; AA, A 373) Among these 2 0 two different meanings, it is of course the latter that is retained by the critical idealism, given its double opposition to the dogmatic assumption of beings in themselves existing outside me and to the correlative realist position which remains fully blind to the ideality of space and time. But the appearance or phenomenon -the Erscheinung -, be it understood as the undetermined object of our empirical intuition, is only considered here as a representation: "in our system, on the contrary, writes Kant, these external things -namely, matter in all its forms and alterations -are nothing but mere representations, i.e., representations in us, of whose actuality (Wirklichkeit) we are immediately conscious." (427; A 371-372 ; trans. modified) From this perspective, that which is immediately conscious is always only a representation, be it internal or external. Kant stresses this important point by writing the following: "Thus there may very well be something outside us, which we call matter, corresponding to this appearance; but in the same quality as appearance it is not outside us, but is merely as a thought in us, even though this thought, through the sense just named, represents it as being found outside us." (434; A 385) This is how the undoubted existence of the outer world is finally dissolved in the undisputed presence in me of its representation, of which I am immediately conscious. The actuality that is proved by following this path is not that of the world or that of the exterior object, but only that of the representation of exteriority which is in me; in more Cartesian terms, it is only the formal reality of the idea or of the representation of the world. But what about its objective reality, that is, what about the existence of the object of this representation?

It is indeed very much significant that Kant will precisely adopt this Cartesian vocabulary (which, as a matter of fact, is quite familiar to him) in the long footnote that he adds at the end of the 1787 Preface, where he claims that the Refutation of idealism is in fact the only veritable supplement (Kant 1998, 121; AA, B XXXIX) i of the second edition of the Critique. The purpose of this supplement was, as Kant reminds it, to provide "a rigorous demonstration […] of the objective reality of the external sense". Undoubtedly, the 1781 resolution 1 of the 4 th Paralogism has mainly focused on the formal reality of my representation of exteriority, by asserting that "every outer perception therefore immediately proves something actual (wirklich) in space, or rather is itself the actuality (das Wirkliche selbst)." (429; A 375; trans. modified) The actuality of exteriority is only the actuality of my representation of it. Otherwise said, "the real (das Reale) in outer appearances is thus actual (wirklich) only in perception, and cannot be actual in any other way." (429 ; A 376) It appears here once again that the resolution of the Paralogism of ideality proposed by Kant in the first edition of the Critique moves itself entirely within the sphere of representation, which corresponds mutatis mutandis to that which Husserl will designate as intentional immanence. From this point of view, one is certainly entitled to say, as Paul Ricoeur in his famous paper on Kant and Husserl (Ricoeur 1986, 235), that the author of the Critique has undeniably acknowledged the level of intentional immanence by going beyond the traditional distinction between transcendence and immanence. Doubtlessly, the differentiation of external and internal objects has no immediate ontological significance in Kant, but only a phenomenological one: their separation is immanent to the realm of appearances (Erscheinungen). As the 1781 edition puts it: "I, represented through inner sense in time, and objects in space outside me, are indeed specifically wholly distinct appearances, but they are not thereby thought of as different things" (Kant 1998, 431; AA, A 379) (insofar as the transcendental object that lies at the ground of these two kinds of Erscheinungen is equally unknown to us). And, for the rest, in the first version of the Paralogisms, Kant faces quite directly the difficulties concerning the status of the intentional object.

Still, the 1787 Refutation of idealism does not please itself with this first solution, but attempts to make a further step towards a satisfying approach of the problem. As the footnote of the second Preface that I have already quoted indicates it, the veritable ground of the Refutation of idealism is not the field of appearances understood as representations, but that of the consciousness of existence, insofar as the purpose is to show that "the empirical consciousness of my existence, [...] is only determinable through a relation to something that, while being bound up with my existence, is outside me." (Kant 1998, 121, note;B XL) In this light, it is easier to understand why the Refutation of idealism is inserted, in the second edition of the Critique, after the presentation of the Postulate of actuality (Wirklichkeit); and also why Kant insists to distinguish, in the same footnote of the 1787 Preface, "the representation of something persisting in existence" on one hand, and "a persisting representation" on the other: there should indeed be no confusion between that which belongs to the objective reality of a representation and that which pertains simply to its formal reality. For only the consideration of the objective reality of representations allows reaching their (outer) correlate and stating something about its existence. This is why the argument of the Refutation of idealism will so much emphasize the actuality of that which is exterior to me, and in this perspective, reality (Realität) and actuality (Wirklichkeit) are to be carefully distinguished. This distinction (which is, unfortunately, not very rigorously honored by both the English and the French translations of the first Critique), corresponding in fact to the one which separates, within the table of categories, the pure concepts of quality and those of modality, is quite decisive when the question of exteriority is at stake.

The fact that the discussion starts progressively to turn around the objective reality of the internal sense indicates that the strategy adopted by the second edition of the Critique in order to escape the realm of representations does not imply relapsing into a realism of a precritical kind, and can at the same time avoid the comfortable path of simply invoking the thing in itself (Kant 2004, § 13, Note 2) : at this level, outside me does not mean in itself, for what is outside me is what is given to me in space; and the exteriority of spatial objects is not the absolute exteriority of things in themselves (which are not, properly speaking, "exterior" in the sense of a spatial relationship). And still, the existence or the actuality of spatial objects is irreducible to the presence or the persistence of their representation in me, even though space is "nothing other than an inner mode of representation." ii (Kant 1998, 430; AA, A 378) 3

Yet, this characterization of space -of the form of exteriority -through its being-interior is undoubtedly dissatisfying: the ambiguity of exteriority is indissolubly that of space itself, considered as an interior exteriority. This is why, in one of the Reflexionen zur Metaphysik that attempt to clarify the Refutation of idealism, Kant will point out the fact that "space is not in me, and still it belongs to the formal subjective conditions of empirical self-consciousness": more precisely, space is not "in me" since it hints at "that which I must represent in another fashion than myself", that is, at that which is exterior to me iii . And given that this representation is intrinsically connected to empirical self-consciousness, this very consciousness is to be defined as the "consciousness of an external relation (Bewusstsein einer äusseren Relation)." (AA XVIII, [Refl. 5653], 307; my translation) The separation between the interior and the exterior seems to lose here all its rigidity, which is ultimately another manner of stating that for me, all interiority is only comparative. And still, this separation covers something more than a sheer difference between two kinds of representation present in me: the empirical consciousness here at stake is always the consciousness of an existence, of something actual outside me iv .

This emphasis on the fact that the Refutation of idealism intends to prove something else than the mere existence of an undoubted representation of exteriority is in fact already present in the Prolegomena, § 49, where one can read the following:

"Outside me empirically is that which is intuited in space; and because this space, together with all the appearances it contains, belongs to those representations whose connection according to laws of experience proves their objective truth, just as the connection of the appearances of the inner sense proves the actuality (Wirklichkeit) of my soul (as an object of inner sense), it follows that I am, by means of outer appearances, just as conscious of the actuality of bodies as outer appearances in space, as I am, by means of inner experience, conscious of the existence of my soul in time -which soul I cognize only as an object of inner sense through the appearances constituting an inner state, and whose being as it 4 is in itself, which underlies these appearances, is unknown to me." (Kant 2004, 88;AA IV Prol., 336;trans. modified) The spatial object -the object that is given to me in space -is manifestly irreducible to my representation, for it exists empirically outside me. Therefore, the consciousness of an existence is just as present in internal experience as in the external one: there is no hierarchy in this respect between the two, as Kant stresses it by writing that "it is just as secure an experience that bodies exist outside us (in space) as that I myself exist in accordance with the representation of inner sense (in time) -for the concept: outside us, signifies only existence in space." (Kant 2004, 89; AA IV Prol., 337) And yet, rather than producing a new asymmetry between the inner and the outer sense, the Prolegomena will only acknowledge their equivalent status: the purpose is not to show that the inner sense depends on the outer one, but only to reject the argument by which the idealist claims that exteriority in general is doubtful.

To this acknowledgment of the equal certainty and immediacy of the representations provided by the inner and the outer sense, only the second edition of the Critique will substitute a genuine reversal, by subordinating internal experience to external experience. The footnote that Kant places at the end of the 1787 Preface anticipates this shift quite clearly:

[…] it is experience and not fiction, sense and not imagination (Erfahrung und nicht Erdichtung, Sinn und nicht Einbildungskraft), that inseparably joins the outer with my inner sense; for outer sense is already in itself a relation of intuition to something actual (Wirkliches) outside me; and its reality (Realität), as distinct from imagination, rests only on the fact that it is inseparably bound up with inner experience itself, as the condition of its possibility." (Kant 1998, 121;AA, B XL, note) This passage is remarkably radical insofar as it inscribes a constitutive relationship to exteriority at the very heart of the inner sense. Furthermore, it is from this relationship itself that the reality of the objects of the outer sense will then be inferred: without such correlates, without an object exterior to me and yet given to me in space, the inner sense itself could not properly function: that which is given through this sense would then be purely evanescent and inconsistent. In the end, the two senses are mutually dependent: on one hand, internal experience seems to have to embrace external experience; but on the other hand, it cannot be self-sufficient, as it so much depends on external intuitions. This means that, just like interiority is only comparative, exteriority is not absolute: "the reality of outer sense is necessarily bound up with that of inner sense, i.e., I am just as certainly conscious that there are things outside me to which my sensibility relates, as I am conscious that I myself exist determined in time." (Kant 1998, 122; B XL, note) And just like the notion of exteriority employed by the Refutation of idealism is not a realist, dogmatic one (it is not an absolute exteriority, but a relative one insofar as it is spatial), the notion of existence only designates here (according to the principle stated by the Postulate of effectiveness) the accordance with the material conditions of experience.

The combat against dogmatic (material) idealism has requested to admit and fully measure the fact that the consciousness of my existence does not imply a certainty superior to that of the existence of objects outside me. The mechanism of the 1787 Refutation of idealism will nevertheless consist in proving that the two are not only equally certain, but that the presumed primacy, priority and superiority of internal experience has to be reversed: it is only then, as Kant eventually realizes it, that the idealist who considers all exteriority as intrinsically doubtful will be completely defeated. This precedence of the outer sense, prescribed by the Refutation of idealism, will even lead to amending the result of the Transcendental Deduction by stating, within the General Remark on the System of Principles (at the end of the Analytics), that in order to grant an objective reality to the categories (as pure concepts of our intellect), "we do not merely need intuitions, but always outer intuitions." (Kant 1998, 335;AA, B 291)

The Refutation of idealism and the inconsistency of the interior

But let us finally consider the shape taken by Refutation of idealism at the end of the Postulate of actuality. The demonstration is well known: its main argument is the fact that only external representations can provide us with a representation of permanence and that "consequently, the determination of my existence in time is possible only by means of the existence of actual (wirklich) things that I perceive outside myself." (Kant 1998, 327;AA, B 275-276) It is in this fashion that Kant intends to "turn against it" the "the game that idealism plays", according to which "internal experience is the only immediate experience". Kant can speak here of a reversal, of an Umkehrung, insofar as his goal is precisely to prove that only "outer experience is really immediate" (Kant 1998, 327;B 276), and that it is the condition, "not [...] [of] the consciousness of our own existence, but [of] its determination in time, i.e., [of] inner experience." (B 277) Significantly, it is also here that reemerges the distinction between the consciousness "able to accompany all my representations" (Kant 1998, 246;B 131), or pure apperception, and internal experience, for which an inner intuition is required, that is, which involves the temporal dimension of the subject of thought. The field of the demonstration is not the mere logical consciousness of the "I think", for at this level, the dependency upon external intuitions would jeopardize the very autonomy of the act of thinking. It is only the temporal determination of existence, associated to the representation of an I, that presupposes a "change in outer relations" (328; B 277), insofar as the inner sense cannot deliver any representation of permanence. The inner sense data do not provide us with anything that could correspond to the representation of a substance: such a representation could not have an objective reality in respect to that which is given through internal experience, and only the matter of external experience could possibly verify this condition. This is how, at the very heart of the Refutation of idealism, we are again confronted to the question of matterabout which, a bit later, in the Amphiboly, Kant will state that nothing absolutely interior is given to me. Thus, it is also the problematic status of the matter of internal experience, or of its specific givenness, that is here at stake; and the second edition of the Critique will even go as far as saying that it is from "the existence of things outside us" that "we after all get the whole matter for our cognitions, even for our inner sense." (121; B XXXIX) This means that, strictly speaking, there are no "immediate data of consciousness", understood as genuine data of the inner sense: the paradox of the inner sense is that it cannot really give anything; or rather, that which is given through it is not really something, for it is only a perpetual evanescent flow. Consequently, for Kant, that which Husserl calls the "originarily giving (originär gebende)" or "originary presentive" (Husserl 1983, 44; Hua III/1, 51) intuition is rather the external intuition. Rigorously speaking, this view is a result of the second edition of the Critique, given that, in 1781, Kant could still assert that "the thinking I is given to inner sense, likewise as substance in appearance." (Kant 1998, 431; AA, A 379) But such a generous interpretation of the giving capacities of the internal sense will not prevail for long: quite the contrary, the second edition will unveil the extreme poverty of the inner sense and, by doing so, will also reveal the indigence of internal experience itself.

For this reason, the 1787 Refutation of idealism has the significance of an even more radical refutation of the substantiality of the soul, thus revealing that the destiny of idealism and that of psychology are intimately connected. It is indeed the lack of permanence in internal experience that the resolution of the Paralogisms accuses by stating that "in that which we call the soul, everything is in continual flux." (432; A 381) From this standpoint, Kant can only reject what will be Husserl's solution to show that the stream of consciousness is not a Heraclitean flow: that is, he refuses to give a specific consistency to the stream itself, to treat it like a kind of autonomous entity. His position regarding this matter is rather to say that, in its flowing, the flux itself cannot be perceived. Otherwise said, time does not have the consistency of something permanent; if there is something in it that never changes, this invariant has simply the "fixity of a transcendental structure" (Bouton 2004, 29), and this is why, for the rest, time cannot be perceived.

The impossibility of an apriorical psychology 9

hesitate to assert that "soul is a substance." (Kant 1997, 78) This suggests that, during this period, "a certain dogmatism of the inner sense" peacefully cohabits with the conception of time as "the form of internal sensibility" (Nabert 1924, 209), and this peculiar dogmatism goes as far as asserting that "the inner sense immediately grasps that which is substantial", and even that it gives "the paradigm of all substantiality." (Nabert 1924, 210) Manifestly, the distinction between the apperception of thought and the inner sense has not been operated yet v , and the limitation induced by the temporal nature of self-knowledge is still ignored. In Husserl's 1913 Ideen I, such an exorbitant credit given to the inner sense and to immanent temporality is also strikingly present, especially when it is admitted that "the total stream of my lived experience is a lived unity of such kind that it is impossible to grasp it wholly and adequately" only to further maintain that "this incompleteness or ''imperfection'' pertaining to the essence of the perception of a lived experience (Erlebnis), is radically different from the incompleteness or ''imperfection'' pertaining to the essence of ''transcendent'' perception" (Husserl 1983, 97; Hua III/1, 94; trans. modified), and that, for this reason, in spite of everything, immanent perception gives access to an absolute.

The gap between Kant's and Husserl's idealism already becomes visible if we pay attention to the terms in which the Paralogism of the substantiality of the soul is refuted by the first edition of the Critique: "in that which we call the soul, everything is in continual flux, and it has nothing abiding, except perhaps (if one insists) the I […]. Yet this I is no more an intuition than it is a concept of any object; rather, it is the mere form of consciousness." (Kant 1998, 432;AA, A 381-382) With this distinction, the surreptitious identification of the unity of thought and of the object of the internal intuition finds itself openly deactivated; thus, "the whole of rational psychology, as a science transcending all the powers of human reason, collapses" (432; A 382), and with it, so does the attempt to ground selfcognition on the inner sense. It is in particular the very project of a psychology pretending to be apriorical, that is, claiming to be something more than an empirical description of the soul, that becomes ultimately inconsistent: critical philosophy cannot 0 lead to disclosing the metaphysical principles of the soul as it will do for the first metaphysical principles of nature (Nabert 1924, 260).

The bankruptcy of rational psychology will be even more virulently stated in the 1787 version of the Paralogisms: since I do not cognize myself "by being conscious of myself as thinking", therefore, "through the analysis of the consciousness of myself in thinking in general not the least is won in regard to the cognition of myself as object. The logical exposition of thinking in general is falsely held to be a metaphysical determination of the object." (Kant 1998, 445;AA, B 406 and 409) Given that there can be no knowledge where there is no relationship to intuition, the mirage of a sheer reflexive selfcognition, obtained in a purely discursive manner, solely through concepts, needs to be dissipated. And that which is given through the inner sense -if there is anything given -has no consistency when isolated from the representation of external objects: otherwise said, it grants no access to a phenomenological sphere of the absolute distinguished from that of the world as merely relative.

For all these reasons, one can legitimately state, following Jean Nabert, that "by depriving internal experience of the privilege of revealing the I in an immediate intuition, Kant broke the chains that kept the subject of thought imprisoned within the boundaries of psychological life." (Nabert 1924, 229) Though, it is somewhat ironical, I would say, that it was precisely Husserl (who, on the other hand, as I have recalled it, restored the view according to which immanent perception grants an access to an absolute) who accused Kant of psychologising the transcendental, given that Kant's main objective in his critique of the Paralogisms was precisely, and quite the contrary, to avoid "objectifying the transcendental through psychologisation." (Grandjean 2009, 112) And in fact, it is quite easy to find, in some places of the second edition of the Critique, what Kant would hypothetically reply to Husserl's recourse to Descartes' "nulla 're' indiget ad existendum" for characterizing egological interiority. Among several eloquent passages, the following is quite remarkable: 1 "Thus if that concept, by means of the term "substance," is to indicate an object that can be given, and if it is to become a cognition, then it must be grounded on a persisting intuition as the indispensable condition of the objective reality of a concept, namely, that through which alone an object is given. But now we have in inner intuition nothing at all that persists, for the I is only the consciousness of my thinking; thus if we stay merely with thinking, we also lack the necessary condition for applying the concept of substance, i.e., of a subject subsisting for itself, to itself as a thinking being." (Kant 1998, 448;AA, B 412-413) It is ultimately the excessive empowerment of internal intuition that is implicitly denounced by Kant, and the confusion between the consciousness that I have of myself while thinking and an intuitive self-cognition: "The unity of consciousness, which lies at the ground of the categories, is taken here for an intuition of the subject as an object, and the category of substance is then applied to it. But this unity is nothing but a unity of thought, through which no object is given, and consequently, to which the category of substance, which always implies that an intuition is given, cannot be applied." (422; B 421-422) For the concept of substance to be legitimately applied to the data of internal intuition, this intuition would have to be an intuitus intellectualis, or a reflexive consciousness of myself in which I am genuinely given to myself. But this case of figure has to be immediately rejected, for "in the consciousness of myself in mere thinking I am the being itself, about which, however, nothing yet is thereby given to me for thinking" (456; B 429) : the purely intellectual or reflexive consciousness of my existence is irremediably void, since it lacks any specific content. In return, "inner empirical intuition is sensible, and makes available nothing but data of appearance" (457; B 430); and yet, these data are ultimately inconsistent and void themselves when no outer intuition is associated to them.

I now come to my conclusion, and my first point will be to stress the fact that the Kantian Critique, according to the final version of its enterprise delivered by the second edition, confronts us with a paradoxical affirmation: that of the ideality of space and time without any correlative or underlying idealism. Should this nuance be taken seriously, one would quite probably have to admit that it can be quite misleading to speak of a Kantian idealism, as Kant suggests it himself when, in his letter to Beck of the 4 th of December 1792, he confesses his willingness to describe the project of the Critique through the "principle of the ideality of space and time", rather than through the confusing expression: critical idealism, and justifies this preference as follows: "I only speak of ideality in respect to the form of representation, while they [the true idealists] speak of ideality in respect to the matter, that is, to the object and to its very existence." (Kant 1999, 445;AA XI, 394-395;trans. modified) Thus, if on one hand, the ideality of space and time suffices for avoiding the perilous temptation of realism, on the other hand, the specific relationship that Kant acknowledges between internal and external experience institutes a comparable distance towards idealism. If there is indeed, as Husserl puts it, an "abyss of meaning (Abgrund des Sinnes)" (Husserl 1983, 111; Hua III/1, 105; trans. (modified)) between consciousness and that which is exterior to it, it is rather external experience that provides an access to a stable and permanent being. There is no interiority for me otherwise than comparatively, insofar as, in itself, interiority is evanescent and inconsistent; and for this reason, that which is interior to me always sends me back to something exterior.

Of course, Husserl has every right to regret, in the Krisis, that "Kant has never penetrated the frightening depth of Descartes' fundamental meditation" (Hua VI, 102), or that he did not contribute to the renewal of psychology; but it is crucial to understand that Kant's reluctance and omission are here entirely deliberate. For in his view, the "self-intuition of the mind (Selbstanschauung des Gemüts)" (Kant 1998, 190;B 69) can never have the meaning of a self-givenness of the I as a phenomenological absolute. When Husserl deplores Kant's empiricist conception of internal perception (Hua VI, 117) he has perhaps not fully evaluated the Kantian critique of Descartes and of rational psychology, and this would also explains his tendency to maintain the privileges and rights of 3 internal experience. Therefore, from Kant to Husserl, one does not have to choose between two versions of idealism, but rather to engage into one of two quite divergent paths. Kant's transcendental project implies "keeping as close as possible to the transcendental and setting aside entirely what might here be psychological, i.e., empirical" (Kant 1998, 675; AA, A 801/B 829), whereas Husserl, in spite of his early critique of psychologism, through his project of a transcendental psychology vi , pleads for a new alliance between psychology and transcendental philosophy. And if Husserl can quite significantly relaunch, at the very end of the Cartesian Meditations, Augustine's famous invitation to explore interiority: "Noli foras ire, in te redi, in interiore hominis habitat veritas" (De vera religione, 39,72) (Husserl 1983, 157;Hua I, 183), in return, by following Kant, one would rather have to praise the richness and resources of exteriority, as the end of § 24 in the Anthropology from a pragmatic point of view clearly suggests it: "The tendency to retire into oneself, together with the resulting illusions of inner sense, can only be corrected if we are led back into the external world and so into the order of things present to the outer senses." (Kant 2006, 164;AA VII, 162;trans. modified) This is the ultimate lesson of the destitution of the primacy traditionally detained by internal experience: being oneself, for Kant, is being in the world and being through the world -and this is why the Kantian cogito can legitimately be called a "cosmological cogito". (Bouton 2004, 30 andBouton 2002, 80) NOTES i Kant writes, more precisely: "The only thing I can really call a supplement". Paul Guyer and Allen W. Wood are manifestly sensitive to this claim while writing, in the Introduction of their English translation: "The argument that while time is the form of all sense, the representation of space is itself the necessary condition for the representation of determinate order in time, which continues Kant's rebuttal of the charge of Berkeleian idealism, is the chief theme of all of the revisions in the "Analytic of Principles" " (Kant 1998, 71).

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ii Kant insists nevertheless in this passage on the necessity "to regard [...] external objects not as things in themselves but only as representations, of which we can become immediately conscious like any other representation, but which are called external because they depend on that sense which we call outer sense; its intuition is space, but it is itself nothing other than an inner mode of representation, in which certain perceptions are connected with one another".

iii Otherwise, "the representation of space would be transformed into a representation of time" (AA XVIII, [Refl. 6311], 611; my translation). iv As Paul Guyer and Allen W. Wood put it, "that which we judge to exist independently of our representation of it, even if we also know that the form in which we represent the independence of such objects is itself dependent upon the constitution of our own sensibility" (Guyer and Wood 1998, 71).

v For an illustration of this perennial distinction, see for instance § § 7 and 24 in Kant's Anthropology from a pragmatic point of view.

vi It is the intention that manifests, for instance, the next to last (72) paragraph of the Krisis, where Husserl states that, from a certain point of view, transcendental psychology is identical to transcendental philosophy (Hua VI,261) .

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Furthermore, in deep connection with the treatment of temporal inner experience, it is the question of psychology (which is the field, for Kant, of the Paralogisms of the soul) that is most likely to unveil the profound divergence between Kant's critical idealism and Husserl's transcendental idealism. When Husserl states (in the Ideen I, § 46) that "immanent perception guarantees the existence (Existenz) of its object" (Husserl 1983, 100; Hua III/1, 96), he does not transgress any Kantian prohibition yet. But when he also claims that "the immanent being is [...], undoubtedly, an absolute being, as far as nulla ''re'' indiget ad existendum" (Husserl 1983, 110; Hua III/1, 104), and when he maintains that external perception is doubtful in principle, he encounters the danger of relapsing, not only into the Paralogism of ideality, but also, to a certain extent, into that of substantiality. The Latin expression adopted by Husserl for characterizing the immanent being (that is, consciousness) is, as it is well known, the one used by Descartes in the first part of the Principles of Philosophy (article 51) to define substance; and Descartes will in fact explain that this definition is, strictly speaking, only verified by God. Of course, in his Ideen, Husserl has no intention of returning to something like a metaphysics of substance; but still, he indisputably emphasizes the absoluteness of the immanent being and, by doing so, posits himself inescapably within the range of action of the Kantian Critique.

On the other hand, and Jean Nabert has legitimately insisted on this point in his remarkable study on "Internal Experience in Kant", it is well known that the refutation of the substantiality of the soul is everything but an early result in Kant's philosophical itinerary. Quite the contrary, "denying to the internal sense any value for the self-cognition of the I understood as a substance was one of the very last steps in Kant's thought before 1781" -and this proves, for Nabert, the solidity of "the resistance that rational psychology opposed to the elaboration of the Critique" (Nabert 1924, 206, my translation). Indeed, the Lectures on Metaphysics that reflect Kant's philosophical evolution between 1775 and 1781 manifest a total trust in the inner sense: for this reason, in one of the sections corresponding to rational psychology, Kant will not