Alda Mari

Enzo Laurenti

Mere-desire and action-oriented bouletics in French

Keywords: bouletic attitudes, experience, action, pathos, rationality

The paper explores a variety of bouletic attitudes in French (and Italian), which it envisions in the light of the distinction between mere-desire and action-oriented volition. It shows that avoir envie (and avere voglia) are not rational and not action oriented, while espérer and vouloir are rational with only vouloir being action oriented. It substantiates these notions by providing several semantic tests, which include consideration of the temporal orientation of the attitudes. The analysis is cast in framework that distinguishes between experiential and actionable spaces for bouletic attitudes and derives the facts from the properties of the modal spaces that are lexically triggered. For vouloir, it proposes a default action-orientation interpretation that can be manipulated by the conditional and adverbs like tellement. The analysis allows the conditional and the adverbs to manipulate the actionable modal base accommodated by default. By setting three different types of modal bases for bouletic attitudes, the paper paves the way for a cross-linguistic systematization that hinge on three different conceptualizations of the attitude holder, as a sentient being, a rational agent or an actor.

Introduction

Like most Romance languages, French has a series of attitude predicates to express volition and desire: vouloir (want), espérer (hope), avoir envie, with no direct English equiv-alent for the last one (with feel like being the best approximate). This paper addresses the question of the meaning of these expressions and attempts to account for the systematic polysemy that cuts across these items.

Building on insights from the philosophical literature (see most notably [START_REF] Davis | The two senses of desire[END_REF] and [START_REF] Hare | Wanting: Some Pitfalls[END_REF]), linguists (see [START_REF] Condoravdi | Anankastic conditionals are just conditionals[END_REF], [START_REF] Grano | The Logic of Intention Reports[END_REF], and [START_REF] Levinson | Probabilistic Model-theoretic Semantics for'want[END_REF] a.o.) have observed that want can be used to describe both a mere-desire and an action-oriented preference. The emergence of one reading or the other depends on the context. In the example below, waiter triggers an action-oriented interpretation of want akin to 'want to add sugar' in this specific case ; diabetes triggers a mere-desire interpretation whereby the addressee is in a state of 'need of sugar'.

(1) After [START_REF] Hare | Wanting: Some Pitfalls[END_REF]: If you want sugar in your soup, a. You must ask the waiter.

b. You must have diabetes.

As we will show, French vouloir does not behave like English want, and it is by default action-oriented : as Ruwet (1984, p. 92) writes, "the object of wanting, is first and foremost the action [. . . ]; when I say Je veux P I convey that I am willing to do whatever it takes to make p true." However the distinction between mere-desire and action-oriented volition is relevant to understand the structure of the notional bouletic domain and its lexicalization in French (and Italian). To this aim, we will primarily focus on the distinction between avoir envie and vouloir, showing that each expression is born as more mere-desire-oriented or more action-oriented. Our empirical investigation shows that this default can be manipulated, but that this manipulation comes at a cost, and most prominently requires adding material such as the conditional mood (see von [START_REF] Fintel | Prolegomena to a theory of X-marking[END_REF]), or dedicated adverbs such as the intensity modifier tellement (so much) or the concessive bien (litt. good / well).

( The paper submits the idea that that all bouletics (more mere-desire-oriented attitudes and volitional action-oriented attitudes) feature two modal bases and that the common feature of all bouletics is a preferential modal base, in line with the long tradition on the study of mood and bouletic attitudes as featuring a preferential semantics (Anand and Hacquard (2013), Farkas (1992), Giannakidou (1999), Giannakidou and Mari (2021), Portner (2018), and [START_REF] Villalta | Mood and gradability: an investigation of the subjunctive mood in Spanish[END_REF] among several others). Differences in meaning across the variety of lexicalizations of volition arise depending on the primary modal bases of the attitudes which range from mere experiential to an actionable space. These modal bases can be manipulated to an extent that our empirical investigation will determine thus generating the variety of interpretations observed.

The paper is structured as follows. In section 2 we present the data. In section 3 we discuss previous accounts. Our analysis is developed in section 4 together with its predictions. Section 5 concludes.

Data

Volitional predicates have often been considered as constituting a rather homogeneous class, mainly built around the opposition between HOPE and WANT. For example, in the recent literature concerning mood selection in Romance (Giannakidou and Mari, 2021;[START_REF] Portner | The semantics of mood, complementation, and conversational force[END_REF]Rubinstein, 2012, 2020;[START_REF] Silk | Commitment and states of mind with mood and modality[END_REF], the rationality of HOPE is summoned to explain its use of indicative in French, whereas the constant selection of subjunctive by equivalents of want across languages is perceived as a consequence of its more 'unrealistic' semantics.

However, the data discussed in this section tend to show that Romance desiderative predicates are more diverse. Italian and French counterparts of want (volere and vouloir, respectively) seem to exclusively target desire that are suitable for action. On the other hand, avoir envie and avere voglia (the Italian counterpart of avoir envie) do not have such a link with action per se; the mental state they describe might certainly constitute, in certain contexts, a motivation for action, but this is not encoded in their lexical meaning. A series of tests will help us making emerge the semantic profile of bouletics.

Desire reports and ascription

It is a well-known fact that Italian and French differ with respect to mood choice with doxastic predicates (see [START_REF] Giorgi | Tense and aspect: From semantics to morphosyntax[END_REF], Mari (2016b), [START_REF] Mari | Actuality entailments: when the modality is in the presupposition[END_REF][START_REF] Mari | Mood variation with belief predicates: Modal comparison and the raisability of questions[END_REF][START_REF] Schlenker | The lazy Frenchman's approach to the subjunctive[END_REF] a.o.).

Importantly, volitional or preferential predicates (in contrast to representational in Bolinger (1968)) pattern similarly in both languages. In Romance languages (and wellbeyond Giannakidou and Mari (2021) for a recent overview), the notional category of desire is firmly associated with subjunctive: Italian selects subjunctive with all desire predicates, and so does French, with the notable exception of espérer [START_REF] Anand | Epistemics with attitude[END_REF][START_REF] Portner | The semantics of mood, complementation, and conversational force[END_REF][START_REF] Schlenker | The lazy Frenchman's approach to the subjunctive[END_REF].

This relative homogeneity with respect to mood selection tends to orient the analysis of desire reports towards an unified core semantics. However, it hides profound contrasts between predicates which seem to appeal to commitment to act and those that do not. As a first approximation, we can observe that the utterance of act, with vouloir, conveys the idea that the attitude holder will act to bring about the prejacent; this inference is absent, or at least not systematic, in ninf with espérer or avoir envie.

(3) a. This tendency to relate to action is to be correlated with a series of semantic properties to which we now turn. French is the main focus of the paper, but we will propose a systematic comparison with Italian.

2.2

The semantic profile of bouletic attitudes in French (and beyond)

Rationality

The compatibility of bouletic attitudes with propositions that describe a state of affairs that cannot be realized in the actual world (for short impossible propositions') is a recurring matter in both the linguistic and the philosophical tradition. Anscombe, 1957, who championed a so-called dispositional conception of wanting the is largely debated since [START_REF] Heim | Presupposition projection and the semantics of attitude verbs[END_REF], who famously discussed the following example (heim) , and noted that want seems at ease with highly implausible propositions, like those describing neverending weekends (see Portner (2018) and references therein).

(4) I want this weekend to last forever. This, however, is not the case for all bouletic predicates. Hope, and its counterparts in many, if not most, languages is not felicitous with propositions that are known or described as impossible. This is also the case with intention reports, that have common properties with both desiderative and epistemic predicates, as shown by [START_REF] Grano | The Logic of Intention Reports[END_REF].

(5) a. #I hope that this weekend will last forever.

b. #I intend this weekend to last forever.

The incompatibility of some attitude reports with impossible prejacents is the consequence of an intrinsic property that can be called rationality. Prototypical rational predicates are epistemics and doxastics, like believe or know that cannot be paired with propositions that are outside the doxastic space (unless the attitude holder entertains irrational beliefs).

One should note that rational predicates are not concerned with metaphysical impossibility per se: the blocking mechanism comes from a subjective epistemic impossibility for the attitude holder.

(6) Adapted from [START_REF] Heim | Presupposition projection and the semantics of attitude verbs[END_REF]:

a. Sam is under the misconception that he has a violin, and he intends to sell his violin. b. Sam is persuaded that square can be round, and he intends to draw a round square.

A good test to identify a rational predicate (see [START_REF] Condoravdi | Anankastic conditionals are just conditionals[END_REF], [START_REF] Grano | The Logic of Intention Reports[END_REF], and Portner and Rubinstein (2020), . . . ) is to first assert the subjective impossibility of a prejacent for an individual (the speaker, in the following example), followed by the assertion that the same individual has a certain attitude toward the same proposition. If the result is infelicitous, the predicate conveying the attitude can be said rational.

Applying the test to French attitudes allow us to observe the trans-categorical aspect of rationality: it is, as expected, a property of the doxastic croire ('believe'), but also espérer and the intention report avoir l'intention ('intend', which patterns similarly). More surprisingly, the volitive predicate vouloir shows a parallel behavior. As we recalled, in English, want is often described as a predicate that is not necessarily rational. However, its French counterpart seems a lot more stable with respect to this property: in the present indicative vouloir is very marginally compatible with impossible prejacents. To be rescued, the force of the utterance must be exclamative (a facts that we do not explain here, but seems to be related to the accommodation of a subjective modal base in a way parallel to what is proposed for tellement cf. infra). This contrast is even more salient if we compare it to its conditional counterparts, or with the desiderative predicate avoir envie.

( Rationality constraints thus seem to affect both action-oriented predicates (vouloir) and (espérer) -which is immune from plannability and actionability1 .

Conjunction introduction

Rationality is observable with an inferential scheme like the introduction of the conjunction, which is verified if and only if the fact that an agent is independently in relation with two distinct propositions p, q entails that she is in relation with their conjunction p&q.

Croire, espérer and vouloir -which are all rational in the sense defined above -instantiate this inferential scheme. Note that these properties are also observable in relation with other action-oriented predicates, like intention reports (ibid.), directives, and, arguably, some but not all interpretations of want-sentences in English (see [START_REF] Condoravdi | Anankastic conditionals are just conditionals[END_REF], [START_REF] Crnič | Getting even[END_REF][START_REF] Levinson | Probabilistic Model-theoretic Semantics for'want[END_REF], a.o). It seems, once again, that rationality is a necessary condition for action-oriented predicates, but not a sufficient one to distinguish them. (We omit the glosses here for readability). ( 10 Rationality and inferential schemes like conjunction introduction are thus properties that allow to distinguish volitional predicates like vouloir ('want') in the present tense from some other desire predicates -its conditional counterpart and avoir envie ('have desire'), for example. -It is nonetheless not a sufficient criterion to identify link to action. Attitudes that are not action-oriented (e.g. hope, doxastic attitudes, . . . ) also support conjunction introduction. The temporal patterns discussed in the next section will allow us to sharpen the distinctions within the volitional class.

Temporal orientation

Temporal constraints on the prejacent of attitude verbs are an important feature which is ground in their semantics [START_REF] Laca | Temporal orientation and the semantics of attitude verbs[END_REF][START_REF] Mari | Actuality entailments: when the modality is in the presupposition[END_REF] 2 : the notional categories of will and desire are tightly linked to future orientation (see Giannakidou and Mari (2021)).

However, it is well-known that HOPE is quite flexible (e.g. Anand and Hacquard (2013)): it supports present, past and future orientation (see Giannakidou and Mari (2021) It thus seems reasonable to argue that the prejacent has a strict future interpretation (see Giannakidou and Mari (2021)), that is non simultaneous to the time of evaluation of the attitude. In contrast, avoir envie and avere voglia seem to be slightly more at ease with present temporal orientation4 , but are still incompatible with past prejacents. Future prejacents, on the other hand, are easily interpreted. ( 17 The difficulty of volere and vouloir to go along simultaneous prejacents distinguish them further from avoir envie and avere voglia. But it also draws a line between espérer and vouloir, which pattern together with respect to other properties such as rationality.

We can make sense of this contrast by going back to our original observation: it is expected that a predicate that semantically refers to action cannot go along a situation which is already true or false at the time at which the intention/request is evaluated.

(19) a. #I intend for this grade to be good.

b. #I request / demand this grade to be good.

Action

The temporal features of bouletic verbs in Romance are important for our main point here, the relation between volition and action. We mentioned earlier that sperare/espérer and volere/vouloir are not felicitous in contexts where the prejacent is presented as impossible (the conditional would be needed). We argue that plausibility follows from the more fundamental property of actionability: a prejacent is actionable if and only if a relevant individual in the context of utterance can do something in order to bring it about.

Introducing a finer distinction we see that certain situations are possible, satisfying an hypothetical rationality constraint, but not actionable: no action accessible to a salient individual in the context of utterance can bring them about. With such prejacents, sperare and espérer are perfectly acceptable, but not volere and vouloir; here, again, there conditional flexion is favored.

(20) Maria must go to the beach with her family this weekend. She wants everything to be perfect, and says: a. It is important to note that this notion of actionability is purely subjective: it is not evaluated given any kind of metaphysical ability 5 , but a subjective one. Indicating that the attitude holder is under the misconception that she has a grasp on outcomes that are, in fact, independent of her action is sufficient to have non-conditional morphology in the matrix clause.

(22) Teresa is under the misconception that she can control the weather / knows some-

Previous analyses

To the best of our knowledge, there is no work on the market that studies the French bouletic attitudes in the light of the distinction between mere-desire, action-oriented volition. A great deal of attention has been paid to the phenomenon of obviation on the one hand and on mood selection on the other (both these bodies of literature are very vast, see Portner (2018) for references). None of the existing works on French has nonetheless leveled the question of the distinction that we are focusing on here as a problem in itself, and avoir envie has remained a largely overlooked predicate. 7 The attention paid to the mere-desire / action-oriented distinction is also recent in the linguistic literature that resorts to possible worlds and that Hintikka had initiated and which we endorse here.

In his pioneering work, [START_REF] Hintikka | Semantics for Propositional Attitudes[END_REF] develops a simple and elegant semantics for attitude reports. Focusing on epistemic attitudes, he proposes that an individual's beliefs might be described as a set of worlds compatible with that individual's beliefs. Informally, Hintikka states that a sentence which has the form of bel is true if and only if, in the context of utterance, the prejacent p -is true in every world of the doxastic mental space of S.

(23) a. S believes that p b. Maria believes that the Colonel Mustard is the murderer.

If Hintikka is primarily concerned with the semantics of epistemics, he explicitly states that he doesn't see reasons for not extending his analysis to other kind of attitudes, including desires (Hintikka (1969, p. 92)) : his semantics is thought as uniformly applicable to all propositional attitudes, which would differ only with respect to their lexical choices of different domains of quantification.

(24) a. S wants that p b. Maria wants the Colonel Mustard to face a tribunal.

Commenting the hintikkian perspective, Stalnaker (1984, p. 89) identifies serious flaws, among which the one of overgenerating true desires.

Suppose I am sick. I want to get well. But getting well entails having been sick, and I do not want to have been sick. Suppose there was a murder. I want to know who committed the murder. But my knowing who committed the murder entails that the murder was committed, and I never wanted the murder to have been committed.

There are many propositions that are not desired but are homogeneously present in the doxastic space -among them, the necessary conditions for effectively desired propositions.

(25) a. Maria wants the murder to have happen.

b. Maria wants to find the murderer.

(26) a. Sam wants to be cured. b. Sam wants to have been sick.

The problem is that the domain of quantification cannot be solely bouletic, because all the situations that are homogeneously present in the mental space of desire are not effectively desired: it is not because Sam wants to be cured that he wants to be sick sam. [START_REF] Heim | Presupposition projection and the semantics of attitude verbs[END_REF], who is primarily concerned with the behavior of presuppositions with attitude verbs, observes that the presuppositions of the prejacent (here, 'Paul has a violin") is projected on the doxastic space when embedded by a desire predicate.

(27) After Heim (ibid.):

(Paul is under the misconception that he has a violin, and Paul wants to sell his violin.

↝ Paul believes he has a violin. ↝̸ Paul wants to have a violin (to sell).

The mental space of desire reports and ascription thus appears to be doxastic: it corresponds to the beliefs of the attitude holder, not solely their desire.

Heim's analysis is essentially the formalization of an idea originally formulated by Stalnaker (1984, p. 89), who states that wanting something is preferring it to certain relevant alternatives, the relevant alternatives being those possibilities that the agent believes will be realized if he does not get what he wants.

This view invites to consider desire reports as a kind of hidden counterfactual conditionals, somehow relativized to the beliefs of the attitude holder: to say that Hercule Poireau wants to catch the murderer is similar to saying that Hercule Poireau thinks that if he catches the murderer, he would be in a more desirable state than if he didn't.

Heim's understanding of desire reports is based on a comparison operator <, that will oppose the prejacent and its negation: the former will be favored in comparison to the latter in the doxastic space. This analysis has been amended by [START_REF] Villalta | Mood and gradability: an investigation of the subjunctive mood in Spanish[END_REF] who considers that the preference is not only between a proposition and its negation, but a class of relevant alternatives. Also revisiting the heimian initial proposal, [START_REF] Rubinstein | Straddling the line between attitude verbs and necessity modals[END_REF] extends the mental space to impossible propositions.8 None of these proposals is primarily concerned with actions.

A conceptual distinction between two types of desires reports is instead often made in a parallel philosophical literature which has been recently adopted by linguists. Numerous labels have been proposed in order to name this distinction: on the philosophical side, [START_REF] Davis | The two senses of desire[END_REF] opposes volitive and appetive desires, and [START_REF] Locke | Beliefs, Desires and Reasons for Action[END_REF] use the term formal and genuine; in the linguistic literature, [START_REF] Levinson | Probabilistic Model-theoretic Semantics for'want[END_REF] uses the terms motivational and partial, [START_REF] Condoravdi | Anankastic conditionals are just conditionals[END_REF] mere-desire and effective preference.

Levinson ( 2003), elaborating on an example from [START_REF] Davis | The two senses of desire[END_REF], insists that a semantics for want must be able to account for cases like contr, where two opposite answers to the same question do not seem to contradict each other. Choosing to assert one answer or the other does not imply any difference with respect to my wanting to share a drink with my classmates: it's appealing, but I can't.

(28) Adaptation from Davis (ibid.):

Q: Do you want to grab a beer after class ? a. Oh yes, I really want to, but I have to finish a paper. b. No (I don't want to), I have to finish a paper.

We will not develop Levinson's analysis here, which is probabilistic and utility-driven. It's sufficient to note that the contrast at stake is the one in focus in our paper, namely the distinction between mere-desire and action-oriented volition.

On the same line, [START_REF] Condoravdi | Anankastic conditionals are just conditionals[END_REF] argues that want is underspecified between two readings, which correspond to the two possible answers to contr, but also to the two different interpretations of the conditionals in soup3, repeated below.

(29) After [START_REF] Hare | Wanting: Some Pitfalls[END_REF]:

If you want sugar in your soup, a. You must ask the waiter. ACTION-ORIENTED interpretation of want. ↝ Asking the waiter is a mean to have sugar in your soup. b. You must have diabetes. MERE-DESIRE interpretation of want.

↝̸ Having diabetes is a mean to have sugar in your soup.

The conditional in anan1 has a very special interpretation, dubbed anankastic in the literature, which present the consequent as a mean to (optimally) obtain the antecedent -note that the desire reports is not present in the paraphrase. anan2, on the other hand, does not have this teleological interpretation. It might be paraphrased as "Because you feel like having sugar in your soup, you must have diabetes", with an explicit reference to the desire expressed in the antecedent.

Anankastic conditionals are a long-standing puzzle in the semantics literature (See Iatridou and Fintel (2005) and [START_REF] Saebø | Necessary conditions in a natural language[END_REF], a.o.) that we will not consider here. Interesting for us is the answer that Condoravdi and Lauer provide9 , which relies on the observation that an anankastic reading emerges in some structure with a particular reading of want, namely the action-oriented one (29a).

They formalize their analysis by injecting preference structures in the model. In every situation of utterance, agents are associated with a set of such structures, each corresponding to their commitments, defined by pairs ⟨P, ≺⟩, where P is the set of propositions and ≺ a strict partial order on P -as they write, "a preference structure can be thought of as an ordering source [from kratzerian semantics] plus an 'importance' ranking" [START_REF] Condoravdi | Anankastic conditionals are just conditionals[END_REF]. The truth of a desire reports depends solely on the top-ranking of the proposition denoted by the prejacent in the preference structure.

If it is said effective, a preference structure is consistent and realistic with respect to an information state10 , i.e. the mental space of the relevant individual. These features are designed as minimal requirements to describe action-relative preference structures: consistency ensures that an agent ranks conflicting propositions; realism just rules out propositions that are believed not to lead to action.

According to the authors, the anankastic reading emerges if and only if the predicate in the antecedent targets an effective preference structure. They argue that want is underspecified with respect to the quality of it's preference structures: if the context feeds it with a structure that has the qualities to be effective, it will have some special properties, including anankastic readings with conditionals and conjunction introduction.

Grano (2017) spells out a semantics for intention reports that relies on hardwired requirement for effective preference structures and RESP-onsibility relation11 between the prejacent and the attitude holder. Moreover, it echoes other observation on distinct structures, like the imperative discussed by [START_REF] Roberts | Conditional plans and imperatives: A semantics and pragmatics for imperative mood[END_REF].

Our account also resorts to preferences. However, as we have noted, the underspecification of vouloir is of a different nature than the one of English want. Vouloir is by default action-oriented. The lexical distinctions between avoir envie as a mere-desire predicate and vouloir as a by default action-oriented predicate are hardwired in their lexical semantics. A special mechanism is envisioned for vouloir, which can turn mere-desire oriented when combined with the conditional and tellement.

Analysis

Recent works on subjunctive have been revolving around two main ideas: (i) the subjunctive articulates two modal backgrounds [START_REF] Mari | Mood variation with belief predicates: Modal comparison and the raisability of questions[END_REF] and [START_REF] Portner | Mood and contextual commitment[END_REF]) and (ii) subjunctive is triggered by non-homogeneity in one conversational background (Farkas (2003), Giannakidou (1999), and [START_REF] Giannakidou | Mixed (Non) veridicality and mood choice with emotive verbs[END_REF]Mari (2015, 2021), a.o.). As bouletic predicates are subjunctive selectors (with the partial exception of espérer, which we do not discuss here, see Anand and Hacquard (2013) in particular), our analysis builds on these two ingredients.

Our proposal is that all bouletic attitudes feature a preferential modal background, but that the flavors and the constraints that we have observed are due to the primary modal base on which the preferences act upon.

We will follow Anand and Hacquard (ibid.) in assuming that espérer is specified, in its lexical semantics, for a doxastic and a preferential modal backgrounds, and we will not discuss further the meaning of this attitude here. We newly propose that avoir envie is lexically specified for a preferential modal background and an experiential one (which is pathos, cf. infra). We also propose that vouloir is lexically specified for preference. Unlike avoir envie and espérer, the primary modal background of vouloir is either accommodated or lexically triggered by extra morphology (the 'conditionnel') or overt lexical items (such as tellement). The default with vouloir (and volere) is an actionable modal space. When specific lexical or grammatical information is added, the default is overwritten by an experiential modal background.

In our analysis, the differences among bouletic predicates result from a difference in lexical specifications. As vouloir introduces a more substantial amount of underspecification (by leaving unspecified one modal background), it allows manipulations that are not observed with the other bouletic predicates.

Modal backgrounds

We first define a preferential modal background P. P are mere preferences of the attitude holder.

(30) Preferences P = {π | π is an option preferred by i over an alternative ¬π given a lexically or contextually determined modal base}

We then define three other types of modal spaces which will intersect the preferential modal background. The first one is the experiential modal space. We consider experience as the anti-rational modal space, that merely encompasses content based on sensory evidence and upon which no rational reasoning applies. w 0 is the actual world and c the context of utterance.

(31) Experiential modal space E(i, w 0 , c) = {ϵ | ϵ is an experience that i undergoes in w 0 in c}

The rational modal space is akin to what is generally referred to as Epist or Dox in the literature on modality and mood (Giannakidou and Mari (2021), [START_REF] Hintikka | Semantics for Propositional Attitudes[END_REF]Portner (2009)), and importantly includes rational information. Note that sometimes Dox has been used to refer to credence and pure subjective evaluations, including irrational one [START_REF] Ippolito | Assessing alternatives: the case of the presumptive future in Italian[END_REF] and [START_REF] Mari | Actuality entailments: when the modality is in the presupposition[END_REF]) and Epist for knowledge that relies on factual information (Mari (2016b)). This is not what R is. R is a rational space, no matter whether knowledge or belief is considered.

(32) Rational modal space R = {ρ | ρ is a piece of knowledge or belief of i which does not rely on credence or irrationality} Here we are using the terms 'experience', 'piece of knowledge' for readability. We consider E, R as modal backgrounds, i.e. sets of sets of propositions.

Our definition of an actionable12 space resorts to branching structures in line with [START_REF] Belnap | Branching space-time[END_REF], [START_REF] Kaufmann | Conditional truth and future reference[END_REF], and Mari (2016a). A three-place relation ≃ on T × W × W is defined such that (i) for all t ∈ T , ≃ t is an equivalence relation; (ii) for any w, w ′ ∈ W and t, t ′ ∈ T , if w ′ ≃ t ′ w and t precedes t ′ , then w ′ ≃ t w. In words, w and w ′ are historical alternatives at least up to t ′ and thus differ only, if at all, in what is future to t ′ . For any given time, a world belongs to an equivalence class comprising worlds with identical pasts but possibly different futures. Let w 0 be the actual world.

For any time t ∈ T , we define the set of actionable alternatives as the set of worlds that are identical to the actual world w 0 at least up to and including t [START_REF] Thomason | Combinations of tense and modality[END_REF]. The actionable modal space contains the worlds in which the set of actions that the subject i can possibly undertake are realized. For any time t:

(33) Actionable modal space A(i, t) ∶= {w | w ≃ t w 0 and such that the actions that an individual i can undertake, take place there}

We do not refine the granularity of the modal base here, but assume that incompatible actions do not take place in the same worlds.

We impose that the actionable space be diverse in the sense of [START_REF] Condoravdi | Temporal Interpretation of Modals -Modals for the Present and for the Past[END_REF] or non-veridical in the sense Giannakidou and Mari (2018), that is to say, it contains both p and ¬p worlds. In other terms there are worlds in which a certain action α (described by p) takes place and others in which it does not [START_REF] Belnap | Branching space-time[END_REF].

According to Belnap (ibid.), nodes of a branching time framework represent choice points at which a certain actor chooses to perform a certain action α.

With these modal backgrounds in place, we can now turn to the lexical semantics of bouletic predicates in French.

Avoir envie

Avoir envie specifies a subtype of experiential modal background, as pathos. Pathos is a type of uncontrollable experience, which, in the case of desire, could be further specified into spanis (an experience of 'lacking of something') akin to thirsty, being hungry, being tired, a fact to which we return here below.

(34) Experiential-pathos

E(i, w 0 , c) = {θ | θ is a pathos that i undergoes in w 0 in c}
We assume that the experiential-pathos modal background contains both desire and non-desire worlds and it is thus non-homogeneous with respect to desiderability. Desiderability results from a double restriction between the experiential-pathos modal base and preferences.

Our analysis of avoir envie is in avoirenvieanalysis2.

(35) [[α avoir envie p]] P,E,i = 1 iff ∀w ′ ∈ P(E(i, w 0 , c))p(w ′ )

All worlds in the experiential-pathos modal base of the judge which also complain with their preferences, p is true.

The analysis accounts for the facts that we enumerated in section 2 and which we recall here. (i) avoir envie supports irrationality, a fact that we explain by resorting to pathos. (ii) avoir envie has a preference for future orientation. This is explained by the fact pathos (as spanis) needs fulfillment, a fulfillment, that, unlike the rational one with espérer, is experiential in nature. In order to be fulfilled, the experiential pathos requires that a change be made in the world of the attitude holder for them to be satisfied thus predicting future orientation.

( (iii) Our analysis relying on an experiential modal base sheds a new light on avoir envie as belonging to the class of other experiential predicates such as avoir faim (be hungry), avoir soif (be thirsty). Note that that they also share the same internal structure with an auxiliary and a bare noun. 13(iv) The lexical encoding of the positive (desirable) experience emerges in the weaknessof-will test, whereby we see that, with negative prejacents, if the action is finally performed (contrary to the initial desire), the interpretation 'being forced' emerges (Goncharov, 2021).

(38) Je n'avais pas envie de partir, mais je suis partie quand même.

I did not want to leave, but I left nonetheless.

The analysis for the first conjunct in weaknessofwill (39) [[α avoir envie p]] P,E,i = 1 iff ∀w ′ ∈ P(E(i, w 0 , c))¬p(w ′ ) All the worlds in the experiential-pathos modal base of the judge which also complain with their preferences, p is false.

Assuming the low interpretation of the negation, the inference arises that, if p becomes true, this was against the initial desire. Note that the semantics does not state that ¬p worlds are never desirable, it only state that all p worlds are. However, this is an inference that persists as the weakness-of-will test highlights.

Vouloir

Turning now to vouloir, we propose that, in French, it features an underspecified primary modal base, thus accounting for the fact that its meaning can range from mere-desire (when combined with adverbs such as tellement) to orientation toward action and formation of intention [START_REF] Condoravdi | Anankastic conditionals are just conditionals[END_REF]Farkas, 1992;[START_REF] Grano | The Logic of Intention Reports[END_REF] We thus assume that, by default, and in absence of contrary grammatical (e.g. conditional) or lexical (e.g. tellement) information, a modal base describing an actionable space is accommodated. The resulting analysis is as follows. We assume for simplicity that vouloir is in the present tense and that the temporal argument can be manipulated by tense. Le t 0 be the utterance time.

(41) Default interpretation of vouloir.

[[α veut p]] P,A,i = 1 iff ∀w ′ ∈ P(A(i, t 0 )) p(w ′ ) All worlds in the actionable modal base of the judge determined at the utterance time which also complain with their preferences, p is true.

This analysis make two immediate predictions. (i) vouloir has mandatory future orientation. An actionable space at a given time t is necessarily future-oriented. A prejacent whose time of interpretation is anterior or simultaneous to the time of interpretation of the attitude predicate is not felicitous with the bare predicate, that has to be modified by conditional morphology or an adverb of intensity in order to be loose its strict future orientation. ( 42 (ii) vouloir is rational both in the sense that its object cannot be something outside of the realm of the reachable beliefs, but also in the sense that two contradictory actions cannot be carried out simultaneously. This would indeed be contradictory with how the world can evolve, and specifically with the fact that two incompatible actions cannot be carried out in the actual world to be. As we said, however, this is a default that can be leveled and in line with von Fintel and Iatridou (2020) we assume that grammar and the lexicon provide means to level the rationability requirement. We propose that tellement ('so much') in tellement, like other adverbs of intensity, introduces the modal base over which preferences operate, and specifically they introduce an experiential-pathos modal base. In this case, the interpretation of vouloir becomes similar to the one of avoir envie.

(44) [[α vouloir tellement p]] P,E,i = 1 iff ∀w ′ ∈ P(E(i, w 0 , c))¬p(w ′ ) All the worlds in the experiential-pathos modal base of the judge which also complain with her preferences, p is false.

As already pointed by von Fintel and Iatridou (ibid.), the conditional (COND) is one grammatical device that also levels the rationality constraint of vouloir, making it compatible with impossible state of affairs, simultaneous events, and everything that avoir envie allows. In our framework, COND has a counterfactual contribution that extends the modal base to worlds in which actions cannot be carried out by i. The mechanism that we envision is reminiscent of the modal base Dox+ used by [START_REF] Heim | Presupposition projection and the semantics of attitude verbs[END_REF], [START_REF] Mari | Actuality entailments: when the modality is in the presupposition[END_REF][START_REF] Mari | Mood variation with belief predicates: Modal comparison and the raisability of questions[END_REF][START_REF] Portner | The semantics of mood, complementation, and conversational force[END_REF]Rubinstein (2020). Dox+ is formed from a DOX, plus irrational worlds. Let A+ a non-rational actionable space, which contains actions that cannot be carried out by the attitude holder.

(47) [[α vouloir.COND p]] P,A+,A,i = 1 iff ∀w ′ ∈ P(A+(i, t)/A(i, t)) p(w ′ ) All worlds in the non-rational actionable modal base of the judge i at a time t which also complain with their preferences, p is true.

Conclusion

This paper has characterized the landscape of bouletic attitudes in French from the perspective of the distinction between mere-desire attitudes and action-oriented bouletic attitudes. The picture that has emerged distinguishes between mere-desire attitudes avoir envie/avere voglia as featuring an experiential modal base, espérer/sperare that appeal to a rational doxastic base and want equivalents vouloir/volere that are underspecified but have a default preference for an actionable modal base. All bouletic attitudes rank the worlds of these modal bases according to preferences. One open question is what are the cognitive underpinnings of these semantic distinctions. We submit, without further justifying the hypothesis, that the modal bases correspond to three different conceptualizations of the individuals as sentient beings, rational agents and actors according to the following systematization.

Representation of the individals

Modal bases Lexicalization

Sentient The paper has shown that these distinctions are ground in the lexical semantics of bouletic attitudes and has provided several tests for (ir)rationality and actionability (and lack thereof). Our discussion seems to point to the fact that there is a consistent amount of homogeneity across French and Italian. How languages beyond these two Romance ones organize their own landscape across these conceptual categories is a question that we leave for future research.

  t know what is in the box, but I want it so much to be an I-Pad !

(

  is impossible but I want to go on the moon.

  know this is impossible, I want to go on the moon. bmove in with Sam and I want to stay in my children bedroom. csummer, I want to go to Rome and I want to go to Dublin. But I do not want to go to both Rome and Dublin.

  want / would want for her to be sleeping / sleeps at her mother's place right now.

Figure 2 :

 2 Figure 2: Lexicalizations of volition in French

  Maria is proud of me. ↝̸ I will act in order to bring about the fact that Maria is proud of me.

	Je	veux			que	Marie	soit	fière	de	moi.
	I	want.IND.1SG	that	Marie	be.SUBJ.3SG	proud	of	me
	I want Maria to be proud of me.
	↝ I will act in order to bring about the fact that Maria is proud of me.
	b. J'espère		que	Maria	est	/	sera	fière	de	moi.
	I hope.IND.1SG	that	Maria	be.IND.3SG	/	be.IND.FUT.3SG	proud	of	me
	I want Maria to be proud of me.
	↝̸ I will act in order to bring about the fact that Maria is proud of me.
	c. Ho	voglia	che	Maria	sia	orgogliosa	di	me.
	have.IND.1SG	desire		that	Maria	be.SUBJ.3SG	proud	of	me
	I want Maria to be proud of me.
	↝̸ I will act in order to bring about the fact that Maria is proud of me.
	d. Je	crois				que	Maria	est	/	sera	fière	de	moi.
	I	believe.IND.1SG	that	Maria	be.IND.3SG	/	be.IND.FUT.3SG	proud	of	me
	I believe that

  Jean believes that he will visit New York this summer, and he believes also believes that he will visit Dublin this summer. But he does not believes that he will visit both New York and Dublin this summer. Jean intends to visit New York this summer, and he also intends to visit Dublin this summer. But he does not intend to visit both New York and Dublin this summer. Jean wants to visit New York this summer, and he also wants to visit Dublin this summer. But he wants to visit both New York and Dublin this summer. Jean wants to visit New York this summer, and he also wants to visit Dublin this summer. But he does not want to visit both New York and Dublin this summer.

	) a. Jean	croit			qu'il	va	visiter	New	York	cet	été,	et	il	croit
	Jean	believes	that-he	will	visit	New	York	this	summer,	and	he	believes
	aussi	qu'il		va			visiter	Dublin	cet	été.	#Mais	il	ne	croit	pas
	also		that-he	will	visit	Dublin	this	summer.	But	he	neg	believes	not
	qu'il			visitera			et	New	York	et	Dublin	cet	été.
	that-he	visit.FUT	and	New	York	and	Dublin	this	summer.
	b. Jean	a			l'intention		de	visiter	New	York	cet	été,	et	il	a	aussi
	Jean	has	the-intention	to	visit	New	York	this	summer,	and	he	has	also
	l'intention		de	visiter	Dublin	cet	été.	#Mais	il	n'a	pas
	the-intention	to		visit		Dublin	this	summer.	But	he	neg-has	not
	l'intention		de	visiter	et	New	York	et	Dublin	cet	été.
	the-intention	to		visit		and	New	York	and	Dublin	this	summer.
	c. Jean	veut		visiter	New	York	cet	été,	et	il	veut	aussi	visiter	Dublin
	Jean	wants	visit			New	York	this	summer,	and	he	wants	also	visit	Dublin
	cet	été.				??? Mais	il	ne	veut	pas	visiter	et	New	York	et	Dublin	cet
	this	summer.	But			he	neg	want	pas	visit	and	New	York	and	Dublin	this
	été.
	summer.
	d. Jean	a			envie		de	visiter	New	York	cet	été,	et	il	a	aussi	envie	de
	Jean	has	desire	to	visit	New	York	this	summer,	and	he	has	also	desire	to
	visiter	Dublin	cet	été.	Mais	il	n'a	pas	envie	de	visiter	et	New
	visit		Dublin	this	summer.	But	he	neg-has	not	desire	to	visit	and	New
	York	et			Dublin	cet	été.
	York	and	Dublin	this	summer.

  ). Such configurations are possible both in Italian spe and in French esp.3 Equivalents of want in Romance are stricter. French vouloir and Italian volere are not compatible with past prejacent. (ibid.).The most litigious point pertains to simultaneity: it is frequently argued that equivalents of want in Romance have a non-past orientation (e.g.Portner and Rubinstein (2020) a.o.). However, simvol and simvoul are impossible in Italian and French, respectively, most notably in comparison with their conditional version, which is much more acceptable.

	b. Vorrei		che	ora		stesse	dormendo	da	sua	madre.
	Want.COND.1SG	that	now	be.SUBJ.IMPERF.3SG	sleep.GER	at	her	mother
	(13) Italian: Volere present perspective and future orientation only: I want her to be sleeping at her mother's place right now.
	a. #Voglio (16) French			che	ieri	abbia	dormito
	Want.IND.PRES.1SG a. #Je veux	that	yesterday qu'elle soit have.SUBJ.PRES.3SG en train sleep.PART.PAST de dormir
	da I	sua want.SUBJ.PRES.1SG madre.	that.she	be.IND.PRES.3SG	in	course	of	sleep.INF
	at / dorme her mother				chez	sa	mère	maintenant.
	I want here to have slept at her mother's place yesterday. / sleep.SUBJ.PRES.3SG at her mother now (11) Sperare present perspective with past, present, future orientation: a. Spero Hope.IND.PRES.1SG che that ieri yesterday abbia have.SUBJ.PRES.3SG b. #Voglio che ora stia dormendo I want her to be sleeping / sleeps at her mother's place right now. dormito Want.IND.PRES.1SG that now be.SUBJ.PRES.3SG sleep.PART.PRES b. Je voudrais qu'elle soit en train de dormir / / sleep.PART.PAST / da at sua her dorma da sua madre. I want.COND.1SG that.she be.SUBJ.PRES.3SG in course of sleep.INF / madre. sleep.SUBJ.PRES.3SG at her mother dorme chez sa mère maintenant. mother I want her to be sleeping / sleeps at her mother's place right now. sleep.SUBJ.PRES.3SG at her mother now I hope she slept at her mother's place yesterday. b. Spero Hope.IND.PRES.1SG che that ora now stia be.SUBJ.PRES.3SG dormendo sleep.PART.PRES dorma sleep.SUBJ.PRES.3SG da at sua her mother (14) French: Vouloir present perspective and future orientation only: madre. I want her to sleep at her mother's place tomorrow. / want.IND.PRES.1SG that sleep.SUBJ.3SG at her mother tomorrow / c. Voglio che dorma da sua madre domani. I would like for her to be sleeping / sleeps at her mother's place right now.
	I hope she is sleeping / sleeps at her mother's place right now. a. #Je veux qu'elle ait dormi
	c. Spero Hope.IND.PRES.1SG I want.IND.PRES.3SG che that that.she domani tomorrow have.SUBJ.PRES.3SG dormirà sleep.IND.FUT.3SG sleep.PART.PAST / / dorma sleep.SUBJ.3SG chez sa mère hier. sua her at her mother yesterday madre. I want her to have slept at her mother's place yesterday mother b. #Je veux qu'elle soit en train de dormir I hope she will sleep / sleeps at her mother's place tomorrow. I want.IND.PRES.1SG that-she be.IND.PRES.3SG in course of sleep.INF da at / /
	(12) Espérer present perspective and past, present, future orientation: dorme chez sa mère maintenant.
	a. J'espère sleep.SUBJ.PRES.3SG	qu'elle at her a mother	now	dormi	chez
	I.hope.IND.PRES.3SG I want her to be sleeping / sleeps at her mother's place right now. that.she have.IND.PRES.3SG sleep.PART.PAST	at
	sa c. Je	mère veux	hier.				qu'elle	dorme	chez	sa	mère
	her I want.IND.PRES.3SG mother yesterday	that-she	sleep.SUBJ.PRES.3SG	at	her	mother
	I hope she slept at her mother's place yesterday demain.
	b. J'espère tomorrow				qu'elle	est	en	train	de	dormir	/
	I-hope.IND.PRES.1SG I want her to sleep at her mother's place tomorrow. that-she be.IND.PRES.3SG in	course	of	sleep.INF	/
	dort				chez	sa	mère	maintenant.
	sleep.IND.PRES.3SG.		at		her	mother	now
	I hope she is sleeping / sleeps at her mother's place right now.
	c. J'espère				qu'elle	dormira	chez	sa	mère
	I-hope.IND.PRES.3SG	that-she	sleep.IND.FUT.3SG	at	her	mother
	demain. tomorrow (15) Italian
	I hope she will sleep at her mother's place tomorrow. a. #Voglio che ora stia dormendo	/
	Want.IND.PRES.1SG	that	now	be.SUBJ.PRES.3SG	sleep.PART.PRES	/
	dorma				da	sua	madre.
	sleep.SUBJ.PRES.3SG	at	her	mother
	I want her to be sleeping / sleeps at her mother's place right now.

)

  Avere voglia: present perspective and present and future orientation:

	b. ?J'ai							envie	qu'elle	soit	en	train	de
	I-have.SUBJ.PRE.1SG	desire	that.she	be.IND.PRES.3SG	in	course	of
	dormir		/	dorme			chez	sa	mère	maintenant.
	sleep.INF	/	sleep.SUBJ.PRES.3SG	at	her	mother	now.
	I want her to be sleeping / sleeps at her mother's place right now.
	c. J'ai					envie		qu'elle	dorme	chez	sa	mère	demain.
	I-have.IND.1SG	desire	that-she	sleep.SUBJ.3SG	at	her	mother	tomorrow
	I would like her to sleep at her mother's place tomorrow.
	a. #Ho				voglia	che	ieri	abbia	dormito	da	sua
	Have.IND.1SG	desire	that	yesterday	have.SUBJ.3SG	sleep.PART.PAST	of	her
	madre.
	mother
	I would like her to have slept at her mother's place yesterday.
	b. Ho				voglia	che	ora	??stia	dormendo	/
	Have.IND.1SG	desire	that	now	be.SUBJ.3SG	sleep.PART.PRES	/
	dorma					da	sua	madre.
	sleep.SUBJ.3SG	of	her	mother
	I would like her to be sleeping at her mother's place right now.
	c. Ho				voglia	che	dorma	da	sua	madre	domani.
	Have.IND.1SG	desire	that	sleep.SUBJ.3SG	of	her	mother	tomorrow
	I would like her to sleep at her mother's place tomorrow.
	(18) Avoir envie present tense: present perspective and present and future orientation:
	a. #J'ai					envie	qu'elle	ait	dormi	chez	sa
	I-Have.IND.1SG	desire	that-she	have.SUBJ.3SG	sleep.PART.PAST	at	her
	mère	hier.
	mother	yesterday
	I would like her to have sleep at her mother's place yesterday

  Symmetrically, if the realization of the prejacent seems to depend solely on the attitude holder actions, sperare/espérer (HOPE) is not felicitous, while volere/vouloir (HOPE) and avoir envie/avere voglia are.(21) Samia just checked the fridge, and saw that everything is there to do here favorite breakfast (scrambled eggs and orange juice).

	d. Ho					voglia	che	il	tempo	sia	bello.
	Have.IND.1SG		desire	that	the	weather	be.SUBJ.3SG	beautiful
	I would like the weather to be beautiful.
											She says:
	a. #Spero				di	avere	un	bicchiere	di	succo	d'arancia	con	uova
	hope.IND.1SG		of	have	a	glass	of	juice	of-orange	with	eggs
	strapazzate.
	scrambled.
	I hope to have a glass of orange juice with scrambled eggs.
	b. Voglio				/	vorrei	un	bicchiere	di	succo	d'arancia	con	uova
	want.IND.1SG		/	want.COND.1SG	a	glass	of	juice	of-orange	with	eggs
	strapazzate.
	scrambled
	I want / would like to have a glass of orange juice with scrambled eggs.
	c. Ho				voglia	di	un	bicchiere	di	succo	d'arancia	con	uova
	have.IND.1SG	desire	of	a	glass	of	juice	of-orange	with	eggs
	strapazzate.
	scrambled
	I would like to have a glass of orange juice with scrambled eggs.
	d. J'espère					(avoir/prendre)	un	verre	de	jus	d'orange	avec	des	oeufs
	I-hope.IND.1SG	(have/take)	a	glass	of	juice	of-orange	with	some	eggs
	brouillés.
	scrambled.
	I hope to have a glass of orange juice with scrambled eggs.
	e. Je	veux						/	voudrais	(avoir/prendre)	un	verre	de	jus
	I	want.IND.1SG	/	want.COND.1SG	(have/take)	a	glass	of	juice
	d'orange	avec	des		oeufs	brouillés.
	of-orange	with	some	eggs	scrambled
	(#)Voglio I want / would like to have a glass of orange juice with scrambled eggs. che il tempo sia bello. (Acceptable under
	Want.IND.1SG f. J'ai		that envie the	weather d' (avoir/prendre) be.SUBJ.3SG un verre beautiful de jus	d'orange	avec
	EXCL) I-have.IND.1SG	desire	of	(have/take)	a	glass	of	juice	of-orange	with
	des	oeufs	brouillés.
	I want the weather to be beautiful. some eggs scrambled
	b. Vorrei I would like to have a glass of orange juice with scrambled eggs. che il tempo sia bello.
	Want.COND.1SG	that	the	weather	be.SUBJ.3SG	beautiful
	I would like the weather to be beautiful.
	c. Spero					che	il	tempo	sia	bello.
	Hope.IND.1SG	that	the	weather	be.SUBJ.3SG	beautiful
	I hope the weather will be beautiful.

  37) Avoir envie present tense: present perspective and present and future orientation:

	a. #J'ai		envie	qu'elle	ait	dormi		chez	sa
	I-Have.IND.1SG	desire	that-she	have.SUBJ.3SG	sleep.PART.PAST	at	her
	mère	hier.
	mother	yesterday
	I would like her to have sleep at her mother's place yesterday
	b. J'ai		envie	qu'elle	dorme	chez	sa	mère	demain.
	I-have.IND.1SG	desire	that-she	sleep.SUBJ.3SG	at	her	mother	tomorrow
	I would like her to sleep at her mother's place tomorrow.

  .

	(40) Je	sais		bien	qu'il		y		a	la	morale,	la	vertu,	mais	je
	I	know.IND.1SG	well	that-it	there	have.IND.3SG	the	moral,	the	virtue,	but	I
	peux	toujours	avoir	cela.	Je	veux		tellement	autre	chose.
	can.IND.1SG	always	have	that.	I		want.IND.1SG	so much	else	something
	I know that there is moral, virtue, but I still can have all that. I want so much
	something else.

See Grano (2017) for a discussion on the proximity of intention reports and doxastic attitudes on the basis of the same properties discussed here.

See also[START_REF] Condoravdi | Temporal Interpretation of Modals -Modals for the Present and for the Past[END_REF] for a detailed analysis on the temporal orientation of modals implemented in a branching-time framework.

We use 'temporal perspective' to refer to the time at which the attitude holds and 'temporal orientation' to refer to the time at which the prejacent is evaluated with respect to the temporal perspective.

Some speakers are reluctant with the association of avere voglia and a simultaneously interpreted prejacent with the gerunds, but with the present subjunctive any unacceptability is far less strong as with volere. The same holds for avoir envie.

See Mandelkern, Schultheis, and Boylan (2017) for a recent analysis on the matter.

Our analysis does not distinguish between non-past and future orientation. SeeGiannakidou and Mari (2018) for finer distinctions. Since non-past is only marginally acceptable even with avoir envie and avere voglia, we do not consider here its precise contribution.

With the exception of[START_REF] Ruwet | Je veux partir/* Je veux que je parte. A propos de la distribution des complétives à temps fini et des compléments à l'infinitif en franc ¸ais[END_REF], which we recalled in section 1.

A kratzerian semantics for desire reports has been spelled out by von[START_REF] Fintel | NPI Licensing, Strawson Entailment, and Context Dependency[END_REF]. Under many circumstances, these analyses make similar predictions. See[START_REF] Crnič | Getting even[END_REF] for a detailed comparison.

See Phillips-Brown (2020) for a recent critique.

Condoravdi and Lauer insist on the fact that realism and consistence are necessary conditions for a preference structure to be effective.

This relation is originally found in[START_REF] Farkas | On obligatory control[END_REF] and might be understood as some kind of (very) special thematic role.

We borrow this term from the NLP literature[START_REF] Kozlowski | A three-level classification of French tweets in ecological crises[END_REF] and references therein)

Interestingly, and as side note, the best approximate of the French avoir envie is feel like that makes visible the two components experiential-pathos (feel) and appetite (like).


Espen Gaarder
email: espenhaug@mac.com

Gianfranco Spavieri
email: gspavieri@gmail.com

A new strong-field type Schwarzschild metric closer to observation in gravity theory

Keywords: general relativity theory, Schwarzschild metric, weak field, strong field, black holes

The Schwarzschild metric is the most commonly used metric solution that can be derived from Einstein's field equation. It is used to predict most gravitational phenomena that can be checked with observation, especially for weak field phenomena. However, in one of the final steps of deriving the final metric, one relies on Newton's theory, which suggests that the standard and well-known Schwarzschild metric is valid for weak fields only. Unfortunately, few sources make this clear, and the physics community does not seem to be fully aware of it. As a result, the weak field solution has been used to predict strong gravitational fields as well, for example predictions about black holes, both large black holes and micro black holes.

We present a new metric that provides the same predictions as the weak field Schwarzschild metric in weak gravitational fields, but gives significant new predictions in strong gravitational fields in particular for black holes, but also for wormholes. Observational evidence related to strong fields is more consistent with this new metric than the weak field approximation metric, which in some cases might have been used improperly to predict results linked to strong gravitational fields.

The Standard Schwarzschild Metric

Einstein's [START_REF] Einstein | Näherungsweise integration der feldgleichungen der gravitation[END_REF] field equation is given by:

R µv 1 2 Rg µv + ⇤g µv = 8⇡G c 4 T µv (1)
Based on the assumption of a non-spinning spherical mass with no electrical charge or angular momentum, as well as setting the cosmological constant to zero, Schwarzschild [START_REF] Schwarzschild | Über das gravitationsfeld eines massenpunktes nach der einsteinschen theorie[END_REF][START_REF] Schwarzschild | über das gravitationsfeld einer kugel aus inkompressibler flussigkeit nach der einsteinschen theorie[END_REF] derived the following metric for spherical polar coordinates:

c 2 d⌧ 2 = ⇣ 1 ↵ R ⌘ dt 2 ⇣ 1 ↵ R ⌘ 1 dR 2 R 2 (d✓ 2 + sin 2 ✓d 2 ) ( 2
)
where ↵ has to be determined before the metric can be used for any practical purposes. The standard methodology in the literature to determine the value of the ↵ is to rely on Newton's [START_REF] Newton | Philosophiae Naturalis Principia Mathematica[END_REF] theory, in short one has

We note that only a few books on general relativity, such as Hobson, Efstathiou, and Lasenby [START_REF] Hobson | General Relativity[END_REF], specifically mention that this is a weak field limit. Other books, such as Weinberg's [START_REF] Weinberg | Gravitation and Cosmology[END_REF], Poisson and Will's [START_REF] Poisson | Gravity[END_REF], and the major work by Misner, Thorne, and Wheeler [START_REF] Misner | Gravitation. Freeman[END_REF], do not point out specifically that the last step in deriving their final Schwarzschild metric is linked to calibrating it to Newton's weak field limit and that the solution is therefore likely valid for weak fields only.

If this is the case, the weak field Schwarzschild metric is not appropriate to make predictions related to strong gravitational fields, including studies of black holes at the centers of galaxies and quasars. For instance, it has been used to predict the escape velocity and the Schwarzschild radius in general relativity theory. We argue that such weak-field metric predictions are likely not valid in strong gravitational fields, which we define as fields where the escape velocity v e is significant relative to c. We do not contest the existence of black holes, but as we will soon see, a new strong-field metric solution gives di↵erent and more logical predictions that even seem to be in line with observations.

To illustrate the weakness of the weak field limit, consider the escape velocity in Newton's theory, which is determined by solving the equation for v:

1 2 mv 2 G Mm r = 0 (4) which gives v = q 2GM r .
It is evident that this formula cannot be valid when v is close to the speed of light because the kinetic energy formula used in the derivation, E k ⇡ 1 2 mv 2 , is only the first term of a Taylor series expansion from Einstein's relativistic kinetic energy, E k = mc 2 mc 2 . However, it is well known that general relativity theory predicts the same escape velocity as Newton, as shown in [START_REF] Augousti | An observation on the congruence of the escape velocity in classical mechanics and general relativity in a Schwarzschild metric[END_REF]. For years, it has been a mystery to us why the escape velocity derived from general relativity theory is the same as that derived from Newton's theory, where the one derived from Newton theory is clearly valid only when v ⌧ c. We think we have found the reason: in general relativity theory, the final Schwarzschild metric is mistakenly assumed to be valid in a strong gravitational field, despite being "calibrated" to Newton for weak field and then used also for strong gravitational field predictions. We claim that the general relativity escape velocity, which is identical to the one we get from pure Newton, is actually valid for a weak gravitational field only, because derived from the Schwarzschild metric, which, in its last step, is calibrated to the weak field Newtonian gravity theory.

So, nothing is wrong with the Schwarzschild metric itself; it is just that one needs to be aware that the last step used to turn it into a practical and useful formula relies on Newton and that the whole solution therefore likely is only valid for weak gravitational fields. The issue, therefore, is how to have the last step calibrated in such a way as to take into account relativistic e↵ects and obtain a Schwarzschild metric solution that holds also for the strongest gravitational fields. We show and discuss this in the next sections.

mc 2 mc 2 = mGM R 1 2 = 1 v 2 e c 2 = ✓ 1 GM Rc 2 ◆ 2 = 1 2 GM Rc 2 + G 2 M 2 R 2 c 2 ✓ v 2 e c 2 ◆ relativity = 2 GM Rc 2 G 2 M 2 R 2 c 2 (6)
where in equation ( 6) the factor gamma appears consistently in the expression of the kinetic energy and the interaction potential energy (a discussion about the "relativistic mass" is given in the Appendix). In the limit when v = v esc ! c and Newton becomes relativistic2 we have the correspondence,

✓ v 2 e c 2 ◆ N ewton ! ✓ v 2 e c 2 ◆ relativity 2GM Rc 2 ! 2GM Rc 2 G 2 M 2 R 2 c 2
Then, the Swartzschild component becomes

⇣ 1 ↵ R ⌘ = ✓ 1 2GM Rc 2 ◆ ! ✓ 1 2GM Rc 2 + G 2 M 2 R 2 c 2 ◆ = ✓ 1 2GM Rc 2 + U R 2 c 2 ◆
where U is a physical quantity related to the gravitation potential in the metric of the Reiser Nordström type [START_REF] Reissner | Über die eigengravitation des elektrischen feldes nach der einsteinschen theorie[END_REF][START_REF] Nordström | On the energy of the gravitation field in einstein's theory[END_REF]. Our full strong field metric is therefore given by

c 2 d⌧ 2 = ✓ 1 2GM c 2 R + G 2 M 2 c 4 R 2 ◆ c 2 dt 2 ✓ 1 2GM c 2 R + G 2 M 2 c 4 R 2 ◆ 1 dR 2 R 2 (d✓ 2 + sin 2 ✓d 2 ) (7)
For all weak field phenomena, it gives predictions that are virtually identical to those of the standard (weak field) Schwarzschild metric, with any di↵erences between the two being too small to be observable in weak field experiments. The first term is identical to the weak field Schwarzschild metric approximation, which is the cornerstone of much of gravitational physics. For large values of R (weak field), the second term is negligible with respect to the first. Most of the very solid tests of general relativity have been done in the weak field, such as gravitational time dilation, gravitational red-shift and light deflection. In many weak field experiments, one can set up experiments where one has direct observations in all parts of the experiment. For example, for gravitational time dilation, all one needs is basically two atomic clocks at di↵erent altitudes. For gravitational red-shift, one can send a light beam down from a tower and thereby have full control of observations of the frequency sent out and received, as first published by Pound and Rebka [START_REF] Pound | Gravitational red-shift in nuclear resonance[END_REF] in 1959. There is no doubt that the weak field Schwarzschild metric approximation gives very accurate predictions for long series of gravity phenomena observed in a weak gravitational field.

Observations from a strong gravitational field are much more indirect, as there is no strong gravitational field on Earth or even in our solar system. We define a strong gravitational field as one where the escape velocity is significant compared to that of light, which means it's close to the radius of black holes as well as in very dense stars such as Neutron stars. In this case, R is small and the second term is no longer negligible and becomes relevant in the observation of black holes, which are found at the centers of galaxies, including quasars only indirectly. The only observations we have from these objects are incoming photons. In other words, we have no observable information about the exact wavelength of these photons when emitted from just outside these black holes. As a result, much of the interpretation of black holes is done through a mathematical lens, which has been the weak field Schwarzschild metric. An interesting question is what our strong field solution predicts about strong gravitational fields and how this compares to observations. This will be the topic of the next sections.

The Implications of Our New Strong Field Metric

The new strong field metric has a series of implications and predictions for gravity in strong gravitational fields. We will discuss some of them here.

Black Holes

The main di↵erence in prediction between the well-known weak field Schwarzschild metric and our strong field metric is that the radius where the escape velocity is equal to the speed of light is now R s,2 = GM c 2 instead of R s = 2GM c 2 . Additionally, the escape velocity that applies to both weak and strong fields is given by v

e = q 2GM R G 2 M 2 c 2 R 2 instead of the Newton weak field limit v e = q 2GM
R , in weak gravitational fields the two escape velocity predictions are indistinguishable. Even if this cannot be measured directly as we would need to hover just outside a black hole, there is as we will see in the sections below indirect evidence from for example high-z quasars.

3.2 The strong field limit gives a perfect fit between the Planck scale and the Planck mass micro black hole

In a recent paper [START_REF] Haug | Micro black hole candidates and the planck scale[END_REF], we showed that the weak field Schwarzschild metric, which has been used to make predictions about micro black holes, cannot match more than one or two aspects of the Planck scale with any mass candidate for a micro black hole. However, when we take into account that the black hole radius is given by R s,2 = GM c 2 (the radius where v e = c) in the strong field metric, then a Planck mass micro black hole fits all aspects of the Planck scale.

We mistakenly claimed that micro black holes in general relativity cannot match the aspects of the Planck scale. However, if our new strong field metric is consistent with Einstein's field equation, then this is all fully consistent with general relativity theory, it is just that one mistakenly has done predictions about strong fields using a weak field approximation metric. To give a few examples, let us assume the micro black holes to have Planck mass size. Then the Schwarzschild radius from the weak field metric is

R s = 2Gm p c 2 = 2l p (8)
One may ask why it is twice the Planck length and not just the Planck length. After all, the Planck length is considered the smallest meaningful radius or length in quantum gravity (see, for example, [START_REF] Padmanabhan | Planck length as the lower bound to all physical length scales[END_REF][START_REF] Adler | Six easy roads to the Planck scale[END_REF][START_REF] Hossenfelder | Can we measure structures to a precision better than the Planck length? Classical and Quantum Gravity[END_REF]). Furthermore, the escape velocity from the Planck length is now greater than the speed of light, with v e = q 2Gmp lp = c p 2. However, one could argue that it is meaningless to calculate an escape velocity within the Schwarzschild radius, and we would agree on that, but what if this is not the correct radius where the escape velocity is c, due to having calibrated the Schwarzschild metric to Newton. Additionally, the density of the Planck mass micro black hole would be only 1/8 of the Planck mass density. Why is that? Alternatively, one could assume that the micro black hole is half the Planck mass, in which case its Schwarzschild radius would be the Planck length. However, the reduced Compton wavelength of the mass would now be twice the Planck length, and it is often assumed that a particle can be compressed at most to its reduced Compton wavelength. Moreover, the surface acceleration would be only half the Planck acceleration. We discuss this topic in much more detail in [START_REF] Haug | Micro black hole candidates and the planck scale[END_REF].

The crucial point is that as soon as we switch to the strong Schwarzschild metric, a Planck mass size black hole fits all aspects of the Planck scale. Its Schwarzschild radius would be the Planck length, the acceleration at the Schwarzschild radius would be the Planck acceleration, and if the Planck acceleration lasts for the Planck time, one would reach the speed of light. The density of the black hole would be the Planck density, and so on. The strong field Schwarzschild metric seems to o↵er much better logic and a perfect match between the Planck mass black hole and all aspects of the Planck scale. This could be important to better understand the Planck scale and to get to a quantum gravity theory.

Wormholes seems forbidden in the strong field limit

In 1916, Flamm [START_REF] Flamm | Beiträge zur einsteinschen gravitationstheorie[END_REF] hinted at the existence of wormholes. In 1935, Einstein and Rosen [START_REF] Einstein | The particle problem in the general theory of relativity[END_REF] were the first to mathematically predict wormholes using the Schwarzschild metric. They used the standard Schwarzschild metric, which is described in Section 1 of this paper, and as is often done when working with the Schwarzschild metric, they set c = 1 and R s = 2GM c 2 = 2m. Next, Einstein and Rosen defined a new variable, u 2 = R 2m, and replaced R with u 2 +2m in the Schwarzschild metric to obtain:

ds 2 = ✓ 1 R s R ◆ c 2 dt 2 dR 2 1 Rs R R 2 (d✓ 2 + sin 2 ✓d 2 ) ds 2 = 4(u 2 + 2m)du 2 (u 2 + 2m) 2 (d✓ 2 + sin 2 ✓d 2 ) + u 2 u 2 + 2m dt 2 (9)
They then discussed the special case when u = 0. In this case, the term g 1,1 = 1 Rs R c 2 dt 2 = u 2 u 2 +2m dt 2 vanishes, while the other terms in the Schwarzschild metric remain well-defined. This was interpreted to mean that one could move in space without moving in time, essentially providing a passage from one part of the universe to another through a wormhole.

Wormhole physics has been investigated by a series of physicists [START_REF] Morris | Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity[END_REF][START_REF] Maldacena | Cool horizons for entangled black hole[END_REF][START_REF] Prat-Camps | A magnetic wormhole[END_REF][START_REF] Lobo | From the flamm-einstein-rosen bridge to the modern renaissance of traversable wormholes[END_REF][START_REF] Gao | Traversable wormholes via a double trace deformation[END_REF][START_REF] Fu | A perturbative perspective on self-supporting wormholes[END_REF][START_REF] Paul | Observational signatures of wormholes with thin accretion disks[END_REF][START_REF] Paul | Traversable wormholes in the galactic halo with mond and non-linear equation of state[END_REF][START_REF] Goto | Replica wormholes for an evaporating 2d black hole[END_REF][START_REF] Numasawa | Four coupled syk models and nearly ads2 gravities: phase transitions in traversable wormholes and in bra-ket wormholes[END_REF][START_REF] Kokubu | Thin-shell wormholes in einstein and einstein-gauss-bonnet theories of gravity[END_REF][START_REF] Zaslavskii | New scenarios of high-energy particle collisions near wormholes[END_REF][31][START_REF] Yusupova | Accretion flow onto ellis-bronnikov wormhole[END_REF][START_REF] Zafiris | The "er = epr" conjecture and generic gravitational properties: A universal topological linking model of the correspondence between tripartite entanglement and planck-scalewormholes[END_REF][START_REF] Fabris | Black hole and wormhole solutions in einstein-maxwell scalar theory[END_REF][START_REF] Maeda | Simple traversable wormholes violating energy conditions only near the planck scale[END_REF], and it remains a hot topic to this day despite the lack of observable findings of wormholes.

However, we will claim that the interpretations of wormholes could be incorrect as they are predicted by a weak field approximation of the Schwarzschild metric, whereas wormholes are related to strong gravitational fields. Also, for simplicity, in our strong field metric, we set c = 1 and R s,2 = GM c 2 when v e = c. For notation purposes, we can set m = GM c 2 . Similar to Einstein and Rosen, we set u 2 = R m. The choice of u is just as in the Einstein-Rosen solution, such that we end up with the dt 2 term vanishing. We can now replace R with R = u 2 + m. We end up with

ds 2 = ✓ 1 2GM Rc 2 + G 2 M 2 R 2 c 4 ◆ c 2 dt 2 dR 2 1 2GM Rc 2 G 2 M 2 R 2 c 4 R 2 (d✓ 2 + sin 2 ✓d 2 ) ds 2 = ✓ u 2 u 2 + m ◆ 2 dt 2 4(u 2 + m) 2 u 2 du 2 (u 2 + m) 2 (d✓ 2 + sin 2 ✓d 2 ) ( 10
)
If we now set u = 0, the dt 2 term vanishes, as expected, similarly to how it did in the Einstein-Rosen modified Schwarzschild weak field metric. However, in our strong field metric, the du 2 term now becomes infinite, meaning that it is mathematically undefined or we can say it goes to a singularity. The fact that the du 2 term is no longer mathematically valid should be interpreted as implying that no valid solution for the metric exists when the dt 2 element disappears. That is, unlike in the weak field Schwarzschild metric, nothing can move in the strong field metric without time passing by. In other words, wormholes are not allowed in this metric. This should naturally be investigated by more researchers, but the conclusion so far is that wormholes do not exist.

Explaining the lack of time dilation in quasars with the strong field metric

In a groundbreaking study of high-z quasars, Hawkins [START_REF] Hawkins | On time dilation in quasar light curves[END_REF][START_REF] Hawkins | Time dilation and quasar variability[END_REF] surprised the scientific community by reporting that these objects showed no evidence of velocity time dilation, contrary to what had been expected. In the words of Hawkins:

"There does not appear to be a satisfactory explanation for the absence of a time dilation e↵ect in quasar power spectra..."

Recently, we have shown in a paper [START_REF] Haug | Does general relativity theory strongly underestimate gravitational redshift for objects such as black holes and quasars[END_REF] that if we use the strong field metric with R s,2 = GM c 2 instead of the weak field metric with R s = 2GM c 2 , then light can be sent out from much closer to the center of the black hole than previously assumed, still outside the event horizon that is now only half the distance predicted by the weak field Schwarzschild geometry. This leads to a stronger gravitational redshift for strong field objects than expected from the weak field metric, with a larger portion of the redshift being due to gravitational redshift rather than velocity (Doppler) redshift. As a result, the velocity time dilation is much lower than expected. Once again, the observations seem to support our new metric.

The maximum mass of Neutron stars corresponds with observations in the strong field limit

In a recent paper [START_REF] Haug | Taking into account lorentz relativistic mass, the maximum mass of a neutron stars is predicted to be 2.147 solar masses versus observed 2.14 ± 0.1m[END_REF], we have shown that the maximum mass of Neutron stars, when taking into account relativistic mass, is fully consistent with our new strong field metric. Our metric predicts a maximum mass of Neutron stars to be 2.147 solar masses, while the largest observed Neutron star is 2.14 ± 0.1M , as reported by Cromartie et al. [START_REF] Fonseca | Relativistic shapiro delay measurements of an extremely massive millisecond pulsar[END_REF].

In contrast, the weak field Schwarzschild metric, using the same logic, predicts a maximum mass of only 0.76M . While several di↵erent approaches to predict the maximum Neutron mass in the literature have been suggested, this again highlights the need for multiple researchers to investigate this further over time. However, we believe that this is a promising development in favor of the new strong field metric.

Conclusion

In this paper, we have presented a new metric solution, valid for weak and strong gravitational field, to the Schwarzschild solution. We believe that our solution is consistent with the general theory of relativity, although it is subject to further discussion and investigation over time. Our solution provides more logical predictions, such as for micro black holes, where the Planck mass black hole now fits all aspects of the Planck scale. This is not possible to achieve in the weak field Schwarzschild metric. Additionally, our solution predicts that wormholes cannot exist. The strong field metric also appears to explain the lack of observed velocity time dilations in high-z quasars.

Overall, we believe that our new metric represents an important step forward in understanding the behavior of strong gravitational fields, and we look forward to future research in this area.

still was somewhat a competitor to Einstein even at this point, even if the two theories strongly overlap. Einstein was certainly the first to suggest relativistic energy of the form E = mc 2 , so he could have arrived at the relativistic mass simply by dividing by c 2 , but he had not done this and had instead derived other formulas for relativistic mass. We will also come back to dividing the relativistic mass by c 2 , as there are also discussions on pros and cons in the literature to this day. Whether it was Lorentz who invented the relativistic mass, which now seemed preferable by most physicists and played a role in Einstein becoming negative towards relativistic mass and abandoning it altogether, or if it mostly had to do with his work on general relativity theory, will likely be unknown.

In deriving his general relativity theory, Einstein relies on relativistic mass given by Max Planck, but now incorporates relativistic mass in fourth-momentum, as well as in the stress-energy tensor. In other words, Einstein does not rely anywhere directly on relativistic mass. Einstein wrote in a letter to Lincoln Barnett, an American journalist, dated 19 June 1948:

It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass M = m/ p 1 v 2 /c 2 concept than the "rest mass", m. Instead of introducing M , it is better to mention the expression for the momentum and energy of a body in motion.

This letter has been actively used among physicists who are negative towards relativistic mass, for example, Hecht [START_REF] Hecht | Einstein never approved the relativistic mass formula[END_REF]. Other prominent experts in general relativity, such as Adler [START_REF] Adler | Dose mass really depends on velocity dad?[END_REF] in 1987 and Taylor and Wheeler [START_REF] Taylor | Spacetime Physics, Introduction To Special Relativity[END_REF], have also been negative towards relativistic mass. One of their main arguments against relativistic mass is, in their own words, "In reality, increases of energy with velocity originate in the geometric properties of spacetime itself." They also claim that relativistic mass "implies the name "mass" -belonging to the magnitude of a 4-vector -to a very di↵erent concept, the time component of a 4-vector." Okun [START_REF] Okun | The concept of mass[END_REF] has been a strong opponent of the concept of relativistic mass in his 1989 paper. Rindler [START_REF] Rindler | Putting to rest mass misconseptions[END_REF][START_REF] Rindler | Relativity, Special, General and Cosmology[END_REF], a defender of special and general relativity theory, however, went out against Okun's arguments and defended the use of the concept of relativistic mass.

Sadnin [START_REF] Sandin | In defence of relativistic mass[END_REF] defended relativistic mass in a 1991 paper and went through many of the arguments against relativistic mass put forward by Okun and Taylor and Wheeler. He concluded that their arguments against it are rather weak and stated, "Relativistic mass paints a picture of nature that is beautiful in its simplicity. We should continue to use relativistic mass along with consistent interpretations of Newton's second law and E = mc 2 in introductory courses. Insisting on its removal as a useful tool from all textbooks, as Okun does, is a form of unnecessary censorship.

Jammer [START_REF] Jammer | Concepts of Mass in Contemporary Physics and Philosophy[END_REF], in his detailed study of mass published in the year 2000, has dedicated a whole chapter to relativistic mass and the pros and cons arguments that have been presented in the literature. He mentions that this has been a debate going on for decades and that it is not over and much about preferences. The debate continues to this day. For example, Atkin [START_REF] Atkin | The teaching of mechanics: some criticisms, and suggestions for a rational approach[END_REF] in 2015 defends relativistic mass and states in his conclusion, "The term mass should mean relativistic mass rather than the currently popular meaning of rest mass." However, Sullivan [START_REF] Sullivan | Comment on 'the teaching of mechanics: some criticisms, and suggestions for a rational approach[END_REF] comments on the paper and refers to the critics of relativistic mass given by Okun, Adler, and Hecht, but also to the defense of relativistic mass by Sadnin [START_REF] Sandin | In defence of relativistic mass[END_REF]. Sullivan states, "Of course, there is nothing wrong with introducing relativistic mass, and some physicists have made a case for its retention [START_REF] Poisson | Gravity[END_REF][START_REF] Misner | Gravitation. Freeman[END_REF]; ultimately, it comes down to an individual pedagogical decision." Dai and Dai [START_REF] Dai | Deriving mass-energy equivalence and mass-velocity relation without light[END_REF], in a recent 2018 paper, rely on relativistic mass when deriving mass-energy equivalence and the mass-velocity relation without relying on light. They state, "In relativity, the inertial mass of a moving particle is not a constant quantity but a function of the particle's velocity."

Field [START_REF] Field | Three routes to relativistic kinematics and time dilation and their connection to quantum mechanical path integrals[END_REF] in a 2020 paper criticizes several of the arguments made by Okun, Adler, and Wheeler on relativistic mass. For example, Field points out that "Okun is erroneously conflating the 'rest mass of a photon' and the entirely di↵erent 'mass equivalent of the energy of a photon'."

Oas [START_REF] Oas | On the use of relativistic mass in various published works[END_REF] in 2008 went through over 600 books and papers in physics and showed that a majority of books and papers mentioning relativistic mass are positive about it. However, many of these books and papers only touch upon the topic, so the fact that a large number of physicists (if not the majority) are still positive about relativistic mass is not a good argument in itself.

Of the recent books that really go into a detailed discussion of relativistic mass, Jammer's seems to be neutral on the topic and only concludes that it is a long ongoing debate with many interesting arguments pro and con. Petkov [START_REF] Petkov | Relativity and the Nature of Spacetime[END_REF] in his 2009 book "Relativity and The Nature of Spacetime" criticizes the critics of relativistic mass. He discusses relativistic mass in quite some detail and concludes, "So, if we cannot talk about relativistic mass, by the same argument we should only talk about proper time, which is invariant, and deny the name 'time' to the coordinate time." as he claims that some of the same arguments used against relativistic mass can be used against relativistic time."

See the appendix for the validity of inserting the Lorentz factor in Newton.

Data Availability Statement:

No data has been used for this study.

Conflicts of Interest:

The author declares no conflict of interest.

Appendix: Relativistic e↵ects before taking into account general relativity

As early as 1981 and 1986, Bagge [START_REF] Bagge | Relativistic e↵ects in the solar system[END_REF] and Phipps [START_REF] Phipps | Mercury's precession according to special relativity[END_REF] suggested modifying Newtonian mechanics to take into account special relativistic e↵ects, resulting in a modified equation of the form:

Where is the Lorentz factor = 1/ p 1 v 2 /c 2 . That is, since the small mass m moves relative to the large gravitational mass M , they suggested it should be relativistic. Actually, as mentioned below, the meaning of the term "relativistic mass" has been evolving through the years and sometimes misinterpreted by some authors. Nevertheless, Phipps had in the same paper claimed that this relativistic correction alone gave the correct prediction of Mercury precession. However, it was shortly afterwards shown by Peters [START_REF] Peters | Comment on "Mercury's precession according to special relativity[END_REF] that Phipps had made a small error in his calculation of Mercury precession, and that the Mercury precession with this method still seemed to be o↵ compared to the observed Mercury precession. Phipps [START_REF] Phipps | Response to "comment on 'mercury's precession according to special relativity?[END_REF] agreed on the mistake made in his calculation but still thought the relativistic adjustment of the Newton formula could be of interest and needed further investigation. Recently, Corda [START_REF] Corda | The secret of planets' perihelion between newton and einstein[END_REF] has shown that if, besides the "relativistic mass", one also takes into account that the mass of Mercury is not insignificant relative to that of the Sun, then one gets the correct prediction of Mercury precession. Haug [START_REF] Haug | Relativistic Newtonian gravitation that gives the correct prediction of mercury precession[END_REF] has looked closer at this problem and has indicated that when one properly takes into account that both M and m are moving relative to a third observer, the Earth observer, then one could get again the correct prediction of Mercury precession. We will not conclude on this issue here, but just point out that this is likely not a fully settled question yet; see also [START_REF] Vossoss | New central scalar gravitational potential according to special relativity and newtonian physics, explains the precession of mercury's perihelion, the gravitational red shift and the rotation curves in galaxies, eliminating dark matter[END_REF][START_REF] Vossoss | Explanation of light deflection, precession of mercury's perihelion, gravitational red shift and rotation curves in galaxies, by using general relativity or equivalent generalized scalar gravitational potential[END_REF].

In general, relativistic modifications to Newton's theory have been dismissed and not looked at mostly for another reason. The main reason for so little interest in adding relativistic e↵ects to Newton has been that parts of the general relativity research community has typically rejected relativistic mass. To understand the pros and cons of relativistic mass, we should go back and look at the history of the debate on relativistic mass.

Lorentz [START_REF] Lorentz | Simplified theory of electrical and optical phenomena in moving systems[END_REF] already in 1899 was the first to introduce the relativistic mass in the form we find it in many textbooks [START_REF] Adams | Relativity: An Introduction to SpaceTime Physics[END_REF][START_REF] Mould | Basic Relativity[END_REF][START_REF] Morris | The Special Theory of Relativity[END_REF][START_REF] Morin | Special Relativity[END_REF] and some papers that we soon will get back to. The Lorentz relativistic mass in today's notation is given by m , where m is the rest mass. In his most famous paper on special relativity theory, Einstein [START_REF] Einstein | On the electrodynamics of moving bodies[END_REF] suggested two types of relativistic mass, namely transverse mass m 2 and longitudinal mass m 3 , neither of which are used in any standard theory today. In 1906, Einstein [START_REF] Einstein | On a method for the determination of the ratio of the transverse and longitudinal mass of the electron[END_REF] tried to come up with experiments that could distinguish between the di↵erent suggested relativistic masses, but with little or no success.

Max Planck [START_REF] Planck | Das prinzip der relativität und die grundgleichungen der mechanik[END_REF] in 1906 was the first to introduce the relativistic momentum p = mv . Tolman and Lewis [START_REF] Lewis | The Principle of Relativity, and Non-Newtonian Mechanics[END_REF] in 1909, as well as Tolman [START_REF] Tolman | The mass of a moving body[END_REF] in 1912, concluded based on conservation of momentum that had been experimentally observed that it was the Lorentz relativistic mass of the form m the only one consistent with this. In other words, they rejected the relativistic mass formulas that had been suggested by Einstein. This was a view soon held by a series of physicists, for example, Veride [START_REF] Vereide | Relativitetsprincippet eller Tidrummets Struktur[END_REF] and later even by prominent physicists like Pauli [START_REF] Pauli | Theory of Relativity[END_REF]. Pauli concludes, "This leads to a complete confirmation of the relativistic (mass) formula, which can thus be considered as experimentally verified. It has not been possible up until now to establish this variability for masses other than that of the electron experimentally, because of the smallness of the e↵ect, even for fast alpha particles..

In his 1965 book titled 'Einstein's Theory of Relativity', Born [START_REF] Born | Einstein's Theory of Relativity[END_REF] describes the relativistic mass of the form m = m 0 and attributes it to Lorentz. Born explains that the Lorentz relativistic mass formula as introduced by Lorentz was only for an electron, but he argues that the formula is correct for any moving mass. Born concludes that to have conservation of momentum, the mass is to have di↵erent values according to the system of reference, according to the velocity of the moving body. Based on conservation of momentum in the case of inelastic collision", Max Born concludes that it is impossible to retain the axiom of classical mechanics that mass is a constant quantity peculiar to each body". The book [START_REF] Born | Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen, (Einstein's Theory of Relativity[END_REF] was first published in 1920 but was updated in 1962 and 1965.

However, it should also be mentioned that other prominent physicists like Wien [START_REF] Wien | Die Relativitätstheorie vom Standpunkte der Physik und Erkenntnislehre[END_REF] mentioned Einstein's relativistic mass as late as 1921 without even mentioning the Lorentz relativistic mass.

Einstein did not seem to have been successful with his relativistic mass prediction formulas, despite the enormous success of the rest of his paper on special relativity theory. We must remember that the Lorentz relativity theory Another interesting point is if we even need relativistic mass to incorporate relativistic e↵ects in the Newton formula. Adler and Bazin [START_REF] Adler | Introduction to General Relativity[END_REF] in a section of their book derives gravitational red-shift in a weak gravitational field based on replacing the small mass with E/c 2 , so in that case we could argue for that one could re-write

when dealing with relativistic e↵ects in Newton theory and that we simply are dealing only with relativistic energy and not relativistic mass.

All we can conclude is that the physics community does not agree on whether relativistic mass is a valid concept or not. The debate has been ongoing for decades, and based on a series of recent papers discussing it, it is clear that the debate is not over. To pretend that the debate is over and come to a conclusion without exploration is seldom the right way to go. The appropriate approach is to fully explore what incorporating relativistic mass leads to in terms of predictions.