• 1 I am working with the Augustinian, rather than Tarskian, theory of truth, so don’t expect such thi (...)

1Can any deontic norms be either true1 or false or have any other truth value, should there be more than two? This is the “keynote” question of this paper.

• 2 But see Di Lucia & Fittipaldi, 2021.
• 3 Such as the morally or legally right and wrong with all the respective variations. The term – not (...)

2I shall not raise the concomitant question of how the truth-value of any norm (with one exception) could be established (I am not sure if it always can, not even in principle – in this sense I am not a cognitivist), nor that of the relation between Is and Ought,2 nor that of the Naturalist(ic) Fallacy (see Carcaterra, 1967), nor that of whether the deontic determinations3 can be discovered by reason alone or also by moral sentiments. These are related to my “keynote” question, but different from it.

• 4 “By the word ‘validity’ we designate the specific existence of a norm” (Kelsen, 1967, p. 10).
• 5 “[Τ]ὸ ὂν λέγεται πολλαχῶς” (Aristotle, Metaphysics, book 4 (Gamma), section 2, 1004b5).
• 6 Aristotle, Metaphysics, book 6 (Eta), section 2, 1026b36, 1027b33. Not just “called”, also studied (...)

4Short of referring him to Kelsen and/or Lotze (see, e.g., Maxsein, 1938), the philosopher may respond along these lines: “A norm is valid if it has been formulated, agreed upon and made known to everybody concerned by a group of people exclusively authorised to create norms”. To which your “man in the street” could reply: “Very well then, I wonder if it is true that the norm about wearing masks in Poland or New Zealand has been created by the authorised people”. Here, the truth or otherwise of the norm gets pushed back one remove from the norm, for it is now the truth about the validity of the norm and not the truth about the obligatoriness of covid masks in Poland or New Zealand that is at issue. But given that the norm is valid (let’s suppose it is), one can say: “Covid masks are obligatory in Poland or New Zealand, and it is so”, meaning: it is so in the mode of being called validity.4 There are many modes, this we know from Aristotle,5 in which we say that something is something else, and there are modes more puzzling than validity: as Miss Anscombe notes (Anscombe & Geach, 1961, p. 23), if the bird dodo is extinct, this is so. A mode of being to be called non- or no-longer-being? Not necessarily so: Aristotle has called it the mode of truth (ὡς ἀληθές).6

• 7 D. Hume, A Treatise of Human Nature, book 3., part 1., section 1. (Hume, 1739-40/1978, SBN p. 469) (...)

5Yet, to those who believe in Hume’s guillotine,7 the idea of an is in the mode of validity, if this validity should be that of a deontic norm, may seem an absurdity even more patent than that of an is in the mode of non-being.

• 8 D. Hume, An Enquiry into the Principles of Morals, Appendix 1 (Hume, 1751/1975, SBN p. 287).
• 9 D. Hume, An Enquiry into the Principles of Morals, Appendix 1 (Hume, 1751/1975, SBN pp. 285-294).
• 10 D. Hume, An Enquiry into the Principles of Morals, section 1.2, (Hume, 1751/1975, SBN, pp. 69-70).
• 11 See, e.g., D. Hume, An Enquiry into the Principles of Morals, section 2, or Appendix 1 (Hume, 1751 (...)
• 12 D. Hume, An Enquiry into the Principles of Morals, Appendix 1, section 14 (Hume, 1751/1975, SBN pp (...)

6Now Hume famously claimed that however we analyse or “anatomize”8 human acts and actions we never find moral qualities in them, as matters of fact or a system of relations between the actions, agents or their mental states9. But moral qualities are not nothing for Hume. On the contrary, at the beginning of his Enquiry into the Principles of Morals he writes that you must be a “disingenuous disputant”10 (or an idiot) to deny the “reality of moral distinctions”. They are real, even if they cannot be found “inside” the acts. Their reality consists – Hume thinks – in commanding universal acclaim, admiration and other positive sentiments.11 Following Hume, we can admit that just like the beauty of the circle is none of its (inherent) properties,12 being obligatory or prohibited in Poland (or wherever) is not an inherent property of the norm but a complex property straddling several subjects and expressible thus:

• 13 None of which is a good example of an empirical reality, nay, their very existence is highly dispu (...)

8A philosopher will remark, perhaps, that property 2. is not, as may be suggested, a fact-like relational property of the norm consisting in its having been enacted, because there is still validity lurking in it, not reducible to a well-behaved empiricist matter-of-factly (mode of) being: the person enacting a norm must have a valid title to do so; she must have been validly elected as a member of the legislative body, or validly anointed, or validly nominated, or the like. And the validity involved in each one of these requires a valid, “canonical”, definition, and so on. Ultimately, we shall arrive at the highest authority, with respect to which such questions as “Have you been validly elected a member of the legislative body” and so on cannot be sensibly asked because anything that comes from an authority like that – be it God, or the Kelsenian basic norm, or the volonté générale or what have you – is valid by definition.13

• 14 In the sense of “pertaining to action”, not in the “thick” sense given this expression by Miss Ans (...)

9Yet our man in the street would not be interested in all that. He would, riding on a bus without a mask and hearing the driver saying to him in a stern tone of voice: “Sir, you must put on a mask immediately or get off the bus”, recognise him immediately as a person of authority (which authority? the right, the relevant authority) and he will not ask where this authority derives from. “So it’s true, you’ve got to do it in this darned country”, he would think, perhaps. But as proclaimed by this bus-driver, the norm is a distinctly practical truth,14 not just a piece of matter-of-factly, sober information concerning the laws valid in Poland, but “also” (perhaps even chiefly) a command, i.e., the application of a general rule to this individual. This use of norms is often overlooked by some (most?) legal philosophers. For Kelsenians who attribute to their Master a clean distinction between Rechtsnorm and Rechtsatz, i.e. a statement about the former (the legal norm), a purely metalinguistic statement involving nothing normative within it except that a norm is its subject matter, with nothing in between, the Kelsenian “norms in the descriptive sense” (Hart, 1983, p. 287) are dismissed as a mistake. Hart has argued (Hart, 1983, pp. 287-295; pp. 328-330), however, that there is something in between, and my driver’s stern reminder about the masks to be worn on the bus would belong to this category (to which Hart did not give any name).

• 16 D. Hume, A Treatise of Human Nature, 2.3.3.5. (Hume, 1739-40/1978, SBN p. 415).
• 17 In any sense of this word, whether Founding Fathers’ or Aristotle’s (incessantly performing virtuo (...)

16This is the hardest part, obviously. Philosophers since Confucius have striven to define “human nature” (性, xìng in Classical Chinese) and so did the great Hume, too, and they typically used their findings as a foundation for a variety of normative statements, such as Hume’s “reason is, and ought only to be the slave of the passions”,16 or the beginning of the American Declaration of Independence: “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness”; is it really self-evidently true that all human beings have certain inalienable rights? I.e., is it true that I may this or that and cannot renounce on this may nor can anyone take it away from me? Or the Universal Declaration of Human Rights: All human beings “are endowed with reason and conscience and [for this reason?] should act towards one another in a spirit of brotherhood”. Should we really, or needn’t we? Is the pursuit of happiness really permitted (by whom?) and is it, perhaps, the case that we must never ever, and under no pretences, nor even for the very best reasons available, hinder anyone from pursuing his or her happiness; and… what is happiness, anyway?17

• 18 As did, e.g., one Irma I. I. Grese (1923-1945), known as the Beautiful/Blonde Beast of Belsen, for (...)

17However, the nature of my investigation commits me to starting not up high, amongst such high-flown ideals as Happiness or the Brotherhood of Man, because not achieving either, not even coming any close, does not (have to) destroy you as a human being – but quite low down. That is: Imagine that there are types of acts whose, as I said above, peculiar feature is that when you perform any such act, you sort of destroy yourself as a human being, become inhuman(e), in certain aspects only, to be sure (you do not necessarily transform yourself in a werewolf) and only – at the beginning – for a limited period of time, but… if you repeat your acts on a regular basis you will (consuetudo est quasi altera natura) earn yourself the name of a “beast”, an “Unmensch”, as the German says.18

• 19 See: https://www.quora.com/Why-shouldnt-I-shoplift/answer/Kimberly-A-Szacik. A perhaps more incisi (...)
• 20 Except that those others must not become the instigators and performers of their sacrifice; this t (...)
• 21 Mock-quotes: the formulation is still tentative and provisional.

19The idea that cruelty destroys the cruel person’s “soul […] life […] conscience” is to be found already in Augustine (see Baraz, 1998). One Kimberly A. Szacik BA in Psychology in Psychology [sic] answers, on Quora, the question “Why shouldn’t I shoplift?”19 with the statement “You know what you are doing is wrong, it will eat away at your soul”. But perhaps, pace Szacik BA, shoplifting, though doubtlessly reprehensible, is not really outright psychophagic. So, let us consider any type of a truly heinous, hideous, terrifying act, e.g., anthropophagy; Ó Gráda illustrates the self-destructive, dehumanising character of anthropophagy with such quotations as “the act of cannibalism symbolizes how far human beings are willing to let themselves fall” or “there was also of course a great deal of psychic decomposition, even right down to some cases of cannibalism” (Ó Gráda, 2020, p. 11). The problem is that most heinous and hideous acts which humans can do to other humans may, under highly unusual circumstances, be pardonable and even commendable, or, at the very least, they may deserve clemency. In the famous case R v Dudley and Stephens (1884, see Hutchinson, 2010, pp. 13-40), in which the defendants, accused of cannibalism, were first sentenced to death, the judges arguing that in certain cases, to preserve one’s moral integrity (one’s being human in the moral sense) one must sacrifice one’s (biological) life for others,20 but eventually served only six months in prison, due to the public consensus and Queen Victoria being in their favour. Torturing might seem to be another good candidate to the title of a type of act you must never do (see Association for the Prevention of Torture, 2007), but then there are the known “ticking bombs” arguments (see, e.g., Blattberg, 2018; Hill, 2007). Many arguments have been put forward to disarm the ticking-bomb arguments, for instance, that they may lead to justifying torturing babies in particularly extreme situations; I do not know if this is true and won’t go into it, but to err on the safe side I shall remain agnostic and not assume that torturing, not even of babies, is something you must never ever do. Instead, I shall propose the following “formula”:21

• 22 Covered are, therefore, beings which are currently non-sentient due to, e.g., I have the honour an (...)

20By “sentient beings” I mean all beings that can suffer, perceive pain, in any sense of this word. Here, there is a lacuna to be filled, for how many sorts of suffering and pain are there, within the categories of the physical and the mental, or whatever other categories of suffering there may be? Also, I take “sentient” to cover cases in which the being in question has lost temporarily or even permanently the ability to suffer in any widest sense of this word,22 which it, however, originally possessed and which typical representatives of its species possess, too.

• 23 See, e.g., Thomas Aquinas, Summa contra Gentiles, lib. 3, cap. 3, n. 7 (https://www.corpusthomisti (...)
• 24 Suffering can, of course, be something good secundum quid, e.g., suffering for a Good Cause or the (...)

21Making someone suffer for the purpose of making someone suffer and nothing else: Is anything like that possible at all? Is it actually done? Is it thinkable? An act like that may well seem absurd because we tend to assume that every act is done sub ratione boni,23 and suffering per se is, I assume, not aliquid bonum nor can it be conceptualised as anything good.24 Unless, of course, there are further purposes in your inflicting suffering, for instance, taking revenge, punishing, training your victim to bear suffering and not break down, or the like. To block such possibilities, I have built into my “formula” the expression “…and for no other purpose”. So maybe the possibility of inflicting suffering for its own sake is not really a possibility and what remains is just “inflicting pain for the pleasure of it”. Again, to err on the safe side, I have built it into my “formula”.

• 25 It would be disingenuous, however, to pretend I haven’t heard of the Tortured Child from The Broth (...)

22Real-life examples are, naturally, rather drastic, which is why I shall not quote any.25 Suffice it to say that in one case known to me the “vocal reactions”, to put it so, of the victim of the torture administered to her were tape-recorded by one of the tormentors and, confiscated afterwards by the police, classified (meaning: made not accessible to the public). However, FBI agents are made to listen to them during their training, the purpose being desensitising them to what they are likely to be exposed to while doing their duty. Acts of this sort I shall call (acts of) pure sadism or sadist acts. Finally, I have to explain that by torture above I meant not all acts of pure sadism but inflicting pain for the sake of extorting such information from the victim as he is unwilling to provide.

• 26 See, e.g., https://www.youtube.com/watch?v=a3HbMAgcOvY.
• 27 Thinking certain thoughts, saying certain words, moving one’s body in a certain way. An action is (...)
• 28 Anscombe insists that neither the idea of “the thing to do” nor that of “doing-well”, “living well (...)
• 29 Anscombe fathers her concept of practical truth on Aristotle, hence this Greek word: Nicomachean E (...)

31I suppose the above could be brought in line with Miss Anscombe’s difficult – but still sparking large (four digit) literature and even YouTube films26 – concept of practical truth (see Anscombe, 1999; Elliott, 2016; Campbell, 2022). Very roughly, practical truth in her sense is a truth about a rational agent’s action which the agent brings about not by making her judgment conform to a passive, contemplative, onlooker’s, description of what she (thinks she) is doing, but by acting in agreement with a scheme of action,27 known, assented to, and bona fide (i.e., not as a pretext or excuse, still less a piece of self-deception or downright lie) made by the agent the main motive and efficient cause of the action. This alone means, in Anscombe’s concepts, that the agent is acting intentionally, whatever nonsense or maliciousness her intention might contain. To create practical truth, the agent must, in addition, believe that his action is “the thing to do” by the agent’s own principles,28 something that goes into her conception of “doing well” (εὐπραξία29) by the agent’s own lights – and it indeed is a way of “doing well”. E.g., someone who, seeing a drowning child, decides to save it and does her best to accomplish it, realises the practical truth of “NN has saved a child from drowning”, given that saving drowning children, should they be within one’s reach, is a way of “doing well”.

• 30 I am not very much of an erudite, but it seems to me that deriving Is from Ought has so far enjoye (...)
• 31 When I was five or six, my mother warned me, without a special occasion, not to pull off flies’ wi (...)
• 32 Ms. Grese was tried, sentenced to death for war-crimes, and executed by the British authorities in (...)

33This would be a rather unexpected kind of deducing Is from Ought.30 The Ought is my “formula”, the Is – an action manifesting the practical truth of, e.g., not causing pain to a sentient being for no purpose except that it is fun, as part of “doing well” and the subsequent “doing-well” of the agent. Unfortunately, however, the practical transition from the Ought to that kind of Is needs a link, and this link is the decision (προαίρεσις), which the agent can well fail to take. If so, he typically won’t ruin his “doing-well” at once and forever and he won’t turn to an Unmensch. But… you know full well you are not supposed to pull off flies’ wings and legs or nail bats on the door of your barn just because it gives you kicks, yet, it heck does give you kicks, you give in to this temptation and forego the chance of enhancing your doing-well and ultimately your living-well by resisting a dehumanising – and a silly, at that31 – temptation. This Is is not your growth, even if it is a “growth” by your own criteria, as long as they are well-pondered and have been conscientiously conformed to, but your piecemeal destruction as a human being, your transformation in an Irma Grese (s. footnote 18), a beast or a hyena, like her.32

• 33 ChatGPT (https://chat.openai.com) has suggested to me the following definition: “Based on concepts (...)
• 34 Why “not too long a stretch of time”? For this author the equivalence of the axiom of choice and t (...)

35In Anglo-American philosophy it is often expected that all premises and conclusions of a piece of philosophical analysis should be “intuitive”, whatever that means (I am not sure I know what that means33). As regards my “formula”: it is under no circumstances allowed to inflict suffering on sentient beings just for the sake of (drawing pleasure from) doing so, I must admit that I do not perceive it as particularly “intuitive”, i.e., in the sense of the word “intuitive” which I am evoking here, my “formula” does not present itself to me as an insight I reach upon turning it in over my mind for not too long a stretch of time34 and which I finally find self-evident: “Yes, this is so, now I see it clearly”. Intuitive in this sense are, e.g., the well-known theorem ascribed to Euclid to the effect that there is no largest prime number or the theorem that the sum of the three angles of a triangle is 180 degrees, or perhaps even the Pythagorean theorem. Intuitive insights can, however, be mistaken. It is intuitively true, e.g., that if a bat and a ball cost 1 euros and 10 cents and the bat costs one euro more than the ball, the latter costs 10 cents, is it not? No, it is not. Or, at least, it shouldn’t be.

• 35 In philosophy, this if anything is [something or other] as an ultimate argument is sometimes emplo (...)
• 36 “Insofar as only the presupposition of the basic norm makes it possible to interpret the […] const (...)

36But my “formula” is not like that at all. Assenting to it does not take turning it over in one’s mind. Rather, it forces oneself on one’s mind so irresistibly as to provoke the judgment that if the words “it is not allowed”, “it is prohibited”, or the like should be applicable to anything at all, they must be applicable, first and foremost, to inflicting wanton suffering for its own (pleasure’s) sake. In other words, if inflicting pointless suffering were not something that is not allowed, then we are hard put to imagine what else could. Certainly, one may decide not to attach any meaning (extension) to the deontic predicate “…it is not allowed”, or treat it as a purely emotive pseudo-predicate, without extension or just with the pseudo-extension of the set of things which at any given time in any given person provoke certain feelings expressible as “…it is not allowed”, “You must not…”, “…one can only condemn this” or the like. But if one insists that that predicate should or could have an extension, one feels that, if anything, my acts of pure sadism are an excellent candidate for what to start building this extension from35. Such acts are prohibited if any acts are. In this sense, the “formula” in question looks rather like a Kant-style “transcendental condition of possibility of any being prohibited”, as does the basic norm in Kelsen with respect to all kinds or (legal) validity36, or perhaps like modus ponens, which, if treated as a truth of logic among others, viz. as “(( p→q ) & p) → q)”, makes all reasoning impossible in that it starts an infinite regress wherever one attempts to apply it, and which has to be accepted as a rule of reasoning before any reasoning has been performed (see Carroll, 1995).

• 37 As Pascal puts it: “[T]rop de vérité nous étonne […]. Les premiers principes ont trop d’évidence p (...)
• 38 In Peano (1889, p. 2), it is a definition of “2”. See Russell, 1919, p. 5.

37If anything, my “formula” can appear “over-intuitive”, like “1+1=2”37, of ordinary Peano arithmetic. That 1+1 makes 2 is nothing to be found out after hard thinking and to be incorporated into our body of intuitive arithmetic truths. It is, rather, a very basic arithmetical truth which we must have already known in order to grasp the meaning of the symbols contained in its linguistic expression: “1”, “+”, “2”, and “=”.38

• 39 D. Hume, An Enquiry into the Principles of Morals, Appendix 1 (Hume, 1751/1975, SBN pp. 289-290).
• 40 D. Hume, An Enquiry into the Principles of Morals, Appendix 1 (Hume, 1751/1975, SBN p. 290).

39The former is sufficient (if correct) for establishing a mathematical truth, while the latter is at best a necessary condition of establishing a moral truth (if there is any such, that is). Is it, e.g., true that 2+3=10/2? The mathematician – Hume thinks – reasons thus: “if ten be divided into two parts, of which one has as many units as the other; and if any of these parts be compared to two added to three, it will contain as many units as that”. The mathematician does not need to know everything about natural numbers, their addition, division and whatnot, it is enough that he should know the relevant ones. “Thence [a mathematician] infers some unknown relation, which is dependent on the former”.39 By contrast, someone interested in a question pertaining to the moral aspect of things, e.g., the question if he should assist his brother, or, rather, his benefactor, or if a certain killing was or was not an act of self-defence, would have to know all the facts and relations between the acts he is “deliberating” about. But “after every circumstance, every relation is known, the understanding has no farther room to operate, nor any object on which it could employ itself. The approbation or blame, which then ensues, [is] [the] work […] of the heart; and is not a speculative proposition […] but a […] sentiment. In [arithmetic, e.g.] from known circumstances and relations, we infer some new and unknown. In moral decisions, all the circumstances and relations must be previously known; and the mind, from the contemplation of the whole, feels some new impression of affection or disgust, esteem or contempt, approbation or blame”.40

• 41 This creates the impression, somewhat unfairly supporting Hume’s point, that problems of mathemati (...)
• 42 A model of a mathematical theory is a set of mathematical entities and relations between them the (...)
• 43 Russell and many others held, in fact, that the Peano axioms capture the intuitive concept of a na (...)

40However, the proposition “2+3=10/2” is a poor example, I think, for any numerate person would immediately “see” (have an intuition of) its truth.41 But it can be rigorously deductively inferred, or “proved” in the mathematician’s sense of this word, and the proof would have to start from certain basic premises, called “axioms”, e.g., the Peano axioms of arithmetic. Mathematics being a purely extensional science, it matters little which particular set of propositions would be taken as that of axioms as long as it is equivalent with any other, i.e., as long as the same propositions can be inferred from each of them; however, for those branches of mathematics which have a certain standard, default, “natural model”,42 such as arithmetic as we learn it in elementary school, and use for everyday dealings, mathematicians usually try to find, and establish as axioms, such propositions which express certain obvious, “over-intuitive”, constitutive and essential properties of the objects populating that standard model – in the case of arithmetic, the natural numbers as “standardly”, i.e., naïvely, conceived. Now, a striking property of the natural numbers as all of us know them, is that they are positioned one after the other, in an “Indian file” and there is one and only one natural number that is not followed by any other. This is coded in Peano arithmetic as axiom 8. and axiom 9. (Peano, 1889, p. 2). The axioms describe – not accidentally, but by their very “gist” – to the best of our knowledge, the natural numbers as we know them,43 and at the same time they define them in the sense of the Carnapian “explication” (Carnap, 2008, p. 7.), i.e., they make our intuitions clearer and more precise, apt to function as premises in rigorous deductive derivations. It would be rather pursuing a will-o’-the-wisp to look for something else that does that job “in” or “around” or “about” the things that the axioms describe. It would be, too, rather like asking “Which inherent properties, relations or states of affairs make the set of all points equidistant from a given point – a circle?” None – nothing makes these points a circle, and there is no place or need for any making, either, because being the set of all points equidistant from a given point is what we agreed a circle to be, in the precise language of Cartesian geometry, not arbitrarily, however, but taking our deepest and firmest “over-intuitions” about the circle as a guide. Similarly, for the number 1’s being the successor of no natural number (the only difference being that it takes, in Peano’s arithmetic, another two axioms to explain the notion of a successor).

• 44 D. Hume, An Enquiry into the Principles of Morals, Appendix 1 (Hume, 1751/1975, SBN pp. 289-290).
• 45 Actually, this is not true: Gödel’s first incompleteness theorem implies, inter alia, that Peano a (...)

41The truth of “2+3=10/2” doesn’t reside in any inherent property, or any components thereof, nor in any fact other than itself, for it is a (mathematical) fact that 2+3=10/2. As for relations “[w]hence [a mathematician] infers some unknown relation”,44 viz., 2+3=10/2, they are those which are sufficient for deriving (the truth of) this proposition from (the truth of) the axioms.45 After the mathematician has derived (inferred, proved) from (some selection of) the axioms, and going through whatever intermediary stages might be necessary, the proposition in question, his mind, like the mind of a moral deliberator, will find “No farther room to operate, nor any object on which it could employ itself” and the mathematician will typically be overwhelmed by a mixture of pleasant sentiments, such as the sentiment of victory over the challenge of establishing whether 2+3=10/2, the sentiment of happiness over finding another truth and the like. Unless an anankastic neurotic, the mathematician won’t go on asking “Well, I have, indeed, proved that 2+3=10/2 in Peano arithmetic and with its methods exclusively, and my proof doesn’t appear flawed, but does it really mean that 2+3=10/2 is true, I mean, true in any model of and preferably the standard model of PA? Shouldn’t I be rather looking, in 2+3, for an inherent property that makes it equal 10/2, or perhaps the other way around? But however I anatomize both 2+3 and 10/2 I can’t find any such property…” Still less will the mathematician raise questions like “OK, the deduction was all right but are the things that the axioms describe really the natural numbers? Each of these thingumajigs has a direct successor, that one that stands directly after it and the one called ‘1’ is no successor and no two different of them have the same successor, this looks very much in common with the natural numbers as we have known them from times immemorial, but… shouldn’t I rather be looking for a more direct witness, an inherent property of what those axioms talk about, a natural-numberhood purely and simply?”

• 46 This is not exact, see the previous footnote, but the nature of the present paper does not admit o (...)

44Truth in arithmetic can be established by means of logical deduction from the axioms.46 From the deontic axioms, such as my “formula” – and there would be much more of them than there are mathematical axioms in any branch of mathematics – various propositions will be derivable logically. However, more importantly, given that deontics, unlike mathematics, is an empirical branch of study, it is to be wished (and I hope, rather to be expected) that it should be possible to establish the truth or falsity of certain norms appealing to the fact that they are related to my acts of pure sadism causally, motivationally or in another empirical fashion, not (just) logically. More simply: It is in relation to – among other things – their empirical: causal, motivational or what have you connections to acts of pure sadism that certain (types of) acts can, or perhaps should, be considered rightly prohibited, or deserving being prohibited – although not always, and probably not even most of the time, i.e., unconditionally. Acts of pure sadism in my sense seldom give rise to other acts deserving being forbidden independently of any circumstances, and a pure sadist may become an inexorably effective, ruthless, no-quarter soldier or mercenary, but under the circumstances of war, being so will be anything but undesirable and forbidden – quite to the contrary!

• 47 If it is not true (as I suspect it is) that all pornography is violent by definition.

45Other examples may be: Doing one’s duty as an executioner or a prison guard or a policeman with a certain “zeal” similar to that which a good pianist, say, displays while performing? Vandalism (this author’s favourite)? Watching/making/distributing certain kinds of films, such as (violent) pornography,47 horror, “snuff” or “crush”? Engaging in kinds of competition which produce, perhaps solely as a side-effect, a desire to triumph over the outcompeted for the only (and wanton) purpose of enjoying the triumph? Or simple indifference to evil acts: “These girls are setting a hedgehog ablaze? Let’em, why should I care, me of all people? Besides, it’s better they take out their frustration on animals than on humans, innit?”.

• 48 “Dort wo man Bücher verbrennt, verbrennt man auch am Ende Menschen” (Heine, 1823, p. 148). The not (...)
• 49 Today: Alten Graben 5, 78462 Constance, Germany.
• 50 See: Cat burning (n.d.). These orgies of antifeline cruelty are usually believed to have taken pla (...)

46To close with an (intuitive, as I hope) example: as Heine put it, those who burn books will end up burning people.48 Now, burning people may not be pure sadism in my sense, because some (top-rank) burners may sincerely (though for wrong reasons) believe their activity beneficial to the humankind or a part of it, as doubtlessly did the legendary elderly lady who, reportedly, contributed a faggot to the stake on which John Hus was about to be burnt, and earned, not Hus’ curse, but his compliment (sort of): “Oh, holy ingenuousness!” (sancta simplicitas!). But for most onlookers – if the execution takes place in public, e.g., in Smithfield, Place de Grève or the meadow Brühl extra muros of Constance49 – it is just great fun to watch someone die this horrible death, especially if they had been told by the “relevant authority” that the person was a “heretic”, the details of which they neither know nor are interested in. I suppose this kind of entertainment can, in some individuals (probably not very few, though this would have to be borne out by relevant empirical research) generate a gusto for watching such grisly spectacles and even for staging them themselves – first on books, then on animals, still just for fun50 and, for even more fun – no weird pretexts such as Wycliffe & realism vs. Gerson & nominalism required – finally on human beings.

• 51 D. Hume, Enquiry Concerning Human Understanding, part III, section 12.34 (Hume, 1748/1975, SBN p. (...)
• 52 For a conspicuous example of empirical considerations to the effect that something should be penal (...)

47The practical conclusion to be drawn appears to be, at first, to declare burning books as such, no matter what their contents may be, in all kinds of ways reprehensible, good candidate for the title of crime and/or to require from any would-be organisers of a book-burning event official permission from the relevant authority. However, it is rather difficult to imagine David Hume as one of those sinister individuals who start by burning books and end up burning human beings; and yet, he did explicitly encourage burning books,51 not all of them, to be sure. No doubt, there are books which – from the universalist-humanist point of view – deserve being “consigned to the flames”, or at least being made inaccessible to general public, no less, if not more, than those which Hume detested: Malleus Maleficiarum, Mein Kampf, Dialectical and Historical Materialism and, perhaps, most novels from the literary school known as nouveau roman français. So, even if Heine is right and burning books can “lead to”52 burning people, prohibiting the former does not need to be unconditional.

• 53 Famous examples: the fifth axiom of Euclid and the two non-Euclidean geometries resulting, Bolyai- (...)

48In arithmetic, and in every branch of mathematics based on an axiomatic system, some truths (typically, a majority) are also conditional, in the sense that they hold under certain conditions (e.g., if a and b are both odd, a+b is even) and ultimately under the conditions articulated in the axioms (postulates), these being assumed true, either because they jointly express the “essence” of what we (think we) know about the corresponding mathematical beings, e.g., our good ole’ friends natural numbers or because they are (seem to be) consistent. In the latter case, mathematicians can, if the axioms do not seem to express the essence of anything known and familiar since times immemorial, themselves construct something whose essence the axioms can be taken to capture, and that from the constants of the theory itself! We philosophers do not have such freedom; acts and omissions to be praised, condemned or neutral are there for us to face and evaluate correctly. Mathematicians have the privilege of being allowed also to ask what happens if an axiom is left out from a theory.53 In deontics, this may have a heuristic sense at best.

• 54 Purely philosophical ones obviously too, e.g., if this or that system of metaethics should be adop (...)
• 55 In Ivo Andrić’s novel The Bridge on The Drina there is a very plastic episode illustrating this.

49In deontics, a more important question would pertain to what has to be added to the sorts of acts covered by my “formula” so as to obtain an as-exhaustive-as-can-be axiomatics of “things we must never do”. The answer to this question will depend not on logic alone, but on many empirical, probabilistic and stochastic considerations54 – which is why it is so difficult to be a deontic cognitivist. Does watching public executions always awake a bloodthirsty beast within (some of) us? After all, they public executions were introduced not as a type of pastime (unlike the Roman ludi circenses) but as a means of, among other things, discouraging acts like those considered done by the poor sucker who’s got to ascend the scaffold or the validity of law in the mind of the watchers, the “positive Generalprävention” of the Germans, and how shall we legislate if the former effect (entertaining) turns out to have more weight and to be richer in consequences than the latter two? Should we ban them regardless, just because in some tender souls, no matter how few, they might generate or reinforce the inclination to acts of pure sadism? If we should, maybe we should abolish death penalty in general, or indeed any punishment whatsoever, because individuals administering punishment may develop a tendency to draw satisfaction from whatever suffering they may be asked to visit on their “customers”, no matter if these have been convincingly proven deserving the punishment. Other professions may not be safe, either: the cremation of human remains doesn’t need, and presumably seldom does, to correspond to, or breed, any sadist inclinations in those who do the job; but see the famous novel Spalovač mrtvol by Ladislav Fuks and the corresponding film by Juraj Herz, The Cremator. In the Roman Catholic Church incineration is even the preferred disposal method of liturgical objects no longer usable. Here again, we should be suspicious of individuals who seem to fill the function with a certain overzealous meticulousness.55 Maybe there should, or maybe there even are, in some countries, laws against employing certain individuals for such functions.

• 56 We still don’t know what exactly makes for suffering done to others for no reason so pleasant (som (...)

51There are so many ways of becoming and being ὅλως κακός, generally vicious; the question arises, which of them are reducible to which, a question analogous to that which pertains to the axioms of any system of mathematics. In this paper, I have been busying myself with just one of these ways, conceivably the most conspicuous one. And perhaps, too, the most mysterious56 – the mystery here being that of evil.