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Kelsen, in what I think his most difficult, but most important work — published posthumouslyWhether the General Theory of Norms referred to as Kelsen’s ‘swan song’ by its translator Michael Hartney (ix) would remain mute or fly like a flamingo, Kelsen, before his death, left open, see the introduction to the Allgemeine Theorie der Normen (n 3), iii.⁶⁾ — asks whether “[…] the logical thought-process of the syllogism occurs in morality and in law, […] whether the relation between a general moral or legal norm and the individual norm by which it is applied to a concrete case has the character of a logical inference, that is, whether the validity of this individual norm is the result of a logical inference,” in other words, whether “[…] the syllogism of traditional propositional logic is applicable — directly or indirectly — to norms,”Kelsen (n 1) 226.⁷⁾ that is, whether “[…] there exists a normative syllogism analogous to the theoretical syllogism”Ibid. 231.⁸⁾.

2. Kelsen’s Answer: “[T]he validity of the individual norm cannot follow logically […] from [that of a general norm].”Ibid. 234.⁹⁾

In answering this innocent enough looking question, Kelsen comes to the rather strange conclusion that “[t]he validity of the individual norm cannot follow from that of the general norm as the truth of an individual statement follows from that of a general statement”Ibid. 238.¹⁰⁾. What! Why? Well, Kelsen compares a statement’s truth with a norm’s validity“By ‘validity’ we mean the specific existence of norms. To say that a norm is valid, is to say that we assume its existence or — what amounts to the same thing — we assume that it has ‘binding force’ for those whose behavior it regulates.” See Kelsen Hans, General Theory of Law and State (trans. by Anders Wedberg, Harvard University Press 1945) 30.¹¹⁾ and claims that while the truth of an individual statement is implied by that of a general statement, the validity of an individual norm isn’t implied by that of a general norm — a difference I’m going to questionCf. comments about the similarity between statements and norms at footnote no. 35.¹²⁾ — but, let’s build his argument step-by-step, before pointing out where, I think, it can and should be mended.

2.1 Kelsen’s ‘Theoretical Syllogism’

Kelsen begins his argument by explaining the syllogism of propositional logic, what he calls the ‘theoretical syllogism’ as “[…] a sequence of statements, in which the truth of […] one statement — the conclusion — is inferred from the truth of […] two other statements — the major and minor premisses”Kelsen (n 1) 228.¹³⁾. Since Kelsen is concerned “[…] particularly with the inference from the universal to the particular, […] from the truth of a general statement to that of an individual statement,” he goes on to point out that “[…] the minor premiss, is the statement that the condition specified generally in the […] major premiss[…] obtains individually,” and gives the usual example:Ibid. 228; for understanding the syllogism this example is insufficient, see n 82.¹⁴⁾

All humansFor consistency’s sake, humans, like flamingos (see footnote no. 114), can be ‘bunte Vögel’ too. ¹⁵⁾ are mortal.

Socrates is human.                                                                                                                (1)

├ Socrates is mortal.

Logic is about consistencyHodges Wilfrid, Logic. An Introduction to Elementary Logic (2^nd ed., Penguin Books 2001) 1.¹⁶⁾ or the validity of arguments what — warning!An argument is valid, if it’s consistent; a norm is valid, if she (?) is binding.¹⁷⁾ — isn’t to be confused with the validity of norms. According to the logic textbookKelsen in a footnote to page 182 of his Allgemeine Theorie der Normen (n 3) cites philosopher Stebbing Susan Lizzie, A Modern Elementary Logic (Methuen & Co 1957).¹⁸⁾ cited by Kelsen “[a]n argument is valid if […] the premisses logically imply the conclusion”See the 1952 revised and 1961 reprinted 5^th edition of that textbook (n 18), 6.¹⁹⁾. It reads: “If the conclusion does follow from the premisses, the argument is valid; if the conclusion does not follow from the premisses the argument is invalid.”Ibid. 9.²⁰⁾ That is, “[v]alidity […] is not dependent upon truth,”Ibid. 8.²¹⁾ but “[…] depends entirely upon the logical form of the argument”Ibid. 9.²²⁾. The above argument (1) has the form of modus ponens:At least in simplified form; being a quantified statement, its major premiss ‘All humans are mortal.’ would have to be expressed not in propositional, but first order predicate logic as ‘∀x (Hx → Mx)’, read: for all objects ‘x’, if ‘x’ is human, then ‘x’ is mortal, what, Socrates ‘s’ being such an object ‘x’, we would have to ‘instantiate’ to ‘Hs → Ms’, read: if ‘s’ is human, then ‘s’ is mortal, before we could argue that ‘Hs→Ms, Hs ├ Ms’.²³⁾

A → B, A ├ B                                                                                                                        (2)

which is a valid form or rule of inference, because as the cited logic textbook points out: “[…] the premisses cannot be true and the conclusion false,” or what is the same “[…] the truth of the premisses necessitates the truth of the conclusion,”Ibid. 6.²⁴⁾ what can be proved with help of a truth table:The argument ‘A → B, A ├ B’ is valid, if its premisses ‘A → B’ and ‘A’ can’t be true and its conclusion ‘B’ false (see n 24), that is, if ‘((A → B) ∧ A) → B’ is a tautology. Truth table (1) proves ‘((A → B) ∧ A) → B’ is a tautology, that is, true under all possible combinations of truth values for ‘A’ and ‘B’ (rows 1–4), hence it’s always or vacuously true, that is, its truth follows from nothing, but its form: ‘├ ((A → B}) ∧ A) → B’.²⁵⁾

Table 1: Truth table for validity of modus ponens

That is, every argument with the logical form of modus ponens (2) — even if one of its premisses should be false — is a valid argument.As truth table (1) shows ‘((A → B) ∧ A) → B’ is true, that is, the column below material implication ‘→’ shows but ‘T’s for ‘true’, under all possible combinations of truth values for ‘A’ and ‘B’ (rows 1–4). ‘((A → B) ∧ A) → B’ is true if both of its premisses ‘A → B’ and ‘A’ are true (row 1) and it’s true if one of its premisses is false (rows 2–4).²⁶⁾ What is more, if the premisses of such a valid argument are true, its conclusions must be true too.Whenever premisses ‘A → B’ and ‘A’ are true (only row 1), so is conclusion ‘B’ (row 1). That is, there are no rows where the premisses are true and the conclusion is false.²⁷⁾ Which is exactly what the passage from the logic textbook says that Kelsen, in a footnote, cites to undergird his explanation of the ‘theoretical syllogism’: “We can know our conclusions to be true only when we know both [!] that the premisses are true and [!] that they imply the conclusion.”Stebbing Susan Lizzie, cited in: Kelsen (n 1) 229.²⁸⁾ Kelsen points out that “[t]o say that the truth of the conclusion is ‘inferred’ from [or implied by] that of the premisses is simply to say that the truth of the conclusion is implicit [!] in that of the premisses,”Ibid. 229.²⁹⁾ in order to, slightly reworded, restate that “[i]f the premisses are true and if the conclusion is implicit [!] in the premisses, then the conclusion is true”. Referring to John Stuart Mill’s ‘System of Logic’,Mill John Stuart, A System of Logic (London 1898).³⁰⁾ Kelsen also points out that “[…] a[ ] [logical] inference is not a thought-process which leads to a new truth; rather it makes explicit a truth already implicit in the truth of the premisses”Kelsen (n 1) 230.³¹⁾.

2.2 Kelsen’s Supposedly ‘Normative Syllogism’

After his inspection of the ‘theoretical syllogism’ Kelsen switches to its supposed ‘normative’ analogue and explains that, like the theoretical, “[a] ‘normative inference from the general to the particular’ is an inference […]”, where the validity of one norm, the conclusion, may — what Kelsen denies — be inferred from the validity of a norm and the truth of a statement,Citing from both Immanuel Kant’s ‘Critique of Pure Reason’ (ibid. 79) and David Hume’s ‘Treatise of Human Nature’ (ibid. 86), Kelsen concludes that “[…] an Ought cannot be derived from an Is” (ibid. 86). However, if our argument’s major premise is a norm, why shouldn’t we be able to derive another norm as the conclusion of our argument?³²⁾ the major and minor premisses. The major premiss, Kelsen points out, is “[…] a general hypothetical norm which decrees some generally specified behaviour to be obligatory under generally specified conditions […]”, the minor premiss “[…] a statement asserting the individual existence of the condition specified in the major premiss […]”, and the conclusion “[…] an individual [categorical] norm which decrees individually that the behaviour specified generally in the major premiss is obligatory.”Kelsen (n 1) 231.³³⁾ Kelsen provides the example:Ibid. 231.³⁴⁾

If someone makes a promise, he is to keep it.

Maier promised Schulze to pay him 1000.                                                                          (3)

├ Maier is to pay Schulze 1000.

Kelsen then points out some, I think rather superficial, differences between the theoretical and normative syllogism. First, while in the theoretical syllogism (1) “[t]he two premisses have the same logical character: both are statements,” in the normative syllogism (3) “[…] the two premisses have different logical characters: the major premiss is a general norm, while the minor premiss is a statement”Ibid. 232.³⁵⁾. Second, and related, while the theoretical syllogism is concerned with the truth of statements about properties of things,Of course, persons — see Bentham, ignore Kant — are not only, but also things.³⁶⁾ the normative syllogism is concerned with the validity or — what is problematic, but for Kelsen the same“That a norm is ‘valid’ means that it exists. A norm which is not ‘valid’ is not a norm since it is not an existing norm.” See Kelsen (n 1) 28; and Kelsen (n 11).³⁷⁾ — existence of norms for the behaviour of persons.According to Kelsen’s (n 1) General Theory of Norms “[…] a statement […] is true or false,” (ibid. 42) (emphasis removed) and “[…] nothing more than a proposition […]” (ibid. 152) “[…] about things or events,” (ibid. 129), in contrast “[a] norm is valid for certain individuals, for a certain area, and for a certain time,” (ibid. 28) and “[its] object […] is the behaviour of a being endowed with reason and will, that is […] human behaviour” (ibid. 89).³⁸⁾ According to Kelsen, “[…] there is no […] analogy between the truth of a statement and the validity of a norm,”Ibid. 175.³⁹⁾ because while “[…] the truth of a statement is not conditional on the act by which it is made, […] the validity or existence of a norm is conditional on the act by which it is posited”Ibid. 170.⁴⁰⁾. Hence Kelsen’s positivist credo: “No imperative without an imperator, no norm without a norm-positing authority[.]”Ibid. 234.⁴¹⁾ That is, while “[t]he statement ‘The earth revolves around the sun’ is true — if it is true [!] — whether or not anyone actually thinks it or utters it,”Ibid. 229.⁴²⁾ the norm “[t]hat murder is to be punished by death is valid only if this norm is posited by the legislator”Ibid. 171.⁴³⁾. Which is also why, I think, Kelsen points out that “[t]he truth of a statement cannot be repealed by derogation, as can the validity of a norm”Ibid. 171; for more, also cf. Kelsen Hans, ‘Derogation’ in Ota Weinberger (ed.), Essays in Legal and Moral Philosophy (trans. by Peter Heath, Springer 1973) 261.⁴⁴⁾. However, think of the retraction not of a statement’s truth, but what could be its ‘existence’ or ‘validity’.Statements are not only propositions, but also assertions of propositions, which is why Bulygin (n 5) 146 says: “[T]here are two opposed views on the nature of norms […] the hyletic and the expressive conception of norms.” And adds that “[…] the controversy between Kelsen and Weinberger [n 5] fits admirably well into these two categories,” outlined in Alchourrón Carlos E., Bulygin Eugenio, ‘The Expressive Conception of Norms’ in Hilpinen Risto (ed.), New Studies in Deontic Logic (Springer 1981) 95. In Weinberger’s hyletic conception norms, like propositions, are abstract normative sentences which can be obligatory, forbidden or permitted (Op, O⌐p, Pp) (ibid. 96). In Kelsen’s expressive conception norms are commands (!p), that is, like assertions, results of speech acts (ibid. 97). While in the hyletic conception normative sentences can be negated (Op and O⌐p) in the expressive conception norms can only be promulgated and derogated (!p and ¡p) (ibid. 105). Bulygin (n 5) 148 concludes: “The expressive convention of norms precludes the very possibility of a logic of norms: if normativity consists in a certain use of language and norms are expressions of illocutionary acts, then there are no logical relations between norms.”⁴⁵⁾ Statements, I think, are fraught with the very same or similar problems as norms, only, unless you believe in God, what makes them true is not a legislator, but reality herself.Roman Goddess Terra Mater, ‘Mother Earth’, like Justitia (see footnote no. 103), is a woman.⁴⁶⁾ Which is also why Kelsen seems (!) to speak in tongues or think in circles when he says that “[a] statement […] is true — if it is true […]”See n 42, that is, Kelsen (n 1) 229.⁴⁷⁾. ‘No truth without reality,’ one could say.According to Kelsen himself “[…] a statement is true[,] if it agrees […] with the reality it is about” (ibid. 175); similarly Karl Popper who, in the talk on ‘Die Logik der Sozialwissenschaften’ cited by Kelsen (ibid. 191) and published in Adorno Theodor W. et al. (ed.), Der Positivismusstreit in der deutschen Soziologie (Luchterhand 1969), explains that “[w]ir nennen eine Aussage ‘wahr’, wenn sie mit den Tatsachen übereinstimmt oder den Tatsachen entspricht oder wenn die Dinge so sind, wie die Aussage sie darstellt,” (ibid. 117) what he calls the ‘absolute[r] oder objektive[r] Wahrheitsbegriff’ as, he points out, it has been ‘rehabilitated’ by Alfred Tarski⁴⁹ (ibid. 117), a Polish logician and mathematician who in an article on ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ (1935) Studia Philosophica 261 translated from his dissertation writes: “[E]ine wahre Aussage ist eine Aussage, welche besagt, dass die Sachen sich so und so verhalten, und die Sachen verhalten sich eben so und so,” (ibid. 268) and explains that “[…] ‘es schneit’ ist eine wahre Aussage dann und nur dann, wenn es schneit” (ibid. 269).^48),Tarski, born Tajtelbaum in Warsaw, was Jewish and emigrated to the United States where, like Kelsen, he first taught at Harvard and then from 1942 until his retirement at the University of Berkeley in California; for his biography read Feferman Anita Burdman, Feferman Solomon, Alfred Tarski. Life and Logic (Cambridge University Press 2004).⁴⁹⁾ What the legislator is to the validity of norms, reality is to the truth of statements. A yardstick to be measured against.According to Kelsen, morality, although separate from, for the law is a ‘yardstick’, see Hans Kelsen, Pure Theory of Law (trans. by Max Knight, University of California Press 1967) 66.⁵⁰⁾ Only, whereas in case of reality you got one stick, in case of law and morality — if like Kelsen you’re not a jusnaturalist, but a legal positivist — many. Which, unlike with reality, makes not only your view of,According to Einstein’s theory of ‘special relativity’ — see Einstein Albert, ‘Zur Elektrodynamik bewegter Körper’ (1905) 17 Annalen der Physik 891 — not only space is relative, because “[e]in starrer Körper, welcher in ruhendem Zustande ausgemessen die Gestalt einer Kugel hat, hat […] in bewegtem Zustande — vom ruhenden System aus betrachtet — die Gestalt eines Rotationsellipsoides […],” (see ibid. 903) but time is relative too, since “[s]ind in den Punkten A und B von [Koordinatensystem] K ruhende, im ruhenden System betrachtet synchron gehende Uhren vorhanden, und bewegt man die Uhr in A mit der Geschwindigkeit v auf der Verbindungslinie nach B, so gehen nach Ankunft dieser Uhr in B die beiden Uhren nicht mehr synchron, sondern die von A nach B bewegte Uhr geht gegenüber der von Anfang an in B befindlichen […] nach” (see ibid. 904).⁵¹⁾ but law and morality themselves relativistic.See Kelsen (n 50) 67 who says: “[R]elative morals cannot […] provide an absolute standard for the evaluation of a positive legal order. […] But this does not mean that there is no such standard — every moral system can serve as such.”⁵²⁾ According to Kelsen, “[j]ust as the existence of a fact cannot follow logically from that of another fact — the ways of thought [Denken] are not the ways of existence [Sein] — so the existence of a norm […] cannot follow logically from the existence of another norm”Kelsen (n 1) 233.⁵³⁾. However, only because from the truth of a statement the existence of a fact can’t follow — that being the privilege of reality — this doesn’t mean that the supposed truth of one statement can’t imply, not that another statement is, but should be true too. Similarly, only because from the existence or validity of a norm that of another norm can’t follow — that being the privilege of the legislator or judge — this doesn’t mean that the supposed validity of one norm can’t imply, not that another norm is, but should be valid as well. Logic, remember, is about consistency or the validity of arguments, it says nothing about the truth of the statements and the validity of the norms in their premisses and conclusions.All it says, is that if (1) the argument is valid and (2) statement and norm in its antecedent true and valid, then (3) the norm in its consequent must be valid, see footnote no. 18 f.⁵⁴⁾ Be that as it may, for Kelsen, I disagree, there can be no analogy between the truth of a statement and the validity of a norm and with that we get into his main argument. Hear, hear!

Remember that, according to Kelsen, the validity of an individual norm — the conclusion — can only follow from the validity of the general norm and the truth of a statement — the major and minor premiss — if it is implicit in the validity of this general norm and the truth of that statement.See Kelsen’s way of rewording the classic ‘implied by’ to ‘implicit in’ at Kelsen (n 28).⁵⁵⁾ Kelsen, however, claims: “[A]bove all, the validity of the individual norm cannot be implicit [!] in the validity of the general norm and the truth of the statement, because the validity of a norm is conditional upon the act of will [!] of which it is the meaning,” and “[s]ince an act of will of which the individual norm is the meaning must intervene between the validity of the general norm and that of the corresponding individual norm, the validity of the individual norm cannot follow logically — i.e. by a thought-process — as the truth of an individual statement follows from that of the corresponding general statement”Ibid. 234 (emphasis added).⁵⁶⁾. That is, Kelsen claims that the “[…] individual norm […] must — like any other positiveAccording to Kelsen’s ‘legal and ethical positivism’, a positive norm is “[a] norm posited by an act of will occurring in reality,” (ibid. 4) and all norms “[are] posited by […] human acts of will” (ibid. 4). According to ‘natural law theory’, Kelsen points out, “[…] norms do not have to be posited by any act in order to be valid. For […] there are norms which are immediately valid […] since they are given in reality or ‘nature’.” (Ibid. 4 f.)⁵⁷⁾ norm — be the meaning of a real act of will distinct from the real act of will whose meaning is the general norm to which the individual norm corresponds”Ibid. 235.⁵⁸⁾. According to Kelsen these “[…] are two wholly different acts of will”Ibid. 236.⁵⁹⁾. That is, according to Kelsen “[t]he relation between the general norm and the corresponding individual norm is not an immediate relation: it is only a mediate relation, mediated by the act of will of which the individual norm is the meaning”Ibid. 234.⁶⁰⁾. But why?

Kelsen explains that “[t]he general norms posited by the legislator normally concern future behaviour which the legislator does not, and cannot foresee”Ibid. 238.⁶¹⁾. He points out that “[…] it would be an absurd fiction to suppose that in the legislator’s act of will of which the general norm is the meaning, there are already implicit all the possible acts of will whose meanings are the individual norms corresponding to the general norm”Ibid. 238.⁶²⁾. “The authority […],” Kelsen says, “[…] which posits the general norm […], that all people are to keep their promises, cannot will that Maier is to keep his promise to Schulze to pay him 1000, since it cannot know beforehand that at some point in the future someone called Maier will promise someone called Schulze to pay him 1000,” and adds: “[One] cannot will that of which [one] knows nothing[.]”Ibid. 236.⁶³⁾ But how then, Kelsens asks, “[…] does the positing of [the] individual norm corresponding to the general norm […] come about?”Ibid. 239.⁶⁴⁾

Kelsen explains that “[t]he positing of the individual norm […] presupposes the recognition of the applicable general norm on the part of the court which is competent to apply it,” because “[…] the act of will whose meaning is the individual legal norm […] can occur only as a result of the recognition of the validity of the general norm”Ibid. 239 (emphasis added).⁶⁵⁾. A judge can, Kelsen points out, “[…] recogniz[e] the validity of the general norm,” but can also “[…] for some reason or other — for example, because he considers it unjust [!]It’s surprising, how similar Kelsen’s legal positivist position is to that of jusnaturalists, difference being that, according to Kelsen, there is no one ‘true’, objective morality.⁶⁶⁾ to apply the general norm to the concrete case — not recognize its validity for the present case and so not posit the individual norm”Ibid. 239.⁶⁷⁾. In this respect, Kelsen adds, “[…] there is no difference between morality and law,”Ibid. 239.⁶⁸⁾ and points out that “[…] in the fact that this recognition of the validity of the general norm is a necessary condition for the positing of the corresponding individual norm,” consists “[t]he so-called autonomy of morality”Ibid. 237 (emphasis added).⁶⁹⁾. According to Kelsen, “[i]f in a concrete case, for some reason or other, the recognition of the validity of the general norm […] and consequently the positing of the corresponding individual norm does not result in any act of will on the part of the individual, the individual norm does not become valid and cannot become valid by means of the logical thought-process of an inference”Ibid. 237.⁷⁰⁾.

Kelsen, who distinguishes between morality and moral science, respectively law and legal science,According to Kelsen, “[i]t is essential to distinguish between a norm and a statement about […] a norm […], between normative science and the object of its cognition […], between ethics and morality […], and between legal science and law” (ibid. 154).⁷¹⁾ concludes that, while “[…] it is obvious and unproblematic that […] [logical] principles are applicable to [legal thinking]” as far as moral and legal science are concerned,Ibid. 245.⁷²⁾ because “[l]egal thinking cannot create or repeal norms […] [and] cannot make any legal norm valid or invalid,”Ibid. 245.⁷³⁾ as far as morality and law are concerned, “[…] there is no justification for the assumption that there can be normative syllogisms in which the validity of an individual categorical norm follows logically from the validity of the general hypothetical norm to which it corresponds”Ibid. 252.⁷⁴⁾. “[C]ases concerned with the making-valid and the making-invalid of norms,” Kelsen says, “[…] cannot be effected by thinking, not even ‘legal’ thinking. [In this sense] [t]here can be no such thing as ‘legal thinking’[.]”Ibid. 245.⁷⁵⁾ I doubt that.

3. Another Resolution of Kelsen’s Conundrum: of Logic in Law with Autonomy of MoralityOf course, the argument is also for ‘logic in morality with the autonomy of law’.⁷⁶⁾

I believe there is such a thing as legal reasoning, that the syllogism of traditional propositional logic is applicable to norms and that the validity of an individual norm can follow logically from the validity of the corresponding general norm. In other words, I think Kelsen is wrong. But, Kelsen is right I think, because like him I believe in the autonomy of morality, that the recognition of the general norm’s validity is a necessary condition for the validity of the corresponding individual norm — and vice versa.That is, the general norm is valid, if its individual norms are valid; and individual norms are valid, if the general norm is valid; cf. the concept of ‘reflective equilibrium’ (see footnote no. 107) which looks circular, but isn’t, because in law — just like reality in science — morality can serve as a separate standard for the evaluation of an individual norm’s validity.⁷⁷⁾ In the following, I propose an alternative interpretation of Kelsen’s argument that argues for the applicability of the syllogism of traditional propositional logic to norms and the need for recognition of the validity of these norms. That is, I argue for legal reasoning without giving up the autonomy of morality.

3.1 A Problem with Kelsen’s ‘Theoretical Syllogism’

To begin with, I think, Kelsen’s understanding of the ‘theoretical syllogism’ is problematic. It is riddled with some of the very same problemsSee the comments about the similarity of statements and norms at footnote no. 35.⁷⁸⁾ and sets an unrealistically high bar for a possible ‘normative syllogism’. According to Kelsen, “[…] the validity of the individual norm is not implicit in that of the general norm as the truth of an individual statement is implicit in that of a general statement”Ibid. 238 f.⁷⁹⁾. But, how is the truth of an individual statement implicit in the truth of the corresponding general statement? All logic claims, remember the textbook cited by Kelsen, is that “[w]e can know our conclusions to be true only when we know both that the premisses are true and they imply the conclusion”Ibid. 229.⁸⁰⁾. In other words, if an argument is valid — that is, of valid logical form — and both of its premisses are true, then its conclusion must be true too. In the ‘nice’ example provided by Kelsen:

All humans are mortal.

Socrates is human.                                                                                                                (4)

├ Socrates is mortal.

the argument has the valid logical form of modus ponens (2) and both major and minor premiss are true, therefore the conclusion must be and is true — most likely we won’t encounter any immortal human beingsWe can’t be sure: heed the cautionary tale of the ‘inductivist turkey’, or the chickens who “[…] expect food when they see the person who usually feeds them,” but at last “[t]he [wo]man who has fed the chicken every day throughout its life […] wrings its neck instead[.]” See Russell Bertrand, The Problems of Philosophy (Henry Holt & Co 1912) 98.⁸¹⁾ — and all is hunky-dory. However, let’s see what happens in the less congenial example provided by Kelsen’s fellow Austrian philosopher of science Karl Popper:The example is used by Popper Karl, Logik der Forschung. Zur Erkenntnistheorie der Modernen Naturwissenschaft (Springer 1935) 1, who says: “Bekanntlich berechtigen uns noch so viele Beobachtungen von weißen Schwänen nicht zu dem Satz, daß alle Schwäne weiß sind,” and before that by Mill (n 30) 20, who writes: “That all swans are white, was a uniform experience down to the discovery of Australia.”⁸²⁾

All swans are white.

This bird is a swan.                                                                                                              (5)

This bird is white.

That argument also has the valid logical form of modus ponens (2) — hence it is a valid argument — but, since Down UnderPopper, born to parents of Jewish descent in Vienna, in 1937 emigrated to New Zealand and then England where until his retirement he taught at the University of London, see Popper Karl, Unended Quest. An Intellectual Autobiography (Routledge 1992).⁸³⁾ some swans happen to be black, its major premiss is false. And, because its major premiss is false, even though the argument is valid, we cannot know what its conclusion must be. It could be true, it could be false.See truth table (1) where if either of the argument’s two premisses ‘A → B’ and ‘B’ is false (rows 2–4), its conclusion ‘B’ can be either true (row 3) or false (rows 2 and 4).⁸⁴⁾ In case we encounter not a mute European ‘cygnus olor’, but a more vocal Australian ‘cygnus atratus’, both can get pretty aggressive,All generalizations are in danger of being overbroad and causing bias and prejudice.⁸⁵⁾ the conclusion is, quite evidently,Evidence, that the conclusion is false, is what makes us question our premisses.⁸⁶⁾ false. And, since the conclusion is false, according to other forms or rules of inference like modus tollens (7) (cf. appendix), one of the premisses must be false too, either the bird is not a swan or not all swans are white.Either ‘A → B, ⌐B ├ ⌐A’ or ‘A, ⌐B├ ⌐(A → B)’, but something must give, see footnote 99 and the following.⁸⁷⁾ Logic is nice, very nice, but all it does, is ensure consistency. It can tell us that if an argument is valid and its premisses true, the conclusion must (!) be true too; and that if an argument is valid and its conclusion false, one of the premisses must (!) be false as well. It can’t tell us whether and whichWhat is known as the ‘Duhem-Quine Thesis’ after French physicist and philosopher of science Pierre Duhem, La Théoirie Physique. Son Objet, Sa Structure (Librairie Philosophique J. Vrin 2015 [1906]) 259 f, according to whom “[u]n physicien [qui] se propose de démontrer l’inexactitude d’une proposition […] ne se borne pas à faire usage de la proposition en litige; il emploie encore tout un ensemble de théories[.] […] si le phénomène prévu ne se produit pas, ce n’est pas la proposition litigieuse seule qui est mise en défaut, c’est tout l’échafaudage théorique dont le physicien a fait usage; la seule chose que nous apprenne l’expérience, c’est que, parmi toutes les propositions qui ont servie à prévoir ce phénomène et à constater qu’il ne se produisait pas, il y a au moins une erreur; mais où gît cette erreur, c’est qu’elle nous dit pas,” and American logician Willard Van Orman Quine who helped Alfred Tarski (n 49) get to the United States, and in his Pursuit of Truth (Harvard University Press 1992) 13 f. explains: “In order to deduce an observation categorical from a given hypothesis, we may have to enlist the aid of other theoretical sentences and of many common sense platitudes that go without saying, and perhaps the aid even of arithmetic and other parts of mathematics. In that situation, the falsity of the observation categorical does not conclusively refute the hypothesis. What it refutes is the conjunction of sentences that was needed to imply the observation categorical. In order to retract that conjunction we do not have to retract the hypothesis in question; we could retract some other sentence of the conjunction instead.”⁸⁸⁾ premisses and conclusion are (!) true or false.See also Harman Gilbert, Change in View. Principles of Reasoning (The MIT Press 1986) 5 who, as an anonymous reviewer has pointed out — owe you coffee and croissant, thank you! — distinguishes on the one hand reasoning like modus ponens with both beliefs (chapters 1–7) and intentions (chapters 8–9) from, on the other hand, argument with principles of belief revision like for example the ‘get back principle’ (ibid. 58), ‘clutter avoidance’ (ibid. 55), ‘minimal change’ (ibid. 59) and ‘logical closure’ (ibid. 12): “[T]here is something wrong with one's beliefs [or intentions, cf. ibid. 82 f.] if there is a proposition logically implied by them which one does not already believe. In that case one should either add the implied proposition to one’s beliefs or give up on one of the implying beliefs.” (Ibid. 12.)⁸⁹⁾ As Kelsen himself rightly points out “[i]t should be noted that logic does not claim that [a statement is true] […], but rather that if it is true […], then […] [the conclusion] is true[.] […] Whether [a statement] is true […] is something to be determined by some other science than logic.”Kelsen (n 1) 229.⁹⁰⁾ Right! But, that doesn’t make logic useless, quite the contrary. As the textbook cited by Kelsen points out “[if] a scientist […] wish[es] to determine whether a possible hypothesis, which would account for the phenomena [s]heSusan L. Stebbing in the United Kingdom was the first woman to in 1933 be appointed to a full professorship in philosophy at Bedford, then Royal Holloway, now King’s College in London, cf. Beaney Michael, Chapman Siobhan, ‘Susan Stebbing’ The Stanford Enyclopedia of Philosophy (edited by Edward N. Zalta, Uri Nodelman, Fall 2022) <https://plato.stanford.edu/entries/stebbing> accessed 20 November 2009.⁹¹⁾ is investigating, is true or false […] [t]he consequences are deduced, and, when possible tested. If the implied consequence is false, there is no reason to accept the hypothesis; if the implied consequence is true, then the hypothesis may be true.”Stebbing (n 18) 8.⁹²⁾ Kelsen even quotes his fellow émigréHans Kelsen (n 3), Karl Popper (n 82) and Alfred Tarski (n 48) all published in German before the stupidity of Nazism, together with many other scientists, intellectuals and artists, drove them out of — Kelsen (n 2), Popper (n 83), Tarski (n 49) — and darkness into the once brilliant German speaking world, cf. Watson Peter, The German Genius. Europe’s Third Renaissance. The Second Scientific Revolution and the Twentieth Century (Simon & Schuster 2010).⁹³⁾ “[…] Popper [directly] [who] says: ‘The most important function of pure deductive logic is that of an organon of criticism […]’,”Karl Popper, cited in: Kelsen (n 1) 191.⁹⁴⁾ and who in the cited 1961 talk on ‘Die Logik der Sozialwissenschaften’ before the ‘Frankfurt School’ in an after the war Tübingen,Popper’s talk launched the ‘Positivismusstreit’ between him and the ‘Frankfurt School’ of Max Horkheimer, Theodor W. Adorno and Jürgen Habermas, cf. Adorno Theodor W. et al. (ed.), Der Positivismusstreit in der deutschen Soziologie (Luchterhand 1969).⁹⁵⁾ goes on to explain that “[w]e can say: if all premisses are true and the inference valid, the conclusion must be true too; and hence, if in a valid inference the conclusion is false, it it is not possible for the premisses to all be true,”My translation of his talk held and published in German: “Wir können sagen: Wenn alle Prämissen wahr sind und der Schluß gültig ist, dann muß [!] auch die Konklusion wahr sein; und wenn daher in einem gültigen Schluß die Konklusion falsch ist, so ist es nicht möglich, daß die Prämissen wahr sind.” See Popper Karl, ‘Die Logik der Sozialwissenschaften’, in Adorno et al. (n 95) 116.⁹⁶⁾ and for that reason speaks of deductive logic as “[…] not only the theory of the transmission of truth from the premisses to the conclusion, but […] also the theory of the re-transmission of falsehoodfrom the conclusion to at least one of the premisses”Ibid. 116; trans- and retransmission remind of ‘reflective equilibrium’ see footnote number 107.⁹⁷⁾. To sum up, if the ‘theoretical syllogism’ — other than about an argument’s validity or consistency — doesn’t say anything about the truth of the statements in its premisses and conclusion, why should we expect the ‘normative syllogism’ to say anything about the validity of the norms?

3.2 Another Solution for a Kelsenian ‘Normative Syllogism’

If, like the ‘theoretical syllogism’, we understand the ‘normative syllogism’ as — apart from an argument’s validity or consistency — saying nothing about the validity of the norms in its major premiss and conclusion, the need for claiming that, unlike in the ‘theoretical syllogism’, in the ‘normative syllogism’ the validity of the individual norm in its conclusion, isn’t implicit in the validity of the general norm in its major premiss, magically disappears. Sorry, but read that again!I try to write as clearly as possible, but sometimes my best isn’t good enough.⁹⁸⁾ If we don’t want the individual norm in the conclusion of an argument to be valid, we can either claim that, because the validity of the individual norm isn’t implicit in that of the general norm, the argument is invalid — and give up logicLogic tells us ‘A → B, A, ⌐B’ is inconsistent, that is, we must give up either logic and consistency — please don’t! — one our premisses ‘A → B’ and ‘A’ or conclusion ‘⌐B’.⁹⁹⁾ — or, if we feel more humble, question lawThat is, we can argue ‘A, ⌐B ├ ⌐(A → B)’ and give up general norm ‘A → B’.¹⁰⁰⁾ and argue that the general norm in the major premiss must be invalid. Of course, what we can also do, is take the easy way out and argue that the statement in the minor premiss is false.Or, we can argue, ‘A → B, ⌐B ├ ⌐A’ and give up statement ‘A’.¹⁰¹⁾ Remember, that for a conclusion to be true or valid, both the argument needs to be valid, that is, the conclusion must follow from the premisses, and (!) its premisses must be true or valid. If, like Kelsen, we want to deny a conclusion’s validity, we can either argue that the argument is not valid, that is, the conclusion doesn’t follow from the premisses, or we can argue the premisses aren’t true or valid. We can give up logic or question law. Kelsen goes for the former, I go for the latter. Why give up logic, when you can question law? Like Kelsen says himself: “[I]t would be an absurd fiction to suppose that in the legislator’s act of will of which the general norm is the meaning there are already implicit all the possible acts of will whose meanings are the individual norms corresponding to the general norm.”Kelsen (n 1) 238.¹⁰²⁾ The legislator is not omniscient. From time to time herJustitia, ‘Lady Justice’, the Roman Goddess is depicted as a woman.¹⁰³⁾ general norms can and will turn out to be at least in part invalid, that is, either overbroad or underinclusive. And, in case the application of a general norm leads to what, we think, is an invalid individual norm, the corresponding general norm must be, at least in part, invalid too. It is overbroad or underinclusive and must be narrowed or broadened by way of teleological reduction or analogy. We must endeavour to make our general norms consistent with our individual norms and since logic is what enables us to assess that consistency, we shouldn’t sacrifice it: While logic without law is worth less, law without logic is worthless.

This rather ‘technical’ fix has some very important consequences — it saves logic — but, I think, otherwise fits quite well with Kelsen’s theory of law and morality. The price to pay is the sacrifice of the ‘unquestionability’ of law’s validity. But, who wants that? — And, considering that, according to Kelsen, a general norm’s validity in order to become an individual norm must be recognized anyway, that’s a small or no price to pay. Kelsen pays it too. But Kelsen pays more, much more: he gives up logic. With the nickles and dimes, Kelsen gives away his wallet and his bank account. If, for whatever reason, we want to refuse to posit an individual norm, we don’t need to claim it isn’t implied by the corresponding general norm, a norm we must recognize anyway, we can just claim the general norm must be invalid, because the individual norm is invalid. That’s enough. Anything more, is too much. We don’t need to give up logic whole, bones and all,I think I’m falling in love with you, crazy little diamond. May Niki be our angel.¹⁰⁴⁾ we can sacrifice a law. Although, in that it re-establishes the analogy between the truth of a statement and the validity of a norm, this ‘small’ change in interpretation is clearly against his word, it doesn’t do away with Kelsen’s theory of law and morality. How so?

In my understanding, one of the central claims in Kelsen’s theory is what he calls the ‘autonomy of morality’. I think it’s one of the things which together with his relativistic theory of justice make Kelsen Kelsen. According to Kelsen, the “[…] autonomy of morality consists […] in the fact that the application of a general norm to a concrete case […] is conditional upon the recognition of the validity of the general norm for the concrete case on the part of the individuals whose behaviour is decreed to be obligatory by the general norms of the [legal or] moral order”Ibid. 237.¹⁰⁵⁾. That recognition depends on the standard used to assess the validity of the general norm and, since, according to Kelsen’s ‘relativistic theory of value’ “[…] every moral system can serve as such[,] […] the standard of evaluation is relative”Kelsen (n 50) 67.¹⁰⁶⁾. If together with logic we insist on the consistency of the validity of general with individual norms we give more weight to the autonomy of morality. In case a general norm of law implies an individual norm that according to our morality shouldn’t be valid, we can argue that the corresponding general norm shouldn’t be valid either. Consistency is what enables us to not only transmit the validity of the general to the individual norm, but also to re-transmit the invalidity of the individual to that of the general norm. It enables us to keep general and individual norm in a ‘reflective equilibrium’.The term was coined by philosopher of law Rawls John, A Theory of Justice (Belknap Press 1971) 20, who uses the method of “[…] going back and forth, sometimes altering the conditions of the contractual circumstances, at others withdrawing our judgments and conforming them to principle,” in order “[to] find a description of the initial situation that both expresses reasonable conditions and yields principles which match our considered judgments duly pruned and adjusted,” what is “[…] an equilibrium [!] because at last our principles and judgments coincide,” and “[…] is reflective [!] since we know to what principles our judgments conform and the premises of their derivation”. Rawls got the idea, see his footnote no. 7 on p. 20, from fellow American philosopher of science Goodman Nelson, Fact, Fiction and Forecast (4^th ed., Harvard University Press 1983) 63 f., who puts it more succinctly: “A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend.”¹⁰⁷⁾ In giving us a separate standard for the evaluation of the general and individual norms of law, the autonomy of morality provides us with a way to critique the law without endangering its internal consistency. However, this critique depends upon both the subject of that critique, morality, and its object, law, being in themselves consistent. If we choose to give up the consistency of either law or morality, we are also giving up the possibility for their critique.Similarly Karl Popper who in the talk on ‘Die Logik der Sozialwissenschaften’ (n 95) that is cited by Kelsen points out that “[d]ie wichtigste Funktion der reinen deduktiven Logik ist die eines Organons der Kritik,” (ibid. 115) because “[…] alle rationale Kritik hat die Form, daß aus der zu kritisierenden Behauptung unannehmbare Folgerungen abgeleitet werden. Gelingt es uns […], dann ist die Behauptung widerlegt” (ibid. 116).¹⁰⁸⁾

Moreover, if like Kelsen, you believe not in an ‘absolute’. but ‘relativistic theory of value’, logic and consistency — together with reality — are the only things that put any kind of restriction on your law and morality. How much of a restriction, is up for debate, but you shouldn’t give that up too.Although I agree with the claim made by ‘Frankfurt School’ recruit Theodor W. Adorno that, just like in law, in sociology “System und Einzelheit sind reziprok und nur in ihrer Reziprozität zu erkennen,” as cited in: Habermas Jürgen, ‘Analytische Wissenschaftstheorie und Dialektik’, in Adorno et al. (n 95) 155, his disciple is, I think, wrong in saying that this “[…] überschreitet […] die Grenzen formaler Logik, in deren Schattenreich Dialektik selber nicht anders scheinen kann denn als Schimäre,” (ibid. 155) because logic doesn’t need to stop at first, but can extend over second and ever higher orders. Also, I can’t be but amazed at their fear of logic: “Argumente, die sich der analytischen Wissenschaftstheorie anvertrauen, ohne auf deren Axiomata einzugehen […] geraten in die logische Höllenmaschine. […] Damit [die Diskussion] überhaupt möglich sei, muß sie nach der formalen Logik verfahren. […] Gedanken indessen, welche die kritische Selbstreflexion des Primats der Logik in sachhaltigen Disziplinen fordern, geraten unvermeidlich in taktischen Nachteil. Sie müssen mit Mitteln, unter denen die logischen sich behaupten, über Logik nachdenken.” Adorno Theodor W., ‘Einleitung’, in Adorno et al. (n 95) 8.¹⁰⁹⁾ I believe that identity, sameness and similarity as three kinds of ever looser ‘consistencies’ for the sake of possibility, predictability and justice — who but bigots, tyrants and psychopaths likes injustice, unpredictability and impossibility? — make for ever stronger restrictions,Idea being, that (1) for the sake of possibility, you shouldn’t make different decisions for one and the same, identical case; (2) for the sake of predictability, you shouldn’t make different decisions for different cases of the same type; and (3) for the sake of justice, you shouldn’t make different decisions for cases of different, but similar type. Which get’s you from (0) a reign of terror, over (1) enlightened absolutist rule, and (2) the iron rule of law and order, to (3) our modern republican ideal of justice.¹¹⁰⁾ but that is for another, longer article: developing a ‘natural law’ out of nothing, but ‘consistency’.

4. Appendix: Modus Tollens and the ‘Material Implication’

In an argument of the logical form of modus ponens, that is, ‘A → B, A ├ B’ (2), we from the major premiss ‘All swans are white.’, together with the affirmation of its antecedent, the minor premiss ‘This bird is a swan.’, have drawn the conclusion that ‘This bird is white.’ (1). In the argument:

All swans are white.

This bird is not white.                                                                                                 (6)

This bird not a swan.

we don’t affirm the antecedent of the major premiss, but deny its consequent and draw the conclusion that the antecedent’s negation must hold. This argument or inference (6) has the logical form of so-called modus tollens:Again, in simplified form; being a quantified statement, its major premiss ‘All swans are white.’, would have to be expressed not in propositional, but first order predicate logic as ‘∀x(Sx → Wx)’, read: for all objects ‘x’, if ‘x’ is a swan, then ‘x’ is white, what, bird ‘b’ being such an object ‘x’, we would have to ‘instantiate’ to ‘Sb → Wb’, read: if ‘b’ is a swan, then ‘b’ is white, before we could argue that ‘Sb → Wb, ⌐Wb ├ ⌐Sb’.¹¹¹⁾

A → B, ⌐B ├ ⌐A                                                                                                                   (7)

Like modus ponens, modus tollens is a valid form or rule of inference, because “[…] the premisses cannot be true and the conclusion false,” or what is the same “[…] the truth of the premisses necessitates the truth of the conclusion,”Again, Stebbing (n 18) 6.¹¹²⁾ what, again, can be proved with help of a truth table:The argument ‘A → B, ⌐B ├ ⌐A’ is valid, if its premisses ‘A → B’ and ‘⌐B’ can’t be true and its conclusion ‘⌐A’ false (see n 112), that is, if ‘((A → B) ∧ ⌐B) → ⌐A’ is a tautology. Truth table (2) proves ‘((A → B) ∧ ⌐B) → ⌐A’ is a tautology, that is, true under all possible combinations of truth values for ‘A’ and ‘B’ (rows 1–4), hence it’s always or vacuously true, its truth follows from nothing, but its form: ‘├ ((A → B) ∧ ⌐B) → ⌐A’.¹¹³⁾

Table 2: Truth table for validity of modus tollens

Modus tollens enables us to take the easy way out and if, our bird isn’t white, argue that it isn’t, because it isn’t a swan, but a flamingo.Flamingos are pink, because with their brine shrimp they eat their carotenoids.¹¹⁴⁾ However, if our bird, although not white, is a swan, we must conclude that there is a swan that isn’t white or, what is the same,‘There is a swan that isn’t white.’ can be expressed in first order predicate logic as ‘∃x(Sx ∧ Wx)’ what is the same as ‘⌐∀x(Sx → Wx)’ or ‘Not all swans are white.’.¹⁰⁵⁾ not all swans are white:

This bird is a swan.

This bird is not white.                                                                                                 (8)

Not all swans are white.

that is, we make an argument (8) of the following logical form:Again, in simplified form; because, while we can argue ‘Sb, ⌐Wb ├ (Sb ∧ ⌐Wb)’ and, since ‘Sb ∧ ⌐Wb’ is equivalent to ‘⌐(Sb → Wb)’ (see n 117), also ‘Sb, ⌐Wb ├ ⌐(Sb → Wb)’, in order to get to quantified statements like ‘There is a swan that isn’t white.’ or ‘Not all swans are white.’ we cannot use propositional, but have to use first order predicate logic. Doing so, because bird ‘b’ is an object ‘x’, from ‘Sb ∧ ⌐Wb’, read: ‘b’ is a swan and ‘b’ isn’t white, we can ‘instantiate’ that there is an object ‘x’ which is a swan and which isn’t white or ‘∃x(Sx ∧ ⌐Wx)’ what is equivalent to ‘⌐∀x(Sx → Wx)’ (see n 115), read: it is not the case that for all objects ‘x’, if ‘x’ is a swan, then ‘x’ is white.¹⁰⁶⁾

A, ⌐B ├ ⌐(A → B)                                                                                                        (9)

which is part of the broader ‘definition’ of the material conditional (‘→’)The material conditional (‘→’) can be ‘defined’ syntactically by way of the equivalences ‘A → B ≡ ⌐A ∨ B’ and ‘A → B ≡ ⌐(A ∧ ⌐B)’ or semantically by way of a truth table where ‘A → B’ is false if ‘A’ is false and ‘B’ is true (row 2) and otherwise true (rows 1, 3, 4).¹¹⁷⁾ and just like modus ponens and modus tollens a valid form or rule of inference, because “[…] the premisses cannot be true and the conclusion false,”One last time, Stebbing (n 18) 6.¹¹⁸⁾ what we, once more, can prove with the help of a truth table:Argument ‘A, ⌐B ├ ⌐(A → B)’ is valid, if its premisses ‘A’ and ‘B’ can’t be true and its conclusion ‘⌐(A → B)’ false (see n 118), that is, if ‘(A ∧ ⌐B) → ⌐(A → B)’ is a tautology. Truth table (3) proves ‘(A ∧ ⌐B) → ⌐(A → B) is a tautology, that is, true under all possible combinations of truth values for ‘A’ and ‘B’ (rows 1–4), hence it’s always or vacuously true, its truth follows from nothing, but its form: ‘├ (A ∧ ⌐B) → ⌐(A → B)’.¹¹⁹⁾

Table 3: Truth table for validity of ‘A, ⌐B ├ ⌐(A → B)’

The article was written for Tomáš Koref and presented at his workshop on legal theory on Friday 29 November 2024 at Masaryk University Faculty of Law in Brno, Czech Republic.