Maurilio Lovatti


Meta-Ethics and Analysis of Language from Wittgenstein to Deontic Logic Systems  

(Analysis and Metaphysics, vol. 6, 2007, pag. 120-135)


In 1971, during a broadcast conversation transmitted by the BBC, K. Popper affirmed that, as he wore spectacles, every now and then he cleaned them. But spectacles have a function, and they function only when you put them on, to look through them at the world. It is the same with language and therefore, concluded Popper, one should not waste one's life in spectacle-cleaning or in talking about language.
The analysis of language and the logic are without doubt useful to the philosopher, sometimes essential (who looks through dirty spectacles sometimes makes a blunder), but under no circumstances should they exhaust the philosophical activity. Vice versa an examination of the twentieth century analytic philosophy shows that many authors, abandoning the moderate and generally accepted thesis according to which language analysis can indeed be useful to philosophy as such, allowing this to assume as far as possible a rigorous status and avoid falling into excessive verbosity as an end to itself, have ended up investing a load on language which, as it is a communication tool, it is not capable of assuming.
It is illogical to think of resolving ontological or ethical problems simply with the analysis of language, because, as Evandro Agazzi rightly comments, "within this philosophy (of language) there's not much to say about the "kind of reality" which is up to the referent and this for the good reason that this is not a linguistic problem." In other words:

" the linguistic version of a philosophical problem may be a useful heuristic device for attacking the problem, just as in deciding certain questions of geography it is useful to translate them into questions regarding the positions of marks on a map. But just as it would be ludicrous to supposed that maps constitute the entire subject matter of geography, so also it would be to great mistake to suppose that philosophy is or ought to be nothing more than the study of language." .

Within this conception of the analysis of language , only the matter of rationality of ethics will be examined, i.e. the relationship between knowledge of the world and ourselves and ethics, in an attempt to delineate some meaningful contributions that can be drawn from the analytic philosophy and the semantics of the deontic logic systems.

1. Wittgenstein and the neopositivism

In the Tractatus (1921) Wittgenstein affirms the total heterogeneity between facts and values: "The sense of the world must lie outside the world. In the world everything is as it is and happens as it does happen. In it there is no value - and if there were, it would be of no value" (6.4.1). Therefore, within the conception of language formulated in this book, it follows that "It is clear that ethics cannot be expressed. Ethics are transcendental." (6.421)
It is a drastic re-proposition of the so-called Hume's law, according to which, starting from factual affirmations (what it is) it is impossible to logically derive prescriptions or judgments of value (what ought to be). Since for the Tractatus the only significant language is that concerning facts (a descriptive language), whoever tries to formulate propositions about ethics, necessarily meets with non-sense sentences. At the end of the Lecture on ethics in November 1929, referring to everything that is attempted to be said on ethics and on values, Wittgenstein affirms:

"I see now that these nonsensical expressions were not nonsensical because I had not yet found the correct expressions, but that their nonsensicality was their very essence. For all I wanted to do with them was just to go beyond the world and that is to say beyond significant language. My whole tendency and, I believe, the tendency of all men who ever tried to write or talk Ethics or Religion was to run against the boundaries of language. This running against the walls of our cage is perfectly, absolutely hopeless. Ethics so far as it springs from the desire to say something about the ultimate meaning of life, the absolute good, the absolute valuable, can be no science. What it says does not add to our knowledge in any sense. But it is a document of a tendency in the human mind which I personally cannot help respecting deeply and I would not for my life ridicule it" .

The neopositivistic interpretation of Tractatus, drawn up by the Vienna Circle, underlines the nonsense of the ethics theories and tends to reduce the propositions containing evaluative terms as mere expression of emotions. In 1931 Carnap writes:

"The judgment (pronounced on the nonsense of all metaphysics) also extends to philosophy of values and norms, to all ethics or aesthetics as a prescriptive subject. Since the objective truth of a value or norms cannot be (...) empirically verified or be deduced from empiric propositions, given this, it cannot be expressed in any way (by a sensible proposition)" .

With similar motivations, the great thinkers of the Vienna Circle took this iconoclast direction which, reducing moral judgments to emotions, removed ethics from philosophy and denied that the rationality performs any role in moral controversies. The only important exception within the Vienna Circle is constituted by the thought of V. Kraft, who tries to deduce the sense of evaluative concepts using the logical analysis of the same and individualizes in impersonality a characteristic of the judgments of value .
In Great Britain, Alfred Ayer with Language, Truth and Logic (1936) is as drastic as the Viennese:

"We can now see why it is impossible to find a criterion for determining the validity of ethical judgements. It is not because they have an "absolute" validity which is mysteriously independent of ordinary sense-experience, but because they have not objective validity whatsoever. If a sentence makes no statement at all, there is obviously no sense in asking whether what it says is true or false. And we have seen that sentences which simply express moral judgments do not say anything. They are pure expressions of feeling and as such do not come under the category of truth and falsehood" .

Therefore it is impossible to dispute about questions of value. Argument is possible on moral questions only if some system of values is presupposed; otherwise, if two persons are stating two opposite moral judgments, they are merely expressing different moral sentiments. "I know that there is plainly no sense in asking which of them is in the right." .

2. Popper, Toulmin and Hare

At the end of the second world war, in the ambit of empiristic philosophy, or more generally among the philosophers who accept Hume's law, there are no well defined ethical theories which do not fall within the emotivistic or the intuitionistic conceptions. The latter was developed in Great Britain starting from the Principia Ethicas of Moore (1903), particularly with Prichard and Ross . The role of rationality in ethics appears to be undermined or in some cases entirely invalidated; ethics is actually expelled from the sphere of philosophy and dissolved in psychology or sociology. It is considered possible to analyze and explain behaviours and customs also from the historical point of view, but not to rationally and critically examine the value of ethical prescriptions as such. An important exception to this tendency is provided by K. Popper. In The Open Society and its Enemies (1943) he maintains a dualism ("a decisive asymmetry") of facts and decision and a dualism of facts and norms: "it is impossible to derive a sentence stating a norm or a decision or, say, a proposal for a policy from a sentence stating a fact; this is only another way of saying that it is impossible to derive norms or decisions or proposal from facts" Maintaining the view that moral norms are conventional, he states that the artificiality of them by no means implies full arbitrariness and he holds that ethical norms and political proposals are open to rational discussion and corrigible for they are critically evaluated. Nevertheless Popper does not process an organic theory of ethics. A definite revaluation of the role of reason in ethics occurs at the beginning of the fifties, with three works that represent milestones in the twentieth century philosophy: An Examination of the Place of Reason in Ethics (1950, but completed in 1948) of S.E. Toulmin , Deontic Logic (1951) by G.H. von Wright , which presents the fundamental notions for applying symbolic logic to ethical language, and The Language of Morals (1952) by R.M. Hare .
The theories of Toulmin and Hare have been influenced, as almost all the analytic philosophy, by the reflection of the later Wittgenstein. The first part of the Philosophische Untersuchungen (published posthumous in 1953) had already been completed in 1945 and Wittgenstein's new ideas (on the meaning of propositions, exclusively determined by the use in a given linguistic game, of language as a family of linguistic games and on the decision to forego searching for an absolute logical base in the procedural formalities of language) broadly circulated in Great Britain by means of the blue and brown books, dictated by the same Wittgenstein between 1933 and 1935 . Wittgenstein's new conception on the nature of language and on the function of the philosophical analysis made it possible to completely abandon the theory of the meaning as a representation (and accordingly the privileged role assigned to descriptive language) and to consider rationality of reasoning no longer solely in function of the empirical verifiability criterions.
Toulmin, in particular, sustains that as moral judgments, and also scientific ones, are made in relation to our experience, they can be subjected to a critical discussion and they do not result therefore, in principle, to be incorrigible. Moral judgments have the purpose of allowing us to separate those cases of actions which seem or appear to be correct and are indeed so, from the other cases where our feelings are a bad guideline and make things appear correct when in reality they are not. "In ethics, as in science, incorrigible but conflicting reports of personal experience (sensible or emotional) are replaced by judgments aiming at universality and impartiality" .
Toulmin's research aimed at identifying the role of rationality in ethics by the analysis of moral language however is strictly related to an assumption which is not logically formal, and on the contrary pertaining to content, which is given as an axiom. For the English philosopher "we can fairly characterise ethics as to part of the process whereby the desires and actions of the members of to community are harmonised" . This delimitation of the content of ethics is assumed simply because "the only context in which the concept of duty is straightforwardly intelligible is one of communal life; it is, indeed, completely bound up with the very feature of communal life, that we learn to renounce our claims and alter our aims where they conflict with those of our fellow." .
In Toulmin's opinion, moral concepts must be analyzed according to their use; therefore it is possible to distinguish different uses of moral concepts and, consequently, also of moral judgments. They can be used both to express our feeling (it is the emotional element, always present in moral judgments, but considered as neither essential nor predominant), and also in coming to decision about an individual action, as well as in criticising and modifying our social practices, and in conclusion for other uses again . In the second case, the rational evaluation is aimed at determining the coherence of an individual action in comparison to a given norm. In the third case however the validity of a regulation is teleological compared to the "utilitarian" improvement of the associated life. Two different kinds of moral reasoning are therefore possible according to the two different kinds of questions that man asks. A more radical and global justification of ethics not only is not possible, but it would also have no sense. The question: "what makes - in general - an ethical reasoning valid?" is in Toulmin's opinion simply badly expressed and without meaning.
Hare's conception of ethics is however more unitary and organic. In Hare's opinion the prescriptive language includes both imperatives and value-judgments, within which there is the moral judgments subset. Imperatives can be singular or universal, while value-judgments are always universal. Prescriptivity is therefore an essential characteristic of moral judgments. Approximately the difference between descriptive statements and prescriptions is delineated as follows: "If we assent to a statement we are said to be sincere in our assent if and only if we believe that it is true (believe what the speaker has said). If, on the other hand, we assent to a second-person command addressed to ourselves, we are said to be sincere in our assent if and only if we do or resolve to do what the speaker has told us to do; if we do not do it but only resolve to do it later, then if, when the occasion arises for doing it, we do not do it, we are said to have changed our mind, we are no longer sticking to the assent which we previously expressed. It is a tautology to say that we cannot sincerely assent to a second-person command addressed to ourselves, and at the same time not perform it, if now is the occasion for performing it and it is in our (physical and psychological) power to do so." . I.e. Hare is convinced that morals have a sense if they direct, or want to direct, human behaviour. After all it is an answer to the question: "what shall I do?", in fact: "If we were to ask of a person "What are his moral principles?" the way in which we could be most sure of a true answer would be by studying what he did." . Subsequently Hare will define prescriptivity in a more formal way: "We say something prescriptive if and only if, for some act A, some situation S and some person P, if P were to assent (orally) to what we say, and not, in S, do A, he logically must be assenting insincerely" .
For Hare in every statement it is possible to distinguish a phrastic element, which aims to point out, that expresses the content, what is being referred to, and a neustic element, that points out the modality (affirmative, interrogative or prescriptive) with which the phrastic element is affirmed or requested or ordered.
In order for the statement to be meaningful, it is sufficient that the phrastic element is meaningful.
In Hare's opinion inference (i.e. the possibility to logically derive a sentence from two or more premises) is also possible in the moral field. It is possible for example to derive singular imperative conclusions from an universally imperative sentence, combined with minor indicative (or descriptive) premises. In order for moral interferences to be valid, it is evidently necessary to respect the rules of the formal logic for what concerns the phrastic element of the sentences. But this is not enough and two further principles have to be introduced: (1) it is not possible to draw any descriptive conclusion if it is not validly obtainable only from the descriptive sentences contained in the premises and (2) it is not possible to draw any valid prescriptive conclusion from a series of premises that does not contain at least one prescriptive sentence. The second principle is a rigorous reformulation of the so-called Hume's law.
With these distinctions related to language now identified, it is possible to observe that the evaluative terms (for instance "good") always have, both in ordinary and philosophic language, a double function: evaluative and descriptive.
The evaluative function is aimed at praising or approving a given object or action and is directly achieved from the prescriptive character that is typical to each judgment which includes an evaluative term (from this point of view in "a good tennis racket" and in "helping the neighbour is a good action" the term "good" has the same evaluative function).
The descriptive function of an evaluative term is related to the ability to transmit information on the conformity of the object compared to the criterion that establishes the application of the same evaluative term, since the evaluative meaning of "good" is very different from explaining one of the various criteria which regulates the application. To clarify further, following example can be considered: if a radio commentator, referring to a football match, affirms that "team N has played a good first half, despite the result is a draw", he mainly wants to inform the listeners who, if they are competent in football, will interpret the statement in accordance to the criteria for which it makes sense to say that a team plays well (if it creates goal actions, if it dominates in midfield, if it maintains ball possession, etc.). But when the coach, speaking to the players in the locker room and referring to the same match, says: "you have played a good first half", he wants to praise them and exhort them to continue with the same commitment, that is he wants to direct their behaviour.
As a direct consequence of this distinction (that is valid for all evaluative judgments, as shown in the example, and not only for the ethical ones) it is deduced that in every moral judgment the prescriptive function is essential and can not be eliminated, while the descriptive function, that is always present, but at different levels, transmits implicit information on the basis of socially approved criteria. This latter aspect can be considered important for example by the sociologist or the psychologist, but it is irrelevant from the point of view of philosophical ethics. The lack of comprehension of this distinction is at the base of many philosophical errors on ethics and, in particular, is at the origin of the trend of considering evaluative adjectives as qualities or natural properties of things (both "good" and "red" are, from a grammatical point of view, qualifying adjectives, but their function in language is considerably different).
Prescriptivity alone is not enough to define moral judgments. In Hare's opinion they also have to be universalizable and overriding. A judgment is universalizable when the condition is satisfied according to which, in all identical cases with regards to their relevant universal properties, the relative moral judgment has to be identical. This means that it is contradictory to formulate different moral judgments of situations where we admit its identity in relation to the universal properties. In particular, universalizability means that a subject, if he affirms to have to perform a certain action towards another person, has to think (if he doesn't want to contradict himself) that the same action has to be done to him, if he was in the same identical situation as the other person.
A judgment, however, is considered predominant when it is believed that what it prescribes should be performed even if it is in conflict with other principles of non-ethical nature (for instance aesthetical principles) or with other non-universalizable prescriptions (for example common desires).
On the basis of these presuppositions, Hare then proceeded to construct an articulated theory of ethics which foresees a distinction in three levels of moral thought (intuitive, critic and metaethical) on which is not possible to report herein. Apart from the contrasting evaluations that have been formulated on the total work carried out by Hare and even on the meaning of evolution according to his thought, it is however remarkable to underline that the characteristics of prescriptivity, universalizability and overridingness of moral judgments are achieved with a method that we can define as transcendental: who uses moral language in a meaningful and effective way cannot set aside (unless he wants to contradict himself) the obligations which derive from these said characteristics.
Obviously, it is always possible, for instance for the hedonist, not to use the moral language: he can, if he wants, act differently from what the morals prescribe him, where also a chess player, if he wants, can make a move in contrast with what prescribed by the theory of openings.

3. Systems of deontic logic

A further contribution to the revaluation of the role of rationality in ethics comes from the remarkable development of the deontic logics over the last decades, starting from the already mentioned essay of von Wright in 1951. In 1926, the Austrian philosopher Ernst Mally (1879-1944) proposed the first formal system of deontic logic, in the book The Basic Laws of Ought: Elements of the Logic of Willing , but the deontic logic is indeed common among philosophers starting from the early fifties. Von Wright was the first to introduce the term "deontic logic" and promoted and presided in March 1975 at the first international Conference on deontic logic, held in Bielefeld (Germany). During this conference, the most important researchers on the subject compared both the specific problems relating to this sector of logic, and the application of the deontic logic systems to ethics, rights and social sciences . The development of this sector of symbolic logic has been impetuous: the bibliography in the appendix of the Conference documents, which reaches and includes the year 1976, consists in an impressive 1460 titles!
It is common knowledge that the deontic logic systems can be considered as semantic interpretations of modal logic systems, which in turn are an extension of the classical logic.
In the deontic logic systems the necessity modality is interpreted as obligation (duty), whilst the possibility is interpreted as permission. From the syntactic point of view the deontic logic systems do not differ at all from the modal logic systems: the rules of inference are identical and include the rules of the classical propositional logic, further to the so-called rule of necessitation, common to almost all the modal logic systems, according to which if a formula P is derivable from a set of formulas N, then the same is worth if N and P are modalised by the operator of necessity.
The semantic aspect is very different. If one takes as reference the relational semantics of Kripke (that is an extension of the Tarskian classical logic), the originally Leibnizian concept of "possible world" of the modal semantics, is interpreted as a "deontic alternative". In intuitive terms, the deontic alternatives of a given world m can be thought as those possible worlds that allow different ways of realizing the obligations present in m.
Many deontic logic systems have been formalized that differ from each other in the inclusion of some axioms. Which philosophically valid differences involve the formalisation of an ethical theory in a system rather than in another? The systems of modal logic generally have in common the axiom according to which, if a proposition P is necessary, then it is also possible. In the deontic logic this means stating that prescribing something implicates the existence of at least an alternate situation to the current status where, what has to be (that is now prescribed) is effective: in other words, what is prescribed has to be at least possible (i.e. allowed). Even if, evidently it is possible that this possibility will never actually be realised: that is, a moral precept, an obligation, can be meaningful and not contradictory even if, in effect, it is never complied with.
All these systems instead exclude the necessity axiom (that vice versa is fundamental in the most known modal logic systems) according to which if a proposition is necessary, then it is also true and possible in every way.
This exclusion is intuitively acceptable. If what is prescribed would necessarily come true under all the possible alternatives, the specificity of the concept of deontic normativity would be forsaken, which would coincide with the physical necessity (given an initial situation and given some physical laws, a certain consequence X must necessarily happen: a body, left without constraints, must "necessarily" fall). However there are also some differences: in some systems there is no cumulativity, that is in the passage from a given world to a deontic alternative there is no maintenance of obligations. These systems, also referred to as minimal systems, represent abstract situations in which there is no unitary practical project, but a new project is proposed in every deontic alternative.
In other systems however there is a cumulativity of obligations; each deontic alternative introduces additional obligations in comparison to those of the former alternatives in the order of succession. Such models are also clearly important from a practical point of view: their worlds correspond to the intermediary steps of the realization of a project, whose construction proceeds only gradually, setting at each step new obligations in addition to those already included in the former situations.
On the contrary, in other systems there can be a decrease of obligations, but not an increase; instead there is a conservativity of permissions. In other different systems conservativity is possible for both obligations and permissions.
In view of the above, it is possible to draw some philosophical evaluations on the rational nature of ethics.
First and foremost it must be said that, if even the semantic models of the modal logic aimed at treating the physical necessity do not play any practical role in the scientist's activity, both in relation to experimental research and the theoretical setup of physics, it is not possible to pretend that the deontic logic systems can be conclusive in establishing the validity of a moral theory in comparison to another. As mathematics alone is not enough to formulate even the simplest law of physics or the rules of chess do not teach one how to win a game. The semantics of the modal systems is nevertheless able to play an interesting role when comparing different conceptual visions from a metatheoric reflection point of view.
The deontic logic shows that the ethical theories - at least in principle - can be expressed in a formal and rigorous language, that makes it possible to emphasize which contents are axiomatically assumed (and therefore cannot be proved), that possible internal contradictions of an ethical conception can be shown in incontrovertible way, and above all that, from a logic point of view, the analysis of an ethical theory can be developed with the same identical rigor of the analysis of a physical theory.
This is enough to show to what extent the emotivistic and intuitionistic conceptions of ethics are inadequate and unsatisfactory. This is also enough to eradicate the classical common place according to which the concepts of ethics must necessarily result approximate and not rigorously definable such as scientific concepts and that ethical prescriptions having universal form are only "usually" valid or in the majority of the cases.

4. Hume's law

Since the philosophical debate on ethics in the Sixties and Seventies, strongly influenced by the thought of Toulmin, Hare and other analytical philosophers, concluded in focusing on the metaethical aspect, i.e. on the linguistic-formal nature of moral judgments, on their prescriptive character and particularly on the validity or not of Hume's law , it can be interesting to ask oneself if the developments of the deontic logic have brought important contributions in favour of the supporters or of the detractors of the Hume's law. It is perhaps surprising that among the most convinced researchers on deontic logic there is no identity of views on this point.
O. Weinberger sustains that if each normative sentence (that is prescriptive) was reducible (that is transformable according to well precise rules) to a descriptive sentence, Hume's law would definitely be disproved. He defines reductionists as those who think that this reduction is as principle possible and normativists as those who sustain the inderivability of the normative from the descriptive. He also affirms that the normativists can recognise with satisfaction that, despite the continuous attempts of reduction, the reductionists are affirming the general recognition of the semantic independence of the normative sentences in comparison to purely descriptive sentences, and that every attempt of reduction is a diagnosis of the failure of the former .

On the other hand G. Kalinowski, using the Tarskian concept of truth in formalized languages, sustains that ethical and juridical norms can be true or false: it follows the negation of the absolute heterogeneity between descriptive and prescriptive sentences. Nevertheless he admits immediately later that the prevailing thesis among the logics is the opposite one (norms are neither true nor false and there is no sense in asking if they are) since the deontic logic systems "can be interpreted in expressions that do not fall into the categories of true and false" in the sense that both these said logical systems, both the internal coherence (consistence) of the existing juridical and the moral norm systems would remain unchanged "even if the norms (moral and juridical) were (contrarily to what I think) neither true nor false" .
By performing a certain level of drastic simplification, all of this can be interpreted in the following way: the deontic logic systems (their axioms, the rules of inference etc.) are neutral towards Hume's law, that is "they work" and have meaning for both whoever believes that the norms have a value of truth, and for whoever sustains the opposite thesis (furthermore the Euclid geometry "works" and is coherent for both those who believe its postulations are true, and for who consider them mere hypotheses or conventions). From this point of view the notion of truth becomes fundamental; in the followings propositions: (1) "it is true that in this room there are five people", (2) "the theorem T is true in the Euclid geometry" and (3) "it is true that you must not steal", the term "true" apparently has the same meaning and, in respect to common sense, it is correctly used in all three cases.
In reality in the first case it is used without implicit conditions: the truth value of the affirmation depends only on the meaning of the terms and from the state of fact. However in the other two cases it expresses the coherence with some premises, with the axioms of a theory or an ethical or juridical normative system: it does not refer to the world, but to a theory. But at the same time the term "true" is used in: (4) "it is true that all statements of a formalized language are divided into descriptive and prescriptive". It follows that, at least in the ambit of the Tarskian conception of truth, the "Great division" (between prescriptive and descriptive) in itself is neither true nor false and Hume's law (i.e. the impossibility to logically derive prescriptive sentences from descriptive premises) is definitely correct, but on the condition of having chosen to adopt the Great division. Therefore the statement "all sentences of a formalized language are divided into descriptive and prescriptive" is not analytical, (his opposite is not contradictory) but it must be assumed (with prescriptive value) if you want to analyze the language of morals (as Hare does) or if you want to develop a deontic logic.
These considerations related to the logical-linguistic point of view can shine new light on the philosophical dispute on Hume's law.
It is perhaps possible to risk a general evaluation: the attempts to disprove Hume's law on the logical-linguistic plan have decidedly failed and therefore the critics of the ethical non-cognitivism can only follow the two remaining roads: (a) Hume's law, valid from the formal point of view, is however "empty", since the purely descriptive plan does not exist; (b) Hume's law is irrelevant from a practical point of view, as there are some evaluative sentences universally approved (of the type: "it is better to be healthy that sick" or "you must do what it is right").
The most important attempts to follow the first road can be brought back to the thought of K.O. Apel, that sustains that even the sciences of nature are not purely non-evaluative (descriptive), but normative-hermeneutical, that can always imply a principle of normative evaluation in the logicality. In Apel's opinion the same inter-subjective communication implies some moral norms: purely constative sentences do not exist, but the performative dimension is always present, even if implicit. With a little forcing also the radical critic of B. Williams on prescriptivism is similar to this position, at least where he sustains that the theorists of the distinction fact-value, even though they count on linguistic analysis, instead of discovering their distinction in language, they put it there themselves .
Less convincing, despite appearances, is the second road. Less convincing in this sense: it is true that normally ethical or political controversies do not concern the validity of the first principles (of the type "all citizens are equal before the law" or "a person's freedom is guaranteed until the same compromises the freedom of others") but the concrete applications of these principles; in such cases the validity (or not) of Hume's law appears irrelevant.
Nevertheless, as F. Oppenheim underlines, the acceptance of Hume's law is an essential premise to formulate non-cognitive meta-ethical theories and, indeed, the cognitive followers think that it is possible to demonstrate the truth or falsehood of fundamental principles through considerations that are located outside the given ethical system, while the non-cognitive followers deny that such a demonstration can be given . It follows that the non-cognitive formulation becomes relevant when conflicting moral principles are being questioned (on the contrary however, for instance, the doctrine of the ethical State implies a cognitive conception of ethics).
This analysis of Oppenheim must however be correctly understood; the non demonstrability of the first principles must not be confused with the ethical relativism or even with the nihilism: since deductive logic does not exhaust the sphere of reasonableness, the non demonstrability of an accepted principle does not implicate an emotional or irrational choice (the motivations adopted by Aristotele for the principle of non-contradiction in the IV book of Metaphysics or the reasons reported by Apel or Habermas for the transcendental foundation of communicative behaviour can without doubt be considered "reasonable" even if not deductively demonstrated). Human rationality is also expounded from the pure demonstration in formalized languages.
From this analysis, partly historical and partly theoretical, in my opinion, the following conclusions can be made:
1) Emotivism and intuitionism are unsatisfactory ethical conceptions. 2) Reason (intended in a logical-deductive sense) plays an effective role both in ethical discussions and in choices. 3) There are some characteristics of the ethical language (prescriptivity, universalizability and predominance) that cannot be eluded (pain the non significativity of the same language) by those who want to morally reason, i.e. by those who intend to regulate their own behaviour on the basis of acknowledged and coherent principles. 4) These characteristics can be found whether or not all possible ontological-metaphysics foundations of morals are taken into account. 5) The deontic logic systems allow the formalization of ethical theories and - at least in principle - a rigorous critical discussion of the same, but obviously nothing can be affirmed on the value of truth of the axioms of a system. 6) The deontic logic systems are neutral with regard to the validity of Hume's law, but they use the Great division between descriptive (not modalised) sentences and prescriptive sentences modalised by the obligation operator and no system includes rules which allow the deduction of obligation sentences from descriptive sentences. In the deontic logic systems Hume's law is assumed as an implicit result of inferential (conventional) rules. 7) The acceptance of Hume's law as a logical-linguistic thesis does not involve the cancellation of values (nihilism) or ethical relativism or indifferentism.


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