Open Journal of Philosophy
2012. Vol.2, No.2, 107-111
Published Online May 2012 in SciRes (http://www.SciRP.org/journal/ojpp) http://dx.doi.org/10.4236/ojpp.2012.22016
Democratized Morality. Formal Preliminaries to
Contractualist Ethics
Christian J. Feldbacher1,2
1Department of Philosophy, University of Innsbruck, Innsbruck, Austria
2Philosophy of Science Department, Salzburg, Austria
Received February 14th, 2012; revised March 18th, 2012; accepted March 28th, 2012
This paper discusses one of the advantages of applying formal methods in ethics. First, an approach from
democratic morality—which is a special case of contractualist ethics that brings together theories of legal
and moral philosophy—will be adopted, in order to argue for the non-trivial thesis that moral norms are
increasingly democratically motivated. To accept this thesis also as a desired way of justifying ethical
principles raises some issues, such as the problem of providing adequate principles for moral opinion
pooling. Secondly, it is therefore shown how formal criteria of rationality provide at least a partial solu-
tion to such problems. In a broad context this results can be seen as formal preliminaries to contractualist
ethics.
Keywords: Contractualism; Moral Opinion Pooling; Problem of Imperfect Community;
Criteria of Rationality; Tolerance
Introduction
Since the development of deontic systems of logic, formal
methods have spread to the field of ethics. This paper discusses
an instance of the application of these methods. We are going to
discuss in detail one of the advantages of the application of
formal methods in the area of legislation. For this purpose, first
the so-called democratization of morality thesis—which is seen
as a descriptive part of contractualist ethics—will be discussed
very shortly and in heuristic and general terms only; the thesis
of democratization of morality refers to the fact that in the laws
of western societies moral norms are increasingly determined
by democratic principles (The Democratization of Morality).
Following this general discussion, some formal criteria of ra-
tionality will be investigated since their use proves very prom-
ising for contractualist ethics (Formal Criteria of Rationality).
This section is a little bit technical, but nevertheless the text
ahead and behind the formal parts should allow a reader who is
not familiar with logical methods to get the main points of the
discussion.
Note, that in this paper the terms “morality” and “moral” are
used for the predication of specific systems of legal norms and
behaviour in accordance with or oriented towards these systems
of legal norms; the term “ethical” is solely used for justifica-
tions of and investigations in the field of ethics.
The Democratization of Morality
This section endeavours to show very generally how changes
in society, in technology and in economy have given rise to a
morality that is more and more democratized. The goal is to
provide a very basic outline of arguments with a restriction to
paradigmatic examples. The reader may note that a reductionist
point of view regarding morality is a very important underlying
assumption of our whole argumentation: we are going to inves-
tigate morality only in the context of legal norms. So, if, e.g., a
legal norm prohibits stem cell research and the legal norm is
fully accepted by a person (where acceptance of a norm is ex-
pressed by acting in accordance with the norm/law), then we
also assume that a prohibition of stem cell research is also the
person’s moral attitude. But let us begin with the examples
now:
Example. Change in European societies: since the foundation
of the European Union, nationality has less impact on judiciary
systems. The members of different societies perceive this fact
in varied ways, since in every country, the media focus on dif-
ferent issues. In Austria, for instance, there was a heated dis-
cussion about opening the water market to foreign countries. In
this context, the question arose whether Spanish contractors for
example would be permitted to buy Austrian water resources. A
similar debate regarding land policy took place in Hungary and
Poland, while Slovakia discussed similar questions regarding
its energy policy. Decreasing the importance of nationality in
judiciary systems does not only result in economic effects such
as these but also in changes in morality. There has been sig-
nificant change, for instance, in moral values regarding the
keeping of animals. It is evident that these changes are due to
democratic decisions, which illustrates how moral systems are
increasingly defined by the system of democracy they originate
from.
Example. Changes in technology that have led to new moral
systems can be found especially in the fields of medical tech-
nology and medical ethics. The extensive discussions on the
subject of embryonic stem cell research for example, call for
adjustments in moral systems. Taking the form of democratic
decisions, they have led to the following results:
 Germany: production forbidden; research allowed;
 England: production allowed; research allowed;
 Italy: production forbidden; research forbidden;
In Formal Criteria of Rationality this example is discussed in
more detail.

C. J. FELDBACHER
Example. The current changes in the economy, caused by the
penultimate year’s financial crisis, and the demand for new
norms in the financial sector it has evoked, serve as a further
example for the increased democratization of morality. The
demands include, for instance, the establishment of national and
supranational boards of control for banks and national budgets.
From a historical perspective, these demands represent changes
in liberalistic programmes by means of democratic decisions:
an increasing amount of the population shares the opinion that
at least some moral norms are necessary in order to regulate the
market adequately.
These examples have two common grounds: firstly, they are
directly concerned with debates about moral norms, such as
norms in animal ethics, medical ethics and business ethics.
Secondly, the moral evaluation of these changes and the en-
forcement of new moral norms was not determined by an au-
thority, but by democratic decisions. The norms were not de-
fined by a patron, a church authority or a lobbyist, but by a
democratically elected cabinet that was chosen to formulate a
democratized morality. This argument may be seen as trivial
according the following line of reasoning: 1) Those who domi-
nate a society determine its moral system; 2) Before they be-
came democratic, western societies were dominated by authori-
ties; 3) Hence, before democracy, the societies’ moral system
was determined by authorities; 4) Since they became democ-
ratic, all members of the societies have been democratically
determining their moral systems. But this argument appears to
be semantically weak, since the moral systems of western so-
cieties were for a long time strongly influenced by authorities
(e.g. by the churches) and since the new way of enforcing and
handling morality—we will call this way here “democratization
of morality”—does not coincide temporally with the democra-
tization of societies (vs.1). In support of our claim we refer to
the empirical fact that the number of popular votes and refer-
enda on the subject of moral issues increased significantly in
western democratic societies.
It is one thing to argue for the thesis of democratization of
morality in some societies’ legal systems (descriptive), and it is
another thing to argue for an acceptance of this thesis as a nor-
mative ideal. Both lines of argumentation have in common that
they have to examine or investigate methods for moral opinion
pooling. The descriptive part is mostly dealt with empirical
studies of cases as, e.g., we have given here. The normative part
is investigated within contractualist ethics, claiming that in
some more or less strict sense all that is to say about moral
principles for societies is to say something about the moral
attitudes of the societies’ members. In the following section we
are mainly concerned with methods of contractualist ethics for
aggregating individual moral attitudes.
Literature. Here the expression “democratized morality” is
used synonymous to “democratic morality” which is descriptive
and comparable to the use of the expressions “Christian moral-
ity”, “morality of the Greeks” etc. (cf. Gert, 2009). Information
about stem cell policy in European countries used for our sec-
ond example is available at: http://www.eurostemmcell.org/
(July, 2011). A popular discussion of ethics codes in economy
is given in (Berman, 2005). Some statistics about referenda on
moral issues in support of the thesis of democratization of mo-
rality is to be found in (Qvortrup, 2002).
Formal Criteria of Rationality
In the preceding section of this paper it was argued in a very
heuristic way and at a very general level that the setting up of
new moral values by means of democratic procedures consti-
tutes a relatively recent way of accepting and enforcing moral
systems. This process of acceptance stands in opposition to
authoritative procedures.
Once the democratization of morality has been agreed on,
issues arise concerning the democratic procedures for aggre-
gating the single acceptances of moral norms. Also rules have
to be set up for the handling of different opinions regarding
moral norms, just like the majority rule which is used in the
case of public elections or the unanimity rule which is used in
the case of specific jury decisions. One such rule or principle
was introduced by the Austrian mathematician Karl Menger.
His proposal, which is applied in formal philosophy, offers a
promising direction towards a solution to the problem of ag-
gregating single moral attitudes in an adequate way. However,
before we go into more detail, the context of discovery of
Menger’s principle shall be explained sketchily here.
In 1934 at a colloquium at the University of Vienna, Menger
presented a mathematical theorem intended for an application
in the field of ethics. This theorem, as well as another highly
interesting one, was transposed into a more modern frame by
Anne Siegetsleitner and Hannes Leitgeb in 2010. The following
is a selection of insights this principle yields: many problems in
ethics arise out of sets of at least two coexisting, intuitively
acceptable but incompatible norms. Thus, for example, from an
intuitive point of view, some people hold that embryonic stem
cell research is morally permissible, while others of an equally
intuitive stance are convinced that it is morally forbidden.
There are at least two possible ways for solving this issue, one
being an orthodox and another being an unorthodox solution.
An orthodox solution to the problem would be to undertake to
find two separate justifications for each proposed (but conflict-
ing) norm. Then one tries to derive some counterintuitive con-
sequences of at least one of the justifications where one may be
gifted by the fact that exactly one of the justifications leads to
counterintuitive principles. In this case it is easy to decide
which norm one should accept since she only has to choose the
norm that has the deepest structure in terms of intuitive accept-
able justifications.
Apart from this orthodox and common approach, there is an
unorthodox one, which seems to be much more applicable and
which was proposed in a technical investigation first by Menger.
Instead of choosing norms by their deepest intuitive and overall
acceptable structure of justification, i.e., instead of choosing
only those principles that are acceptable to a whole group for a
group’s moral system, Menger proposes to investigate the
moral attitudes of the group’s members and to try to find ways
for partitioning the group in such a way that only non-conflict-
ing members are in contact. So he thinks that one should not try
to find an overall and per se acceptable system of moral norms,
but one should find possibilities of restructuring a group in such
a way that people with coincident moral opinions act together
and people with varying moral opinions stay untouched in
situations they disagree.
We shall go into more detail here and therefore introduce
some technical vocabulary (explanations of the definitions and
theorems are offered below).
Definition 1. ,, []WN is a Menger*-model of language L
iff it holds that:
1) W is a non-empty set of sets of formulas of L, and:
2) N is a mapping from W into and: (()) {}W 
108

C. J. FELDBACHER
3) [ ] is a mapping from the set of formulas of L into ()W

that fulfils the following conditions:
a) For all formulas A of L it holds that:




~
A
WA
and:
b) For all formulas A and B of L it holds that:






&
A
BAB and:
c) For all formulas A of L and for all it holds that: w W



wOA if for all


X
Nw it holds that


X
A
[~O and: d) For all formulas A of L it holds that: . []PA ~A]
Commentary. L is a language containing an operation (and
closed under the operations) for negation (~), conjunction (&),
obligation (O) and permission (P). W represents a set of possi-
ble worlds; N represents those moral systems that are accepted
by the population. This acceptance is technically expressed by
relativization of N to the set of possible worlds W; it is intended
to map each person to a possible world (the person’s point of
view) so that every person is mapped via N to those possible
worlds that are seen as ideal from the concerned person’s point
of view. NB: if, e.g. w1 reflects a person’s P1 point of view and
if N(w1)={{w2}, {w2,w3}}, then person P1 accepts as moral
system (regarding a specific norm that is valid in w2, w3 and
perhaps in some more possible worlds) exactly the moral sys-
tem N(w1). Norms are seen as sets of possible worlds—those
possible worlds in which the norm under consideration is valid
and systems of norms are seen to be sets of norms. [ ] repre-
sents a mapping of formulas of L into the set of possible worlds
so that each formula is mapped to those worlds in which it is
valid. The usual rules of deontic logic apply with respect to [ ],
inasmuch as no norm is valid and invalid in one and the same
possible world etc. Furthermore, illustrated by an example, the
following holds: if q represents “A specific team carries out
research with stem cells in Germany”, and if w is the set of
those formulas that are true and valid in our world, and if there
really is a specific team carrying out research with stem cells in
Germany, then w ∈ [q]. Of course w cannot be seen as to be
ideal in general, because it is not, for instance, ideal from the
Pope’s point of view wP: {w}N(wP).
In accordance with usual semantics one can define deontic
validity as follows:
Definition 2. A formula A of the language L is deontic valid
iff for all Menger*-models M = ,, []WN of L it holds: [A] =
W.
It can be shown that the deontic system D is an adequate
calculus with respect to the given semantics.
Theorem 1. (cf. Leitgeb in Siegetsleitner & Leitgeb, 2010: p.
211). A formula A of L is deontically valid iff A is derivable in
the system D (whereas the axioms of the system are formulated
in L).
We will not make use of this result, because the interesting
question, namely how to create optimal democratic decisions
regarding moral systems, is much more easier dealt with in the
given semantics than in an expansion of the system D1.
Different people accept different systems of norms, however,
not all modes of accepting norms seem to be of equal rational-
ity. Menger proved that only modes of acceptance that are—as
defined below—fully rounded are rational:
Definition 3. (cf. Siegetsleitner & Leitgeb, 2010: p. 213). A
set of moral systems N is fully rounded iff for every person,
assigned to a possible world w, it holds that:
 Principle of Intermediacy. A person who accepts two sys-
tems of norms, also accepts a system included between
them. Technically: if X ∈ N(w) and Z ∈ N(w) and X ⊆ Y ⊆ Z,
then Y ∈ N(w).
 Restricted Principle of Conjunction. A person who accepts
two systems of norms, also accepts a system of norms re-
stricted by combination in case that the norms are noncate-
gorial. Technically: if X ∈ N(w) and Y ∈ N(w) and |X ∩ Y| >
1, then X ∩ Y ∈ N(w).
 Principle of Adjunction. A person who accepts two systems
of norms, also accepts system of norms expanded by com-
bination. Technically: if X ∈ N(w) and Y ∈ N(w), then X ∪ Y
∈ N(w).
Menger showed that these three principles are criteria of ra-
tionality, by proving the following theorem which he called “a
sentence on finite sets with application to formal ethics”:
Theorem 2. (cf. Menger, 1998). A system of systems of
norms N is fully rounded iff for every person assigned to a pos-
sible world w it holds: the, with respect to w, accepted set of
systems of norms N(w) contains only ethical norms (permis-
sions, restrictions, oughts, etc.).
This theorem shows that if a person accepts systems of
norms according to the criteria given above, only the classical
types of moral norms are accepted.
As we are now finished with the introduction of our technical
vocabulary, one may ask for what purpose we are armed in
such a strong way. In particular one may ask why these criteria
of rationality should be so promising in the debate around de-
mocratized morality? The answer is simple: there is an issue
with moral opinion pooling in democratized morality, which
Nelson Goodman called in a much broader context “the imper-
fect community problem”. The problem of imperfect commu-
nity is that although all members of a community resp. a group
may accept pairwise a moral system of norms, there neverthe-
less may be no moral system that is acceptable for the whole
group. Therefore, despite the fact that bilateral debates are suc-
cessful within the group, there may be no result that is satisfac-
tory to the group altogether. Let us illustrate this problem by an
exam- ple: let w1 be the ideal possible world from person P1’s
point of view, w2 the ideal possible world for person P2 and w3
the ideal possible world for person P3. Furthermore, let these
persons accept the following moral systems:
 N(w1) = {{w5}, {w6}, {w5, w7}, {w6, w7}}
 N(w2) = {{w5}, {w7}, {w5, w7}}
 N(w3) = {{w6}, {w7}, {w6, w7}}
Furthermore let us assume the following model: {w5} ⊆ [p],
{w7} ⊆ [q] and {w6} ⊆ [r] with the following representations:
 p: “P imports embryonic stem cells (st)”.
 q: “P does research with st”.
 r: “P produces st”.
So P1 accepts the permission of import of st as a moral sys-
tem, the permission of production of st as a moral system, the
permission of import of and research with st as a moral system,
the permission of production of and research with st as a moral
system, but no moral system, for example, that permits import
of, production of and research with st jointly. P2 accepts import
of st only, research with st only and both: import of and re-
search with st, while P3 accepts production of st only, research
with st only and both: production of and research with st, but no
import. P2 is obviously the legal person’s position in Germany.
P1 and P3 are fictitious, where P3 seems to be a justifiable posi-
1For example, the principle of intermediacy, formulated in Definition 3, is
only expressible in an expansion of D with multiple modal operators: (O1A
& O3C & (C(BA)))O2B, where as bridge principle between the mo-
dalities it would be assumed that O3AO2A and O2AO1A.

C. J. FELDBACHER
tion. P3, e.g., could represent a legal person that may argue for
the permission of producing st, although she thinks that im-
porting st should be forbidden, because she seeks to prevent the
economization of st production.
The problem of the imperfect community is now made evi-
dent by this example. Each pair of persons—P1 and P2, P2 and
P3, P1 and P3—accepts a common system of norms, namely:
 P1 and P2 agree: N(w1) ∩ N(w2) = {{w5}}
 P2 and P3 agree: N(w2) ∩ N(w3) = {{w7}}
 P3 and P1 agree: N(w3) ∩ N(w1) = {{w6}}
But what causes the problem at hand is that the whole group
P1-P3 doesn’t accept a single system of norms. P1, P2 and P3 do
not agree in any moral system of norms: N(w1) ∩ N(w2) ∩ N(w3)
= {}. Therefore, although the bilateral discussions were suc-
cessful, the group as a whole is not. But who is to take the
blame for this? As we can see, according to the criteria pre-
sented above, P2’s and P3’s acceptance of their norms is ra-
tional, that of P1 is not. So it is clear that P1, although she is
rather tolerant, is one way or another not acting on rational
grounds—why would one accept import of, production of and
research with st but reject it as a whole and as a single norm?
With the help of the following theorem, Leitgeb and Sieget-
sleitner have shown that it is always the irrational members of a
society who are the culprits:
Theorem 3. (cf. Leitgeb in Siegetsleitner & Leitgeb, 2010: p.
215). For all Menger*-models M = ,, []WN and all groups
W’ ⊆ W it holds that if N is fully rounded, then:
 If each member of W’ agrees with the others in at least one
moral system (that is: for every w ∈ W’, w’ ∈ W’ it holds
that: N(w) ∩ N(w’) ≠ {}), then it holds that:
 There is a moral system acceptable for the group altogether
(that is: there is a X ⊆ W such that X ∈ ∩ w ∈ W’ N(w)).
According to this theorem, the problem of the imperfect
community is avoidable, provided that all members of the
community have rational attitudes towards norms.
The key idea of this theorem would be that if bilateral talks
are successful and all members of a group are rational, then the
group as a whole will be successful. As we have seen, P1 be-
haves in an irrational manner and is therefore the person re-
sponsible for the group’s failure to find a common system of
norms. How would a rationalized version of P1, called P1’, and
represented below, affect the group’s overall success in agree-
ing on a common system?
 N(w1’)={{w5},{w6},{w5,w6},{w5,w7},{w6,w7},{w5,w6,w7}}
P1’ satisfies all criteria of rationality and obviously represents
England’s position in this matter: import, production and re-
search of st is allowed—in a single norm, in combination and
generally as a whole. So what is the common system of norms
regarding st? England, Germany and the fictitious position
agree on permitting research with st, which means that on the
subject of st they form a community of interest: N(w1) ∩ N(w2)
∩ N(w3) = {w7}. So they can agree on a common policy on
research with st, but have to handle production and import
separately.
What one can learn from this problem and the given solution
is the circumstance that a moral opinion pooling method should
presuppose these rationality constraints in order to be effective
for contractualist ethics. So these constraints seem to be a nec-
essary (but of course no sufficient) basis for contractualist eth-
ics.
The criteria of rationality which are given here allow one to
show another very interesting result on tolerance:
Corollary. (By us). For all Menger*-models M1 = 1 ,, []WN
and M2 = 2 ,, []WN and all groups W’ ⊆ W it holds that if N1
and N2 are fully rounded, and:
 If each member of W’ agrees with the others in at least one
moral system—that is: for every w ∈ W’, w’ ∈ W’ it holds
that: N1(w) ∩ N1(w’) ≠ {}and N2(w) ∩ N2(w’) ≠ {}, and:
 N2 is more tolerant than N1—that is: for every w ∈ W’, w’
∈ W’ it holds that: N1(w) ∩ N1(w’) ⊆ N2(w)N2(w’),
Then a fully acceptable moral system based on N2 is also at
least as tolerant as a fully acceptable moral system based on N1—
that is: there is a X ⊆ W and a Y ⊆ W so that X ∈ ∩ w ∈ W’
N1(w) and Y∈ ∩ w ∈ W’ N2(w) and X ⊆ Y.
According to this corollary, a group’s whole system of norms
is the more tolerant, the more tolerant the bilateral talks within
the group are, whereas it holds that a person, assigned to the
point of view w, is more tolerant in accepting a system of
norms than another person (w0), if all systems of norms ac-
cepted by w0 are also accepted systems of norms of w. The
modified key idea would be: If every person undertakes to be
successful, rational and tolerant in bilateral discussions, than
the group’s system of moral norms will also be successful and
tolerant.
Literature. For Menger’s theorem, see (Menger, 1998: p.
293f). For Goodman’s presentation of the imperfect community
problem, see (Goodman, 1951: p. 125). For a discussion of the
criteria of rationality by Siegetsleitner and Leitgeb, see (Sieget-
sleitner & Leitgeb, 2010: p. 211ff). For a general discussion of
opinion pooling methods cf. (List & Pettit, 2002). A general
overview on Menger’s ethical theory is given in (Leonard,
2010).
Conclusion
In this paper we have established a heuristic and general line
of argumentation in favour of what is termed the thesis of de-
mocratized morality which states that moral systems are in-
creasingly enforced by democratic than by authorities’ deci-
sions. One of the issues that arise when moral systems are ac-
cepted by means of democratic processes (contractualist ethics)
is the imperfect community problem. This problem indicates
the fact that although all pairs of people within a group may
find a system of norms acceptable to them, there may be no
moral system that is acceptable to the whole group. We have
presented here a solution to this problem of moral opinion
pooling that is provided by Siegetsleitner and Leitgeb in their
discussion of criteria for rationality in moral opinion formation
and extended their result by showing that their solution meets
also other intuitions on moral opinion formation, namely intuit-
tions on tolerance: the more people are tolerant in bilateral talks,
the more the whole system of norms is tolerant. This is the
reason why we think that Siegetsleitner’s and Leitgeb’s ap-
proach in the spirit of Menger could serve as a viable solution
for problems in the democratization of morality and hence may
serve as formal preliminaries to contractualist ethics.
Acknowledgements
This research was supported by the Philosophy of Science
Department Salzburg, Austria.
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