CC BY
8Journal of Siberian Federal University. Humanities & Social Sciences 5 (2015 8) 901-911
y^K 111.1
Two Worlds, Two Languages, Two Semantics, Two Linguistic Principles of Compositionality, and Two Kinds of Nonsenses (Criticizing Wittgenstein's Philosophy of Morals and of metaphysics by means of Discrete mathematical modeling a Formal-Ethical Aspect of His Worldview)
Vladimir O. Lobovikov*
Institute of Philosophy and Law 16 Sofi Kovalevskaya Str., Ekaterinburg, 620990, Russia
Received 21.01.2015, received in revised form 14.03.2015, accepted 01.04.2015
The paper represents a systematical critique of Wittgenstein's attitude to semantics of the natural language of ethics and metaphysics. The critique is implemented by means of a discrete mathematical simulation of the famous principle of separation of facts and values. For precise mathematical formulating this separation principle a two-valued algebra of formal ethics is exploited. Being equipped with the fact-&-value-separation principle the author submits systematical separating two worlds, two opposite aspects of natural languages, two formal semantics, two kinds of meanings, two different principles of linguistic compositionality of meanings, and two kinds of nonsenses. The twin worlds, twin aspects of natural languages, twin formal semantics, twin kinds of meanings and twin kinds of nonsenses are inter-excluding and inter-complementing ones. The first elements of the twins are related to the world of "Tractatus". The second elements of the twins are related to the world of pure values which world is transcendent to the one of "Tractatus". The paper is targeted at explicating and precise tabular defining formal-axiological meanings of words and compound word-combinations of the natural language of morals and metaphysics. The author proclaims that according to the submitted (novel) formal-axiological principle of linguistic compositionality (of meanings), formal-axiological meaning of a compound word-combination (of the natural language of morals and metaphysics) is a composition of such moral-evaluation-functions which are formal-axiological meanings of the parts of the compound word-combination. The idea of computing formal-axiological meanings of compound word-combinations (of the language of morals and metaphysics) is exemplified by the submitted discourse about proper knowledge, alethic faith, and alethic tolerance. In the algebraic system offormal ethics a precise definition of the formal-ethical-equivalence relation among moral-evaluation-functions is given and formal-ethical equations are generated by means of computing relevant moral-evaluation-tables. Equations linking moral-evaluation-functions "knowledge", "assumption", "faith", "doubt" are used as representative examples.
© Siberian Federal University. All rights reserved Corresponding author E-mail address: vlobovikov@mail.ru
*
Keywords: world, language, formal, logic, ethics, algebra-of-formal-ethics, semantics, linguistic-principle-of-compositionality, moral-evaluation-function, axiological, meaning, nonsense.
Research area: philosophy.
***
The title of this paper is to irritate those who are funs of Ludwig Wittgenstein and know his biography and writings very well. Why? First of all it is so because Wittgenstein used to write and speak about: the world but not (two) worlds; the language but not (two) languages; the nonsense but not (two) kinds of nonsenses. Hence this paper is devoted not to creating a precise realistic picture of Wittgenstein's philosophy as such but to criticizing his worldview by means of discrete mathematical modeling a formal-ethical aspect of it. According to logic, methodology, and philosophy of science, it is normal that model and original do not coincide: they must be similar but not completely identical; otherwise model has no heuristic value. Obviously Wittgenstein did not undertake discrete mathematical modeling a formal-ethical aspect of his worldview. He did not undertake a formal-ethical investigation as well. Sometimes he spoke and wrote of ethics but not of formal one. Moreover he summoned and tried to avoid explicitly talking of (positive) ethics: his talks (and even the lecture) of ethics were negative: positive talking of ethics (and of metaphysics) was labeled as meaningless. One can paradoxically characterize his "Tractatus logico-philosophicus" as a treatise about ethics but the "Tractatus" defines ethics only negatively and implicitly: it does not contain manifestly defining and substantiating positive moral values. Wittgenstein believed that positive moral values are to be shown in human conduct instead of being spoken about (as speaking of positive moral values has no meaning). According to Wittgenstein's biography he had shown his positive moral values in his moral and religious behavior. Nevertheless below I undertake
investigating possibility of manifest (explicit) formulating quite a positive ethical system (a formal-ethical one) of moral evaluations in spite of the well-established and recognized fact of flexibility and relativity of moral assessments of elementary moral actions. That is why funs and connoisseurs of Wittgenstein shall be irritated by the below presented formal-ethical discourse. Notwithstanding this expectation I believe that the below submitted discourse is worth taking seriously and discussing systematically.
In times of Wittgenstein the descriptive-indicative meanings of empirical sentences and the formal-logical semantics of the language of science were investigated carefully. On the contrary, the possibility of construction and systematical application of a formal-axiological semantics of evaluative sentences (of ethics, aesthetics, religion, metaphysics, etc.) was not recognized. (I think that it is not recognized properly even today.) Investigating the evaluative (formal-axiological) semantics of the natural language was underestimated and even ignored. Probably at the level of sub-consciousness Wittgenstein perceived this asymmetry situation and therefore instinctively tried to correct it by attracting attention to semantics of the natural language which combined both aspects: the factual (formal-logical) and the evaluative (formal-axiological) ones.
According to Wittgenstein's "Tractatus", the world is a totality of facts [22]. Let the symbol Wi stand for this world. Values do not exist in the world W1. Hence even "truth-values" belong not to the world of facts but to the one of values: "Logic is transcendental" [22]. Ethics, aesthetics and other axiological disciplines are transcendental as well [22]. That language which is isomorphic
to the world of "Tractatus" (let that language be called Li) must be not used in any talks about pure values: otherwise the talks become meaningless. Using the language L1 one must abstain from saying something about values. Otherwise using the language L1 heads to nonsenses.
Nevertheless, as strange as it is, Wittgenstein himself was not perfectly silent with respect to values; he did not absolutely abstain from discussing them at the level of natural language. Many facts of his private life [23], philosophical texts, and confessions of the people with whom he communicated demonstrate that he shared quite definite religious and moral values and norms, attempted to follow them systematically in his life [3; 4; 7; 10; 15; 22—27]. Thus he really lived in the world of values or at its border-line (let the world of values be called W2). By definition, the world W2 is a totality of values (and only values). Facts do not belong to W2. The two worlds W1 and W2 exclude and complement each other. Their union makes up the universe of discourse accomplished by means of the natural language. That language (L1), which is isomorphic to the world of "Tractatus", is an important subsystem of the natural language as a system. Another important subsystem of the natural language system is such a language (let it be called L2), which is isomorphic to the world of pure values (W2). L2 must be not used in any talks about pure facts: otherwise the talks become meaningless. Using only the language L2 one must abstain from saying something about facts as such. Otherwise the usage of L2 heads to nonsenses.
There are two different kinds of nonsenses. One kind of them (let us call it N1) is a result of using L1 for talking about W2. Another kind of nonsenses (let us call it N2) is a result of using L2 for talking about W1. The relationship < W1, L1> makes up the descriptive-indicative (formal-logical) semantics to be called S1. The relationship < W2, L2> makes up the evaluative (formal-
axiological) semantics to be called S2. As the first is well-studied and the second is almost unknown, hereafter we shall discuss systematically the formal-axiological semantics dealing with formal-axiological meanings (let M2 stand for these meanings) of words and word-combinations of the natural language. (Let, respectively, M1 stand for the descriptive-indicative meanings of the natural one.)
The present paper is aimed at explicating universal and immutable laws of the world of pure values. However many humans believe that universal and immutable laws of the world of pure values do not exist. The overwhelming majority believes that being of such formal-axiological laws is impossible as values and assessments are necessarily relative and undergo permanent change.
Many humans believe that any relativism is incompatible with objective knowledge. In particular, they think that if moral evaluations of concrete contents of moral actions (and agents) are relative to evaluators, then objective moral laws (=necessarily universal and immutable positive-moral-evaluations of actions) do not exist as they are impossible on principle. However, in my opinion, objective knowledge is compatible with some forms of relativism [13]. For instance, it is compatible with a relative relativism, i.e. such relativism, which is not an absolute one.
This general statement may be exemplified by the relativistic physics. In the special-relativity-theory it is demonstrated that (if x is a physical body then) mass of x, length of x, time of x are necessarily relative: they necessarily depend upon that physical systems, in relation to which they are measured; measuring in relation to different systems gives different results. Nevertheless there are some physical qualities, which invariantly exist in relation to all physical systems. These invariant physical qualities are considered as objective laws of the special-relativity-theory.
Thus physics has made a precedent to be applied to analogous cases. The situation in relativistic ethics is analogous to the one in relativistic physics. Therefore the experience of creating relativistic physics is heuristically important for creating relativistic ethics as a system of objective knowledge of absolute laws of the moral-value-relativity [11; 13].
The special-relativity-theory was precisely formulated and developed by means of the mathematical language. It was impossible to create and develop this theory by means of the natural language. In formal ethics the situation is analogous to the one in physics. It is impossible to create and develop a theory of relativity of moral evaluations (as a system of absolute laws of their relativity) at the level of natural language. For departing from the old-fashioned absolute-moral-relativism to precise mathematical formulations of absolute formal-ethical laws of moral-evaluation-relativity [11; 13], it is necessary to construct an artificial language of formal ethics for investigating a mathematical model of the system of moral evaluations of actions and agents. Hereafter let us start constructing the artificial language and the mathematical model.
Below the possibility of mathematical representation of moral activity is demonstrated by the elementary mathematical ethics—two-valued algebra of good and evil [11; 13]. This algebra is based upon the set of acts. By definition, acts are such and only such operations which are either-good-or-bad ones in the moral meaning of the words "good" and "bad". Algebraic operations defined on the set of acts are moral-evaluation-functions. Moral-evaluation-variables of these functions take their values from the set {g, b}. Here the symbols "g" and "b" stand for the moral values of acts "good" and "bad" respectively. The functions take their values from the same set. The symbols: "x" and "y" stand for moral-forms of acts. Elementary moral-act-forms deprived of
their contents are independent moral-evaluationvariables. Compound moral-act-forms deprived of their contents are moral-evaluation-functions determined by these variables.
Let symbol £ stand for the moral evaluator, i.e. that person, in relation to which all evaluations are generated. In the moral-evaluation-relativity theory, £ is a variable: changing values of the variable £ can result in changing moral evaluations of concrete acts and agents. However if a value of the variable £ is fixed, then moral evaluations of concrete acts and agents are definite.
DEFINITION DF-1 (of invariant law of moral-relativity theory): in two-valued algebra of formal ethics, a moral-evaluation-function is called formally-ethically (or invariantly) good one, if and only if it acquires the moral value g (good) under any possible combination of moral values of its variables.
DEFINITION DF-2 (of formal-ethical contradiction): in two-valued algebra of formal ethics, a moral-evaluation-function is called formally-ethically (or invariantly) bad one, if and only if it acquires the moral value b (bad) under any possible combination of moral values of its variables.
DEFINITION DF-3 (of formal-ethical-equivalence-relation): in two-valued algebra of formal ethics, moral-evaluation-functions x and y are formally-ethically equivalent (this is represented by the symbol "x=+=y"), if and only if they acquire identical moral values (from the set {g, b}) under any possible combination of moral values of the variables. In the natural language the equivalence relation "x=+=y" is represented by the ambiguous word-homonym "is" [11; 12]. Its ambiguity and homonymy was noticed and recognized by many prominent logicians and philosophers including Wittgenstein [22, p. 55]. For adequate understanding the present paper here it is worthy of note that "is" as the
well-known logical connective, and "is" as a linguistic means for representing the relation "x=+=y" in the natural language, are not synonyms. Hence substituting them for each other is strictly forbidden [12].Violating this prohibition produces linguistic illusions of logic contradictions with facts.
Taking into an account the above-given definitions, one can make an important discovery: the invariant laws of moral-relativity theory do not depend upon possible changes of the moral evaluator E. If x is a formal-ethical law, then x is morally good in relation to every moral evaluator E.
Moreover, in the moral-relativity theory under review, formal-ethical contradictions of complex moral conduct also do not depend upon possible changes of the moral evaluator E. If x is a formal-ethical contradiction, then x is morally bad in relation to every moral evaluator E.
Finally, if there is the above-defined formal-ethical equivalence-relation between moral-evaluation-functions x and у, then the functions x and у are formally-ethically equivalent ones in relation to every moral evaluator E.
Hence, in spite of the flexibility and relativity of elementary moral evaluations, there are absolute invariants (immutable universal laws) of the moral relativity [11; 13]. Thus the moral relativity is not absolute but relative one.
To exemplify the above-said let us discuss moral-evaluation-functions "properknowledge (or knowledge proper)", "alethic (true) faith", "doubt", "assumption", "toleration" and "tolerance" in two-valued algebraic system of formal ethics. To begin discussing these functions let us introduce the symbols standing for them in the artificial language of this algebra and then precisely define formal-axiological meanings of the introduced symbols by means of corresponding tables.
The glossary for the Table 1: The symbol KExy stands for the moral-evaluation-function "x's
Table 1: "Proper episteme" and "assumption"
x y KExy ADxy IDxy NExy DXxy DMxy
g g b g b g g b
g b b g b g g b
b g g g b b b g
b b b b g g b g
Table 2: "Alethic faith" and "alethic doubt"
x y FAxy DNxy FNxy DTxy SCxy NSxy
g g b g b g g b
g b b g b g g b
b g g g b b b g
b b b b g g b g
knowing (what, whom) y (in the proper episteme meaning of 'knowing')". ADxy - the evaluation-function "x's assuming y (as a proper episteme)". IDxy - "x's not-assuming y (as a proper episteme)". NExy - "x's not-knowing (what, whom) y. DXxy -"y's being a doxa of (for) x". DMxy - "y's having a determined epistemic quality for x". The moral-evaluation-functional sense of these operations is defined by the Table 1.
The glossary for the Table 2: The symbol FAxy stands for moral-evaluation-function "x's alethic (true) faith (not-revisable belief) in (what, whom) y". DNxy - "x's alethic doubt (not-removable one) in not-y". FNxy - "x's true faith (not-revisable belief) in not-y". DTxy - "x's alethic doubt (not-removable one) in y". SCxy - "x's alethic (true) skepticism concerning y, i.e. x's alethic doubt in both: y and not-y". №xy - "nonbeing of x's alethic skepticism concerning y", i.e. "either x's alethic faith in y", or "x's alethic faith in not-y". The moral-evaluation-functional sense of these operations is defined by the Table 2.
The glossary for the Table 3: The symbol NNxy stands for "x's alethic (true) non-toleration of
Table 3: "Toleration" and "alethic tolerance"
x y NNxy TOxy NOxy TNxy T°xy NTxy
g g b g b g g b
g b b g b g g b
b g g g b b b g
b b b b g g b g
not-y", or "x's not-standing (what, whom) not-y". TOxy - "x's alethic toleration of y", or "x's standing y". NOxy - "x's alethic non-toleration of y". TNxy -"x's alethic toleration of not-y". TCxy - "x's alethic tolerance to y, i.e. x's standing both: y and not-y". NTxy -"nonbeing of x's alethic tolerance to y", i.e. "either x's alethic non-toleration of y", or "x's alethic non-toleration of not-y". These operations are defined by the Table 3.
Using the above-given definitions one can demonstrate the following equations.
1) KExy=+=BFxy: proper knowledge is alethic faith.
2) BFxy=+=KExy: alethic faith is proper knowledge.
3) AExy=+=DNxy: assuming means doubting-in-the-contrary.
4) NAxy=+=BNxy: not-assuming is alethic faith-in-the-contrary.
5) NKxy=+=DTxy: non-being of proper knowledge means doubt, i.e. non-being of alethic faith.
6) DExy=+=S°xy: proper knowledge-indifference is equivalent to alethic faith-indifference.
7) RExy=+=BPxy: non-being of proper knowledge-indifference is equivalent to non-being of alethic faith-indifference.
According to these equations, the knowledgemodalities and the corresponding faith-ones are formally-ethically equivalent to each other. This outcome of mathematical modeling is surprising for those who are used to the opposition of
"knowledge" and "faith", hence, they could estimate 1)-6) as paradoxes. However there are only illusions of paradoxes caused by the ambiguity of the natural language. For destroying such illusions of paradoxes in algebra of formal ethics there is a formal principle of autonomy of facts and values, which is precisely formulated as follows.
Let fix stand for an act of informing (true or false affirming) that x takes place in reality. Concerning the relationship between "=+=" and "logic equivalence", the principle in question may be formulated as the following rule (A&B):
(A) From the truth of x=+=y it does not follow logically that logic equivalence of fix and fiy is true;
(B) From the truth of logic equivalence of fix and fiy it does not follow logically that x=+=y is true.
The illusion of paradox concerning equations 1)-6) is destroyed by (A&B). This illusion is a result of not-recognized "jumps" from formal-ethical equivalences of evaluations to formal-logical equivalences of facts (and back from the formal-logical equivalences of facts to the formal-ethical equivalences of evaluations). In algebra of formal ethics such bridging the gap between facts and values is strictly forbidden by (A&B), which is an explication of important particular case of the general principle of mutual formal-logic autonomy of corresponding facts and values (propositions and evaluations). The rule (A&B) can be universalized in the following way. Let us call this generalization "(Y&Z)";
(Y) From x=+=y it does not logically follow that (fix©fiy);
(Z) From (fix©fiy) it does not logically follow that x=+=y.
Here the symbol "©" stands for any element of the set of all binary formal logic operations.
As to the unary operations of algebra of formal ethics, the general value-&-fact-autonomy
principle can be precisely formulated as the following rule (U&Q):
U) From ß@x it does not logically follow that ßx;
Q) From ßx it does not logically follow that
ß@x;
Here the symbol stands for any element of the set of all unary operations of algebra of formal ethics [11; 13; 14].
Now taking into an account the above-said let us consider the famous linguistic principle of semantic compositionality of meanings of compound word-combinations [9; 16-21]. According to this compositionality principle, the semantic meaning of a complex phrase is a function determined by meanings of parts of the complex phrase. If parts of the complex phrase are functions determined by meanings of their parts, then the semantic meaning of the complex phrase under consideration is a composition of the functions. Here the terms "function" and "composition of functions" are used in their proper mathematical meanings.
According to algebra of metaphysics considered as algebra of formal axiology [11], in particular, as algebra of formal ethics [13], semantic meanings of words and word-combinations in the natural language of ethics and metaphysics are nothing but moral-evaluation-functions determined by a finite number of moralevaluation-variables [11-14]. Semantic meanings of compound word-combinations in the natural language of ethics and metaphysics are nothing but compositions of the moral-evaluation-functions which are formal-axiological meanings of the parts of the compound word-combinations under consideration. (Here the terms "function" and "composition of functions" are used in their proper mathematical meanings as well.) It is easy to see that in the language L2 the linguistic principle of semantic compositionality of meanings of compound word-combinations
is a very specific one. Let this specific formal-axiological compositionality-principle be called C-P2. Hence, respectively, the linguistic principle of semantic compositionality of meanings of compound word-combinations in the language L1 is to be called C-P1. The functions and compositions of functions implied by the two compositionality principles (C-P1 and C-P2), are significantly different ones. How does the principle C-P2 work? For showing a concrete example of its functioning let us consider the epistemic paradox of George Moore [1; 2; 5; 6; 8; 14]. To do this we need some additional moral-evaluation-functions to be introduced and defined by the below glossaries and tables.
The glossary for the Table 4: The symbol K2xy stands for the binary moral-evaluation-function "uniting (conjoining) x and y in a conduct as a whole". (Here the index 2 indicates that the indexed letter stands for a binary operation.) T2xy - the moral-evaluation-function "destruction, termination, annihilation of x by y". P2xy - the evaluation-function "preservation, conservation of x by y". O2xy - "y's offensive, assault (aggression), attack against x". D2xy -"defense of x by y". V2xy - "y's violence over (what, whom) x". J2xy - "y's nonviolence over (what, whom) x". U2xy - "excluding moral choice of the best between x and y (combined with realization of the chosen and non-realization of the not-chosen)". A2xy - "not-excluding moral choice (and realization) of the best among such moral alternatives which can be made by means of x and y". W2xy - "uniting (conjoining) non-realization of x and non-realization of y (in a conduct as a whole)". E2xy - "moral identification of x and y", or "morally equalizing x and y". C2xy - "realizing y in response to realization of x". X2xy - "y's contradiction to (what, whom) x".
The glossary for the table 5: The symbol Nx stands for the unary moral-evaluation-function
Table 4: Binary moral operations in two-valued algebra of formal ethics
x y K2xy T2xy P2xy O2xy Dxy ^xy J2xy LT 2xy ^xy E2xy C2xy ^xy
g g g b g b g b g b g b g g b
g b b b g b g b g g g b b b b
b g b g b g b g b g g b b g g
b b b b g b g b g b b g g g b
Table 5: Unary moral operations in two-valued algebra of formal ethics
x Ax Bx Gx Fx Lx Mx Yx Ox Px Ix Zx Sx Cx Jx Dx Wx
g b g g g g g b g g b b b g g g b
b g b g b b b b b b b b b g g g b
"nonbeing (nonexistence) of x". Bx - the moral-evaluation-function "being (existence) ofx". Gx -"God ofx". Fx - "faith in x". Lx - "alethic necessity of x". Mx - "alethic possibility of x". Yx - "alethic accidentalness (contingency) of x". Ox - "making (what) x obligatoryor "x's being obligatory". Px - "permitting (what) x", or "x's being permitted, or "permission of x". Ix - "deontic indifference to x". Zx - "alethic tolerance to x". Sx - "x's self-destruction, self-termination (suicide)". Cx - "x's self-preservation, self-conservation". Jx - "x's self-salvation". Dx - "x's self-defense". Wx - "x's moral self-contradiction", or "inconsistency in moral form of x's activity'.
Using the above-given definitions one can substantiate the following equation of two-valued algebra of formal ethics.
S K2KExyABFxy=+=b.
According to the above definitions DF-2 and DF-3, this formal-ethical equation means that the epistemic paradox of George Moore is a formal-ethical contradiction, i.e. an inconsistency in moral form of x's activity [14]. This conclusion is very interesting and important one in a wide philosophical context, but in the present paper I concentrate attention mainly on the
fact that computing the equation (8) necessarily exploits the above-discussed principle of compositionality of formal-axiological meanings (C-P2).
Moreover demonstrations of the following formal-ethical equations also imply using the
formal-axiological compositionality principle (C-P2).
9) C2NGxPy=+=g: if God does not exist then everything is permitted (F. Dostoyevsky).
10) C2PSxPy=+=g: if suicide is permitted then everything is permitted (L. Wittgenstein [23]).
11) C2NPdNPSx=+=g: if some (action) d is not permitted, then suicide is not permitted (L. Wittgenstein [23]).
The discrete mathematical models (of moral and metaphysical principles) considered in this paper are interesting not only from an abstract philosophical theory viewpoint, but also from the ones of theology and philosophy of religion, ethics (philosophy of morals), legal philosophy of the natural law, criminology (philosophy of crime), psychology, and even psychiatry. Important practical work aimed at prevention
of committing suicides unites all the mentioned them with the abstract fundamental investigation disciplines in one activity and necessarily links undertaken in this paper.
References
1. Almeida Claudio. What Moore's Paradox Is About // Philosophy & Phenomenological Research. 2001. Vol. 62. Issue 1, pp. 33-59.
2. Cholbi Michael. Moore's Paradox and Moral Motivation // Ethical Theory & Moral Practice. 2009. Vol. 12. Issue 5, pp. 495-510.
3. De Angelis William J. Ludwig Wittgenstein - A Cultural Point of View. Boston, MA, USA: Northeastern University, 2007.
4. Goldstein L. Clear and Queer Thinking: Wittgenstein's Development and his relevance to Modern Thought. London: Duckworth, 1999.
5. Green Mitchell S. and Williams John N. (eds.) Moore's Paradox: New Essays on Belief, Rationality and the First-Person. Oxford: Clarendon Press; New York: Oxford University Press, 2007. 247 р.
6. Green Mitchell; Williams John. Moore's Paradox, Truth and Accuracy //Acta Analytica. 2011, Vol. 26. Issue 3, pp. 243-255.
7. Hacker P. Wittgenstein's place in Twentieth Century Analytic Philosophy. Oxford: Blackwell, 1996.
8. Heal Jane. Moore's paradox: A Wittgensteinian approach // Mind. 1994. Vol. 103. Issue 409, pp. 5-23.
9. Horwich P. The composition of meanings // Philosophical Review. 1997. Vol. 106. pp. 503533.
10. Jareño-Alarcón Joaquin. Religion y Relativismo En Wittgenstein. Barcelona: Ariel, 2001.
11. Lobovikov V. Mathematical Ethics, Metaphysics and the Natural Law (Algebra of metaphysics as algebra of formal axiology). Yekaterinburg: The Institute of Philosophy and Law of the Ural Division of the Russian Academy of Sciences, 2007. 408 p.
12. Lobovikov V. A Digital Turn in Philosophy and Wittgenstein about "Is" // Philosophy of the Information Society. Papers of 30th International Wittgenstein Symposium (August 5-11, 2007, Kirchberg am Wechsel). Volume XV / Edited by Herbert Hrachovec, Alois Pichler, Joseph Wang. Kirchberg am Wechsel (Lower Austria): The Austrian Ludwig Wittgenstein Society, 2007. P. 134-137.
13. Lobovikov V. Algebra of Morality and Formal Ethics // Looking Back to See the Future: Reflections on Sins and Virtues / Edited by Katarzyna Bronk. Oxford, United Kingdom: InterDisciplinary Press, 2014. P. 17-41.
14. Lobovikov V. Moore's paradox in the light of algebra of formal ethics // Tidings of the Ural Federal University. Series: Social Sciences. 2014. N. 1. pp. 44-57.
15. Malcolm Norman. Wittgenstein: A Religious Point of View? London: Routledge, 1993.
16. Pagin P. Communication and strong compositionality // Journal of Philosophical Logic. 2003. Vol. 32. pp. 287-322.
17. Pelletier F. J. The principle of semantic compositionality // Topoi. 1994. Vol. 13. pp. 11-24.
18. Pelletier F. J. Did Frege believe in Frege's Principle? // Journal of Logic, Language, and Information. 2001. Vol. 10. pp. 87-114.
19. Pelletier F. J. Context-dependence and compositionality // Mind and Language. 2003. Vol. 18. pp. 148-161.
20. Principle of compositionality // Wikipedia, the free encyclopedia. URL: http://en.wikipedia. org/wiki/Principle_of_compositionality (21.10.2014).
21. Werning M., Hunzen W., Machery E. (eds.). The Oxford Handbook of Compositionality, Oxford: Oxford University Press, 2012. 745 p.
22. Wittgenstein Ludwig. Tractatus logico-philosophicus. London: Routledge and K. Paul, 1949.
23. Wittgenstein Ludwig. Notebooks 1914-1916 / G.E.M. Anscombe (trans.). Oxford: Blackwell,
1961.
24. Wittgenstein Ludwig. Lectures and Conversations on Aesthetics, Psychology and Religious Belief / Edited by C. Barrett. Oxford: Basil Blackwell, 1966.
25. Wittgenstein Ludwig. A Lecture on Ethics // Philosophical Occasions (1912-1951) / Edited by J. Klagge and A. Nordman. Indianopolis: Hackett, 1993. P. 36-44.
26. Wright G.H. von. Wittgenstein. Minneapolis: University of Minneapolis Press, 1982.
27. Wright G.H. von. Culture and Value. Revised Edition / Edited by G.H. von. Wright. Oxford: Blackwell, 1998.
Два мира, два языка, две семантики, два лингвистических принципа композиционности и два вида бессмыслицы (Критика философии Винтгенштейна о морали и метафизике с использованием дискретного математического моделирования формально-этического аспекта его точки зрения)
В.О. Лобовиков
Институт философии и права Россия, 620990, Екатеринбург, ул.Софьи Ковалевской, 16
В статье представлена систематическая критика точки зрения Винтгенштейна о семантике естественного языка этики и метафизики. Критика основана на дискретном математическом моделировании известного принципа разделения фактов и ценностей. Для точного математического формулирования данного принципа разделения используется двузначная алгебра формальной этики. Используя принцип разделения факта и ценности, автор предлагает систематическое разделение двух миров, двух противоположных аспектов естественных языков, двух формальных семантик, двух типов значений, двух различных принципов лингвистической композиционности значений и двух видов бессмыслицы. Парные миры, парные аспекты естественных языков, парные формальные семантики, парные типы значений и парные виды бессмыслицы являются
взаимоисключающими и взаимодополняющими. Первые схожие элементы относятся к миру «Трактата». Вторые схожие элементы относятся к миру чистых значений, мир которых трансцендентен по отношению к миру «Трактата». Целью данной работы является толкование и точное табличное определение формально-аксиологических значений слов и составных словосочетаний естественного языка морали и метафизики. Автор отмечает, что в соответствии с представленным (новым) формально-аксиологическим принципом лингвистической композиционности (значений), формально-аксиологическим значением составного словосочетания (естественного языка морали и метафизики) выступает состав морально-оценочных функций, являющихся формально-аксиологическими значениями составных частей словосочетания. Идея вычисления формально-аксиологических смыслов составных словосочетаний (языка морали и метафизики) иллюстрируется представленным дискурсом соответствующих знаний, алетической веры и алетической толерантности. В алгебраической системе формальной этики дано точное определение соотношения формально-этической эквивалентности между морально-оценочными функциями. Формально-этические уравнения создаются посредством вычисления соответствующих морально-оценочных таблиц. В качестве иллюстрирующих примеров приводятся уравнения, связывающие морально-оценочные функции «знания», «допущения», «веры» и «сомнения».
Ключевые слова: мир, язык, формальный, логика, этика, алгебра формальной этики, семантика, лингвистический принцип композиционности, морально-оценочная функция, аксиологический, значение, бессмыслица.
Научная специальность: 09.00.00 - философские науки.
