U r s z u l a W y b r a n i e c - S k a r d o w s k a
ON TRUTH, EDUCATION AND LOGICAL CULTURE
Th e need to know about the world has been present in us since childhood. Getting to know the reality is discovering the truth, approaching the truth and searching the truth. Without a specifi c freedom culture, which enables us to discover the world, without referring to the truth acquiring a thorough knowledge of the world as well as sharing with the knowledge becomes fraudulent or even impossible.
Yet, what is the truth? Is it possible to distinguish numerous kinds of truth or is there one, common, objective truth? What is the aim of science or philosophy? What is the specifi city of a scientist’s or an academic educator’s work in conducting research, teaching and educating the youth, as well as in forming logical culture of a university student? Th eses and other questions have tormented philosophers for over two and a half thousand years.
From the ancient point of view, as well as modern history, philosophy and logic, the author of this short article endeavours to provide in a concise and simple man-ner some answers to the above mentioned questions, stressing and accepting in this respect the concepts and views of outstanding representatives of the world famous Lvov – Warsaw School1, including the semantic concept of truth by Alfred Tarski.
1. Historical introduction
I will begin from short commentaries connected with traditional philosophical problems referring to the term “truth”.
It is possible to assume that the modern understandings of truth are rooted in the ancient Greek philosophical thought, which was the foundation of European philosophy2.
In the ancient Greece, philosophers, i.e. “the lovers of wisdom”, allocated to themselves the monopoly on the truth, to be precise: on looking for the truth and wisdom. In the 5th - 4th centuries B.C. In Greece, mainly in Athens, Sophists activ-ity could be noticed. Th ey were travelling teachers of “wisdom” and educators, who off ered for money education in subjects useful both in public and personal life3. Although they did not constitute one unifi ed philosophical school, they invented the style of new rational thinking about the natural and social reality. Th ey are considered to be the fi rst humanists in the history of ancient philosophy, since the issue of their interest was the life and activities of humans, a human himself. “A hu-man is the measure of everything”, as Pythagoras claimed, one of the most famous thinkers among Sophists. Sophists recognised the relativity of human cognition and of whole knowledge, since it is based on fallible sensory perception. Th e truth is relative, Sophists claimed, it has the character of human assumption, which can
be , for our own use, formed in any way with argumentation, i.e. skillful convincing to our own views. According to Sophists, there is no one common and objective truth, there are better (more useful) and worse (less useful) ones. Th e choice of better truth is determined by its bigger usefulness and benefi t. Th e justifi cation of the truth is conditioned by a practical aim. Wise men are the ones that can choose more useful truths, not only as far as cognition is concerned but in the areas of ethics, religion and legal norms, as well.
Th e pragmatism of Sophists contributed in time to overuse of knowledge by using unreliable argumentation in justifying their theses, creating so called
soph-isms, i.e. skillful, seemingly right deductions which conceal deliberately hidden
logical fallacies. Th e attitude of Sophists led to recognising the view that it is pos-sible to conjure two contradictory, yet true statements about every thing. It re-quired fl uency and skill in proving the claimed theses, even the wrong ones, as well as in rebutting the theses of an opponent. Numerous Sophists succumbed also to the temptation to teach rich Greek young men aiming at making a political career how to use misleading, abstruse arguments which had hardly any connection to 2 Th ales of Miletus is considered the “father” of European philosophical thought (the 7th / 6th century B.C.), who was the fi rst to try to answer the question why and how the world came into being (see Słownik kultury antycznej, L. Winniczuk (ed.), Warszawa 1989, p. 477 and following).
3 See Słownik kultury antycznej, L. Winniczuk (ed.), p. 483 and following; K. Szymanek, Sztuka argumentacji, Warszawa 2001, p. 293 and following; W. Tatarkiewicz, Historia fi lozofi i, v. 1, Warszawa
the truth. As a consequence, the word “a sophist” gained a pejorative meaning; the
term began to be used for pseudo scientists and teachers of pseudo wisdom, spe-cialists of conning, though convincing arguments. And such an understanding of a sophist has survived until today.
Th e teachings of Sophists on relativity of the truth was opposed by Socrates (469–399), who descended from their circles and is considered to be one of the most outstanding ancient thinkers4. Th ere is only one, objective and common truth, Socrates, the teacher of Plato, claimed, and the only way to fi nd the truth and to show it is in a dialogue, called later a Socratic dialogue, preserved later in so called
Plato Dialogues. Socrates, venturing into a polemic with the theses of Sophists and
seeming truths, underlining at the same time the consciousness of his own igno-rance (“I know that I know nothing”), used two methods in his dialogue: 1) a neg-ative, critical (elenctic) one, in which through irony and questions he proved to his interlocutor the fallacy of his knowledge, leading his consecutive theses to absurd, due to which overthrowing his arguments, and a positive, constructive (maieutic) one, in which, by suggesting the right answers to the asked questions, Socrates tried to reach the true answers, the truth together with the interlocutor.
Socrates declared the cult of the truth, believed in the existence of absolute good and absolute truth. He considered knowing the objective truth and leading people towards the knowledge as a primary ethical value. His teachings and methods, which dealt with ethical problems and problems of human life, infl uenced his students, among which there were also politicians. For “not recognising the gods that the state recognised” and for “negative infl uence on the youth” he was for-mally tried and sentenced to death by drinking cicuta.
Th e views of Socrates, especially on the truth, known mainly from the writings of Plato, have been present in further development of philosophical and ethical thought not only in the ancient times, but in the Middle Ages and modern times, as well. Various schools in various times have referred to his views, sometimes contradictory ones, ones unequivocal in understanding the truth.
Both Plato – the founder of the famous philosophical school known as Plato
Academy (it survived 10 centuries, until the 6th century) – as well as Aristotle
(384–322), an old student and associate of Plato, contradicted the cognitive relativ-ism of Sophists, recognising the primacy of the truth in science (the objective truth), opposing the rhetorics exercised by Sophists.
Aristotle, one of the greatest and most versatile academics of the ancient times, created the foundations to almost all academic teachings. Predominantly, he
lated logic from philosophy and became known as the “father” of formal logic. It is Aristotle to whom we owe the classical defi nition of the truth in the cognitive sense that has been functioning until today. Th e relative, utilitarian truth and the
pragmatist defi nition of the truth is replaced by the objective truth and by Aristotle, correspondence defi nition, according to which, to summarise, the truth is
a corre-spondence of thoughts and the things that are subjects of the thoughts.
To the classic, Aristotle defi nition of the truth we will refer in a further part of this work. It constitutes the foundation of the modern, semantic defi nition of the truth, provided by Alfred Tarski.
However, is there one, objective truth, or are there many truths? Th e answer to the questions needs some analysis of the term “truth” itself.
2. The truth and the criteria of the truth
“What is the truth?”, a question which was tauntingly uttered by Pilate (without expecting an answer), a question which is quoted by a famous English statesman and philosopher, Francis Bacon (1561–1626), in the introduction to his essay Of
Truth, and following him, other great thinkers, has never found a satisfying answer.
No wonder, since the issue of the truth is one of the most diffi cult and the most disturbing philosophical and not only philosophical problems.
Let us begin from the fact that the truth can be perceived as: 1) the object of cognition, i.e. substantially,
2) a feature, a property of descriptive sentences or logical claims5 expressed by them, or of cognition whose results are these claims,
3) a cognitive and ethical value.
In the fi rst case, the word “truth” is used as a noun, e.g. as in a sentence:
Th e fact that the Vistula is a Polish river is the truth .
Or as an auxiliary, e.g. as in a sentence:
It is the truth that the Vistula is a Polish river.
Such a use assumes that the truth is something existent, that it is an abstract subject, a collection of partial truths (in the exemplary sentences a partial truth is the fact that the Vistula is a Polish river), that it is something unique that “can be discovered in the never ending eff ort of humanity”6. In addition, the truth is
objec-5 Logical claims are meanings of sentences-types (compare footnote 8). Resultantly, they are not psychological claims (some thoughts) of particular people.
tive, in consequence independent of the cognitive subject, time, circumstances, or context. Th e truth perceived in such a way becomes then a philosophical,
onto-logical term. It is possible, then, to talk about the ontic truth7.
In the second case, the word “truth” is used as an adjective, meaning that the truth is a property of sentences (or the respective claims), which is based on their “truthfulness”. Th en, the word “truth” is replaced by the word “truthfulness”, which means a certain domain of descriptive sentences treated as sentences-types8. Such a use assumes then the existence of such sentences. We can deal with them, e.g. in the expression:
Th e sentence “Th e Vistula is a Polish river” is true.
Th e truth understood in such a way becomes then a logical, semantic term. We can talk then about a semantic understanding of the truth. Th e truth of the sentence is here a domain, the possessing or not possessing of which by a given sentence depends on whether between it (respectively what it expresses – a thought, a claim) and what it (respectively she, he) concerns – the widely understood reality – exists a specifi c relation, in Aristotle, classical defi nition – correspondence. Th e truth of the sentence becomes then an objective feature, it does not depend especially on whether we consider the sentence true according to some criteria. Th en, the con-tradiction of the truth is a falsehood.
It must be noticed here that the feature of truthfulness is ascribed not only to sentences or their thought equivalents or to cognition, results of which are true sentences; in the last case we can talk about epistemological truth. We talk also about truthfulness in respect to someone or something that is not a sentence, a claim or cognition using expressions: “a true human”, “a true friend”, “a true communist”, “a true Pole”, “true life”, “a true work of art”, “a true doctrine”, “a true theory”, and so on. We use then the word “true” in its secondary, not primary meaning, possibly meaning a fulfi llment of the essence of an object, its internal coherence, harmony,
correspondence with some ideal, cultural model, a model idea, or criteria.
In the third case we use the word “truth” to specify something that is good, pre-cious, worthy of human desire, something that is an aim of human endeavours, that is an axiological value. When we talk about “knowing the objective truth”, the
truth is perceived as a cognitive value. When we talk about the point of “pursuing
the truth” and “stating the objective truth”, the truth is for us moral in character.
7 In philosophy there exists also the term of ontological truth.
8 Sentences-types are abstract objects, not physical ones. Th ey can be perceived as classes of physical, specifi c sentence inscriptions, to some extent identifi able, e.g. due to their shapes, see U. Wy-braniec-Skardowska, Th eory of Language Syntax, Boston–Dordrecht–London 1991.
Is there a connection among the ontic, semantic, epistemological and axiologi-cal understanding of the truth?Exploring the constantly discovered single partial truths (the ontic truth), we also get to know true sentences (the semantic and epistemological truth) about the reality that interests us, and if searching for the truth (the ontic or semantic one), stating the truth (true sentences), familiarising with the truth ( with true claims) is the aim of our endeavours, the truth is for us cognitive-ethical in character.
Th e word “truth” in ontology (a general theory of beings, metaphysics), logic (logical semantics), epistemology (a theory of cognition), and in axiology (a study of values) has various, though in the perspective given above, close meanings.
Various truths in particular branches of knowledge are also oft en discussed. Is it the right thinking? Th e truth in the branches is specifi ed using various methods, various ways of checking the truth of claims, by means of various criteria. Conse-quently, if the meaning of the word “truth” is relevant for the criteria of the truth, and these can be diff erent in distinct areas of knowledge, various kinds of the truth are sometimes mentioned, or even numerous truths. We usually mean, then, the truths (rules) relativised to a particular branch of knowledge, e.g. to ethics, phi-losophy of language, theory of cognition, logic, physics, geometry, etc.9 Subject
evidence is considered a well motivated, eff ective criterion of the truth, one which
is inner in relation to cognition and connected with the way in which the subject of cognition (the state of the matter) is given to the subject in the act of cognition, providing the truthfulness (faithfulness) of the cognitive result10.
Nevertheless, it should be clearly emphasised that the criterion of the truth – the basis following which we can recognise the truthfulness of cognition, or the condi-tions enough for some sentence, view or belief (claim) to be considered true – it cannot be identifi ed with the defi nition of the truth, with the defi nition of a cogni-tive sentence. Th e classical defi nition of the truth does not refer to any of its crite-ria. Th e defi nition was clearly diff erentiated from the criterion by Bertrand Russell and Jan Łukasiewicz. Following Kazimierz Ajdukiewicz, it is possible to assume that the acceptance of the classical defi nition of the truth allows to entirely elimi-nate the criterion of the truth11.
9 E. Agazzi, O różnych rodzajach prawdy [in:] Znaczenie i Prawda, Warszawa 1994, pp. 285– –307.
10 See: Leksykon fi lozofi i klasycznej, (ed.) J. Herbut, Lublin 1997, pp. 438 i 439.
11 K. Ajdukiewicz, O stosowaniu kryterium prawdy [in:] idem, Język i Poznanie, v. I, Warszawa 1985, pp. 11–13.
3. The classical definition of the truth and competitive definitions
Th e classical defi nition of the truth, known also as a correspondence one, is con-cerned with semantic truth, with the truthfulness of sentences (logical claims). It was formed by Aristotle in no. IV, ch. 6 of Metaphysics and, quoting Tadeusz Czeżowski, it relates »the truthfulness of a sentence with the existence of a subject which is claimed in the sentence: a true sentence is one which states about an exist-ing subject that it is there or about a non existent one that it is not there. In an imprecise conclusion, the defi nition is as follows: “the truthfulness of a sentence is its correspondence with reality” – taken from the defi nition of Saint Th omas Aqui-nas, and the full version of which…«12, in free translation from Latin is : “Th e truth is a correspondence of reason (thoughts) and the matter of fact, which is based on the fact that reason (thought) notifi es the existence of what is there or the non existence of what is not there13.
Th e relation between correspondence, more specifi cally – its happening, was not always perceived as it should be, evoking long lasting disputes. Th e understand-ing of the relations a kind of “sensual reaction”, followunderstand-ing the model of some spatial relation between reason (thought) and reality, evoked among the philosophers of the end of the 19th century and the beginning of the 20th reactions directed against the classical defi nition of the truth (since a thought can be connected only with another thought, not with reality).
Th ey started to seek diff erent than objective truthfulness criteria of scientifi c righteousness of claims, replacing the classical defi nition with others.
A coherency defi nition (Spinoza, Kant, Bradley, Neurath) states that the
truthful-ness of scientifi c claims is based on mutual correspondence of the thoughts ex-pressed by them, conditioning the truthfulness of a theory sentence on the fact whether it constitutes an ingredient of a coherent, uncontradictory whole, where it is not satisfactorily stated what is the essence of this correspondence.
12 T. Czeżowski, Uwagi o klasycznej defi nicji prawdy [in:] idem, Odczyty Filozofi czne, Toruń 1958, p. 68. In the original defi nition given by St. Th omas Aquinas, the defi nition sounds as follows: Veritas
est adequatio intellectus et rei, secundum goud intellectus dicit esse, goud est, et non est, quo non est
(comp. also W. Krajewski, Słownik pojęć fi lozofi cznych, Warszawa 1996, p. 159). Alfred Tarski showed in his concept of the truth what is the nature of the statement adequatio intellectus et rei (see part 5 of this work).
13 See: Leksykon…, p. 437. Th e defi nition quoted here implicates the following defi nition of the epistemological truth: cognition is true when and only when the substance of cognition corresponds with the subject (the state of the matter) with which the cognition is concerned, meaning when it is exactly how the cognition defi nes or how it is claimed in the cognition.
An evidential defi nition conditions the truthfulness of sentences on the criterion
of subject evidence (subjective) or of the mentioned subject evidence (objective).
A pragmatic defi nition conditions the truthfulness of a sentence, a thesis on
some pragmatic criteria: usefulness for predictions and practical use, convenience, and the economical aspect. American pragmatists of the 20th century (W. James, CH.S. Peirce, J. Dewey) claimed that the truthfulness of sentences or claims is defi ned by the widely understood criteria of usefulness. Rejecting the classical defi nition of the truth and gaining theses that constitute a solid basis of our knowl-edge, pragmatists condition the truthfulness of sentences on some aims and ac-tions, they bestow the truth with a comparative character, and cognition – relative. Recognising the primacy of cognition over thinking, and of practice over theory, pragmatists approach the views of Sophists.
It is possible to form a charge against the pragmatic defi nition, just as facing other non classical defi nitions of truthfulness, that – to some extent – it is justifi ed by assuming the classical defi nition14. Moreover, as mentioned above, the classical defi nition does not require relating to any criteria of the truth. “Th e term of truth-fulness is a natural and basic characteristic of science, most fully diff erentiating science from other creations of mind culture”15.
Th e aim of science is to pursue the objective truth. Th e endeavour grants the truth with a cognitive value and defi nes the way of education, especially academic one.
Polish philosophers and logicians gathered in the internationally famous the Lvov – Warsaw School ( Szkoła Lwowsko-Warszawska; abbrev: SLW) supported the Aristotle defi nition.
4. The truth as the primary value in the Lvov–Warsaw School
Th e attitude of philosophers in the Lvov–Warsaw School (SLW)16 was formed by its founder and the “teacher of teachers”, Kazimierz Twardowski, who as a 29-year-old professor, in November 1895, came from Vienna to Lvov to accept the chair at Jan Kazimierz University. When Twardowski took the post, various infl uences of European philosophy crossed in Poland. Nevertheless, Twardowski worked out
14 See: Leksykon…, p. 439. 15 T. Czeżowski, Uwagi…, p.70.
16 A monograph devoted to the SLW was written by Jan Woleński; see idem: Filozofi czna Szkoła Lwowsko-Warszawska, Warszawa 1985. Most of the comments or remarks connected with the SLW
a specifi c philosophical style, both due to his contribution to science (especially to general theory of knowledge), and to his own example, his teaching work as a pro-fessor of the university and an organiser of the work of his students and circles on which he had impact. Twardowski had about 40 students, and in the SLW circles, almost 80 people worked17. Th e charisma of Twardowski, the scientifi c and ethical values he emphasised (veracity, responsibility for words, reliability, and respect for others and their views) aff ected not only his particular students who accepted the values, but the whole school, as well.
Th e SLW was unifi ed not as much by common views on various philosophical problems, as by common ideas and common intellectual and ethical attitude. Th e most important connection among the members of the SLW was an opportunity to fulfi ll intellectual values, the cult of the objective truth, the discovery of scien-tifi c truth and pursuing the objective truth as a value of scienscien-tifi c and educational ethics.
Already in 1904, Twardowski, in his speech, at the fi rst sitting of the Polish Philosophical Society, he was one of the founders of, defi ning the aims of the so-ciety, claimed, “We want all the directions of work and views in our Society to pursue one aim: to enlighten the truth. Scientifi c criticism is a means to achieve this”18. Two years later, Twardowski published in writing his speech on veracity19, and in a speech celebrating the fact that he was granted a honoris causa doctorate by Poznań University, in 1932, he spoke amazingly beautifully and correctly – like no one else – about the primacy of the objective truth in academic work and teach-ings, and about the fact that pursuing the objective truth has a clear ethical sense20.
Here we will quote a few statements from this speech. Emphasising the function of academic work in university activities, the importance of spreading the skill to reach the objective truth, the objective character of a research, Twardowski stated about the last issue that “it has only one task: to reach correctly justifi ed true claims, or at least probable […]”21. Th is aim “[…] carries for humanity a light of pure knowledge, it enriches, deepens science, gains new truths and probabilities – in one
17 Famous students of Twardowski were, already mentioned in this work, Kazimierz Ajdukiewicz and Tadeusz Czeżowski.
18 K. Twardowski, Przemówienie na otwarciu Polskiego Towarzystwa Filozofi cznego, “Przegląd Filozofi czny” VII/2, pp. 241–242.
19 K. Twardowski, Prawdomówność jako obowiązek etyczny, “Przegląd Filozofi czny”, IX/1. 20 K. Twardowski, O dostojeństwie Uniwersytetu, Poznań MCMXXXIII.
word it creates the highest intellectual values that a man can be granted”22. Next, Twardowski claims, “University is founded to serve scientifi c truth, objective knowledge, and to perfect methods of research. It should predominantly teach academic thinking as the right thinking to lead to the truth”23. Continuing his speech on the tasks of a university school, Twardowski talks about the University (which is surprising even in modern times), “It must be separated from everything that does not serve acquiring scientifi c truth, it must sustain the proper distance between itself and the current that fl ows near its walls: everyday life, the noise of clashing social, economic, political and all other currents, among the struggle of the various currents the University should stand like a lighthouse, which shows ships with its light the way through the raging waves, yet it never immerses its light in the waves. Having done so, the light would disappear, and the ships would re-main without the guiding light”24. Continuing about the function of a university school, Twardowski emphasises that it has to walk two paths: of educating the youth and publishing academic works, “yet the University is not only the research-ers that work there […], there are also students who are supposed to acquire the skills of academic thinking and working […]”. talking about educative tasks includ-ing students, Twardowski states, “education […] is based on awakinclud-ing and deepen-ing in young minds the understanddeepen-ing of the considerable importance that the objective truth and activities to reach it contain for people; […] the youth, im-mersed in the academic and researching atmosphere of the University, will learn to look for the objective truth in everything, instead of succumbing to great-sound-ing statements and fallgreat-sound-ing into the nets of various soul hunters… And realisgreat-sound-ing that in every case there is only one objective truth, the youth will fi nd common grounds in searching for it; […] the love of the objective truth and a belief in constant pur-suit of the truth must become a powerful factor of educating the youth to be hu-mans that understand one another and are understanding for one another, that are able to cooperation where subject reasons are above individual ones, common interests above individual one”25. On the role of an academic teacher and a man of science Twardowski continues as follows: “An academic teacher is fi rst of all a serv-ant of the objective truth, a representative of the truth and its spokesman among the youth and society. […] the one who can really see the meaning of life in reach-ing and teachreach-ing the objective truth, who, so to say, is a man of science, […] he can
22 Ibidem.
23 Ibidem, pp. 9–10. 24 Ibidem, p. 11. 25 Ibidem, pp. 13–14.
be deaf to the deceitful whispers of various ambitions and defend against the temp-tation of playing any role where it is not really about the truth but about power, infl uence, honours and titles, or simply about money!”26. Twardowski defi nes the role of philosophy, and in searching for the truth, he wonders about it and about the perfect methods of reaching it. He claims that “philosophy is located in the focal point of all sciences. By considering the truth itself as the core of its study, by enlightening the paths that lead towards it, philosophy becomes an ally and leader of everyone who in any fi eld of human investigation follow the truth”27.
It must be stated here that philosophy in the SLW is sometimes identifi ed with logic, and somewhat correctly, because the body of the school, next to Twardowski, was formed from such outstanding logic philosophers as Kazimierz Ajdukiewicz, Tadeusz Czeżowski, Tadeusz Kotarbiński, Stanisław Leśniewski and Jan Łukasiewicz. Among the enumerated scholars, the two last ones are the creators of the Warsaw Logic School.
Warsaw School of Logic [Warszawska Szkoła Logiczna (abbrev: WSL)] was an uttermost achievement of the SLW. It was active in the inter war period and worked together with Warsaw University, reactivated once Poland regained independence. Its founders were students of Kazimierz Twardowski: Jan Łukasiewicz and Stanisław Leśniewski, and their common student was Alfred Tarski, who to the greatest ex-tent, due to his semantic concept of the truth (truthfulness), contributed to WSL’s fame in the world. Th e consciousness of Twardowski’s heritage and traditions of the SLW had undoubtedly a considerable infl uence on the teachers of Tarski, on Tarski himself, and on the philosophical background of his concept of the truth28.
WSL conducted new original study in the area of mathematical logic, bases of mathematics and science methodology. Its creators were philosophers, but they were off ered chairs in the mathematics – nature department! From the very foun-dation, the school has been connected with mathematical society, who not only supported its activity, but ventured into close cooperation with the school, as well.
26 Ibidem, pp. 14–17. 27 Ibidem, p. 19.
28 Tarski, mathematically educated, felt also a student of Tadeusz Kotarbiński, and his academic results, just as the results of other representatives of the school, were philosophically “concerned”. Stanisław Leśniewski – the professor advising with Tarski’s doctorate thesis – expressed his views on the truth (his belief that the truth is absolute, eternal and age-long) and on the need to pursue abso-lute truthfulness of cognition not only in his earlier works, but also in a dissertation Is the truth only
eternal, or is it eternal and age-long, published in a pedagogical periodical “Nowe Tory” of 1913, no.
10, pp. 504–505. He called sentences in a material supposition that had the feature of truthfulness the truths.
Th us, the members of the school on the one hand cooperated with a group of mathematicians, on the other hand – with philosophers, especially with a student of Twardowski, Tadeusz Kotarbiński.
5. On the semantic concept of the truth by Tarski
Alfred Tarski, as the fi rst one in the history of philosophy, worked out in a scien-tifi c, mathematical way a semantic defi nition of the truth for the specialist lan-guages of deductive studies (1933)29; his concept of the truth is considered one of the most important individual achievements of WSL30. Th e traditions of the SLW explain the choice of a sentence as a carrier of the objective truth. Tarski defi ned the term of a true sentence performing an explication of the classical defi nition of the truth. According to the classical defi nition of the truth, the truth and falsehood, so called logical values, are semantic properties of sentences since they are ascribed to sentences due to their correspondence with states of matters described by the sentences. Accepting the following, according to Tarski intuitive, formation of the defi nition by Kotarbiński:
A true sentence is a sentence which expresses that there is such and such a state of the matter, and this is what the state of the matter really is,
Tarski incorporates it into a known scheme:
(*) “p” is a true sentence when and only when p, in which “p” is the name of sentence p.
A specifi cation of the scheme (*) is a partial defi nition of the true sentence: “Th e Vistula is a Polish river” is a true sentence when and only when the Vis-tula is a Polish river.
However, used in such an intuitive way, the term of a true sentence causes dif-fi culties, which can become a source of contradiction and of a so called liar’s
para-29 A. Tarski, Pojęcie prawdy w językach nauk dedukcyjnych, “Prace Towarzystwa Naukowego Warszawskiego, Wydział III Nauk Matematyczno-Fizycznych” 1933, no. 34, vii+116. Th e book has been translated to a few languages, such as German, English, Italian, French. A reprint of the original work of 1933 can be found [in:] A. Tarski, Pisma logiczno-fi lozofi czne, v. 1, Prawda, (ed.) J. Zygmunt, Warszawa 1995, pp. 13–172.
30 I discuss the achievements of Tarski in detail in the essay Alfred Tarski – człowiek, który zde-fi niował prawdę, “Ruch Filozozde-fi czny”, no. 4 (2007), in print.
dox31. Th e paradox has numerous versions. One of them, which can be recon-structed in the (*) scheme, can be described in the following way32:
(s1) I stated a falsehood. Th en:
(s2) If I said the truth, then (s1) is true and according to the (*) scheme I stated
a falsehood.
(s3) If I stated a falsehood, then (s1) is neither true nor following the (*) scheme
I did not state a falsehood, I said the truth.
A logical conclusion:
(s4) I stated a falsehood and I did not state a falsehood (I am a truthful liar). A formally corrected scientifi c theory must be, of course, free from any paradox. Such a theory of the truth had been expected for centuries. Alfred Tarski (1933) presented such a theory.
Tarski, in his concept of the truth, explained in detail why the defi nition of thee truth cannot be created for everyday language. Namely, some sentences of the natural language, such as statement (s1), lead to contradiction, and the source of the contradiction lies in not diff erentiating there between two levels of language:
the subject language (which does not include the word “falsehood”, stated about
sentences) from the metalanguage (in which we talk about expressions of the sub-ject language, especially about its sentences)33.
Resultingly, defi ning the term of a true sentence in everyday language causes the danger of contradiction and evokes the necessity to create a defi nition of the truth for a particular language. Th is convinced Tarski to form a defi nition of a true sentence only for the formalised languages of deductive sciences, and only using the proper metalanguage. Tarski creates a detailed defi nition of a true sentence using the language of a particular famous deductive theory – classes algebra. Si-multaneously, he presents the general conditions showing how to use his method of defi ning the term of a true sentence for the languages of other deductive sci-ences34. A basic means that serves Tarski to defi ne the term of the truth
(truthful-ness) is a supporting term – the semantic term of satisfying. Th e term of satisfying 31 It comes from a famous representative of the eristic school (eristic – the art of arguing), Eu-bulides of Miletus, and was known already to Aristotle.
32 Comp. J.J. Jadacki, Człowiek i jego świat, Warszawa 2003.
33 Th e diff erentiation of subject language from metalanguage to solve the problem of antinomy was performed by Stanisław Leśniewski.
34 Th e method is in a simple way presented by Jan Woleński in Filozofi czna Szkoła…, pp. 162– –165. A wider discussion of Tarski’s concept can be found in chapter 16 of Logika formalna. Zarys
encyklopedyczny, edited by W. Marciszewski, elaborated by S. Krajewski, Warszawa 1987, pp. 144–
is understood here just like in school mathematics, when we say that e.g. subject-number 5 satisfi es the formula-inequality “x < 8” (with a free variable x) in the area of natural numbers, since a sentence “5 < 8” is true. Generally, a formula with free variables is satisfi ed by specifi c subjects when replacing in the formula the free variables respectively with names of the subjects we achieve a true sentence. Th e limits of the work make it impossible to plunge into the subtleties and details of the adequate defi nition of the truth by Tarski. Nevertheless, leaving the subtleties aside, it is possible, following his concept, to conclude that the simplest formula “Tx” of a deductive theory is satisfi ed by subject a only when Ta, namely only when “Ta” is true. Reversing the order, it is possible to receive a classical condition of
truthfulness adequacy: “Ta” is a true sentence only when Ta35.
In the concept of the truth by Tarski, a sentence (a sentence has no free varia-bles) is true when it is satisfi ed by any subjects. Th e truth understood in the
classi-cal sense, as a correspondence of a sentence and the reality outside language, de-pends here on the interpretation of the symbols of variables and the domain of the subjects which the variables concern (which the variables undergo)36. Nevertheless, the substantial correctness of the concept has the proper argumentation that sug-gests that the defi nition given by Tarski specifi es the sense of the term “a true sentence” in agreement with the classical defi nition of the truth.
It should be added here that the theory of the truth by Tarski was the fi rst step to build a theory of models. Th e term of truthfulness is the basic term of this theory – one of the most prominent branches of mathematical logic. Th e semantic theory of the truth by Tarski has had an enormous infl uence on the development of the theory of models aft er the war and this is the nature of its logical importance. Th e possibility to defi ne semantic terms in logic, including the term of a true sen-tence as understood in the classical defi nition of the truth and having excluded semantic paradoxes, has simultaneously an unusually great philosophical meaning, since the term belongs as mentioned above, to the basic terms of the theory of cognition37.
35 Th e subtleties spoken hereof are connected with the fact that (*) scheme is an expression of metalanguage, and its right part includes an ingredient belonging to the subject language, namely a sentence whose truthfulness is supposed to be specifi ed. For the classical defi nition of the truth to be correct, the ingredient must be replaced by its synonym – “translation” into metalanguage. In the concept of the truth by Tarski, the argument is of considerable importance.
36 Th e charges of the opponents of the classical defi nition of the truth that we should not connect thought with reality, only with another thought are strongly rejected by T. Czeżowski; see idem,
Uwagi o klasycznej defi nicji prawdy, pp. 70–71.
37 25 years have passed from the death of Alfred Tarski, jone of the greatest logicians of all times aft er Aristotle. A quarter of a century is a long period. It is surprising then, that the achievements of
Tarski gained the biggest world fame from the members of WSL. Th is happened not only due to his semantic concept of the truth, but also because of his aca-demic work, which, as a logician, he conducted aft er the war in Berkley (USA), where he created Californian School of Logic – an outstanding worldly research centre in logic and bases of mathematics. Th e school, similar in its “philosophical component” to Warsaw School of Logic, has become not only a forge of talents, but a forge of knowledge and exchange of international academic thought, as well38.
Th e achievements of Tarski and other distinguished representatives of Warsaw School of Logic and their students contributed to distinguishing from logic, as a science, so called Polish Logic. Resultantly, Polish logic has today international, good prestige.
Th e wheel of history goes on. Th e enormous success of logic and semantic re-search in the circles that stemmed out of the Lvov – Warsaw School was possible only due to the assumptions of work in education of its Master and Founder – Kazimierz Twardowski, and his remarkable, aforementioned, students. And the assumptions included educating in the name of the truth, criticism, precision and accuracy, as well as everything that is an element of logical culture.
6. The truth and spreading logical culture
How many times have we heard that we need logic here and there? Whereas, logical
culture of Polish school and university youth, and in general of Polish society, is
constantly decreasing. Th us, there arises a question: Why? Th e reason seems to be in reach: it lies in Polish educational system, which makes it impossible to acquire or perfect logical culture by the youth. Th e sense of logic in education was ques-tioned in the aft er war history of Poland. Exercising logic became political then… Later, mainly due to Kazimierz Ajdukiewicz and Tadeusz Kotarbiński, logic returned as a school subject to the last years of secondary schools, and later to universities. However, in the times aft er Solidarity, it is possible to notice a systematic elimination of logic in teaching programs. Why is that? Maybe because in our nation such values as the necessity of acquiring objective knowledge or the benefi t of mind culture have not rooted strong enough. Th ey have been replaced by mind-enslaving media and virtual knowledge, and by the ever present pragmatism.
Tarski in the fi eld of logic are still alive, and his semantic defi nition of the truth still evokes discus-sions and comments.
38 Tarski, in spite of his academic achievement, did not live long enough to receive praise in Poland, since until the end of the inter war period he was not granted a chair at Polish university.
Th e cultural patterns present today, such as the truth is created by a human, a human is the measure of the truth, are similar to the views of a Sophist, Protago-ras. Th e ever stronger tendencies to accept relativity of truth, weakening of the role of the objective truth in cognition and human activity cannot shape the views of children and the youth, neither, more importantly, can they direct the educators working with them every day, because, according to the thought of Jan Zamoyski39, it is time to consider the saying:
Commonwealths will be such as the upbringing of their youth.
Education, including logic education of the youth, is one of the most salient tasks and responsibilities of the state. Teaching logic is essential for popularisation of logic culture as an important element of the widely understood humanist
cul-ture, which already in the ancient times was considered the ideal of paideia.
Ventur-ing into logic culture should render individuals sensitive to the truth and false-hood, to logical mistakes, implement criticism towards our own and other views. Logical culture is necessary in private and social life since it protects us against accepting unjustifi ed claims, it does not allow to implement opinions that are not supported by logical thinking, it also teaches carefulness in making our own opin-ions, propagates humility when faced with the objective truth in, protects against belligerence or demagogy.
Acquiring logical culture is connected with educational work. Basing on their knowledge, an educator should form in a student the need to fi nd the objective truth and the skill of critical thinking, speaking and reasoning. To do so, the teach-er must achieve or pteach-erfect his logical culture himself. It is possible through study-ing logic, whose teachstudy-ing program cannot in any case depend on political, cul-tural, or social factors.
Logic has been the basis of all sciences and the basis of teaching. It is a tool, useful in every branch of knowledge, life and technique, in accordance with the intentions of its creator, Aristotle, whose logical works have been named
Organon,which means a tool. It can be perceived as an ideal model of rationality,
and as paidagogos – the educator and teacher of philosophical wisdom, one that allows to realise the primary value which is the objective truth, the truth so much cultivated in the Lvov – Warsaw School and the truth so much attacked in all places where there is no reliability and decency in thinking or acting, where a lie is a weapon.
39 A politician and a protector of humanism, a founder (1595) of Zamoyski Academy, which was known for its high level of teaching and education.
“And now logical culture – Tadeusz Czeżowski writes – is bound to ethical and social culture. It lift s people above the contradictions that divide them and con-nects them with binds of general solidarity, pointing the way to the age-long ideals of the truth and of the inseparable from the truth goodness and beauty”40.
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SUMMARY
Th e paper addresses the ages-old problem of truth, considered from a scientifi c, ethical and educational point of view. Approaching the issue from the perspective of ancient as well as modern history of philosophy and logic, the author attempts to outline, in a concise and intelligible manner, some answers to such questions as: What is truth? Can we speak of many kinds of truth, or is there just one, universally valid and objective truth? What is the aim of science, philosophy? What is the role of teachers in conveying reliable knowledge about the surrounding world? What is the value of objective truth in the education of school children and university students? How can we disseminate logical culture among the youth and within society? Th e answers are based on the ideas and notions of the re-nowned Lvov-Warsaw School of Philosophy, and particularly of its founder Kazimierz Twardowski.
Th e dissertation essay paper also briefl y discusses the semantic concept of truth devel-oped by Alfred Tarski, a representative of the Lvov-Warsaw School who substantially con-tributed to the School’s international repute.
