Józef Maria Bocheński’s logical analyses of Question I of St. Thomas Aquinas’ Summa Theologiae

Bocheński claims that it would be very useful to apply logical tools to philosophical and theological investigations. His viewpoint can be ascribed to the fact that during Bocheński’s youth logic and reflections on the foundations of mathematics flourished. His seminal work on these issues is the book Gottes Dasein und Wesen. Logische Studien zur Summa Theologiae I, qq. 2–11 (2003). Due to the fact that it was necessary to introduce numerous corrections to it, the book was published over a decade after submitting the manuscript to the publishing house in 1989 (according to certain sources, in 1991). There exist two manuscripts: one German (1989b) and one Polish (1993b). The latter contains also Bocheński’s unpublished works, including the analyses of Question 1 from St. Thomas Aquinas’ Summa Theologiae. In this Question, Aquinas focuses on the ways of understanding the term sacra doctrina. Bocheński’s text, which is a logical analysis of that Question, seems to be almost completed. With reference to the topic and the method of analysis, the text constitutes a whole together with the analyses of Questions 2–11, published in Bocheński (2003).


Introduction
It is impossible to talk about attempts to utilize logical tools in the philosophy of God without introducing the person and works of Fr. Józef Maria Bocheński (1902Bocheński ( -1995. The inter-war period was the time of the activity of the so-called Cracow Circle. Besides 1. There is an urgent need to resume studies on God. 5 2. A human being has only three ways of knowing God: direct experience, reasoning, and faith. 3. It is necessary to learn about the scholastic research into the issues connected with God. 4. The results of the scholastic doctrine of God should be judged critically. 5. An urgent task is to examine critically the Kantian and neo-positivist reservations concerning the possibility of knowing God, including the proofs of His existence. 6 6. Looking at what an average believer's experience of God demonstrates gives rise to two tasks: (1) to determine what ''experience'' and similar words mean; (2) to examine how such experiences, in both the broad and the narrow senses, are possible, or if they really exist.
2 On the left-hand side, the abbreviation used to refer to a given work has been provided. 3 Bocheński (1991). 4 Cf. IIa, 7-16; IIb, 2-9; III, 17-28. 5 In IIb Bocheński adds that he means philosophical studies. Cf. IIb, 3. 6 In IIb Bocheński is talking about the objections to the proofs of God's existence, and in IIa and III about the doubt about the possibilities of knowing God. Cf. IIb, 5 and 9; IIa, 11 and 16; III, 21-22 and 28.
7. The scholastic doctrine of God should be studied with the tools of mathematics and logic as well as the critical method. 8. A believer does not need a proof of God's existence because he believes in this existence. 9. The type and the way of acceptance by a believer of God's existence requires detailed logical and theological studies. 10. It is necessary to develop a theology that is concerned first of all with God Himself.
For Bocheński, the main subject of the formal-logical research in the above program was St. Thomas Aquinas' Summa Theologiae. After a detailed analysis of Aquinas' text, Bocheński formalized Questions 2-11 and then, on the basis of the results, he presented the preliminary axiomatization of the theory of the Absolute. 7 He also analysed the Kant's cosmological criticism of the argument for the existence of the Absolute. The results of these works were published in the book Gottes Dasein und Wesen. Logische Studien zur Summa Theologiae I, qq. 2-11 and can be found as well in the German and Polish manuscripts. In addition, the latter work contains the following texts: Wiara i wiedza. Matematyczno-logiczny komentarz do pierwszego rozdziału Sumy (Faith and Knowledge. A Mathematical-Logical Commentary to Chapter I of the Summa) and Powszechniki jako treści cech w filozofii św. Tomasza z Akwinu (Universals as the content of properties in St. Thomas Aquinas' Philosophy). 8 Their absence from the other works can be explained by the fact that the Polish manuscript of the book dates from 1993 and constitutes the latest work of all the works in which the topic is discussed (with regard to the time of writing and editing by Bocheński). The German manuscript was sent to the publishing house in Munich either in 1990, as Hans Burkhardt writes in the introduction to the book, or in 1991, as Bocheński reports in the introduction to the Polish manuscript. 9 Because Bocheński did not authorize the amendments introduced to the book by the publishing house, the Polish manuscript constitutes his latest text. It should be noted that the text we are interested in is not included in the introduction to the manuscript and in the table of contents. These two additional texts can be found in the manuscript following the list of contents. 10 So far, they have not been published.
The aim of the present work is to carry out a critical analysis and reconstruction of the first of the above mentioned texts, that is, Bocheński's formalization of Question 1 of the Summa Theologiae. It can be useful in the future edition and publication of this study. Because Bocheński's text is not known to a wider public, it will be presented in detail so that the relevance of a commentary can be demonstrated. That is also why the character of the present study is descriptive rather than critical or polemical. 7 The formal analyses used by Bocheński are often called formalizations. By this is meant the translation of a text written in a natural language into a formal language. Cf. Ajdukiewicz (1978), (the original text: Ajdukiewicz (1934)). 8 The translation is by the author of the present paper. 9 IIb, 1; III,9. 10 IIb, 83-97; IIb, 97-106.

Bocheń ski's logical analyses
Why did Bocheński actually undertake the logical analyses of Question I of St. Thomas Aquinas' Summa Theologiae? This question can be answered in the following way. First, such a study constitutes a whole together with Questions 2-11 which were analysed previously. Second, as the author emphasizes, although the fragment of the Summa describes the meaning of a very important term sacra doctrina (sacred doctrine), ''in the writings on the topic we often encounter a mistake: either ignorance of this text or a hagiographical attitude towards the author who is treated like an infallible god.'' 11 According to Bocheński, what is required is an honest analysis.
The first problem he points to is the understanding of the expression sacra doctrina. In the first Article of the Question we are interested in finding arguments to show that the doctrine is indispensable for salvation, and in the second Article that the doctrine is a science. How should we understand the term then? Is it about faith or about theology? Bocheński claims that in both cases there is a contradiction. He shows it in the following way: The abbreviations: dn =: sacred doctrine is indispensable for salvation, ds =: sacred doctrine is a science, fs =: faith is a science, tn =: theology is a science, ts =: theology is indispensable for salvation.
Bocheński tries to show the contradiction in the following way 12 : Article 1 Article 2 1: ds ! ts 1 0 : dn ! fn 2: dn 2 0 : dn 3: $ ts 3 0 : fn from l and 2 by means of modus ponendo ponens we obtain: 4: ts 4 0 : fn and from 4 and 3 by means of conjunction introduction we obtain: 5: ts^$ ts 5 0 : fn^$ fn Thus, there is a contradiction. Unfortunately, the above reconstruction is incomplete. There is no information about the meaning of the expression ''fn'' which is used in the formalization referring to Article 2. Besides, verse 4 in the formalization of Article 1 does not result logically from verses 1 and 2, and the meanings of the expressions ''tn'' and ''fn'' seem to be swapped (''n'' means necessity and ''s'' means science).
The above text is criticised by Bocheński, who introduces two additional abbreviations: f =: sacred doctrine is faith, t =: sacred doctrine is a (scientific) theology.
The main problem is the interpretation of the term abstrahit. It is translated as together. According to Bocheński, it refers to a logical sum. The same interpretation is suggested by the term sive in sentence 2b. If this is so, then, according to Bocheński, Cajetan assumes that: Article 1 Article 2 1: f _ t ! tn 1 0 : f _ t ! fs but at the same time he claims that these sentences do not imply false sentences: 2: t ! tn 2 0 : f ! fs : As Bocheński observes, this is a mistake because the relevant directives of reasoning are correct. He uses the following schema of reasoning: The contradiction can be also avoided, according to Bocheński, not by rejecting but by accepting the content of relationship 2. This is the case because knowledge of scientific theology is indispensable for humanity as a whole, such that indirectly it is indispensable for each individual. Such an interpretation of Aquinas' text is common, although Bocheński does not find any real basis for it. Even if we accept this interpretation, sentence 2 0 remains a false sentence.
The contradiction can also be avoided by assuming that, because in the Question under discussion the Bible is called scientia (science) by St. Thomas, the noun is used in a different sense than in the other texts. It is then possible to say that faith too is a science. However, such an interpretation is rejected by Bocheński. In his view, science means here an orderly set of sentences with axioms (principia), as defined by Aristotle. Besides, in such an interpretation of the term sacra doctrina it is impossible to understand it as a teaching activity. Bocheński notices also that the term appears four times in the discussed Question (3.2; 8.6; 9.3 and ad tertium), and it is equivalent to sacra scriptura. This equivalence is stated directly (2. ad 2: sacra Scriptura seu doctrina). It seems then that, according to Bocheński, the use of the term sacra doctrina is incoherent. It is not surprising that the term is also translated by means of the expression sacred science.
After conducting a critical review of Cajetan's commentary, Bocheński introduces his own analysis of the specific Articles of Question I of the Summa Theologiae. In order to do that he usually lists the abbreviations and inference rules used in the commented fragments.
The abbreviations: The directives of reasoning given by Bocheński include three rules of the logic of sentences, four non-syllogistic directives of first-order predicate calculus, and the syllogism Barbara, which is used in two versions. In the text under discussion, Acquinas uses this syllogism exceptionally frequently (according to Bocheński, in 70 % of the verses in proofs). In the first version, the mood is used 8 times, in the other version it is used 9 times. 17 Unfortunately, while listing the directives of the calculus of predicates, Bocheński commits mistakes in all four schemas. Nevertheless, they do not influence following the analyses. 18 For the sake of the completeness of the analyses, let us provide the directives of the predicate calculus as well as the versions of the Barbara syllogism: The simplicity of the above inference rules shows, according to Bocheński, the simplicity of reasoning in this part of the Summa.
Question 1 The Nature and Extent of Sacred Doctrine 19 Article 1 Whether, besides philosophy, any further doctrine is required? But the end must first be known by men who are to direct their thoughts and actions to the end.

1.3.
Unde necessarium fuit homini ad salutem, quod ei nota fierent quaedam per revelationem divinam, … Hence it was necessary for the salvation of man that certain truths … should be made known to him by divine revelation.
The above text justifies the need to reveal the truths about God. Part I (1.1-1.3) concerns the truths that are inaccessible to natural cognition, and Part II (1.4-1.6) concerns the truths that are accessible to natural cognition. According to Bocheński, the content of the latter part is original and it constitutes St. Thomas' novelty, pointing to a kind of scepticism towards metaphysics.
Besides, Bocheński points to the fact that the name sacra doctrina is absent from corpus articuli. We only find it in the reply to the second objection. In this fragment there is also the term theologia. 20 It is understood as a discipline whose only subject of study is the existence and the essence of God.
The above Article is reconstructed by Bocheński in the following way: The abbreviations: According to Bocheński, the first and the third premises are obvious philosophical statements and for this reason they are considered to be analytical. The other premises are included in the Christian Credo. Next, Bocheński presents his proof. … because the truth about God such as reason could discover, would only be known by a few, and that after a long time, and with the admixture of many errors. Therefore, in order that the salvation of men might be brought about more fitly and more surely, it was necessary that they should be taught divine truths by divine revelation. 20 ''Theologia quae ad sacram doctrinam pertnet, differt secundum genus ab illa, quae pars philosophiae ponitur.'' (''Hence theology included in sacred doctrine differs inkind from that theology which is part of philosophy.''). For Bocheński, the reasoning is progressive-deductive. He presumes also that for St. Thomas it was a kind of ''reasoning in Barbara''.
It is not difficult to notice that the above reconstructions contain numerous mistakes. For instance, verse 5 is a repetition of verse 1 (so verse 2 is unnecessary); in order to obtain verse 6, verses 3 and 4 are insufficient, and in verse 7 the constant d is provided instead of the variable x. Besides, in the formalization, the constant d should appear in the right domain of the predicate RV(x,y), and not in the left domain (according to the meaning of the abbreviation). We should also notice that the predicate OB(x,y) from the list of abbreviations is absent from this formalization. Then, the predicate EX(x,y), which is present in the list of abbreviations in the formal reconstruction, is unary. Thus, we propose the following modification of Bocheński's formalization: Thus, premise 2 is unnecessary in our reconstruction, and verses 5 and 6 follow in a way different from Bocheński's. When it comes to the predicate EX(x,y), it can be understood in the following way: EX(x,y) =: x excedit y in comprehensionem rationis The second part is formalized by Bocheński as follows: The premises: 8: $ 9 x RVðx; dÞ ! prl 9: prl ! cs The proof: 10: $ 9 x RVðx; dÞ ! $ cs 8; 9; Syll; 11: cs ! 9 x RVðx; dÞ 10; Transp: Here we can notice that there is no direct connection between parts one and two. Besides, Bocheński does not explain the abbreviation ''prl''. Noting the way the abbreviation ''cs'' is introduced we can understand it in the way presented below: prl =: veritas de Deo per rationem investigata a paucis et per longum tempus, et cum admixtione multorum errorum homini proveniret Thirdly, it should be noticed that verse 10 does not result from 8 and 9, which is the consequence of the lack of negation in the second argument of the implication in verse 9. Thus, it should be: Question 1 The Nature and Extent of Sacred Doctrine Article 2 Whether sacred doctrine is a science?
Bocheński claims that this Article is the most important one in Question I. It points to the difference between faith and knowledge and gives the first known relativization of the notion of the scientific system. In Aquinas' time, on the basis of Posterior Analytics, science or knowledge, described with the Greek term epirselg was the deductive system based on obvious axioms; everything else was dona, mere opinion. Bocheński points to the fact that as knowledge of the Posterior Analytics grew Christians faced the task of determining the relationships between scientific methodology and the Christian faith. They did this in various ways. Bocheński reminds us that St. Peter Damiani (1007-1072) rejected Aristotle's treatise, judging it to be a work by Satan. St. Anselm (1033-1109) considered it possible to prove the content of faith on the basis of the principles of reasoning. St. Thomas chose none of these ways. He claimed that although the content of faith cannot be proven, sacred doctrine is a science. For the sake of this claim, Aquinas changed the meaning of the term axiom. It was no longer necessary for the axiom to be obvious for everyone. It was enough when it was obvious for God and the saved people (the saints). From this viewpoint, theology remains a science despite the fact that not all its axioms are obvious for everyone. Bocheński notices also that the term lumen naturalis intellectus (verse 2.2) is used in contrast to the direct intellectual insight, and not to revelation. This is proven by verse 2.5.
The abbreviations: Ks(x) =: x is a knowledge obtained by deduction, Sci(x) =: x is a science When analysing this fragment, Bocheński notices that in sentence 3.1 the expression potentiae et habitus is understood as a type of mental disposition (meaning is subjective) and not as a set of sentences (the objective meaning). Besides, he claims that verse 3.2 is unnecessary in the entire process of reasoning, and the term sciptura should be replaced by the term doctrina. It is impossible to agree totally with Bocheński because premise 3 in his formalization is based on this very verse. In another terminological remark he refers to verse 3.3. Instead of revelabilia it is better to use revelata. Otherwise, theology would be a universal science covering everything.
The abbreviations: Crr(x) =: x considerat aliquem secundum quod sunt revelata, 22 Cur(x) =: x considerat aliquem secundum unam rationem, Us(x) =: x est una scientia. According to Bocheński, the above Article consists of two fragments. The first (4.1-4.5) shows that sacred doctrine is a theoretical and practical discipline, and the second (4.6-4.7) emphasizes the primary character of the previous claim. Doctrina sacra understood in this way means theology, not faith.
The abbreviations: Ah ( Bocheński notices that, as in the case of the previous Article, only the Barbara syllogism was used in the reconstruction. Because the formalization of the second part contains small mistakes (premise 6 is rather controversial, and apart from that verses 8 and 9 do to result from the verses presented by Bocheński in the way he suggests), this fragment needs to be reconstructed. In order not to distort the original formulae we suggest the following modification: Question 1 The Nature and Extent of Sacred Doctrine Article 5 Whether sacred doctrine is nobler than other sciences? Because of some visible inaccuracies in the above schema we suggest a small modification: Bocheński remarks (as seen also in the above schema) that St. Thomas' reasoning in this Article is virtually only regressive.
The abbreviations: CE(x,y) =: x est certior y, Cld(x) =: x habet certitudinem ex lumine divino, 24 Cop(x) =: x considerat obiecta scientiarum practicarum prout sunt congnoscibilia lumine divino, DG(x,y) =: x est dignior y, FN(x,y) =: x est finis y, Spr(x) =: x est scientia practica, Ssp(x) =: x est scienta speculativa, Ulf(x,y) =: x est ulterior y. 25 Part one: 24 In the original version, there is Cld(s) on the left-hand side of the equation, which we treat as an obvious mistake. 25 In the list of abbreviations there is only the predicate ULf(x,y), but in the formalization there is Ulf(x,y). If we want to be faithful to Bocheński's way of creating abbreviations, we should use the predicate Ult(x,y) here. The form of premise 1 provided above raises numerous controversies. Besides, it is easily noticeable that verse 6 is totally unnecessary and obscure (because of the use of the constant/variable r). 27 Verse 7 does not result from verses 1 and 2 on the basis of the Barbara syllogism (even if the lack of the symbol of negation in the first element of the antecedent of the formula in verse 7 is taken into account), and verse 8 does not result from verses 7 and 3 on the basis of the d schema. Besides, the predicate Cop(x) is absent from the formal reconstruction, although it appears in the list of abbreviations. There is also no recollection of the way of understanding the predicate OB(x,y). Perhaps in this place the formalization should take the following shape: 26 This is a slight modification of the Barbara syllogism (verse 7). 27 Probably it was supposed to take the following shape: 8 Obviously, it is possible to formalize the second part of the Article in a different way, in order to avoid the propositions that Ulf(d,d) or DG(s,s), which can be done, for instance, in the following way: Question 1 The Nature and Extent of Sacred Doctrine Article 6 Whether this doctrine is the same as wisdom?
In the commentary to this fragment Bocheński points to two issues. First, sacred doctrine, according to Aquinas, is wisdom in the highest degree (not only wisdom), and apart from that, he talks about it in 6.1-6.2, when describing a wise man, and not wisdom itself. The abbreviations: Ac(x) =: x est altissima causa, OB(x,y) =: x obtinetur ab y, Sm(x) =: x est maxime sapientia. The abbreviations: OB(x,y) =: x est obiectum y, REF(x,y,z) =: x refertur in y sub ratione z. It is necessary to notice the different understanding of the predicate OB(x,y) from the one in the previous Articles (where it was an abbreviation for x obtinetur ab y).
Obviously, in this case it is possible to ask if it is the same relationship but 29 Here we deal with a slight modification of the syllogism Barbara 2-o. 30 The inference rule used here is different from Barbara 2-o. expressed by means of a different Latin term. Besides, because of Aquinas' text certain doubts are raised by premise 1. We suggest the following modification: Question 1 The Nature and Extent of Sacred Doctrine Article 8 Whether sacred doctrine is a matter of argument?
The abbreviations: Cis(x) =: cognitio x initium habet a sensibus, M(x) =: convenienter in sacra Scriptura traduntur x spiritualia sub metaphoris corporalium, Nsi(x) =: est naturale x ut per sensibilia ad intellgibilia veniat. Here, Bocheński only makes the comment that the text is exegetic and refers to Holy Scripture, not to sacred doctrine.
Bocheński's concludes his analyses with a comparison of the Thomistic theory of faith and the contemporary theory of the world-view. The most import differences are as follows: 1. Religious faith is the only world-view known in the Middle Ages. The present notion of the world-view is a generalization and secularization of the notion used in the Middle Ages. The notion consists of the synthesis of a subject's knowledge, answers to existential questions, and moral code. 2. In the Middle Ages, people did not differentiate between faith and knowledge. 3. It was accepted in those times that a sentence needed to be deduced from obvious premises in order for it to be a scientific claim.
Bocheński presents the obtained results in the following way: The In order to achieve his goal, a man needs revelation, that is faith The answer to the most important questions can only be given by a world-view The content of faith cannot be proven; faith must be accepted by means of a free decision The content of a world-view cannot be proven and must be accepted by means of a free decision The axioms of theology are not obvious for us (although they are obvious for God) Axioms of theoretical sciences are not obvious Despite that, theology can be a science Despite that, systems based on such axioms can be scientific Bocheński's analyses cease, or rather are interrupted here. There is no broader summary although it was typical of Bocheński to prepare one. The absence of a summary concerns, for instance, the matter of relationships in the conceptual net constituted by the notions sacra doctrina, knowledge, theology, religious faith, and world-view, as well as assumptions used throughout. The impression that the work was unfinished remains despite the fact that on the last page (p. 97) the next unpublished text begins, titled Powszechniki jako treści cech w filozofii św. Tomasza z Akwinu (Universals as the content of properties in St. Thomas Aquinas' Philosophy).

Conclusions
Despite the rough character of Bocheński's text it deserves appreciation for the following reasons: 1. It is the first attempt to formalize Question I of St. Thomas Aquinas' Summa Theologiae.
2. It constitutes a whole (with regard to the subject and the method of analysis) with the published commentaries on Questions 2-11 of the Summa Theologiae.

After introducing certain necessary corrections, the material prepared by
Bocheński can be the starting point for creating a formal theory of the notion sacra doctrina. 4. Bocheński's formalizations have contributed to the precision of the notions present in the discussed Question. 5. Connecting the notions appearing in the analysed Question with the notion of the contemporary world-view is both bold and revealing. 6. Bocheński skillfully identified the chains of reasoning in St. Thomas' text and reconstructed them in a formal way.
It seems that Bocheński's analyses were nearly completed. The main question that arises in regard to them is: how to understand the term sacra doctrina, used by Aquinas? After identifying the difficulties and the ways used previously to overcome them, Bocheński suggests his own solutions. The key issue seems to be the notion of the religious world-view. Bocheński claims that it is a generalization of the theory of faith presented by St. Thomas. Thus, the Articles of Question I are a description of what can be named the religious world-view today. However, Bocheński does not provide anywhere in the text the answer to the question: how to solve the problems encountered in Question I of the Summa Theologiae in case the term doctrina sacra is understood in this way? In the formal analyses we have discussed we also find a surprising, for Bocheński, role assigned to formalizations. In the case of quinque viae they allowed Bocheński to assess the value of Aquinas' particular arguments; in the case of the formalizations of the following Questions of the Summa Theologiae they permitted him to identify the most appropriate description of the Absolute and to create the preliminary axiomatization of the theory of the Absolute. When it comes to the first Question, the formal relationships seem to play a secondary role. The final conclusion claiming that we are dealing here with a world-view, results from the content of this Question, but is not connected directly to the formalizations. We need to admit that the reconstruction of St. Thomas Aquinas' reasoning in a formal language and the demonstration of its correctness are valuable results, but in our case, this does lead to the final conclusion, which shows the similarities between the theory of faith presented by St. Thomas and the contemporary theory of the world-view. A number of questions resulting from this problem remain unanswered.
The formal anlyses of Question I of the Summa Theologiae conducted by Bocheński are an insightful and scrupulous study carried out with the use of formal logic. The study has a final conclusion. Nevertheless, the work seems unfinished. This offers encouragement to continue investigations in line with Bocheński's ideas. Let us hope that this encouragement will be answered properly by those who cherish both theology and logic.
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