Faith and science

It is wellknown that the Enlightenment philosophy raised the issue of the conflict between reason and faith. The basic motivation is the fundamental Aristotelian character of the Enlightenment approach which in fact is based on classical Aristotelian logic. Indeed that the Aristotelian philosophy is in contradiction with the faith had already been established at the time of Thomas of Aquinas (see Note 1).

This viewpoint was confirmed by Joseph Ratzinger in his famous book “Introduction to Christianity” (1). In fact, according to Ratzinger (his viewpoint is clearly expressed in the first chapter of the same book), the crisis of the Enlightenment/Modernistic viewpoint which raises the conflict of reason with faith, depends on the philosophical premises adopted by the Enlightenment viewpoint. However, in the same book he expressed also his hope and personal convinction that somehow such a conflict could be overcome. His hope was essentially based on his faith in God omniscient and creator, and thus creator of science, which led him to believe that reason (i.e., science) and faith should be mutually consistent, so that they should not contradict each other in any way.

The goal of this paper is to prove that such a mutual consistency indeed is well founded.

In particular, we intend to show that this depends very much on how logic can be actually established in the two cases, i.e., for reason/science and faith, and to ascertain whether – at least in some cases – there is a unique common logic.

The non-standard 3-valued logic of physics:

Concerning physics, in particular, it has recently been discovered that the logic of both quantum and classical physics (2-6) coincide with the 3-valued non-standard boolean logic. Such a logic is endowed with the logical values true, false and undecidable while furthermore it satisfies a corresponding 3-valued Principle of non contradiction (whereby the 3-valued logical values are mutually incompatible). We stress that in difference with the classical (Aristotele’s) logic, such a logic is non-deterministic in the sense that its logical truth value do not coincide necessarily with the truth value true and false but can also be undecidable (in the sense that it is impossible to decide whether it is true or false).

The logic of faith

Concerning faith, there is only one that has been revealed to us by God himself. This is the faith in the Son of God and God incarnated, namely Jesus Christ, born of a Virgin in Bethelem and of King David’s descent. Who is also the Biblical Messiah and is called as “the alfa and the omega”(Revelation 1:8), the Kyrios (κύριος, Revelation 1:9), the Lion of Judah (Revelation 5:5), the Savior (Isaiah 43:11, Luke 2:11, John 1:29), the Lamb of God (John 1:29), the Good Shepherd (John 1:11-18), the Light of the World (John 8:12), Emmanuel (God with us, Matt 1:23) and King of Kings (Revelation 19:16). But foremost Jesus claimed himself to be (John 14:6) “the way and the truth and the life” stating that “No one comes to the Father except through me.” Therefore, as such, it follows that everything He has revealed to us is certainty and truth. Which means that the logic of his Revelation and therefore the logic of faith in Him is, by definition, the 2-valued logic of deterministic logic, i.e.,the classical Aristotele’s logic.

Now Jesus’s Revelation deals in particular about the trascendent, i.e., not only God himself but the infinity of the spiritual world which is beyond or above the range of physical human experience. This includes the heaven, the purgatory and the hell.

However, the revelation does not open us to the full knowledge of trascendent but only to the way, that is represented by Jesus himself, to reach the ethernal life in God’s heaven. Even notions and concepts that have been revealed to us, may be such only in a partial sense. For example, Jesus has revealed to the Apostle his second arrival but not the time and date of such an event.

This means that the trascendent has not (yet) been completely revealed to us. Therefore an unrevealed trascendent remains which is therefore unknown and undecidable to us.

The conclusion which we intend to reach is that the logic of the Revelation, and more generally of the non-revealed trascendent, should coincide necessarily with the 3-valued non-standard boolean logic.

The only possible common logic between physics and the unrevealed trascendent

Neverthless is obvious that in case one of the elements of the unrevealed trascendent is actually revealed then it should obey the same logic of Revelation.

This leaves us with the (only) remaining possibility for establishing a common logic. That is, the unrevealed trascendent should actually obey the same 3-valued non-standard boolean logic reached in the case of physics. In other words all logical sentences which involve the unrevealed trascendent should remain undecidable to us. This means that, in contrast to the revealed trascendent, the unrevealed trascendent does not obey to the Aristotile’s classical logic.

The Thomas of Aquinas viewpoint

An interesting issue, however, remains to be analyzed. This concerns the viewpoint of Thomas of Aquinas concerning the revelation which is expressed in his masterpiece “Summa contra Gentiles” (7). The question in fact is whether Thomas of Aquinas remains faithful to the Aristotile’s classical logic or whether he departs from it in a clearcut way. It is well known that Thomas of Aquinas can scarcely be considered a follower of the Aristotele’s philosophy in general (8). However different is the opinion regarding the Aristotele’s classical logic. Nevertheless, contrary to a popular view which emerges among some of the experts in the field (i.e., logic scientists, philosophers and teologicians), Thomas of Aquinas acknowledges the existence of the unrevealed trascendent. In fact, the notable aspect of his thought, expressed in the cited reference, is that he agrees that the unrevealed trascendent should remain undecidable to any man. Indeed he states (Book 1, Chapter 9) that “the wise man must accept two types of trascendent truths and deny their negation: for the first type a rational investigation is possible, but for the second one, it overcomes the capacity of our mind“. The consequence is therefore that Thomas of Aquinas takes into account the possible existence of the undecidable trascendent! In other words, the logic he adopts must necessarily overcome the Artistotile’s Classical logic! The remaining question, of course, is to establish a full formal consistency with the 3-valued non-standard boolean logic reached in the case of physics.

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Bibliography

NOTE 1: This is the reason why originally Pope Urban IV (1261-64) entrusted the defense of the Christian faith against the influence of the philosophy of Aristotle, to Thomas Aquinas.

1 – Joseph Ratzinger, “Introduction to Christianity“, Ignatius Press, San Francisco, 1968; second edition 2003.

2 – M. Tessarotto and C. Cremaschini, “The Common Logic of Quantum Universe—Part I: The Case of Non-relativistic Quantum Mechanics“, Foundations of Physics, Volume 52, Issue 1, id.30 Pub Date: February 2022 DOI: 10.1007/s10701-022-00547-z 

3 – M. Tessarotto and C. Cremaschini, “The Common Logic of Quantum Universe—Part II: The Case of Quantum Gravity”, Foundations of Physics, Volume 52, Issue 2, id.39 Pub Date: April 2022 DOI: 10.1007/s10701-022-00548-y 

4 – Tessarotto, Massimo , Cremaschini, Claudio,  Asci, Claudio Soranzo, Alessandro  Tessarotto, Marco,  Tironi, Gino The non-standad logic of physics: the case of the Boltzmann-Sinai hard-sphere system, eprint arXiv:2412.19716 Pub Date: December 2024 DOI: 10.48550/arXiv.2412.19716 

5 – Tessarotto, Massimo, Asci, Claudio,  Soranzo, Alessandro ,  Tessarotto, Marco , Tironi, Gino, A new type of Multiverse, Gödel theorems and the nonstandard logic of classical, quantum mechanics and quantum gravity, eprint arXiv:2501.04045 Pub Date: January 2025 DOI: 10.48550/arXiv.2501.04045 

6 – Tessarotto, Massimo , Cremaschini, Claudio, Quantum Gravity Spacetime: Universe vs. Multiverse, Entropy, Volume 27, Issue 11, id.1168 Pub Date: November 2025 DOI: 10.3390/e27111168 

7 – S. Tommaso d’Aquino “Somma contro i Gentili“, UTET, Torino 1998.

8* – William F. Wertz, Jr, “Why St. Thomas Aquinas Is Not an Aristotelian“, https://archive.schillerinstitute.com/fidelio_archive/1993/fidv02n01-1993Sp/fidv02n01-1993Sp_049-why_st_thomas_aquinas_is_not_an.pdf