Theological notes

Sixtus Cartechini, S.J., explains the so-called theological notes in his 1951 work De Valore Notarum Theologicarum (On the Value of the Theological Notes). (It's also available in Italian translation.) A theological note is classification of the proximity of a theological proposition to revelation. Cartechini calls notes 1 through 6 "Catholic doctrine": "The expression Catholic doctrine [#6] is sometimes applied to truths of a higher order also, but never of a lower one."

1. Theological note: Dogma.
   Equivalent terms: Dogma of faith; de fide, de fide Catholica; de fide divina et Catholica.
   Explanation: A truth proposed by the Church as revealed by God.
   Examples: The Immaculate Conception; all the contents of the Athanasian Creed.
   Censure attached to contradictory proposition: Heresy
   Effects of denial: Mortal sin committed directly against the virtue of faith, and, if the heresy is outwardly professed, excommunication is automatically incurred and membership of the Church forfeited.
   Remarks: A dogma can be proposed either by a solemn definition of pope or council, or by the Ordinary Magisterium, as in the case of the Athanasian Creed, to which the church has manifested her solemn commitment by its long-standing liturgical and practical use and commendation.
2. Theological Note: Doctrine of ecclesiastical faith
   Equivalent term: De fide ecclesiastica definita
   Explanation: A truth not directly revealed by God but closely connected with Divine revelation and infallibly proposed by the Magisterium.
   Example: The lawfulness of communion under one kind.
   Censure attached to contradictory proposition: Heresy against ecclesiastical faith.
   Effects of denial: Mortal sin directly against faith, and, if publicly professed, automatic excommunication and forfeiture of membership of Church.
   Remarks: It is a dogma that the Church's infallibility extends to truths in this sphere, so one who denies them denies implicitly a dogma or Divine faith.
3. Theological Note: Truth of Divine faith.
   Equivalent term: De fide divina.
   Explanation: A truth revealed by God but not certainly proposed as such by the Church.
   Example: Christ claimed from the beginning of His public life to be the Messias.
   Censure attached to contradictory proposition: Error (in faith).
   Effects of denial: Mortal sin directly against faith, but no loss of Church membership. May incur a canonical penalty.
4. Theological Note: Proximate to faith.
   Explanation: A doctrine all but unanimously held as revealed by God.
   Example: Christ possessed the Beatific Vision throughout his life on earth.
   Censure attached to contradictory proposition: Proximate to error.
   Effects of denial: Mortal sin indirectly against faith.
5. Theological Note: Theologically certain.
   Equivalent term: Dogmatic fact; theological conclusion.
   Explanation: A truth logically following from one proposition which is Divinely revealed and another which is historically certain.
   Example: Legitimacy of Pope Pius XI.
   Censure attached to contradictory proposition: Error (in theology).
   Effects of denial: Mortal sin against faith.
6. Theological Note: Catholic doctrine.
   Equivalent term: Catholic teaching.
   Explanation: A truth authentically taught by the Ordinary Magisterium but not as revealed or intimately connected with revelation.
   Example: Invalidity of Anglican Orders; validity of Baptism conferred by heretic or Jews.
   Censure attached to contradictory proposition: Temerarious.
   Effects of denial: Mortal sin indirectly against faith.
   Remarks: The expression Catholic doctrine is sometimes applied to truths of a higher order also, but never of a lower one. In some cases the appropriate censure may be graver than "temerarious".
7. Theological Note: Certain.
   Equivalent term: Common; theologically certain.
   Explanation: A truth unanimously held by all schools of theologians which is derived from revealed truth, but by more than one step of reasoning.
   Example: The true and strict causality of the sacraments.
   Censure attached to contradictory proposition: Temerarious.
   Effects of denial: Usually, mortal sin of temerity.
   Remarks: Proportionately grave reason can sometimes justify an individual who has carefully studied the evidence in dissenting from such a proposition; since it is not completely impossible for all the theological schools to err on such a matter, although it would be highly unusual and contrary to an extremely weighty presumption.
8. Theological Note: Safe.
   Explanation: Affirmed in doctrinal decrees of Roman Congregations.
   Example: That Christ will not reign visibly on earth for a thousand years after Antichrist.
   Censure attached to contradictory proposition: Unsafe/temerarious.
   Effects of denial: Mortal sin of disobedience and perhaps imprudence.
   Remarks: Exterior assent is absolutely required and interior assent is normally required, since, though not infallible, the Congregations possess true doctrinal authority and the protective guidance of the Holy Ghost.
9. Theological Note: Very common/commoner.
   Explanation: The most solidly founded or best attested theological opinion on a disputed subject.
   Example: Antichrist will be of the tribe of Dan.
   Censure attached to contradictory proposition: None.
   Effects of denial: None.
   Remarks: Very common or commoner opinions can be mistaken and there is no obligation to follow them though prudence inclines us to favour them as a general policy. It should be noted that an opinion which is "very common" is less well established than one which is "common" which implies moral unanimity of theological schools.
10. Theological Note: Probable.
    Explanation: A theological opinion which is well founded either on the grounds of its intrinsic coherence or the extrinsic weight of authority favouring it.
    Example: Judas received Holy Communion at the Last Supper. Judas did not receive Holy Communion at the Last Supper.
    Censure attached to contradictory proposition: None.
    Effects of denial: None.
    Remarks: The better founded of two conflicting opinions is referred to as more probable; but Catholics are free to prefer some other opinion for any good reason.

^{For a good history of the development of these notes, see The development of the theological censures after the Council of Trent: (1563-1709) by John Cahill, O.P.
source: this answer}

Theological conclusion

Example:

1. All that exists has God as primary cause. ← truth of faith
2. Human acts exist. ← truth of reason
3. Therefore, human acts have God as primary cause. ← theological conclusion

^{source: this answer, originally from here}

Fr. Hardon's definition:

Religious truths that are derived from two premises, one of which is an immediately revealed truth, and the other a truth of natural reason. Since one premise is a truth of revelation, theological conclusions are also called mediately revealed. And they are said to call for ecclesiastical faith when such truths are proposed for acceptance by the faithful, even at times in solemn definitions of the Church. Some prefer to say that theological conclusions are virtually revealed, and their belief, then, is called mediate divine faith.

Truths of Reason

Cartechini, ibid. pp. 51-52 lists many of these truths of reason (or preambles of faith):

1. That truth exists and that we are capable of knowing the truth, against skepticism (cf. the thesis on the one God).
2. The objectivity of cognition, against idealism or immanentism (cf. condemned Modernism)
3. That truth is absolute, i.e. the same for everyone; against relativism: for if truth were only what appears now, there would not be a standard of comparison for distinguishing between true and false; thus every affirmation would be equivalent to its negation.
4. That our concepts, at least in some ways, are universal: for if no universality is admitted, there would be no distinction between nature and person, and the mystery of the Trinity and Incarnation would be a contradiction.
5. That merely natural, even non-scientific certitude is nevertheless true, as in simple human faith.
6. That man is capable of reasoning, for it is theologically certain that he can demonstrate the existence of God. (D. 1670)
7. And thus: the first principles of being, that of contradiction, sufficient reason, causality, and finality. One cannot say that according to the logic of Kant or Hegel these principle do make sense, for that logic is absolutely heretical.
8. The objectivity of relations, such as causality, similarity for knowing the existence and essence of God, which is a dogma against the agnostics.
9. Somehow: the existence of substance and accident (albeit not necessarily with all the Aristotelian determinations). For otherwise Transubstantiation and grace, which is not the same as the soul yet is in the soul, cannot be explained.
10. That changes exist: for it is a dogma that man can lose grace, and that he can grow in it.
11. Distinctions of reason with a foundation in reality, e.g., in the Trinity.
12. That extended things or bodies exist.
13. That to be in place and time is said of something real, or that time and space have a foundation in reality; for otherwise it would not make sense that Christ lived in such-and-such a place or time.
14. In general that spiritual beings exist, against materialism.
15. That man has a spiritual and immortal soul.
16. That the soul in man is one only: because if the sensitive soul were other than the intellectual soul, the sensible pains of Christ would not have been pains of some spiritual soul.
17. That man is man from the union of soul and body: the soul is the form of the body.
18. That in man the senses are not the same as the intellect, because concupisecence, which arises in the sensitive part, is distinguished from sin, which requires the will and avertence of the moind.
19. The man has freewill, which is a dogma of the faith.
20. That man can know and demonstrate the existence of God with only the light of natural reason.
21. That God is distinct from the world, against pantheism.
22. That God is a free, personal being Who can speak with us.
23. That we can know God as a personal being, because we know Him as principle and end.
24. That man is obliged to religion, and if God speaks, that he is obliged to hear Him.
25. From the very nature of things, there is a distinction between good and evil; that man can know this distinction; and that he is thus obliged to do good and avoid evil.
26. That it is easy to know and make first applications at least of the natural law: such as to love one's parents, not to murder, to help one's neighbor.

^{my transl. of the Latin, with comparisons to the Italian}

cf. also:

• Sacred Congregation of Studies, 24 Thomistic Theses
• Wuellner, Summary of Scholastic Principles