¹ Werner Heisenberg, ‘Was ist ein Elementarteilchen?’ Lecture presented at the Tagung der Deutschen Physikalischen Gesellschaft, 5-3-1975. Reproduced in Die Naturwissenschaften 63 (1976), pp. pp. 1–7. In page 5 he affirms: “daß heute in der Physik der Elementarteilchen gute Physik unbewußt durch schlechte Philosophie verdorben wird.”

² Shimony, Abner, ‘The Reality of the Quantum World’, in Russell, , Clayton, , Wegter-McNelly, and Polkinghorne, (eds.), Quantum Mechanics. Scientific Perspectives on Divine Action (Vatican City – Berkeley: Vatican Observatory – CTNS) pp. 3–16, p. 3Google Scholar.

³ Dirac, Paul, The Principles of Quantum Mechanics (Oxford: Clarendon Press, 1958), p. 73Google Scholar.

⁴ The superposition principle asserts that from any two quantum states of a system further states can be formed by superposing them. Physically the operation corresponds to forming a new state that ‘overlaps’ each of the states from which it was formed. See Penrose, Roger, The Road to Reality. A Complete Guide to the Laws of the Universe (London: Jonathan Cape, 2004), pp. 541ssGoogle Scholar.

⁵ Penrose, The Road to Reality, p. 498.

⁶ Hughes, R.I.G., The Structure and Interpretation of Quantum Mechanics (Cambridge, Massachusetts and London: Harvard University Press, 1989), p. 113Google Scholar.

⁷ Published as ‘Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik’, Zeitschrift für Physik 43 (1927), pp. 172–198CrossRefGoogle Scholar.

⁸ Conjugate variables are pair of variables mathematically defined in such a way that it is possible to transform them into one-another, through a mathematical operation called the Fourier transform. Some examples of canonically conjugate variables include the following: Time and frequency; time and energy; position and momentum; angular position and angular momentum.

⁹ Heisenberg, Werner, Principles of Quantum Theory (New York: Dover Publications, 1930), p. 20Google Scholar.

¹⁰ Heisenberg, Werner, Physics and Philosophy (New York: Prometeus Books, 1958 [1999]), p. 129Google Scholar.

¹¹ Heisenberg, Physics and Philosophy, p. 81.

¹² Heisenberg, Physics and Philosophy, p. 34.

¹³ Cfr. Heisenberg, Physics and Philosophy, p. 185.

¹⁴ Heisenberg, Physics and Philosophy, p. 180–181.

¹⁵ Cfr. Heisenberg, Physics and Philosophy, p. 54.

¹⁶ Heisenberg, Physics and Philosophy, p. 53.

¹⁷ It is important to note that Heisenberg has not written on this topic in any other papers, thus he has not gone deeper into this concept of ‘potentiality’ or ‘tendency’ in his philosophical interpretation of quantum phenomena. But it is also necessary to say that this work on which we have worked, Physics and Philosophy, is a mature work after which he moves to different questions in physics and in philosophy.

¹⁸ In his Introduction to Heisenberg's Physics and Philosophy edited in 1958, F. S. C. Northrop says in page 16 that “it would be an error, therefore, if the reader, from Heisenberg's emphasis upon the presence in quantum mechanics of something analogous to Aristotle's concept of potentiality, concluded that contemporary physics has taken us back to Aristotle's physics and ontology.” This is certainly a strong claim, and it is a shame that Northrop does not expand on what he understands by “Aristotle's physics and ontology”, although I have my suspicion that it assumes an incomplete reading of the history of science. However, I must admit to agree with this claim to a certain extent. There is no need to “go back” if one can understand that the notions of act and potency are as important today as they were for Aristotle and even Thomas Aquinas.

¹⁹ See Richard Connell, Nature's Causes (New York: P. Lang, 1995), p. 241: “Inanimate entities and their properties are similarly determined in their behaviour; and so we see why and in what sense necessary propositions can be formed about entities that can either exist or not exist. Natural activities are determined to one alternative.” Brock, Stephen L., ‘Causality and Necessity in Thomas Aquinas’, Quaestio 2 (2002), pp. 217–240, p. 220CrossRefGoogle Scholar, expresses this by saying that “it cannot be denied that St Thomas does associate causality with necessity.”

²⁰ Thomas Aquinas, Summa Contra Gentiles III, 64.

²¹ Thomas Aquinas, De Malo, 16, 7, 14.

²² Events which occur ut semper are, for Aquinas and Aristotle, those which take place in the heavens: the movement of heavenly bodies. For Aristotle and Aquinas, heavenly bodies cannot fail in their actions because their forms actualise all the potentiality of matter, leaving no potency to another form. Thomas Aquinas, Summa Theologiae I, 84, 3, 1: materia coelestium corporum est totaliter completa per formam, ita quod non est ei potentia ad aliam formam. See also Summa Contra Gentiles II, 30.

²³ Summa Contra Gentiles III, 39. See also Summa Theologiae I, 63, 9, co; In I Peri Her., XIV, 172; De Veritate, 3, 1, co; De Malo, 1, 3, 17; In II De Caelo et Mundo, 9, 4; In VI Metaphysicorum, 2, 16; In VI Metaphysicorum, 3, 22; Summa Contra Gentiles III, 99.

²⁴ In all these cases (ut semper, ut in pluribus, ut in paucioribus y ad utrumlibet), Thomas is talking of secondary (natural) causes, which act according to their own power. He does not understand them to be the primary cause, neither to be acting with the power of the primary cause. That is why contingency is distinguished from miracle. See De Malo, 16, 7, 15: voluntas divina est universaliter causa entis, et universaliter omnium quae consequuntur modum necessitatis et contingentiae. Ipsa autem est supra ordinem necessarii et contingentis, sicut est supra totum esse creatum. Et ideo necessitas et contingentia in rebus distinguuntur non per habitudinem ad voluntatem divinam, quae est causa communis, sed per comparationem ad causas creatas, quas proportionaliter divina voluntas ad effectus ordinavit; ut scilicet necessariorum effectuum sint causae intransmutabiles, contingentium autem transmutabiles. Besides, God creates natural agents to act contingently. See In I Peri Herm., XIV, 197: ex ipsa voluntate divina originantur necessitas et contingentia in rebus et distinctio utriusque secundum rationem proximarum causarum: ad effectus enim, quos voluit necessarios esse, disposuit causas necessarias; ad effectus autem, quos voluit esse contingentes, ordinavit causas contingenter agentes, idest potentes deficere. Et secundum harum conditionem causarum, effectus dicuntur vel necessarii vel contingentes, quamvis omnes dependeant a voluntate divina, sicut a prima causa, quae transcendit ordinem necessitatis et contingentiae.

²⁵ Beltrán, Oscar, ‘La doctrina de la contingencia en la naturaleza según los comentarios del Card. Cayetano y S. Ferrara’, Studium 6:11 (2003), pp. pp. 41–75, p. 51Google Scholar: “Para Santo Tomás la cuestión no se dirime en términos meramente extrinsecistas, como el puro hecho de darse siempre o no darse nunca, o el de no poder ser o dejar de ser impedido, sino, valga subrayarlo, conforme a la naturaleza intrínseca de las cosas. En resumen, la posibilidad del impedimento como hecho extrínseco reclama su fundamento en el orden intrínseco.” See also Summa Contra Gentiles III, 86: Impressiones enim causarum recipiuntur in effectibus secundum recipientium modum. Haec autem inferiora sunt fluxibilia et non semper eodem modo se habentia: propter materiam, quae est in potentia ad plures formas; et propter contrarietatem formarum et virtutum.

²⁶ Connell, Nature's Causes, p. 242.

²⁷ See Connell, Nature's Causes, p. 242: “The actions of natural agents can be sometimes defective because of extrinsic active causes or because of inadequately prepared materials or because of an indisposition resulting from a stray, incidental active cause.”

²⁸ Thomas Aquinas, In VI Metaphysicorum, 3. See also Summa Contra Gentiles III, 99: multae enim naturalium causarum effectus suos producunt eodem modo ut frequenter, non autem ut semper; nam quandoque, licet ut in paucioribus, aliter accidit, vel propter defectum virtutis agentis, vel propter materiae indispositionem, vel propter aliquod fortius agens.

²⁹ Cfr. Thomas Aquinas, Summa Contra Gentiles III, 74.

³⁰ Cfr. Thomas Aquinas, Summa TheologiaeI, 116, 1, co.

³¹ Thomas Aquinas, Summa TheologiaeI, 115, 6, co: quod autem est per accidens non habet causam quia non est vere ens, cum non sit vere unum.

³² Thomas Aquinas, Summa TheologiaeI, 115, 6, co.

³³ Thomas Aquinas, Summa TheologiaeI, 116, 1, co.

³⁴ Beltrán, ‘La doctrina de la contingencia’, p. 54: “Todo aquello que es per se tiene una causa necesaria. Luego, si alguna causa no resulta necesaria en virtud de un impedimento, aquello que se origine bajo tal circunstancia no será un ens per se, sino per accidens, ya que propiamente no tiene causa, o la tiene como algo extraño a él. Entonces, habida cuenta de la proporcionalidad entre el ser y sus causas, se dice que la causa relativa al ser per accidens es una causa per accidens.”

³⁵ Thomas Aquinas, In XI Metaphysicorum, 8, 13: Si aliqua causa sit ad quam non de necessitate sequitur effectus, sed ut in pluribus, hoc est propter impedimentum, quod per accidens contingit. See also In V Metaphysicorum, 22, 21–23 and Summa Contra Gentiles III, 86.

³⁶ Thomas Aquinas, Summa TheologiaeI, 116, 1, co: id quod est per accidens, non est proprie ens, neque unum; unde impossibile est quod id quod est per accidens, sit effectus per se alicuius naturales principii agentis.

³⁷ Innocenzo D'Arenzano, ‘Necessità e contingenza nell'aggire della natura secondo San Tommaso’, Divus Thomas (1961), pp. 28–69, pp. 41–42.

³⁸ Connell, Nature's Causes, p. 253.

³⁹ Brock, ‘Causality and Necessity’, p. 228: “The concursus will be a mere coincidence.”

⁴⁰ Charles De Koninck, ‘Réflexions sur le problème de l'indéterminisme’, Revue Thomiste (1937), pp. 227–252 and pp. 393–409, p. 248. See also Connell, Nature's Causes, p. 245: “Chance is a contingent, incidental union of effects coming from two or more determinate agents, none of which is antecedently ordained to the union.”

⁴¹ Connell, Nature's Causes, p. 246.

⁴² Thomas Aquinas, In I Peri Herm., XIV, 183.

⁴³ D'Arenzano, ‘Necessità e contingenza’, p. 46: “S. Tommaso ammette come fonte di indeterminazione, negli esseri corporei, la ‘debilitas agentis’, in forza del principio pasivo che, come potenza di contrari e causa di contingenza, ogni essere naturale sublunare (quinde anche l'essere meramente materiale) possiede: la materia prima.”

⁴⁴ D'Arenzano, ‘Necessità e contingenza’, p. 47: “Infatti, la forma determinata del corpo materiale non domina perfectamente la materia che tiene sotto di sè: resta quindi la possibilita che la materia, in quanto appunto sfugge dal completo dominio della forma, si costituisca essa stessa, parzialmente, in causa indipendente, rendendo in tale modo imprevedibile la reazine esatta che dovrebbe avere dall'azione dell'agente esterno.”

⁴⁵ Connell, Nature's Causes, p. 242.

⁴⁶ Cfr. Thomas Aquinas, In I Peri Herm., XIV.

⁴⁷ Thomas Aquinas, Summa Contra Gentiles III, 86: Haec autem inferiora sunt fluxibilia et non semper eodem modo se habentia: propter materiam, quae est in potentia ad plures formas; et propter contrarietatem formarum et virtutum.

⁴⁸ Cfr. D'Arenzano, ‘Necessità e contingenza’, p. 48. Cfr. Comm. Caietani in Summa Theologiae I, 115, 6: Ratio contingentiae potest dupliciter assignari: uno modo, ex parte complementi; alio modo, ex parte radicis. Radix quidem huiusmodi contingentiae est natura potentiae inventa in naturalibus, qua et possunt deficere in minori parte, et sunt in potentia contradictoris… Complementum vero contingentiae est concursus accidentalis causarum, sive activae et passivae, sive activarum inter se, etc. Et propterea non opposita dixit, sed utrumque assignavit in diversis locis divus Thomas…

⁴⁹ Beltrán, ‘La doctrina de la contingencia’, p. 66: “la causa material, en cuanto es intrínseca y necesaria a la naturaleza de las sustancias físicas, se plantea como un factor potencial e indeterminado, que no puede ser asimilado de ninguna manera al orden de las causas en acto.”

⁵⁰ D'Arenzano, ‘Necessità e contingenza’, p. 58: “l'agire dei corpi, in forza dei principi attivi intrinseci di operazione, debe essere, per principio metafisico, determinato ‘ad unum’ e, nello stesso tempo, ma sotto un aspetto diferente, può godere di una certa indeterminazione.”

⁵¹ Brock, ‘Causality and Necessity’.

⁵² Brock, ‘Causality and Necessity’, p. 235.

⁵³ Thomas Aquinas, De ente et essentia, 3.

⁵⁴ Thomas Aquinas, De ente et essentia, 3. See also Summa Contra Gentiles III, 69; De Spiritualibus Creaturis, pro., 1, 25; Compendium Theologiae I, 74.

⁵⁵ Thomas Aquinas, De ente et essentia, 4.

⁵⁶ Velde, Rudi te, Aquinas on God: The ‘Divine Science’ of the Summa Theologiae (Aldershot: Ashgate, 2006), p. 132Google Scholar.

⁵⁷ Thomas Aquinas, In I Sententiarum, 39, 2, 2, 4: In naturalibus invenitur triplex gradus; aliquid enim est quod habet esse tantum in actu; et huic nullus defectus essendi advenire potest: aliquid autem est quod est tantum in potentia, sicut materia prima; et hoc semper habet defectum, nisi removeatur per aliquod agens reducens eam in actum: est etiam aliquid quod habet actum admixtum privationi; et hoc propter actum dirigentem in opere recte operatur ut in majori parte, deficit autem in minori, sicut patet in natura generabilium et corruptibilium. See also De Veritate, 8, 6, co: Sicut enim est gradus actus et potentiae in entibus, quod aliquid est potentia tantum, ut materia prima; aliquid actu tantum, ut deus; aliquid actu et potentia ut omnia intermedia. Also In De Memoria et Reminiscentia, 2, 6; In Boethii de Trinitate III, 5, 4, co2.

⁵⁸ Thomas Aquinas, Summa Theologiae I, 83, 3, co: Est autem unumquodque contingens ex parte materiae, quia contingens est quod potest esse et non esse; potentia autem pertinet ad materiam. Necessitas autem consequitur rationem formae, quia ea quae consequuntur ad formam, ex necessitate insunt.

⁵⁹ Selvaggi, Filippo, Causalità e indeterminismo, La problematica moderna alla luce della filosofia aristotelico-tomista (Roma: Editrice Università Gregoriana, 1964), p. 153Google Scholar.

⁶⁰ De Koninck, ‘Réflexions sur le problème de l'indéterminisme’, p. 237: “Si les êtres naturels sont hiérarchisés selon le degré de détermination de la forme, ils constituent une hiérarchie de natures. Il y aura gradation dans l'ordre de l'activité : les effets ne seront pas légalement déterminés dans leur cause, mais dans la mesure de la perfection de la nature.”

⁶¹ Selvaggi, Causalità e indeterminismo, p 153: “andrà assumendo proporzioni sempre maggiore, finchè al fondo della scala, al livello degli elemento primordiali della materia, potrà raggiungere un livello anche directamente osservabile nell'esperienza.”

⁶² I am clearly leaving aside the discussion of human free will.

⁶³ Selvaggi, Causalità e indeterminismo, p. 390: “La necesita e la determinazione fisica sono fondate sull'atto in quanto atto, la probabilità e l'incertezza sull'atto in quanto limitato dalla potenza, in cui è ricevuto.”

⁶⁴ Beltrán, ‘La doctrina de la contingencia’, p. 69: “La indeterminación de la materia no basta para explicar la contingencia, porque ella de por sí es pura potencia, pura disponibilidad, y no tiene nada propio en virtud de lo cual resistir a la forma sustancial, por débil que ésta sea. Por eso su resistencia o capacidad de impedir ha de asumirse bajo una cierta disposición, que se atribuye a la forma que actualmente posee, y que puede guardar un grado diverso de adecuación con la del agente que pretende obrar sobre ella. Y dicho agente, si se trata de una sustancia natural, aun del orden celeste, sólo puede efectivizar su influjo ad modum recipientis.”

⁶⁵ Cfr. Selvaggi, Causalità e indeterminismo, pp. 381–382.

⁶⁶ Cfr. Selvaggi, Causalità e indeterminismo, p. 386.

⁶⁷ Cfr. Selvaggi, Causalità e indeterminismo, pp. 386–388.

⁶⁸ See Thomas Aquinas, De Potentia Dei, 3, 4, 14: in educendo res de potentia in actum multi gradus attendi possunt, in quantum aliquid potest educi de potentia magis vel minus remota in actum, et etiam facilius vel minus faciliter.

⁶⁹ Selvaggi, Causalità e indeterminismo, pp. 389: “Abbiamo quindi una reale potencialita, che non è pura potenza, ma è costituita in un certo grado di attuazione e determinazione. Ed è proprio questa potenzialità parzialmente attuata che, a nostro parere, costituisce il fondamento reale ontologico della probabilità a priori che regola i fenomeni quantici.”