1453	Fall Of Constantinople
1517	Start Of Reformation
1543	Copernicus Published
1545- 1563	Council Of Trent
1564	Galileo Born
1609- 1610	Telescope, Kepler’s Laws Starry Messenger Published
1613- 1616	Attacks Begin; Letters To Castelli and Grand Duchess; First Inquisition.
1618	Thirty Year War Begins
1623	Barberini Becomes Pope; The Assayer Is Published
1632	Dialogue Concerning The Two Chief Systems Of The World Published; Second Inquisition
1633	Galileo’s Trial, Abjuration, And Sentence.
1638	Two New Sciences Published.
1642	Galileo Dies.
1820- 1835	Church Recognizes Earth’s Motion As True; Dialogue Removed From Ban.
1893	Church Officially Rejects Fundamentalism.
1979	Pope Confesses Guilt.

One century separates the publication of the Revolutionibus by Copernicus from the death of Galileo. Within that period, the Scientific Revolution was begun, its Declaration Of Independence from Religion was declared, and its intellectual battle for independence from religion was concluded. The crucial action took place in the 25 year period between Galileo’s development of the telescope in 1609 and the abjuration of Copernicanism forced on him by the Roman Inquisition in 1633.

Many factors contributed to the Church’s decision to subject Galileo to an Inquisition: pressures arising from the Reformation, the Counter Reformation, and the Thirty Year War; the decline in power and consequent political alignment of the Florentine court (Galileo’s patron) with Spanish interests against the Pope; the power struggle between Dominicans and Jesuits; Galileo’s own combative personality; the sensitivity of Pope Urban VIII to Galileo’s perceived slights; the sensitivity, jealousy, defensiveness, and vindictiveness of Aristotelians both in and out of the Church. None of these factors, however, caused the dispute in the first place. That cause was a fundamental disagreement over nature of truth which has not gone away. Things that bother people today concerning scientific claims to truth are virtually the same as those that bothered Church leaders 350 years ago. The record of Galileo’s trial lets us examine them with the advantage of hindsight and the perspective of centuries.

Christianity like all great religions derives its truths via written and oral traditions which evolve in time, for any system of beliefs which survives long enough to be called ancient must evolve. It must be sophisticated enough to continually re-interpret its basic texts. Moreover, it must provide a range of interpretations to be able to serve the uneducated as well as the educated, the child as well as the adult, and the sinner as well as the saint. A child may need to interpret the "hand of God" literally, but a reasonably mature adult can understand it to mean something else. Fundamentalism, a single, simple, literal interpretation of Scripture, was never an essential characteristic of Christianity.

Certain basic miracles, especially that of the Resurrection, could not be allegorized by the Church, but a belief in miracles by itself did (and does) not make the Church an enemy of science. In fact reason was needed by the Church to demonstrate to pagans whom they wished to convert that apparently miraculous events not described in Scripture were not due to sources of power independent of the Christian God. This was especially true when those powers could be identified as pagan gods or the demons into which they had been transformed by the Church. That reason depended on the existence of natural law, and that is what science seeks to establish. The comprehensibility of the world requires that natural law be obeyed at least almost all the time.

The Church burned witches and wizards but no natural philosophers. Even philosophers who directly contradicted Church teaching had little to fear. As late as 1440, Nicholas of Cusa had argued–brilliantly, but alas with no factual evidence–that the universe was infinitely large, could have no fixed center, and was populated with an infinite number of worlds; and though this contradicted a literal reading of Scripture, he was made a cardinal. The Church, in any case, did not feel overly threatened by mere speculations of philosophers whose spider-like webs, spun from their own imagination, had neither the backbone of mathematics, nor the flesh of observation.

One century later however, conditions had changed, and Copernicus dared publish his great opus only from the safety of his deathbed. Yet even then astronomy was not greatly affected. Sensible people still agreed that theories such as heliocentrism, were merely clever calculational techniques, not descriptions of ‘truth’. The Church still had no compelling interest in banning a book on a form of astronomy which seemed to merely amount to clever mathematics.

Finally, however, only two years after publication of De Revolutionibus, on 8 April 1546, the Council of Trent, that had convened in response to the Protestant Reformation, promulgated Decree 786:

Thus, the Reformation had challenged, and the Council had begun to defend more closely, traditional Church prerogatives, which included the sole authority to interpret Scripture.

Complex issues motivated this re-assertion of power. Through the spread of printing, the Scriptures were for the first time available to all believers, and Protestantism held that these new readers, properly illuminated by the Holy Spirit, could interpret Scripture by themselves. But who was properly illuminated?.

One way to maintain control was to undermine the Protestants’ source of revelation: stand-alone Scripture. The Catholic Church thus began a historical critique of Scriptural text in order to show that the Protestants would be reduced to complete doubt about religion as long as they based their case on their personal reading of it.

Suppose you are given a book called The Bible, but is it? Maybe it contains errors in transcription or translation; and even if not, still, how do you know what the writing means? Ancient Hebrew is still poorly understood; making sense of it relies heavily on scholarship and tradition. The idea that you are reading the original and making up your own mind, that you are an independent agent, is an illusion; in fact you are heavily dependent on authority. If everyone could read a perfect rendition of divinely inspired Scripture the meaning of which was perfectly clear, then there would be no need for a hierarchy to interpret the text. But this is not the case. Thus the need for a tradition of interpretation.

This kind of radical skepticism was extended to include natural philosophy. Galileo talked about the ‘Book of Nature’ but was that Book, as presented to our senses "The Book"? And how clear was its interpretation? Did that not also need Church guidance?

Another part of the Church’s effort to maintain control was the elevation at that time (1567) of Thomas Aquinas to the status of an official Doctor of the Church. The weight of Aristotelian natural philosophy, which he had wedded to Catholic theology three centuries before, was thereby more firmly committed to the support of that theology.

Particularly important was Aquinas’ Aristotelian interpretation of the Eucharist. The central question was the miracle of transubstantiation: bread and wine becoming the body and blood of Christ. The Council stated:

The council’s statement is phrased in terms of Aristotelian metaphysics¾ the distinction, utilized by Aquinas, between ‘substance’ (or the ‘reality’, the ‘essence’ of a thing), and ‘species’ (or the ‘outward appearance’, the ‘accident’ of a thing). The idea is that the outward appearance of bread and wine remains the same although it actually turns into flesh and blood. The immediate purpose of making Aquinas’ view orthodox was to exclude the teachings of Luther who professed uncertainty over the matter and criticized Catholic refusal to discuss it. Besides that, three centuries of similar interpretation had been based on St. Thomas and Aristotle and the Catholic Church naturally felt that it had a great stake in the omniscience of both philosophers.

The philosophic issue is the distinction between outward appearance and inner truth. It is an issue in interpretation of Scripture--its outer versus inner meaning--that was addressed by Plato in his parable of the cave, and in his theory of Forms. It was to lie at the heart of the dispute between Galileo and the Church.

The question of vouchsafing miracles also re-appears here, this time with Protestants in place of Pagans. Perhaps Transubstantiation and in addition, other miracles were being granted to Catholics by divine favor but denied to Protestants? To support such a claim, Catholics had to be able to convincingly identify an event as being a miracle, that is, as being supernatural as opposed to being natural.

Thus, miraculously, Protestantism was an added goad towards an ever more serious study of natural philosophy by the Catholic Church In all these considerations, the presupposition was always the rule of Reason. A miracle was a phenomenon which could only be proven to be indeed miraculous, to be inexplicable by other than supernatural intervention, through the use of reason,.

In summary, at the start of the 17th century, biblical interpretation had become associated with burning theological and social issues, and the Church was vigorously reasserting its authority as the sole interpreter of Scripture. It was also vitally interested in natural philosophy and was prepared to more thoroughly extend its authority to this area. And finally, in conjunction with all this, it felt more strongly than ever committed to defending Aristotelianism.

Before engaging the deeper meaning of Galileo’s trial, it is worth dispensing with the secondary issue of fundamentalism. Galileo’s views are clear, and worth repeating in detail.

On Dec. 12, 1613, Father Benedetto Castelli, a former student, current friend, and collaborator of, and successor to, Galileo at the university of Pisa, was invited to dine at the Medicis. Those present included the Grand Duke Cosimo II, his Grand Duchess Maria Maddalena of Austria, the Grand Duke’s mother the Grand Dowager Duchess Christina of Lorraine, her confessor, and a fellow professor at the university, Cosimo Boscaglia, who taught Aristotelian philosophy and enjoyed the patronage and friendship of the ducal family. What happened was related in a letter Castelli sent two days later to Galileo:

The events surrounding this incident and the increasing attacks upon Galileo since his development of the telescope and publication The Starry Messenger in 1610, made it clear that the faithful Castelli had been set up. He had known he was being drawn into a dangerous discussion of theology, had "expressed the appropriate disclaimers", but then had gone ahead anyway. Prof. Boscalgia said nothing because Her Ladyship, his cats paw, did all that he had hoped for. It was not necessary to win a theological argument, only that natural philosophers be seen as encroaching upon the domain of theologians.

Galileo wrote back one week later. He had since been told more details of the meeting, and after complimenting and reassuring his nervous follower, he made the following comments. They explain the separate domains of science and religion, and the case against fundamentalism. Key portions are indicated in boldface and the whole is summarized at the end.

His major points in brief are as follows:

1. Scripture is true but interpreters may err. Galileo sets up the analogy between two assumed sources of fact: scripture and phenomena. Both are and need to be interpreted. The meaning of Scripture depends on the meaning of its words, and word meanings are notoriously slippery. The meaning of experience is filtered through our sensory apparatus. Both scripture and phenomena must be fitted and are fitted to the templates within us that determine what is information and what is noise. This view is partially Sophistic. Does it say (along with Protagors) that Man is the measure of all things; and does it say (along with Nietzsche) that All is interpretation? Well, yes, but, that depends on what you mean by all, by things, by is ! Man is also the measure of what this words mean
1. It is already well known that Scriptural interpretation is necessary since literal meanings lead to internal inconsistencies and violations of basic religious principles.
2. In order to adapt itself to the understanding of all people, it was appropriate for the Scripture to say many things which are different from absolute truth, in appearance and in regard to the meaning of the words. The job of the wise interpreter is to explain the true meaning and origin of these inconsistencies. In talking about absolute truth Galileo distinguishes his sophistic thinking for the normal kind. Clearly, absolute truth, whatever it is, cannot be subject to interpretation. Absolute truth is itself reached by correct interpretation, by passage–education-- from the cave of ignorance to the light of reality.
3. Both Nature and Scripture ultimately come from God (equally derive from the divine Word).
4. Nature is not required, like Scripture, to tailor the truth to fit the mental capacities of all people.
5. Since Nature presents the straight truth concerning physical phenomena while Scripture is not so constrained, lessons learned from Nature via sense and reason must take precedence over Scripture.
6. It is not prudent to base religious belief on statements which may turn out to be demonstrably wrong by a science whose future bounds are unknown to us. Somewhat later in support of this, Galileo quotes St. Augustine as follows [ Ref. , p. 186]: whenever the experts of this world can truly demonstrate something about natural phenomena, we should show it not to be contrary to our scriptures.
7. We do not know if those who argue from Scripture are divinely inspired, but they certainly seem to be unable to understand Science.
8. It seems unreasonable that the same God who has furnished us with senses, language, and intellect would want to bypass their use and teach Science in another way, especially through Scripture which barely discusses it.

In addition to these points, Galileo discussed the specific passage in Joshua the interpretation of which had been brought up at the Medicis. This unfortunately was what Galileo’s enemies had hoped for because first Castelli and then Galileo had now both done what the Council of Trent had forbidden; they had interpreted Scripture according to a Copernican illumination.

Copies of this letter gradually circulated, one finally finding its way to a Dominican named Lorini, a Florentine professor of ecclesiastical history and member of an anti-Galileo conspiracy which had formed when Galileo had publicly espoused Copernicanism. He sent it via a sympathetic Cardinal to the Congregation of the Holy Office, "by the mercy of God, cardinals of the Holy Roman Church, Inquisitors-General throughout the Christian Commonwealth against heretical pravity". Thus, on February 7, 1615, two years after Castelli’s gentle inquisition at the hands of the Medici family, the Roman Inquisition heard of the incident.

Lorini accompanied the letter with the following comments

Lorini doctored his copy of the letter to Castelli sent to the Inquisition so as to make Galileo look bad. Despite this, the Inquisitor assigned to the case found nothing of consequence to censure. In particular, nothing was wrong with Galileo’s contentions (1) that the language of Holy Scripture does not mean what it seems to mean; or (2) that in discussions about natural phenomena the last and lowest place ought to be given to the authors of the sacred text which in effect means that a literal interpretation of Scripture does not take absolute precedence in determining the truth of natural phenomena. The Inquisitor did not question Galileo’s denial of this fundamentalist assumption.

Furthermore, in none of the subsequent controversy between Galileo and the higher echelons of the Church was fundamentalism ever the basic issue. The points Galileo made in the letter to Castelli were not questioned. By default, the Church agreed that Scripture did not teach natural philosophy but that instead, natural philosophy, using (God-given) senses, language, and intellect, determined the proper interpretation of descriptions of the natural phenomena found in Scripture. And although it took the Church almost three hundred years to do it, they finally explicitly reaffirmed in writing their basically non-fundamentalist tradition. As St. Augustine had said: whenever the experts of this world can truly demonstrate something about natural phenomena, we should show it not to be contrary to our scriptures.

Thus despite ambiguities and waverings under fire, the Catholic Church, at least as it was defined by its highest leaders and in accord with its highest interests, was not fundamentalist. Its basic argument with Galileo was about far more fundamental issues than simplistic fundamentalism. It was about the very nature of truth.

We have an insight into the thinking of the Church’s chief theologian during this period. In 1615 a small pro-Copernican book was published by Carmelite Father Foscarini. He had asked for Cardinal Bellarmine’s opinion of it, and the answer made the following points (Ref. , pp.98-100):

The heart of his first argument is: To say that …. all the celestial appearances are explained better [by Copernicus than by Ptolemy] …..is to speak with excellent good sense …. [and]…. is enough for a mathematician. But to want to affirm [this] in very truth …..is a very dangerous attitude. Bellarmine is, in effect, distinguishing between scientific and metaphysical truth. The first is that which, on the basis of what has been discussed as reduction, leads to a simpler and wider understanding of phenomena, the second is, as it were, God's, or absolute, or Real, or… Truth.

The second of the arguments quoted concedes that real proof of truth is attainable outside Scripture, and admits that scriptural interpretations must be revised when in disagreement with truth. Bellarmine thus shows himself to be a non-fundamentalist (in fact, he had been one of the leaders in the Jesuit’s attack on Protestant fundamentalism discussed earlier). But, although he says what it is not, he does not say what real proof is.

Sometime during the period (1615-1616) now being discussed, while Barberini, the future pope, was still both a cardinal and a friend of Galileo, they are reported to have discussed Copernicanism. Barberini’s views as expressed in their conversation has been imaginatively reconstructed by Santillana from a number of sources (Ref. , p.166) as follows.

In fact, astronomy, the first of the mathematical sciences, was already known to provide three equivalent ways of looking at the world: that due to Ptolemy, Copernicus and Tycho. Maybe there were even more. In the sense that each agreed with observation, each was true. So in general, how would you ever know whether all versions of truth have been found and which of them, if any, is the one favored by God? Thus Barberini maintained his intellectual right to believe (concerning that miracle in Joshua which since Castelli’s meal at the Medici’s was still serving as the framework of these discussions) that there was a truth favored by God in which the Sun really had stopped.

The story of this conversation ends with the statement that Galileo finally fell silent. The understanding, at least of the storyteller (Barberini’s papal theologian), was that the future Pope had won the argument.

Elsewhere Bellarmine contended that mathematics is a shaky guide to the truth; it may provide hypotheses but not proofs. The whole tradition of Aristotelian philosophy supported this view and some of its rationale goes as follows:

1. Mathematics makes exact statements whereas nothing can be measured exactly. Mathematics distorts the world with this innate and unrealistic idealization.
2. Number and quantity are ‘accidental’ as opposed to an ‘essential’ property of matter. Thus mathematics is limited to specifying and predicting outward appearances.
3. Numbers are ideas abstracted from reality but abstractions are not real.
4. Mathematics cannot describe motion and change which is the heart of physics.

The first three are interrelated metaphysical points which will be treated first. In some more detail:

1.A asks what mathematics’ perfect circles, perfectly straight and infinitely thin lines, and so on, have to do with a reality which seems to be, instead, a ‘more or less’ kind of world, a place of fuzzy edges and fuzzy logic? This is perhaps the most commonly expressed worry about the ability of ‘pure’ mathematics to describe the ‘impure’ world our senses inform us is out there.

1.B refers to statements such as: the number of sheep in a flock has nothing to do with the essence of being sheep; or, lengths and angles might describe the shape of a stone sculpture, but nothing about stoniness–the essence of being a stone. A more recent versions of this is: number might describe the behavior of all the chemicals which make up the human body, but how can it describe the essence of being human (life, consciousness, emotion, …).

1.C is the idea that the number one does not exist–only one something exists–in external reality.

In contrast to the first three points, the last one (1.D) requires some preliminary explanation. It comes from the difficulty we have in describing the continuum: what is the relation between the real number system, mathematical points and lines, and physical space and time?

Every direct distance measurement, from that of a wooden ruler to an atomic wavelength, must always yield a rational number. Similarly, direct measurement of the coordinate distances along axes (Figure 1) as well as the distance to the origin of points with those coordinates will all yield a rational numbers. This seems to imply that every physical distance corresponds to a rational number: that the ratio between the distance between any two points and some unit of distance is of form m/n where m and n are integers. This conclusion was believed by everyone before about the 5th century BCE and is still believed by many today. Nevertheless, it is logically contradictory to maintain all these distances are truly rational.

The Pythagorean discovery of the non-commensurability of the legs and hypotenuse of an isosceles right triangle destroyed this idea. For the next two thousand years, as long as number meant integers and rationals, this discovery stalled the Pythagorean program for physics. It was still doing so during Galileo’s trial, as Bellarmine’s first point demonstrates. People near the start of the seventeenth century understood the rational but not the real number system. And in particular, they had not made the connection between the points on a straight line and the real numbers. Thus, for them, number could not exactly describe space.

This left geometry–still logically distinct from arithmetic until Descartes–for the description of space. However physics could not rely on geometry alone because physics described change and hence also involved time and when space and time are mixed, even geometry had problems. These trace back to Zeno of Elea (circa fifth century BCE) who presented them in the form of four paradoxes which purported to show that motion is impossible. All have a similar character, and the first, called the Dichotomy, will be enough for our purposes. As quoted by Aristotle it says:

There is no motion because that which is moved must arrive at the middle [of its course] before it arrives at the end.

Replacing the end by the middle, the same thing must be said about arriving at the point midway to the middle. This can be repeated forever: each middle becomes an end which is preceded by another middle. If the process never ends, how can something in motion ever arrive at its endpoint, and thereby end the process?

The usual response is that the series of times taken to travel between ‘middles’, say at constant speed, adds up to a finite sum proportional to (1/2 + 1/4 + 1/8 + …= 1) so the moving object gets to its end in a finite time. This is true but does not answer the question. It tells us how long the arrow would take to get to the end, if it could, but does not explain how it can. How can an endless process actually end. There is an inconsistency in the way we talk about space, time and motion revealed by the paradox which needs to be clarified.

It is not necessary to know whether or not Cardinal Bellarmine understood the problems of non-commensurability and dichotomy in any depth. It is sufficient that he judged that various experts who did understand them were not the obstructionist fools which simplistic histories have made them out to be. Mathematics, as then understood seemed to be quite possibly not up to the job of describing space and motion let alone questions affecting both ultimate truth and reputation of Christianity.

Galileo and the Church were not arguing over the possibility of miracles; both agreed that they occur.

Neither were they arguing over fundamentalism. Although fundamentalists could be found throughout the Church hierarchy, its authoritative heads were free of it because of both religious tradition and the then current fight against Protestant predilections towards it. Galileo’s arguments on this point, as expressed in his letter to Castelli, were never seriously disputed.

Neither was freedom of speech or of inquiry central to these discussions. Although here again the hierarchy’s actions were not blameless, neither were they very different from modern practice in free societies.

Neither did they argue over the data. Galileo did engage in important scientific disputes with natural philosophers as part of the normal course of doing science (and these comprise the great bulk of his writings), but Bellarmine and Barberini were not competent or interested in such technicalities. They were willing to grant both the observations, and the efficacy of Copernicanism in describing them.

Similarly, although much has been made of the fact that early telescopes were hard to use and could give untrustworthy results, this also was not important. If the testimony of the telescope had been seriously suspect, Galileo’s influence would have rapidly vanished. He would have posed no threat and no trial would have occurred.

What were the core issues. They depend on with whom one argued, Barberini or Bellarmine. The former denied our ability to discover Truth except through revelation; thus science could not discover it. The latter, on the other hand, allowed that science could discover Truth but would not recognize the authority of mathematics to describe it much less provide the criteria (the mathematical simplicity of Copernicanism) for it. These core issues remain unsettled to this day.

There is a pragmatic meaning to truth which not in dispute. People have always given such a sense to the word; they take to be true whatever they perceive as useful to be so taken--whatever works. Since Galileo the area in which science has gained (what William James called in a definition of pragmatism) a cash value in experiential terms has continually expanded. Today, certainly in this sense, we know that to say something is scientifically true is to award it top honors for reliability and utility, and hence, for truth.

At that time, Bellarmine did not think that Copernicanism had proved itself pragmatic. Although it agreed with astronomical data, so did the Ptolemaic theory. Although it was mathematically simpler, that just made it useful for mathematicians. It did not agree with the generally accepted physics of the day. And it violated the cosmology that had been developed over the centuries to support Christian tradition and morality. He could reasonably argue that, in net, it was not yet true.

Galileo, who was also a pragmatist, nevertheless insisted to the contrary, that Copernicanism was true. He concluded this from an understanding of physics that was deeper than that of his opponents, the Scholastic followers of Aristotelian, upon whose expert views Bellarmine necessarily depended. Evidence of this depth appears throughout his writings in which he exposes their inconsistencies, vagaries, and factual errors. Even taking into account that it is Galileo their opponent who is describing them, and created the modern viewpoint from which we are seeing them, they perform surprisingly poorly in these accounts. Why did these Aristotelians, successful and presumably intelligent men of their time, put on such a hapless performance?

Their views strikes us today as not even wrong--not even to the point, from another, an intellectually foreign, world. Their physical reasoning rarely went beyond verbal classification, referring to things which liked to rise, or liked to fall, things which were pure or impure, and so on. They were not prepared to proceed beyond this: to give any other than verbal, qualitative explanations based on classification. Classification is a process that characterizes the first stage of knowledge in any field, and remains characteristic of it as long as the field resists deeper analyses. It is the process by which we create and given names to sets of objects sharing certain properties. By doing this we identify those properties deemed essential to understanding behavior preparatory to then classifying behavior patterns in terms of them.

The property of being heavy is shared by all members of the set of heavy things. It is understood through muscular sensation. If a thing is heavy, we can predict something about how it will feel to hold it. But then we can also predict that it is likely to fall. By establishing a connection between muscular sensation and possible movement, heaviness aids in data reduction. We need not create and carry along in memory another classification of objects: those with a "tendency to fall". Heaviness predicts this other property.

This kind of tool has been discussed before under the topics of ideals and of abstractions: heaviness does not exist in the phenomenal world, the world of Becoming, but is an idea abstracted from it. It is a Platonic ideal; it exists in the world of Being. Ideals/abstractions discussed previously included 'one' and 'sheep'.

Most sciences have gotten beyond this stage of analysis and reduction only within the last century. Astronomy, through the use of mathematics, was the first study to do so. There were very few other naturally occurring systems here on Earth that were not too complex to be similarly analyzed. Because they were so rare, it took rebellious genius to sense that this approach could extend beyond astronomy. It also took time for mathematics to develop to where it could be used in these new situations. It took time to realize that systems could be made (unnaturally) available to analysis through the technique of experimentation. Part of that time was required for examples of early pioneers to accumulate; part, to develop technical abilities in manufacture; part, to develop social conditions in which to learned men devoted themselves to experimentation. When that time came, and the fuel was in place, the spark of just a few set off the intellectual conflagration that is modern science, and with it, the modern world.

Abstraction, classification, naming, etc., define one level of understanding, and along with it, one level of pragmatic truth. Galileo was one of the few who recognized the possibility of a deeper, essentially mathematical, level of truth. In his Dialog Concerning Two World Systems, the character representing Galileo asks that representing Aristotelian philosophy (Simplicio) to describe by what cause heavy bodies are conducted downward. The reply is that anyone knows that it is gravity, to which Galileo's character rejoins, You are mistaken, Signor Simplicio, you ought have said: anyone knows that it is called gravity. We have named a cause and can classify phenomena as being due to it, but that does not mean we know anything about it.

With the example set by the development of the Copernican system, Astronomy provided the example of how to proceed beyond this intellectual dead end. Astronomy did much more than classify heavenly bodies and their orbits. It measured precise trajectories, and this knowledge revealed the higher simplicity (= higher in the ladder of forms) of the Copernican system. Thus a precise measurement of the trajectory of projectiles might lead to similar insights, similar higher simplicities, which of course it did. Knowing that projectile trajectories were of constant downward acceleration and constant horizontal velocity still did not teach us the cause of either that acceleration or velocity--the causes are still just given names like gravity and inertia-- but nevertheless we did learn a lot. We learned useful, pragmatic truths at higher, more abstract, levels: concepts such as velocity and acceleration which precisely connect large varieties of phenomena and thereby provided greater amounts of reduction.

The discussion of pragmatic truth addresses only the objections of Bellarmine. In that context, events have shown Galileo to be correct: Copernicanism was the truth. But the objection of Barberini concerning a level of truth that remains hidden from scientific inquiry--a God's truth--is unaffected by this. Such truth is paradoxical. On the one hand, being hidden from science implies that it concerns facts that have no effect on phenomena, for if they did, they would no longer be hidden. On the other hand, through their influence on human behavior, they do effect phenomena. Thus beliefs affect behavior irrespective of their truth. Furthermore, hidden truth can never be tested and therefore, never proven nor disproven.

The classic definition of being real is being able to influence phenomena. If spiritual beliefs/truths can indirectly even indirectly effect phenomena, they are real even though the things about which they purport to be true may not be real (by the same definition)! All this emphasizes the fact that what is real and true is not as unambiguous as it is sometimes made out to be, and that talk about the existence of a 'spiritual' truths needs to be rather carefully addressed.

When Galileo heard Barberini's argument he is said to have offered no response. This can be interpreted in more than one way and Galileo may have been even wiser than commonly thought.