No branch of science, except fundamental particle physics, rests on so many basic philosophical assumptions as does cosmology. Yet neither cosmology nor any other branch of science can justify those assumptions in its own terms (pp. 264-5).As he has already pointed out by this point in the book, Goedel's (in)completeness theorems, rule that out. When I read Cambridge Prof. Roger Penrose's book, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), I saw that he too had taken Goedel's theorems on board, and makes some very cogent arguments that confirm Fr. Jaki's assessment here. (Unfortunately for me, I lent that book to a friend, and have not seen it since he moved away. I hope it's not just sitting on a shelf!)
The point is that all sciences start from first principles, or assumptions, which they take as given, and then apply their methodologies and insights to draw further conclusions. And the scientific method requires that hypotheses be tested with data, which data need to be measured (and therefore measurable) somehow. That is why modern science is "culture neutral"; its hypotheses and their measurements and tests are reproducible (in principle) by any other human being anywhere on earth.
Continuing, Jaki tells us:
One of those assumptions is that there is a universe, or a totality of consistently interacting things, an assumption of special relevance for cosmology. For if there is no reasoned assurance about an entity called cosmos, or universe, the word cosmology should be banned from science. Instead of cosmology there should be a science of supergalactology. Unlike congeries of galaxies that can be observed, the universe cannot. Surprising as this may seem, science cannot obtain, in its own terms, a reasoned assurance about the reality of a cosmos as defined above. This reasoned assurance is the fruit of philosophical exercise, which scientists like to take lightly, at times even prefer to jettison.I should mention that Prof. Penrose is not a scientist of the sort Jaki is mentioning here, as we will see in a moment. Jaki gives his definition of the universe early in the book, and it is the same as he defines it here, the totality of consistently interacting things. Early in the book he has made the point that Einstein's relativity adjustments to Newtonian physics is what has brought the universe back into focus for scientists, after having been in the wilderness of Newtonian "steady-state" physics. Why wilderness? Because the assumption of a Cartesian-coordinate-like physics entailed infinities along all axes, and there can be no science about infinities, and therefore, "no thing" to be measured.
As Thomas Aquinas holds, there cannot in reality be an actual (in actu) infinity, but only potential infinities. An actually infinite cosmos could never be known, since no "infinity" can be measured. Thus, the "universe" gradually was lost from view by scientists while under that model.
But the "universe", as Jaki says, cannot be observed either, as if it were one or more galaxies. If for no other reason than because there is some portion of it which is forever lost to our observation due to the horizon created by the speed of light being absolute. Unless photons from the early, or far away, cosmos can reach us given the speed of light, they will be forever unobserved by us. But the theory of relativity holds that "given a proper frame of reference, physics is everywhere in the universe the same." That is the assumption, and a reasonable one, that physics makes its own, but cannot prove. The evidence of it can accumulate, however, much like the evidence for the scientific theory of evolution has accumulated, and continues to accumulate. The evidence that has accumulated for the "physics everywhere the same" assumption is very great.
All of which just goes to show us a nexus between modern science and realist philosophy (ontology) in us human beings, i.e., in our minds. But modern science constrains itself to a more limited range of reality than philosophy, i.e., to those quantitative aspects of reality which are susceptible to measurement and testing.
As an example of a man, capable of holding in his own mind both realms of knowledge, there is this statement of Prof. Penrose, taken from the documentary A Brief History of Time:
There is a certain sense in which I would say the universe has a purpose. It's not there just somehow by chance. Some people take the view that the universe is simply there and it runs along–it's a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don't think that's a very fruitful or helpful way of looking at the universe, I think that there is something much deeper about it, about its existence, which we have very little inkling of at the moment.