[Right Wing Professor]

The natural sciences rest on metaphysical presuppositions such as the idea that natural laws are uniform and predictable; that the universe is ordered and predictable; that scientists can trust the evidence of their senses; that something cannot both be, and not be, in the same sense and at the same time; that the whole is greater than its parts; that mathematics has objective value and existence; that objective truth exists, etc.

You raise some serious issues that I will try to discuss seriously

• - that natural laws are uniform and predictable, and that universe is ordered and predictable, are metaphysical presuppositions. I dispute both contentions. That natural systems are uniform and predictable is an empirical observation, and one that is not universal. Quantum mechanical systems in some cases exhibit randomness which we believe to be unavoidable; some dynamical systems exhibit chaos - behavior that is determinisitic but diverges rapidly towards unpredictability. We do seem to have discovered some universal laws, but I submit they are universal only because we haven't yet found counterexamples; not because we make the assumption they are universal.
• that scientists can trust the evidence of their senses. There is some justification for calling realism a metaphysical presupposition, but it's not unique to science. The assumption of realism is universal to all human endeavors (except, perhaps, some religions). And I'd make the argument that it's a byproduct of experience as much as a presupposition. When we're infants, we notice that we cry, and mommy comes. Thence we discover that we can affect the world around us, and can do so in ways that have pleasant results.
• that something cannot both be, and not be, in the same sense and at the same time. This is an empirical observation, and not a universal one. Before a measurement, a quantum mechanical system is generally in a superposition of states. If you ask if a hydrogen atom is in the 1s state; the answer is yes; if you ask is it not in the 1s state, the answer is also yes. Once you do the measurement, you force the system to 'make up its mind', if you like.
• that the whole is greater than its parts Sometimes it is; sometimes it isn't. Empirical observation.
• that mathematics has objective value and existenceMathematics has done a pretty thorough job of analyzing its own structure as a mathematical problem. I'm not really competent to discuss that; but I agree that it does appear that mathematics is not a closed, complete system; some small number of presuppositions are necessary. As to whether math exists and has value: again, I'd say that's far more an empirical observation than a presupposition. Some fields of science are highly mathematical; some are still mostly qualitative; the extent to which math. is valuable depends to a great extent on the maturity and the complexity of the field.
• that objective truth exists Apparently, yes, there are some universal constants, but their 'objectivity' is a matter of scientific observation. Einstein emphasized that GR, which is all about what are universal, objective measurements and what are based on reference frame, stood or fell by experimental test, not by the beauty or mathematical consistency of its structure. Observationally, there are some entities, like the speed of light, that have an objective value irrespective of reference frame. But the key word is 'observationally'.

To conclude; I agree that science requires a small number of metaphysical presuppositions. Those presuppositions are, however, so limited and so universal beyond science that they don't really support the contention that philosophy (or less yet, theology, which presumes an entity whose existence many scientists don't accept) have some sort of essential underlying structural role in science, or that they determine its scope. What philosophers think of science has seldom had any impact on us at all.

[Aquinasfan]

That natural systems are uniform and predictable is an empirical observation, and one that is not universal. Quantum mechanical systems in some cases exhibit randomness which we believe to be unavoidable; some dynamical systems exhibit chaos - behavior that is deterministic but diverges rapidly towards unpredictability. We do seem to have discovered some universal laws, but I submit they are universal only because we haven't yet found counterexamples; not because we make the assumption they are universal.

Is this universally true? Is this assessment based on observation of every known aspect of the universe at all times? Or is this a judgment?

that scientists can trust the evidence of their senses. There is some justification for calling realism a metaphysical presupposition, but it's not unique to science.

Nevertheless, metaphysics lies outside both the nature and definition of the natural sciences. Moreover, the materialist nature of scientism makes a realist metaphysics impossible. Nominalism, and its inherent contradictions, follows necessarily from scientism.

The assumption of realism is universal to all human endeavors (except, perhaps, some religions). And I'd make the argument that it's a byproduct of experience as much as a presupposition. When we're infants, we notice that we cry, and mommy comes. Thence we discover that we can affect the world around us, and can do so in ways that have pleasant results.

Realism is true. The problem is that the presuppositions of scientism make a logical explanation of moderate Realism impossible. See the link above.

that something cannot both be, and not be, in the same sense and at the same time. This is an empirical observation, and not a universal one.

No, it is a first principle. It is an eternal truth, since its truth is independent of time and place. It is the presupposition inherent in all thought. And thought precedes all empirical analysis.

that the whole is greater than its parts Sometimes it is; sometimes it isn't. Empirical observation.

This reductionism is one of the central errors of scientism.

A Ford Mustang is greater than its components scattered across the garage floor. There is a difference between a car and its components. The difference is real, and the whole car is superior to its parts, since the whole car possesses real, additional qualities that the group of components do not. Similarly with all things.

that mathematics has objective value and existence. Mathematics has done a pretty thorough job of analyzing its own structure as a mathematical problem. I'm not really competent to discuss that; but I agree that it does appear that mathematics is not a closed, complete system; some small number of presuppositions are necessary.

I'm getting at something less complex. Has anyone ever observed a number? Number is essentially a non-material or spiritual reality.

Quantity (except for unity) is an accidental quality of any particular substance. Any particular thing may be grouped, for example, as number 8 of ten things or number 6,589 of a million things. Both numberings can be true, and we can know both numberings to be true. Therefore, this real characteristic of things is a real, non-essential (or accidental), non-material (or spiritual) aspect of things.

truth exists

Apparently, yes, there are some universal constants,

I thought there were no universals? And how would you know empirically if there were without observing every part of the universe at all times?

...but their 'objectivity' is a matter of scientific observation. Einstein emphasized that GR, which is all about what are universal, objective measurements and what are based on reference frame, stood or fell by experimental test, not by the beauty or mathematical consistency of its structure. Observationally, there are some entities, like the speed of light, that have an objective value irrespective of reference frame. But the key word is 'observationally'.

The law of non-contradiction is an eternal truth, since its truth is independent of time and place. The first principle of ethics, that the good is to be done and evil avoided, is also true and eternal since it too is independent of time and place. Eternal truths, which are essentially spiritual (non-material) truths are beyond the realm of the natural sciences, which are limited to the material.