1. Philosophy and Science
- or -
Does it matter if we know
what we’re talking about?

2. Science: “Systematized knowledge covering general truths or the operation of general laws, esp. as obtained and tested through scientific method.”
Philosophy: “The study of the most general and abstract features of the world and the categories with which we think. In philosophy the concepts with which we approach the world themselves become the topic of enquiry.”

3. Yeah? What’s that to me?
You have all had some training in physics & math. So:
What is mass?
What is electric charge?
What is energy?
What is infinity?
Why aren’t there more complex numbers than there are real numbers?
How do I measure ?

4. Brown’s Paradox
Magnetic domain wall motion explains the quantitative properties of iron.
- but -
The math tells us magnetic domain walls cannot form.
Lab experiments tell us they do.

5. Rationalism vs. Empiricism
Brown’s Paradox is an example of the clash between rationalism & empiricism. (In this instance it looks like rationalism loses).
The great rationalists: Plato, Descartes, Leibniz, Newton, Maxwell, Einstein, De Broglie, Bohr.
The great empiricists: Aristotle, Locke, Berkeley, Hume, Newton, Faraday.
The great materialists: There aren’t any.

6. The Bandwidth Paradox

7. What do we get when we measure a signal’s spectrum?
We get a “signal” plus “noise”

8. What is this really?
Plato: The “signal” signal and the “noise” signal are both real. The “signal” bandwidth is really infinite. The only reason we can’t perceive it is because our senses are limited and deceptive.
Aristotle: What we see is what is real. There is only one signal. To say otherwise is mere speculation. It is absurd to say the bandwidth is infinite because infinity does not really exist. It is merely a ‘becoming’. The form of a thing changes to a new form, and this becoming is called enérgeia. ‘Signal’ and ‘noise’ are just names by which we call different aspects of the form. It is Plato’s world that is not real.

9. No, really. What is this?
Kant: The measurement shows us the appearance of a real object. But this appearance looks like it does because of the way our powers of perception work. Plato is wrong to say the signals are really Ideas and our senses err. Aristotle is wrong to say the object stamps its impress on our minds. We understand the object through our concepts of it. But we must be very careful not to let our concepts go beyond what we can actually experience because we cannot know what we cannot actually experience. We call our understanding of the world ‘Nature’. Nature is our model of the world.

10. Kant’s Philosophy Rationalism by itself does not work
Empiricism by itself does not work
Both take ontology as their center
Ontology is our understanding of objects
Epistemology is the science of knowledge
Ontology must come out of epistemology
We must first understand knowledge. Only then can we understand objects.
Objects will conform to our powers of cognition, not the other way around.
This science is called Critical Philosophy.

11. The Critical Question
Principal Quantities: Those parts of “B” that correspond to measurements made in “A”
Secondary Quantities: Those parts of “B” that are abstractions making equations solvable but which have no counterparts in “A”

12. Scientific Constructs

13. How far can constructs go?

17. What must we do to trust math?

19. Other Implications Differential Calculus
Newton’s absolute ‘evanescent quantities’
Einstein’s relativity
Slepian’s rule again. No physical infinitesimals

20. Infinity Math says the infinite set is an axiom
There exists at least one set W with the properties
This means the set is made up of
What the heck is this? A big set of nothing? It is a definition of ‘counting’ in disguise.

21. How to get into trouble 0 = 0 = 0 + 0 + 0 + . . .
0 = (1 + -1) + (1 + -1) + (1 + -1)
= 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) =
= 1
Infinite series are a matter of limits. Whenever things like this come up math has to go back in and fix them. They call this ‘analysis’.
The moral: “Infinity is a becoming”.

22. Okay, what about logic?
In the village of Cleancheeks, Nebraska, everyone is clean-shaven. The village has one barber and his name is Joe. Joe shaves everyone who does not shave himself and he shaves no one who does shave himself.
Sounds pretty reasonable, does it not?

23. Well, then, Who shaves Joe?
Option 1: Joe shaves himself. But Joe does not shave anyone who shaves himself. Therefore Joe does not shave himself.
But (option 2): Joe shaves everyone who does not shave himself. Therefore Joe shaves himself.
But . . .
This is known as the Russell Paradox.
Kant: Logic must have both a formal part and a transcendental part that deals with objects.

24. The Lessons to be Had
Do not mistake ‘mathematical reality’ for ‘physical reality’
Know where the objective validity for your ontological objects come from
Know what the principal quantities you need from your math model are
Make sure these quantities are not sensitive to small changes in the secondary quantities of your math model
Simulations are not experiments. Go to the lab once in awhile

25. Thanks for listening!