Articles: Many, many… please see CV.
ArXiv: Computer Science and Metaphysics: A Cross-Fertilization (May 2019)
_____ Mechanizing Principia Logico-Metaphysica in Functional Type Theory, 2017
Axiomatic theory of abstract objects
Books: Intensional Logic and the Metaphysics of Intentionality, MIT Press, 1988
_____ Abstract Objects: An Introduction to Axiomatic Metaphysics, Reidel, 1983
Twitter (Zalta event, 2015)
YouTube (and other videos): Towards Leibniz’s Goal of a Computational Metaphysics
Fifth email: Friday, July 16, 2020
Our guests have returned home, and within the morning quiet, I begin thinking about “there is an ‘object-theoretic’ analysis of the objects…”
You are so quick (and me so slow), it may take some time to process your object-theoretic analysis because my hypostatized objects are de facto spatio-temporal and within a mathematical causal order yet are so far removed from the particles (as an atom is from the solar system)… so now I accept this object-theoretic analysis as a homework assignment to be turned into when new insights if and when a deeper understanding prevails.
It may well take awhile! Thank you, Ed.
PS. Perhaps consulting with others, such as those within the Langlands and Witten coteries, could be helpful. I am envisioning a massive “computer-like” grid starting with base-2, yet within that first doubling we initiate a unique expansion for prime 3 expansion. And then, for every subsequent prime number doubling, a new type of mathematical expansion, right through to the 202nd base-2 notation. That would provide 45 different mathematical systems, i.e. each resulting from the primes, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197 and 199. Perhaps such a grid or matrix, numbers as numbers, might provide an outline to guide our reification, instantiations and hypostatizations, particularly about the very nature of a second and a meter. -BEC
Fourth email: Thursday, July 15, 2020 (in process)
Does the sphere qualify?
(P2) Mathematical entities are indispensable to our best scientific theories.
(C) We ought to have ontological commitment to mathematical entities.
Could the sphere further qualify?
2. …given it is a dimensionless constant?
3. Yes, are the never-ending, never-repeating numbers of pi infinite?
So, I thank you for your note: Sun, Jul 12, 2020 at 6:19 PM (PST). I am still reflecting on it.
Also, as a result of following your notes within your September 2011 lecture at the MCMP Workshop for Computational Metaphysics, LMU Munich, 11.06.2011, I am also reading the manuals regarding the downloading Prover9 and I apologize in advance if my questions could be answered therein.
I am having a great time of discovery. I feel like an undergraduate student! Thank you!
I am also reading and re-reading your essays like your work with Uri Nodleman, Foundations for Mathematical Structuralism. Yes, like the kid in a candy shoppe, I am trying to take in too much too quickly, so please excuse my silliness.
Thank you for your understanding.
PS. It is a bit like being in this candy shoppe where the sign says, “Free! Up to $25.” I am on a tasting frenzy! -BEC
Third email: Sunday, July 12, 2020 at 1:34 PM (CST, TZ-18)
Dear Ed –
Please bear with me as I naively start with your statement: “For every set of properties, there is exactly one object that encodes exactly that set of properties and no others.”
I profoundly agree.
So now, if I were to choose to grasp an unique set of properties for a thing unto itself (as well as for all things, everywhere, for all time), I would turn to the Planck base units of space (Length) and Time. These two provide the unique set of properties — dynamic properties that constantly expand — and these properties are numerical (very much like pi (π), never-ending and, logically, never-repeating). Another layer of identification could readily be alphabetical, but it would be secondary identification.
There appears to be very few people who are examining the possibility that the intellectual and logical starting points for space and time are the Planck base units. Max Planck’s numbers are a study of dimensionless constants yet have a natural definition of the empirical whereby the first instant of space (Length) is in a dynamic relation with Planck Time. When that length is divided by that time, the relation equals the speed of light. The result rendered is within .001% of the laboratory definition used by the National Institute of Standards and Technology (NIST) and the International System of Units (SI) which was re-confirmed as recently as 2019.
Each of those primary calculations by Max Planck is a key.
There is one that defines Planck Length and another that defines Planck Time. And, because each involves dimensionless constants, it tacitly opens questions about the finite-infinite relation. Then, his definition for the derivative formula, Planck Length divided by Planck Time is equal to the speed of light tells us yet another story and it all warrants our attention and further key questions.
Several years ago, I was quite surprised to see an actual number for the age of the universe, the 13.81 billion years, stated in seconds. Seeing so few actual numbers taught me something new about very large numbers and very small numbers: The age of the universe, 13.81 billion years is just 436,117,076,900,000,000 seconds (436 quadrillion, 117 trillion, 76 billion, 900 million seconds). It wouldn’t take much to define uniquely each “thing” as well as everything, everywhere for all time. Then, special consideration would be given to Notations 10 to 64, whereby every concept, every idea, every intuition, could also have its unique definition. Nothing-but-nothing would be exempt from a specific-and-unique and dynamic definition.
What am I missing?
I can hear you say, “Everything!” But, maybe not.
Second email: Friday, July 10, 2020 at 9 PM
Let me further engage your work so I can re-context Planck’s base units in light of your axiomatic theory of abstract objects. I’ll be back! Thanks.
First email: Friday, July 10, 2020 at 10 AM
Dear Prof. Dr. Edward Zalta:
I so enjoy your Stanford Encyclopedia of Philosophy (SEP). Thank you for all your work with it. It is a trusted resource and helps fill in some of my many blanks. Now, I am so old I remember many lectures with Quine and Putnam, even a spirited dinner with them at Quine’s Beacon Hill home. Thank you also for your work to follow-up the Correspondence with the video of your lecture, Towards Leibniz’s Goal of a Computational Metaphysics.
I have a quick question.
Could a cogent metaphysics and physics start with the Planck base units? If we were to assume the sphere is the first physical manifestation of space-time-matter-energy, might we also assume sphere stacking and cubic-close packing of equal spheres (such that a base-2 notation emerges)? The first second is in the 143rd notation and the current age-and-size of the universe emerge in 202nd notation. It seems that our old friend, John Wheeler, might celebrate its simplicity.
I know how totally idiosyncratic it is, but maybe with such a different look at all the old problems, we can get beyond some of the more dastardly impasses within science today.