Find the fallacy…

On page 45 of Programming the Universe, Seth Lloyd says,

The universe began just under 14 billion years ago in a massive explosion. What happened before the Big Bang? Nothing. There was no time and no space. Not just empty space, but the absence of space itself. Time itself had a beginning. There is nothing wrong with beginning from nothing. For example, the positive numbers begin from zero (the “empty thing” [Sanskrit: shunya]). Before zero, there are no positive numbers. Before the Big Bang, there was nothing––no energy, no bits.

I find one of Lloyd’s central claims here highly dubious, for at least two reasons. Before I state my reasons, however, I wanted to invite readers to give their two (or three) cents about the quotation. Why am I dubious? Should I be? Is Lloyd just right, or just out in left field?

Okay, now I will explain my reasons for looking askance at Lloyd’s obiter dicta on, literally, nothing and everything. I appreciate the good insights others offered, some of which will be shown to anticipate my own ideas.

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Counting to infinity by infinity…

MAJOR PREMISE: It is not possible to measure an infinite magnitude.

POSTULATE: The very act of measuring, or quantitatively delimiting, puts an incoherent ‘cap’ on infinity.

MINOR PREMISE: It is possible to measure the universe. It is possible at the very least to measure matter, and material objects, as the constitution of the universe.

CAVEAT: The inability to measure the universe to an infinitely precise degree does not negate the fact of its measurability per se. Indeed, the very ability to challenge or refine one measurement, is itself based on a competing standard of measurement (viz., a measurement obtained in and of the actual spacetime manifold can only be refined, or, indeed, rejected by measuring it against other quantifiable objects). This is significant, because potentially infinite divisibility (i.e., by increasingly precise measuring devices), does not equate to actual infinity. If everything were actually infinite, then anything we measured, at any scale, would be infinite, not measurably finite, as our measurements report.

CONCLUSION: The universe is not of an infinite magnitude, and is not itself a material ‘entity’ of infinite magnitude. Nor can it, therefore, be eternal.

DENOUEMENT: I would even go so far as to say the idea of an infinitely large material substance, as well as an eternally ‘old’ temporal object, is incoherent, since in either case, the categories of materiality and temporality presuppose finite divisibility, i.e., quantitative divisibility and measurability as distinct objects in spatiotemporal relation to others. To be an object of empirical scrutiny is to be quantitatively delimited by others, and to delimit others objects in the same way. This holds for objects’ fourth dimension as well. Unless one is prepared to deny science can measure anywhere in the cosmos––i.e., sectors or ‘levels’ of the universe are metaphysically simple––then one admits the universe, from top to bottom, is subsumed by the finite categories of quantitative spatiotemporal extension. To reject the universe’s ‘subsumption’ under finitude is to posit an inifnite (and eternal) universe. Again, though, an infinitely extended quantity is incoherent on the grounds that an infinite magnitude cannot be a “quantum” (i.e., a discrete amount). One infinity cannot be more “magnus” than another, and therefore neither can be of any magnitude.