Reading over this chapter from Steve more than once got me thinking about it. Zero is a fascinating case where abstract mathematical reasoning crosses into something almost philosophical: it’s a symbol of nothingness but simultaneously “something” because it’s a defined, manipulable concept within mathematics.
Just as Steve discusses that some truths are accepted within specific frameworks (like mathematics) without empirical falsifiability, “zero” represents a similar kind of “truth.” It’s a construct that we accept based on an axiomatic system. We can’t empirically observe “nothing,” yet zero is a critical part of mathematical logic and arithmetic. In the same way that some scientific theories or metaphysical beliefs require an initial leap of faith or a foundational assumption, zero requires us to accept an abstract notion—that “nothing” can have form and can even be operated on.
Philosophically, zero also evokes ideas of Faith and Belief, echoing the article’s discussion on fideism. Zero doesn’t exist as a physical entity, yet we treat it as “real” within math; is part of the Reals! This is similar to how certain metaphysical truths or beliefs are accepted on faith despite a lack of empirical basis. Zero is both the absence of value and a key player in mathematical structures, illustrating how abstract “nothingness” can become foundational—a paradox that also appears in discussions of absolute truth and belief.
Nice — yea the reals are a great example of math meets reality. We use the number “2” as a model of things in the real world like quantity of apples or whatever but the number itself is an abstract concept. We can build up the integers, reals, arithmetic from an axiomatic basis (see Peano arithmetic for example). So zero (or negatives) is part of that model and has a lovely application in the physical world, but the number itself, in a mathematical sense, is fabricated and only has meaning within its constructed context
Zero is part of the Reals.
Reading over this chapter from Steve more than once got me thinking about it. Zero is a fascinating case where abstract mathematical reasoning crosses into something almost philosophical: it’s a symbol of nothingness but simultaneously “something” because it’s a defined, manipulable concept within mathematics.
Just as Steve discusses that some truths are accepted within specific frameworks (like mathematics) without empirical falsifiability, “zero” represents a similar kind of “truth.” It’s a construct that we accept based on an axiomatic system. We can’t empirically observe “nothing,” yet zero is a critical part of mathematical logic and arithmetic. In the same way that some scientific theories or metaphysical beliefs require an initial leap of faith or a foundational assumption, zero requires us to accept an abstract notion—that “nothing” can have form and can even be operated on.
Philosophically, zero also evokes ideas of Faith and Belief, echoing the article’s discussion on fideism. Zero doesn’t exist as a physical entity, yet we treat it as “real” within math; is part of the Reals! This is similar to how certain metaphysical truths or beliefs are accepted on faith despite a lack of empirical basis. Zero is both the absence of value and a key player in mathematical structures, illustrating how abstract “nothingness” can become foundational—a paradox that also appears in discussions of absolute truth and belief.
Nice — yea the reals are a great example of math meets reality. We use the number “2” as a model of things in the real world like quantity of apples or whatever but the number itself is an abstract concept. We can build up the integers, reals, arithmetic from an axiomatic basis (see Peano arithmetic for example). So zero (or negatives) is part of that model and has a lovely application in the physical world, but the number itself, in a mathematical sense, is fabricated and only has meaning within its constructed context