Further Discussion on Emergentism

However, the logic of (c) may have more significance than it initially seems. Specifically, “British Emergentism,” which is also known as property dualism, appears to be such a case. Consider, for example, an object with a mass of 10 tons resting on a road. This ball is attributed with the property of heaviness. According to (c), the position of property dualism argues that the physical property of 10 tons of mass and the property of heaviness are entirely different, having no mutual influence and being irreducible to one another. This argument seems to echo discussions about the connection between mathematics and the real world. For instance, explaining how the physical world fits mathematical descriptions so well is quite a challenge. We might agree that nature does mathematics rather than philosophy, but exactly why this is the case remains a mystery. If mathematics were part of the physical world, humans would have discovered all of mathematics purely through empirical experience. Historically, numbers such as natural and whole numbers were discovered by people counting physically—thus experience-dependent. However, much of mathematics beyond this is not experience-dependent. Not all mathematical systems are countable; it is impossible to empirically discover the concept of transfinite numbers as studied by Hilbert or Cantor. Pure mathematics like mathematical logic, topology, or complex analysis cannot be demonstrated experimentally. Mathematics contains far more concepts discovered through imagination rather than hands-on experimentation. Some argue that these mathematical concepts are proven by physics. However, this is demonstrably untrue. If the claims were accurate that mathematical systems and physical-world experience match up precisely, then Gödel’s incompleteness theorems—which showed the systematic impossibility of proving all truths within a system—would have led to the collapse of the physical world. Yet the real world remained intact after Gödel, Church, and Turing emerged. Even Wittgenstein discussed this at length in his philosophy of mathematics. A simpler example would be the claim that physics proves the existence of a mathematical system: it would be equivalent to saying, “The real world should only validate the proposition 1 + 1 = 2, and not the proposition 1 + 1 = 10.” These two propositions may seem contradictory, and classical logic does not allow for both. However, we know that these two propositions can coexist—1 + 1 = 10 is valid in a binary system, as proven by the development of modern computing. Such propositions are now acceptable under non-standard logic or quantum logic after developments beyond classical logic. We intuitively understand that the collapse or reestablishment of a logical system has no impact on the physical world. While this discussion may seem digressive, the conclusion we reach is that while some parts of mathematical discovery are experience-dependent, others are experience-independent; thus, mathematics cannot be entirely dependent on the physical world. How, then, does mathematics exist in such a way, and how do we humans engage with it? There are two main hypotheses. One view is the transcendent view, which holds that mathematics is entirely independent of the physical world and has no relationship with it whatsoever. However, this view seems inadequate, given how extraordinarily well mathematics is used as a tool to explain natural phenomena. Thus, another view is the Kantian approach: mathematics is independent of the physical world, but it is an a priori concept for the physical world, and we can somehow perceive it (though we do not yet understand how exactly). As a result, interpreting the relationship between mathematical systems and the physical world in this manner can be quite convincing, and I find that (c) is making a similar type of argument. Rather than claiming that there exists a soul or some independent mind, it suggests that psychological properties that lead us to think of ourselves as “I” indeed exist. These psychological properties—just like the relationship between mathematical systems and the physical world—are independent of physical properties, do not influence each other, and yet somehow manifest in the physical world. This is what British Emergentism argues (assuming I have correctly understood it). While opinions may vary, (c) seems more promising in the long run compared to (a) or (b).