Relations: An Improved Foundation for Mathematics, Science, and Philosophy (Perennial Philosophy) ペーパーバック – 2019/8/1
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Relations are peculiar things. The author gives the example of a cup of coffee: the coffee is in the cup and this 'in' is a relation. We can both perceive and describe the cup and the coffee, but can we perceive and describe the 'in'? If we can perceive it, what does it look like? We cannot say, because it does not have any looks: it has no colour or shape; nor can we taste it, or smell it, or touch it, or hear it. So how can we perceive it? And we can certainly describe the 'in': it is asymmetric, since although the coffee is in the cup, the cup is not in the coffee; and it is transitive because if we put a spoon in the coffee then the spoon is in the cup. But asymmetry and transitivity, like the relation in, have no looks, tastes, smells, etc., so how can we perceive them? Indeed, are they all even real? We have to say that we can perceive the 'in' because otherwise we could not know whether the cup had coffee in it. And we have to say that the in is real because if it wasn’t how could we drink our coffee? So what has gone wrong?Another question arises with the concept of a structure. Protons and neutrons are structures of quarks, atomic nuclei are structures of protons and neutrons, atoms are structures of nuclei and electrons, molecules are structures of atoms, single-celled organisms are structures of molecules, multi-celled organisms are structures of single-celled organisms, species are structures of single-celled organisms, habitats are structures of species, and the biosphere is a structure of habitats. At each level of these structures novel properties emerge, such as life, organs, brains, and mind. This pyramid of structures is here called the Grand Structure. It is important in philosophy of science because every branch of science is concerned with some part of it: it is the focus of all the sciences. But what is a structure? Can you define it?Read this book for answers to these questions, and much more fascinating stuff about relations.