Herb Silverman is the Founder of the Secular Coalition of America, the Founder of the Secular Humanists of the Lowcountry, and the Founder of the Atheist/Humanist Alliance student group at the College of Charleston. Here we talk about Platonism, the nature of mathematics, the real and the unreal, and more.
Scott Douglas Jacobsen: What defines Platonism? How does this relate to the nature of mathematics? What defines antirealism? How does this relate as a counter to the previous descriptions about the nature of mathematics — and a previous session’s definition of numbers? What seems like the majority view of the practicing mathematicians now? Are numbers in the head, in the world, or both?
Professor Herb Silverman: Platonism says abstract objects exist even when they do not exist in space or time, and so they are therefore non-physical and non-mental. For instance, numbers are abstract, non-physical objects. Most mathematicians probably think that mathematical objects exist (as concepts) independent of our human intellect, and that such mathematical objects can be used in determining how any conceivable universe would work. This is an example of Platonism.
However, the existence of mathematical objects, as mathematicians understand the notion of existence, is based on the set of axioms mathematicians use. Different axiomatic theories can be useful to model different physical processes, and mathematics is the combined set of all mathematical theories. While we can postulate any axioms we wish, we usually choose only sets of axioms that yield theories we find useful. Platonists would probably try to find an axiomatic theory that is the theory of the universe.
Platonists contend that abstract objects exist in a framework of reality beyond the material world. Platonism argues that these abstract objects do not originate with creative divine activity. There appears to be no place for a divine being in Platonism. Theism, on the other hand, contends that God is uniquely necessary, eternal, uncaused, and is the cause of everything that exists. Some theists, however, try to reconcile theism and Platonism by concluding that necessarily existing abstract objects have their origin in the creative activity of God.
Before discussing anti-realism, we need to define realism. Realism is the belief that reality can lie outside the human mind. Realism focuses on what can be observed, as well as things that exist independently of what the human mind believes to be true. An example of realism is that a tree exists in nature whether or not a human is able to recognize it as a tree. Realism has nearly nothing to do with the human mind, but has everything to do with the way the world functions outside of the mind. Realists believe in rational thought and will only perceive things the way that they are truly seen, without any type of interpretation. Realists tend to believe that whatever we believe now is only an approximation of reality, whose accuracy and understanding can be improved. Realism can be applied to the past and the future as well as mathematical entities like natural numbers
In anti-realism, the truth of a statement can be demonstrated through internal logic, in contrast to the realist notion that the truth of a statement must correspond with an external, independent reality. For the anti-realist, most of what we believe to be the case about the world is due to how our minds project or create certain features or characteristics of what we perceive. Anti-realist arguments contend that natural thought processes can account for mathematical reasoning. Because anti-realism encompasses statements containing abstract ideal objects, like mathematical objects, anti-realism may apply to a wide range of philosophical topics, including science, mathematical statements, mental states, the past and the future.
Realism is also sometimes applied to moral categories. Moral realism is the belief that ethical positions exist objectively, independent of subjective opinion. Moral anti-realism and moral skepticism deny that moral propositions refer to objective facts. I’ve been in several debates about whether humans can be moral without input on morality from a supreme being (God). My opponent always takes the position that an objective morality exits and it comes from God.
What follows is the more nuanced view I’ve taken in debates about whether there is an objective morality.
Most atheists believe that ethical values are derived from human needs and interests; are tested and refined by experience; and that morality should be based on how our actions affect others. I think morality is a necessary invention of humans to construct a livable society. But morality requires flexibility because circumstances under which we live continue to change and we discover what works better. So I don’t think there’s the kind of objective morality that can be attributed to a deity.
But suppose, for the sake of argument, that we could demonstrate the existence of objective morality. I’ll first give a math analogy. There are essentially two kinds of mathematical proofs: Constructive and Existential. Here’s an example of a constructive proof, which shows that between any two numbers there’s another number. We simply construct the new number by taking the average of the two. So a new number between 7 and 8 is 7.5. On the other hand, Euclid gave an existential proof that there are infinitely many prime numbers. His proof did not give us a way to actually make such an infinite list. We only know in theory that such a list exists.
Suppose we could carefully define “morality” and come up with a set of axioms on which we could all agree. Then we might, and I stress might, be able to show that there is some sort of objective morality. But that would be an existence proof, not a constructive proof. In other words, it would be a theoretical objective morality and not one that we could readily apply to our daily lives.
Different people today and in past centuries have claimed an objective morality, but these sets of objective morals often contradict one another. They were handed down by different gods or religious authorities, all claiming to have the objective Truth with a capital “T.” And deviations from these so-called objective moralities often had dire consequences for heretics.
Our morality today differs significantly in many ways from biblical morality. Throughout history, the Bible has been quoted to justify slavery, second-class status for women, anti-Semitism, executing blasphemers and homosexuals, and burning witches and heretics. Some actions that were deemed moral 2000 years ago are considered immoral today. Morality evolves over time as our understanding changes about human needs within a culture.
Christians who claim to have the one true universal morality can’t seem to agree on what it is. The same occurs within other religions. Associating God with morality can be very problematic, especially for those who view this life as just a prelude to an afterlife. To put love of an imagined god above the love of real human beings is immoral. One biblical character, Abraham, is revered as a prophet in all three monotheistic religions: Judaism, Christianity, and Islam. He is admired for having such great faith that he was willing to kill his son because God told him to do it. Reasonable people may disagree on the right thing to do in a given situation, but there is no reason to imagine that a supernatural belief system, based what you think a god wants, can offer anything over a secular morality based on reason and compassion.
Jacobsen: Thank you for the opportunity and your time, Professor Silverman.