​https://medium.com/question-time/ask-dr-silverman-13-by-the-godless-integers-people-mathematicizing-secular-activism-5967952df538
The concept of separating church and state is often credited to the writings of English philosopher John Locke. According to his principle of the social contract, Locke argued that the government lacks authority in the realm of individual conscience, something rational people could not cede to the government. Locke’s views were influential in the drafting of the United States Constitution. Though the separation phrase is not explicitly in the Constitution, Thomas Jefferson used the metaphor of the “wall of separation between church and state” in an 1802 letter to the Baptist Association in Danbury, Connecticut. This phrase, as the Supreme Court noted, has come to be commonly accepted as an authoritative declaration of the scope and meaning of the First Amendment to the Constitution. Having seen the religious wars in Europe, our founders viewed religion as a private matter, without government involvement. The U.S. Constitution is a godless document, with no mention of any deities. It begins with the words “We the people,” not with “Thou the deity.” Secular government guarantees freedom to follow any religion or none. It allows people to explore religious questions according to individual conscience, but does not take sides itself. Those who wish to promote Christianity, other religions, or atheism, are free to do so—but without government assistance. All beliefs are protected, which is what guarantees religious freedom. 

​https://www.canadianatheist.com/2019/07/ask-herb-12-jacobsen/
 
I’ve debated many fundamentalist Christian ministers, and it’s often the first time that members of a mostly Christian audience get to hear an atheist point of view from an atheist, rather than from their Christian minister. Many atheists, myself included, have been overly optimistic that rational arguments will change minds. I’ve since learned that you can’t reason someone out of a belief that he or she didn’t find unreasonable through reason. I now think the best we can do is make good points in a reasonable and pleasant manner. I emphasize “pleasant” because many in the audience are affected more by the debater’s personality than by arguments. This was difficult for me to understand at first, since it’s so different from my world of mathematics, where smiling and a sense of humor are useless. I look for opportunities to change atheist stereotypes and to raise questions some Christians may never have considered. 

​https://medium.com/question-time/ask-dr-silverman-12-nominally-platonic-platonically-nominal-fictionalism-neo-meinongianism-a8f672b0bd4e
 
Mathematical nominalism, also known as mathematical nominalism factionalism, is the view that mathematical entities, such as, numbers, functions, and sets do not exist. The opposing view, mathematical realism or platonism, holds that at least some mathematical entities exist. Nominalists say that mathematical entities do not seem to be the kinds of things that have space-time locations or causal powers. So, if they exist, we can’t have knowledge of them. On the other hand, mathematical entities play crucial roles in any area of science. Nominalists see the benefits of and applicability of mathematics, but refuse to recognize abstract objects. I think these arguments are mostly semantical, and not particularly interesting to me. Neo-Meinongianism, named after the Austrian philosopher Alexius Meinong, holds that there are non-existent objects, including mathematical and other abstract objects. For example, a round square is a non-existent object. Of course, there are things that could possibly exist, but don’t—like world peace. Everything is an object, even if unthinkable. It then has the property of being unthinkable. I’m not a philosopher, so these arguments don’t interest me either, because they also seem mostly semantical.
 

​https://www.canadianatheist.com/2019/07/ask-herb-11-jacobsen/
 
True, the history of humankind must include the history of warfare. Even our prehistory, through archeological findings, shows that there have always been wars. From our hunter-gatherer past, through the Middle Ages and approaching fairly modern times, the norm across many societies included mutilation of the enemy, murder of enemy infants, routine rape, routine torture of prisoners, and other hideous, cruel and unusual punishments. Public executions for the amusement and instruction of the populace were also common. There is a long list in both time and practice of man's inhumanity to man. Today, more than ever, humans have the capacity to use weapons of mass destruction to do away with just about all other humans, as well as the ability to affect climate change that could devastate human life on our planet.

https://medium.com/question-time/ask-dr-silverman-11-nature-antirealism-and-realism-cc4ef32867a1
 
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.

https://medium.com/question-time/ask-dr-silverman-10-mathematical-objects-number-ology-not-numerology-82fcf0492528

​Mathematicians don’t much think about types of mathematical objects. A mathematical object can be anything that mathematicians work on, including functions, sets, vectors, numbers, points, lines, circles, ellipses, matrices, infinite series, and so on. The various specialties of mathematics, like linear algebra, abstract algebra, topology, real analysis, complex analysis, geometry, combinatorics, and many more, can be organized by the type of mathematical objects they primarily concentrate on. Different areas of mathematics have some objects in common. For instance, most mathematical areas deal with objects like numbers, functions, and sets. 
 
 

​https://medium.com/question-time/ask-dr-silverman-9-numbers-numbers-numbers-16ed68d12c95
 
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, …., which were extended to take in 0 and the negative integers. This later included rational numbers (fractions), irrational numbers (real numbers that are not rational) like pi and the square root of 2, and complex numbers like the square root of -1.Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the number 13 is regarded as unlucky. Some people also believe in numerology, whichattributesa divine or mystical significance to numbers. One such example, espoused by many Christian fundamentalists, is fear of the number 666, which they refer to as  the Mark of the Beast. Numerology is also associated with the paranormal and astrology. Of course, numerology is a pseudoscience, a superstition that uses numbers to give their subject a veneer of scientific authority.
 

https://medium.com/question-time/ask-dr-silverman-8-infinity-behind-every-real-infinite-is-a-silver-lining-infinite-ca48e718070

​Early puzzles about the infinite might have begun with the ancient Greek philosopher Zeno. One version of his paradox of the infinite is this: “An arrow goes halfway to its target. It then goes another halfway, and repeats the processan infinite number of times. Therefore, it can never reach its target.” But, of course, the arrow does reach its target. Zeno lived long beforethe concept of a limit (the basis of calculus) was discovered independently by Newton and Leibniz. They showed that infinite sums can converge to a finite limit. In Zeno’s case, we can begin with one half, then add half of that (one fourth) and keep adding halves. This infinite series has the limit 1, which is the Zeno target.  
 

​
https://medium.com/@scott.d.jacobsen/ask-dr-silverman-7-infinity-1-2-3-4-until-you-cant-count-anymore-171a7297f5c5 
 
There is no middle ground between the finite and the infinite, but there are some strange, non-intuitive things we can say about infinity, some of which I’ll describe. In mathematics, a set (of numbers) is said to be infinite if it can be put into a one-to-one correspondence with a proper subset (not all the numbers) of itself. For instance, the positive integers (1, 2, 3, 4, …)  form an infinite set because there is a one-to-one correspondence between them and the proper subset of positive even integers (1~2, 2~ 4, 3~6, 4~8, 5~10, etc.). A set of numbers that is not infinite is called finite. There is no one-to-one correspondence between the set of numbers {1, 3, 7, 13, and 18} and a proper subset of itself. We say that the cardinality of this set is 5 because it has 5 elements, the same as the cardinality of {10, 20, 30, 40, 50}. 

​Although the 19th-century mathematician Gauss crowned mathematics the “queen of the sciences” because mathematics is essential in the study of all scientific fields, an argument can be made that mathematics is not really a science. Science is empirical, meaning based on observations of nature, and it is potentially falsifiable by new observations of nature. In other words, new evidence can lead us to revise scientific theories, so scientific ideas can never be proved absolutely.Some mathematical ideas, on the other hand, can be absolutely proved. 
For a mathematical statement to be accepted as a theorem, its conclusion must be known to always be true whenever its hypotheses are satisfied. Mathematicians accept that a conclusion must be true based on a proof rather than empirical evidence. The Pythagorean Theorem, for example, can be proved.