It is argued that logic, and in particular mathematical logic, should play a key role in the undergraduate curriculum for students in the computing fields, which include electrical engineering (EE), computer engineering (CE), and computer science (CS). This is based on 1) the history of the field of computing and its close ties with logic, 2) empirical results showing that students with better logical thinking skills perform better in tasks such as programming and mathematics, and 3) the skills students are (...) expected to have in the job market. Further, the authors believe teaching logic to students explicitly will improve student retention, especially involving underrepresented minorities in STEM, whose rate of attrition is higher than for non-minority students. Though this work focuses specifically on the computing fields, these results demonstrate the importance of logic education to STEM (science, technology, engineering, and mathematics) as a whole. (shrink)

In this article, I will discuss some of the arguments for and against the existence of God, in particular the monotheistic God believed in the Abramahamic religions (Judiasm, Islam, and Christianity) as well as Babism, the Bahai Faith, and Sikhism. Arguments for the existence of God try to argue that either God exists (based on other things people agree with) or that belief in God is reasonable. Arguments against the existence of God try to argue that the existence of God (...) leads to some contradiction or other absurdity. (shrink)

The problem of evil is one of the most significant challenges to theism and Christianity in particular, asking why there seems to be so much evil if an omnibenevolent (all good), loving God exists. The problem of evil, as posed by many atheists and agnostics today, (following Epicurus) often asserts that the following premises cannot all be true: 1. God exists, and is omnipotent (all-powerful) 2. God exists, and is omnibenevolent (all-good) 3. God exists, and is omniscient (all-knowing) 4. Evil (...) exists Christian thinkers over the past two thousand years have given various responses to the problem of evil in the form of various theodicies, or attempts to explain why evil exists (or appears to exist) given the existence of an Omniscient, Omnipotent, Omnibenevolent God. This document serves as a brief overview of different theodicies offered by Christian thinkers throughout history. (shrink)

Frequency-based arguments against rational belief in a miracle occurring have been present for centuries, the most notable being from David Hume. In this essay, the authors show Hume's argument rests on an equivocation of probability, with him using the term interchangeably to refer to two different and incompatible perspectives: Bayesianism and Frequentism. Additionally, the authors show that any frequentist arguments against miracles relies on a view of probability that is only dubiously linked to rationality. In other words, the frequentist cannot (...) have it both ways: if probability is indeed frequency, then miracles are indeed improbable but not necessarily irrational to believe. On the other hand, if probability is an agent's confidence in a given belief, than under certain assumptions miracles are indeed highly probable and thus rational to believe despite their rarity. As a result, regardless of which view of probability one takes, it does not follow that believing in a miracle is irrational simply because miracles are rare. (shrink)

It is argued that Maximum Likelihood Estimation (MLE) is wrong, both conceptually and in terms of results it produces (except in two very special cases, which are discussed). While the use of MLE can still be justified on the basis of its practical performance, we argue there are better estimation methods that overcome MLE's empirical and philosophical shortcomings while retaining all of MLE's benefits.

The vast majority of grading exams that contain true-false and multiple choice questions encourages students to guess. This leads to two issues: the first is it incentivizes students to be overconfident rather than honestly quantify their level of belief and the second is that instructors cannot see which questions students are certain about versus these where students guess. This paper explores how Bayesian Grading solves these issues, encouraging students to be honest about their true beliefs and discouraging them from guessing. (...) Bayesian Grading evaluates both cognition and metacognitive reflection simultaneously, teaching students to become aware of the sources of their uncertainty and encouraging them to be self-directed learners. (shrink)

Anti-intellectualism involves general mistrust of scholars, academics, and ex- perts, often as pretentious or power-motivated. While scholars have described currents of anti-intellectualism in American public life, evangelical Christianity, in responses to COVID, and rural identity, to my knowledge none have looked at how anti-intellectualism specifically manifests in the New Atheism movement. In this work, we explore the way anti-intellectualism is commonly found and expressed in New Atheism and the modern Skeptical Movement, including scientific skepticism more generally.

In this article, I define a cultural epistemology as a set of socially reinforced assumptions about how knowledge and truth are produced. Unlike a philosophical epistemology, a cultural epistemology is largely the product of culture and largely invisible. As products of culture, cultural epistemology are relatively unquestioned and, in many cases, philosophically unsophisticated. There are three common types of cultural epistemologies, influenced by who holds power in a given society: an epistemological monarchy, an epistemological oligarchy and an epistemological democracy. A (...) given cultural epistemology subsequently influences the legitimacy of culture and government itself. I argue argue that Americans tend to hold an "epistemological democracy" with two distinct facets: a trust in consensus, linked to living in a democratic republic, and a trust in their own self-interest, linked to market economics and capitalism more generally. These two facets combine, interact, and even oppose each other to legitimize and challenge American culture and its political and economic systems. (shrink)

In this paper, I give a brief overview of ideas from Reformed Epistemology, and the relationship between faith, evidence, and belief. I discuss what makes belief in God rationally warranted, and how reformed epistemology strikes a middle ground between fideism and evidentialism. In effect, reformed epistemology avoids the fideist idea that belief in God must be taken on "blind faith," but also avoids some of the epistemic issues present in evidentialism, such as its self-referential incoherence. The reformed epistemologist says belief (...) in God is rational, but not for the reasons demanded by evidentialists. (shrink)

In this paper, I wish to criticize the notion that consensus is an epistemology. While I have never seen it explicitly claimed that “consensus is an epistemology,” I have nonetheless seen it implied in many scholarly (and layperson) articles. This occurs whenever articles cite, “a majority of scholars agree that…” or “most scientists/researchers think…” In our democratic, individualistic society, we put a value on high value votes and the quantification of majority viewpoints, whether it be in political polls (due to (...) living in a democracy), online on websites with ranking or voting systems such as Reddit, YouTube, or Instagram. The danger here is we may defer too much to the consensus view without appropriate justification. I will give several reasons why we should be skeptical of appeals to consensus (including a consensus of experts), which include its non-obvious link to ontology, the fact that consensus changes, and a lack of specificity of who counts as an ``expert,'' the lack of specificity on how to handle consensus (if it does occur), and epistemic undercutting defeaters from evolutionary epistemology. While an appeal to consensus may not tell us much about whether a theory is true, they can give us practical or pragmatic reasons for trusting a position. (shrink)

This work deals with problems involving infinities and infinitesimals. It explores the ideas behind zero, its relationship to ontological nothingness, finititude (such as finite numbers and quantities), and the infinite. The idea of infinity and zero are closely related, despite what many perceive as an intuitive inverse relationship. The symbol 0 generally refers to nothingness, whereas the symbol infinity refers to ``so much'' that it cannot be quantified or captured. The notion of finititude rests somewhere between complete nothingness and something (...) having no end. -/- My concern is that many of the philosophers arguing for or against the ontology (or possibility) of an actual infinite set are unaware or unfamiliar with the mathematical literature attempting to clearly and rigorously define these terms. I believe it is a mistake to leave mathematicians out of this conversation, as analysts in particular have defined (and used) infinity in a way that is relevant to the ongoing debate between philosophers. -/- For this paper, I have selected examples from Principles of Analysis by Walter Rudin, which has become a standard text for Real Analysis classes taken by pure mathematicians and engineers. I will also restrict the scope of examples to Euclidean spaces for simplicity. Finally, I will be using addition, + and multiplication * in their usual way. (shrink)

For years, the European world saw millions of swans, and all of them without exception were white. If inductive reasoning is valid, one may conclude that all swans are white. However, this would be incorrect: in 1667 Dutch explorer Willem de Vlamingh observed black swans in Australia, falsifying the hypothesis that all swans are white. While often used as a cautionary tale for the use of induction, such as with Popper’s falsification principle, I want to explore a slightly different idea: (...) does the existence of fabricated or otherwise failed accounts of Black swans give me a reason to ignore future arguments or doubt their existence? I argue that while faulty or fabricated reports do not give us a logical reason to reject a claim, they can give us a practical one for refusing to consider future arguments. This practical vs logical distinction gives an inductive reason for believing that future arguments will be invalid, but keeps one from being able to necessarily deny the claim in question without further argumentation. (shrink)

Western, secularized capitalism appraises the “worth” of a worker through a wage, a numerical value assumed to reflect the value of one’s time (in the case of hourly jobs) or contribution (in the case of salary or commision-based work). Computers and AI models are capable of matching and even exceeding human performance on a variety of tasks such as mathematical computation, handwritten digit recognition, and even complex tasks such as playing the game Go. Furthermore, they can work around the clock (...) with no need for sleep, healthcare, or even a salary. As a result, computers are more “valuable” than humans under capitalism because they are more productive (in terms of quantity and, in many cases, quality of work). Combined with an erosion of the religious idea of explicit human worth or dignity, other humans are seen as mere means to the ends of those powerful enough to exploit them. Any hope of reducing inequality or promoting justice must come from an explicit belief in the “value” of human life independent of his or her ability to produce. (shrink)

This book serves as an introduction to mathematical logic for STEM (Science, Technology, Engineering, and Mathematics) students, written for undergraduates (in particular, 1st and 2nd year undergraduates). A focus on this book is on logical thinking, not simply rote memorization, with a focus on examples and analogies relevant to students aimed at becoming technical leaders and problem solvers. This book includes propositional logic, set theory, functions and relations, and more, with coding examples provided in the Python programming language.

Linear Algebra is an extremely important field that extends everyday concepts about geometry and algebra into higher spaces. This text serves as a gentle motivating introduction to the principles (and philosophy) behind linear algebra. This is aimed at undergraduate students taking a linear algebra class - in particular engineering students who are expected to understand and use linear algebra to build and design things, however it may also prove helpful for philosophy majors and anyone else interested in the ideas behind (...) linear algebra. Linear algebra is used extensively in statistics, mechanical engineering, circuit theory, signal processing, economics and data science/machine learning. I have found in my teaching career that students tend to struggle the most with motivating the "why" behind the abstract concepts discussed in linear algebra. This can be difficult for professors to understand because we are so used to using the language of linear algebra we take for granted why these questions are important in the first place. In other words, we may understand the “why” (after years of using these tools), but our students may not. This text seeks to explain this “why” in an accessible, engaging way. (shrink)