Critical thought in the 21st century requires familiarity with traditional skills (of logic, argument, and fallacy-detection-and-avoidance) but also the most relevant aspects of cognitive science and Bayesian reasoning. Both of those new techniques are the centerpiece of the training program at the Center for Applied Rationality (or CFAR) especially in a forward-thinking application (helping people make better decisions in the future), but the same knowledge can be applied to examine past or current claims and beliefs for the possibility of fallacies, biases, or errors, and to protect yourself from both dubious and nefarious attempts at influence or persuasion.
For a complete guide to traditional critical thinking, covering all the standard principles of logic, questioning, and inquiry, see Christopher DiCarlo's How to Become a Really Good Pain in the Ass [print or kindle]. For the following, see my PDF slides and video.
Bayesian Reasoning: Finally, although Bayes' Theorem has been around since the 18th century, it has finally come into its due. It is now widely recognized as an essential component of human reasoning. In fact it happens to be the correct mathematical model for all valid empirical reasoning, and as such, it is crucial to understand it, so you can better understand how to detect weak or flawed arguments and build strong and valid ones. I have done my best to explain it (and its applicability to many tasks in critical thinking) for an audience of humanities majors in Proving History (2012) [print | kindle] (no more than primary school math required). I have also arranged an online calculating tutorial [Bayesian Calculator] and provided a video that really brings it down to basics [Bayes' Theorem: Lust for Glory!]. A good brief and basic intro to all statistical and Bayesian reasoning (especially for non-mathematicians) is Thinking Statistically (Uri Bram, 2012) [print | kindle]. For a more advanced but elegant explanation of why Bayesian reasoning underlies all sound scientific reasoning, see Scientific Reasoning: The Bayesian Approach, 3rd ed. (Colin Howson & Peter Urbach, 2005) [print]. But for beginners, it's essential to understand even basic statistical and probabilistic reasoning, and to that end, start with Innumeracy: Mathematical Illiteracy and Its Consequences (Paulos, 1988) [print | kindle], A Mathematician Reads the Newspaper (Paulos, 1997) [print], and Proofiness: How You're Being Fooled by the Numbers (Seife, 2010) [print | kindle]. For basic skills, most of the math you'll ever really need is in Math Doesn't Suck (McKellar, 2008) [print].
A Reliable & Consistent Epistemology: Most important is how you know what you know, and what standards and methods you apply to the task of forming reliable beliefs. It's essential that your epistemology be, in fact, demonstrably reliable. See my thorough treatment of that subject (for forming your own reliable worldview) in Sense and Goodness without God [print | kindle] and Peter Boghossian's skillful treatment of the subject (for challenging others to form a reliable worldview) in A Manual for Creating Atheists [pre-order print | kindle edition in the works]. It's also essential that your epistemology be applied fairly and consistently (and thus applied even to your most cherished or certain beliefs, with the same standards you apply to all other claims and beliefs). You should apply the principles in John Loftus, The Outsider Test for Faith [print | kindle], to all beliefs and claims (not just religions, which is only the example Loftus deploys), including moral beliefs, political beliefs, and everything else.
The Principles of Critical Thought:
[Originally assembled in 2013 as a helpful resource. May be revised over time.]
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