Formal Logic 101 – Part 1: Introduction

[Author's note: From February through April of 2021, Atheism Resource's Facebook page featured a series of posts on formal logic. These posts are being reproduced here, along with practice problems that were presented alongside those posts. While I am not proud enough to believe that these posts constitute a replacement for a proper university course on Logic, I hope that these posts will at least serve as a decent primer in the study of formal logic.]



As promised, welcome to Atheism Resource Presents: Formal Logic 101. This introduction is intended to provide a general overview of some of the more important concepts and terms of logic. If you reach the end of this post and feel like you don’t really understand many/all of the concepts, no need to fret. Everything in this post will be covered in much greater detail in subsequent posts. If you get to a later post and think “I feel like I heard something about this once before back in the introduction”, my purpose in writing this post will be accomplished.


What is logic all about?

I think most folks know that logic is a form of reasoning, and we generally understand that it’s a good one. It’s not at all uncommon for people engaged in a heated argument to say “I’m being logical!” and mean “The position that I’m arguing for is correct”. That said while logic is extremely useful, being logical does not necessarily mean that you’re right.


To understand this, let me digress briefly to cover the main parts of an argument:

  • Conclusion: This is what you intend to prove by your argument.
  • Premise: Propositions that are presented as evidence for your conclusion.
  • Proposition: A statement that has a truth value. For instance, “the pen is broken” is a proposition because it can be either true or false, but not both. “Please open the door” is a statement, but not a proposition because it’s not the sort of statement that can be deemed true or false.
  • Sub conclusion: an “intermediate step” that can be proven from your premises and – in turn – can serve to help prove your Conclusion.
  • Inference: A mental step that is taken to connect ideas together. For instance, consider the premises: “All copper is metal” and “All pennies are copper” an inference is the mental process that lets us conclude “all pennies are metal” from those premises.

So then, how is it that one can be logical and wrong at the same time? Put simply: logic is not about producing truth, but rather about preserving truth. To accomplish this, logic uses what are called “valid” inference rules. If you will indulge me two more definitions:
  • Valid Inference Rule: An inference that – if applied to premises that are all true – must necessarily, without even one possible exception, lead to a true conclusion. (If an argument exclusively uses valid inference rules, the result is a valid argument.)
  • Invalid Inference Rule: An inference that – even if applied to premises that are all true – may lead to a conclusion that is false in even just one instance.

You see, the rules of logic are designed so that the conclusion is as true as the premises that we put in.
That said, the rules of logic do not assess the truth of the premises. Logic merely assumes that the premises put in are true and looks to see what conclusions can be reached. I am fully within my rights to present the premises: “All cats can fly” and “all flying things are lampshades” and conclude that “all cats are lampshades”. The conclusion necessarily follows from the premises, so the argument is valid, and I’m being perfectly logical. The problem is that my premises are preposterous.
For the sake of formal logic, you can put in whatever asinine premises you may like, so long as you apply valid inference rules, your argument is valid. That said, you will typically not be very convincing in an actual argument unless you begin from premises that the people you intend to convince are likely to agree with.


Thank you for coming with me on this brief “meet and greet” with Formal Logic. I hope I’ve at least piqued your interest enough that you’ll show up next time as we start in on actual topics. 

For that matter, if you’re the anxious sort who’s reading this thinking “this sounds interesting, but I’m way too dumb to learn logic” send the page a message and I’ll see what I can do to help. I’m going to go out on a limb here and say there’s a 99% chance that you’re NOT too dumb to learn logic and your anxiety is just messing with you.


Lastly, I would like to thank my former logic professor for their gift of some of the textbooks I’m referencing while writing these posts. My former professor is presently doing some outreach work around their university to promote the use of logic, and asked to not be named in these posts so as to avoid the appearance of religious or political bias in their own work. But these posts would certainly not have been possible without them.

Continue to Part 2

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