Author: Eugenia Cheng
I’ve always prided myself on being a logical person. My choice of career, hobbies, and even conversation topics make no secret of this. So naturally, a book on the application of logic to life’s questions, written by a Cambridge mathematician, would be right up my alley. Surely this book reaffirmed my unwavering faith in logic as the primary weapon in my decision-making arsenal? In fact, the opposite is true. Cheng helps me realize the limits and follies of logic, and why life seldom seems to follow its rules.
“Logic makes our arguments rigorous but emotions make them convincing” (Introduction p. xii) – The core idea of this book. Importantly, it is worth noting that logic and emotion are not (logically) opposites, though this quote may trick you into believing this false dichotomy. This statement has varying degrees of applicability person-to-person but remains fundamentally true in its implication that neither logic nor emotion should exist alone.
“At some point people realize that the thing they liked about ‘math’ up until then was jumping through hoops and getting the right answer. They liked being able to get the right answer easily, and once they got to this exploratory world of math they run away.” (p. 8) – Not inherently related to the topic of this book. This was simply a quote that resonated strongly with me as a prospective PhD student who is on the cusp of crossing the bridge between jumping through hoops and finding my own hoops.
“you can be alogical without being illogical, and indeed being alogical is unavoidable and sometimes beneficial or even crucial, whereas being illogical is undesirable” (p. 24) – Being alogical means you are not governed by logic alone. Being illogical means you are incorrectly attempting to act logically. Being illogical is blaming your teammate for missing when you gave a terrible pass. Being alogical is NOT blaming your teammate for missing because you know they already had a bad day.
“a useful way to be a rational person is to look for the sense in which things are true rather than simply deciding if they are true or false.” (p. 125) – Tortured philosophers often believe it is difficult to know anything with certainty. Yet why are we always so eager to put knowledge into these discrete bins? I urge you to take something you strongly believe to be false, and look for a sense in which it may be true. For example, I believe the earth is not flat. However, I can see a sense in which it may be.
“Things that are true are not necessarily illuminating.” (p. 139) – Without context, this statement is an example of its own point. This statement is true, but how is it useful? We can easily come away from reading this quote feeling like we are none the wiser. In context, this statement encourages us only to pursue truths that are useful to the matter at hand. Practically, this means avoiding straw man arguments, personal attacks, and stupid brain teasers that realistically only serve to waste my time.
Gödel’s Paradox: “This statement is unprovable.” – The Kryptonite of math?! Nothing profound here, just good fun. Let’s dissect.
- IF the statement is false, this implies you can prove that “this statement is unprovable”. Consequently, you have proved the statement to be true, contradicting the original falseness. Therefore, your statement cannot be false.
- THEREFORE, your statement must be true yet unprovable since that is what you’re stating.
So can you just substitute “this statement” with any math problem and be right? Unfortunately no. Gödel’s Paradox, as with all circularly logical paradoxes, lies in the self-referential nature of the statement. Once you reference an external problem, the paradox breaks down. For example “I am lying right now” is a paradox, while “he/she is lying right now” is not.
“one way to be powerfully logical is to convert logic into feelings” (p. 172) – How often do we truly act out of logic? This is different from acting logically, as you can act logically but not out of logic. For example, when we run away from a rabid dog, are we thinking: dog is running toward me snarling – does it intend to cause me harm – if it does… if it doesn’t… else…? No. We run away out of fear. Fear is an emotion. Ultimately, the most logical action in said situation is indeed to run away, yet our decision to do so was driven by fear. The same can be generalized to all of our actions. The best way to reinforce your logical decisions is to charge them with feelings that make you act with conviction.
“In mathematics, the things we decide to start with are called axioms, and in life these are our core beliefs.” (p. 183) – This insight helped me understand why some disagreements just seem to be impossible to resolve. Oftentimes, such arguments are unfruitful and result in a stalemate born out of differing personal axioms. In such cases, rather than alienate the other party due to some misconception of their intelligence or stubbornness, we should try to identify which of their personal axioms differ from ours and be accepting of said axioms despite their misalignment with our own.
“If you feel something then the fact that you feel it cannot be argued down by logic” (p. 271) – A simple yet powerful statement that left me feeling disappointed in myself for not realizing sooner. In the past, I have admittedly been bewildered at people who I felt were feeling unjustifiably ‘sad’ or ‘frustrated’. Though I would rarely articulate my thoughts, in my head I was trying to logically understand WHY this person was feeling this way. Although I still maintain it is not useless to attempt to logically understand your feelings, I now see that it is inappropriate to either invalidate or resolve them with logic alone.
“a good argument, at root, is one in which everyone’s main aim is to understand everyone else.” (p. 296) – Unlike we are often led to believe, the aim of an argument is not to win. In fact, even if you ‘win’ an argument by convincing the other party of your perspective, you have ultimately failed if you yourself do not understand the source of the other’s original perspective.
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