The Beauty of Argument Reconstruction (First Edition)pdf
The Beauty of Argument Reconstruction (First Edition)pdf
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  2. The Beauty ofArgumentReconstructionJason ChenFirst Edition2024This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of the license, visit https://creativecommons.org/licenses/by/4.0/
  3. For those who desire to make patterns with ideas.
  4. Table of ContentsPreface.........................................................................................................1Introduction.................................................................................................2Chapter 1 -Concision.................................................................................5Chapter 2 -Linearity.................................................................................14Chapter 3 -Progression.............................................................................22Chapter 4 -Nestedness..............................................................................31Chapter 5 -Application.............................................................................36Aristotle’s Argument for Perfectionism............................................37The Problem of Evil..........................................................................42Death is Nothing to Us......................................................................46Sartre’s Argument for Freedom.........................................................51Kant on Why Autonomy Deserves Respect......................................55Conclusion................................................................................................59
  5. 1Preface.When I was in graduate school, I read A Mathematician’s Apologyin which G.H. Hardyexplains how mathematical theorems can be beautiful. Admittedly,I could not appreciate the beauty of Euclid’s proof of the existence of an infinity of prime numbers or any otherexamples he cited, but I never doubted his assertion. I always believed there was something beautiful in math. Consequently, reading the essay left me feeling envious of those more able to experience this higherdimension of human existence. I hoped that one day I would be able to see what was not easily seen. Unfortunately, that day still has not come; Ihave yet to appreciate the beauty of math. However, I have come to recognize the potential for beauty in argument reconstruction, which is, in one sense, similar. Hardy likens a mathematician to a painter or poet because they are all makers of patterns. A painter makes patterns with shapes and colors, a poet with words, and a mathematician with ideas. To this,I would add that philosophers can also be artists, that we can also be makers of patterns.Though it may seem strange at first, breaking down argumentsinto premise-conclusion form isnot only a tool but a craft. And like any other craft, its product can be madesuch that it instantiates aesthetic properties intended by the maker. It can be molded, refined, chiseled, sculpted, shaped, and polished. It can be a thing that is more beautiful than the material from which it came. Hopefully, by reading this book, you can also become an artist, a patternmaker of ideas.
  6. 2IntroductionThe followingworkis for those who desire to make beautiful reconstructions of deductive arguments. It is not a resource that will teach you the basics; hence, in that sense, it is an advanced guide. The reader should already be familiar with premises and conclusions, validity and soundness, and the different patterns of deductive arguments. The target audience for this book includes philosophy majors and graduate students. However, anyone familiar with the subjectmay be interested. To be clear, mygoal is not to teach you how to make beautiful arguments; rather, itis to teach you how to make beautiful argumentreconstructions. Those are two different things. What I will showis that reconstructions can be more or less beautiful depending on their structure. Soan argument presented formally may be beautiful even if the argument itself is not, and vice versa.This is to say that this project goes beyond accuracy. It is not aboutensuring the author’s conclusion is at the bottom, their premisesare at the top, and the reasoning in between is valid. The reader should already know how to do that; rather, this project is about becoming an artist.You may be wondering why anyone would care about the aesthetic properties of reconstructions. That is a good question. Beautiful reconstructions arelike well-taught classesthat guide the reader through the lesson in a clear way. There are nodistractionsor obstructions; there are only propositions listed in logical order. Written well, a reconstruction should leave readers with a greater understanding of the ideas being discussed with as little effort as necessary.Beautiful reconstructions also have instrumental value in the sense that they are pleasurable to consume. When I read (and write) beautiful reconstructions, I experience what John Stuart Mill refers to as a higher
  7. 3quality pleasure, a pleasure only available to rational beings like us.Those of you who can appreciate other forms of art know what I am referring to.There is also something to be said about beautyhaving noninstrumental value, but I will not speak about thathere. I will leave that discussion for others to debate. That said, I find its instrumental value to be a sufficient reason to care. Here is a summaryof the aesthetic properties that I have been speaking of.Generally, beautiful reconstructions are •concise,•linear,•progressive,•andnested, when appropriate.Each property has corresponding general rules, which I list below.ConcisionC1 –Propositionsshould be combined ifdoing so does not negatively affect flowor dialectical usefulness.C2 –Supporting argumentsshould be removed if they are uninteresting and unimportantto the main argument, and if the spirit of the mainargument can be maintained.C3 –Propositions should be implicit ifthey areunimportant anduncontroversial.LinearityL1 –Broad premises should be listed first.L2 –If there are equally broad premises, their order does not matter unless they belong to different arguments, in which case they should be placed in their respective arguments.
  8. 4L3 –Conditionals should be listed first but shouldbe placed in their respective arguments.ProgressionP1 –Every conclusion should be directly preceded by the minimum number of necessary premises that belong to the argument.P2 –Main conclusions should follow every proposition prior to them.Follow the trail of logic backward to determine if this is true for any reconstruction.NestednessN1 –Nested listsshould be utilized when they are not distracting and can help the reader understand the argument.N2 –Different colors may be used to designate a nested list if it is helpful to present the argument clearly. N3 –Collapsible lists should be used when possible.Following these rules improvesthe flow, and therefore beauty, of a reconstruction. This will become clearer as we dive deeper into the topic. Chapters1-4 are each dedicated to one aesthetic property. Chapter 5 includes demonstrations of how these properties are to be incorporated.
  9. 5Chapter 1 -ConcisionThe purpose of a reconstruction is to promote understandingof the argumentby clearly presenting the logic. Generally, this means a reconstruction with fewer propositionsis better, all else equal. So,it is good practice to combine premisesif it does not make the argument more difficult to understand. Consider the following:1.All catsshould be petted.2.Abbey is a cat.3.Bob is a cat.4.Therefore, Abbey and Bobshould be petted. (This follows 1-3.)Premises2 and 3 can be combined.1.All catsshould be petted.2.Abbey and Bob are cats.3.Therefore, Abbey and Bobshould be petted. (This follows 1 and 2.)This reconstruction conveys the same argument while being more concise. Thus, it is more beautiful.Sometimes it is not as clear if combining premisesis ideal because it may negatively affectthe reconstruction’s flow. Consider the following:1.People who have made good health choices should not have to suffer from any of the consequences of other people’s bad health choices.2.One way that people who have made good health choices suffer the consequences of other people’s bad health choices is not being able to be treated at hospitals due to a lack of medical resources caused by other people’s bad health choices.
  10. 63.Therefore, people who have made good health choices should not be prevented from being treated due to a lack of medical resources caused by others who have made bad health choices. (This follows 1 and 2.)4.People who have decided to get vaccinated belong in the category of those who have made good health choices.5.People who have decided not to get vaccinatedbelong in the category of those who have made bad health choices.6.Therefore, people who have been vaccinated should not be prevented from being treated due to a lack of medical resources caused by people who have decided not to get vaccinated. (This follows 3, 4, and 5.)This is what the reconstruction would look like if 4 and 5 were combined.1.People who have made good health choices should not have to suffer from any of the consequences of other people’s bad health choices.2.One way that people who have made good health choices suffer the consequences of other people’s bad health choices is not being able to be treated at hospitals due to a lack of medical resources caused by other people’s bad health choices.3.Therefore, people who have made good health choices should not be prevented from being treated due to a lack of medical resources caused by others who have made bad health choices. (This follows 1 and 2.)4.People who have decided to get vaccinated belong in the category of those who have made good health choices, and people who have decided not to get vaccinated belong in the category of those who have made bad health choices.5.Therefore, people who have been vaccinated should not be prevented from being treated due to a lack of medical resources caused by people who have decided not to get vaccinated. (This follows 3and 4.)
  11. 7You may think the original reconstruction flowed a little better because the combined premisebecame longer, and longer premises tend not to flow as well, oryou may not. I believe there is room for personal preference here.Combining premisesalso runs the risk of rendering the reconstruction less dialectically useful in the sense thatit allows different people to disagree with the same premiseeven though they disagree with different parts of it.Remember,we want reconstructions to presentthe logic of an argument clearly such that we know exactly what we agree and/or disagree with. In the lastexampleabout vaccinations,if you disagree with onepart of premise 4, my guess is that you probably disagree with the other, and vice versa.This is why I think combining them is a reasonable option. But if that is not true, if you think enoughpeople would disagree with onepartbut not the other,then the uncombined premisesare preferable.Here is another example.1.Everyinstance of unjustified killing is wrong.2.Capital punishment is unjustified killing, and killing in self-defense is unjustified killing.3.Therefore, capital punishment and killing in self-defense are wrong.We can imaginemany people agreeing with one partof premise 2but not the other. For that reason, splitting it into two premises would render the reconstruction more dialectically usefulin the sense that it allows us to better pinpoint which part of the argumentwe disagree with. Of course, this is a simple argument, so the benefits are minimal; I just used it to make a point.Sometimes reconstructions can be more concise by simply eliminating one argument.For example,1.Those who have strong attachments to their material possessions will have a lot of emotional trouble when their things are taken
  12. 8away from them, and those with weak attachments will have less emotional trouble when their things are taken away from them.2.Many things will ultimately be taken away somehow.3.Therefore, those who have strong attachments to their possessions will have a lot of emotional trouble, and those with weak attachments will have less emotional trouble. (This follows 1 and 2.)4.You should constantly try to do whatever you canto minimize emotional trouble.5.Thus, you should constantly try to have weak attachments to possessions. (This follows 3 and 4.)This reconstruction has two arguments, with one supporting the other.Argument 1-3 supports argument 3-5. We could remove the first argument and reformulate the second in the following way: 1.Havingweak attachments to possessionswill minimize emotional trouble when you inevitably lose those possessions.2.You should constantly try to do whatever you can to minimize emotional trouble.3.Therefore, you should constantly try to have weak attachments to possessions. (This follows 1 and 2.)This new reconstruction takes fewer steps to reach the conclusion while still being faithful to the argument.(I would actually flip premises 1 and 2 because 2 is broader, but Iwill discuss this in a later chapter.)To be clear, since complicated arguments consist of multiple arguments, you could always make them more concise by removingsupporting arguments. This does not mean that itshould always be done. It depends on what is interestingandimportant, as well asthe intentions of the author. In the case above, I do not think the supporting argumentis interesting. I also do not find it to be important in the sense that it does not contribute to the clarity of the overall argument. Lastly, I believe the new premise 1 captures the point of the supporting argument, so the author's intentionis not lost.
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