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By Study and Faith – Episode 3: Logic

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by Zachary Wright

Introduction

If you’ve ever listened to an argument, you’ve probably heard someone angrily protest to the other “You’re not being logical!”, or something to that effect.  When I heard the term “logic” previously, I usually thought of things like “facts” or “math,” or even more vague ideas like “things that make sense.”  This is mostly true, but there’s a bit more to it than that – and that “bit more” is what we’re going to talk about today.  Logic, at its core, is a methodology for creating and evaluating arguments (1).   Of course, when I say “arguments” I don’t mean shouting matches like the one in the previous example, rather, I mean “a reason given for or against a matter under discussion” (2).  We make these kinds of arguments daily: at work, at home, and even in church. You see, we as people run into problems, and have to make decisions all the time to survive, maintain relationships, and accomplish the tasks we set for ourselves.  As critical thinkers, it’s important to understand what “logic” is, because logic is key in helping us convince other people of our ideas, evaluate the arguments of others, and can help us make those decisions based on the information we have obtained (like from the good sources we learned to evaluate in our last article).  No matter who you are, logic can help you accomplish your goals, make informed decisions, and be the kind of people God wants us to be.  That being said, there is a lot of information to cover.  First, we’re going to be talking about the history and basics of logic, then we’re going to talk about how to make a logical argument, then finally we’ll talk about the difference between deductive and inductive reasoning.  Let’s begin.

Logic: Terms and Tomatoes

The roots of logic trace back to Greek philosophers, specifically Aristotle.  Most of you watching have probably heard of him at some point in your educational lives, but suffice it to say that he lived through a LOT of significant Greek history.  For example, he studied at Plato’s (another very important philosopher you’ve probably heard of) academy for 20 years (3) and also got to see Greece transition from being a Republic to being an empire under Alexander the Great (whom Aristotle personally tutored) (4).  More important to our discussion today, though, is the fact that Aristotle is one of the forefathers of modern logic as we now understand it.  As one website put it, “Aristotle’s logic, especially his theory of syllogism, has had an unparalleled influence on the history of Western thought.” (5)  As I explain what Aristotelian logic is, you’ll probably begin to understand why; but first let’s take some time to build the foundations of logic by defining some terms.

Now, there are a lot of explanations of logic out there, and a lot of them have some pretty complicated figures and materials if you don’t look at them carefully.  Here are some things that we can say though:  Logic is based chiefly on propositions.  Consider the following synopsis from British Philosopher A.C. Grayling:

“Aristotle took it that the fundamental unit of logical interest is the proposition, the ‘what is said’ by an utterance, this ‘what is said’ being either true or false.” (6)

Okay, that’s easy enough…Aristotle focused on what each claim was actually saying, and what the parts of a claim are.  What are the parts of a claim?  Well, that’s where tomatoes come in handy.  I’m personally not super fond of tomatoes in their raw form, but it’s actually pretty easy to describe tomatoes, especially ones like this:

Ignoring the stems and seeds, if I were to say “The tomato is red,” that would be a proposition.  A proposition can be a singular sentence, or expressed in multiple sentences.  For example, if I were to say “The tomato is red” and “The redness quality is shown by the tomato,” those two sentences would share the same proposition:  in other words, they make the same claim.  I borrow this description from Grayling’s book again, where he makes the same point using “white” and “snowflakes.” (6)  Easy, right?

Next, we need to talk about the subject phrase and predicate/verb phrase (7).  The subject is the chief noun that’s being discussed or described by the predicate.  In our statement “the tomato is red,” the subject phrase would be “the tomato,” and the predicate phrase would be “is red.”  As you can see, the subject is described by the predicate phrase.  Try playing around with descriptions of things in your head, and identify the subjects and predicates of each proposition or statement you make.

Next, we have universal/particular propositions (8), and affirmative/negative propositions (9).  This part is a little more self-explanatory: universal/specific propositions have qualifiers that describe the subject, and affirmative/negative propositions have qualifiers found in the predicate.  Let’s explore what that looks like for a moment.  A universal proposition is one that explains that all of the subjects have a specific predicate.  For our tomato example, it would be like saying “all tomatoes are red,” not just “some tomatoes are red.”  Particular propositions are the opposite – they just refer to specific subjects, very much like our example of “the/this tomato is red.”  Not all the tomatoes are red…just this one.  Affirmative and negative propositions describe subjects as having (or not having) specific characteristics or qualities.  “All tomatoes are red” would be a universal affirmative proposition, seeing as it affirms that all of the subject does have a specific description.  The proposition “all tomatoes are not red” would be a universal negative proposition, as it’s negating the idea that the subject has the predicate’s description.  Consider this example here about birds (10):

In this chart talking about propositions about birds, “A” describes a universal affirmative proposition, “E” is a universal negative proposition, “I” describes a particular affirmative proposition, and “O” describes a particular negative proposition.  You can do a decent amount with propositions like this, but there are a few more things we need to go over as we build our logical foundation.

We’ve already touched on “quantity” (universal/particular) and “quality” (affirmative/negative) classifications, but there are a few more that might be useful to discuss before we learn how to build an argument.  Grayling states that Aristotle had several categories that he classified things into when he was looking at propositions (6).

  • Species: a definition of the essence of a thing. It’s what makes something that something.  For our tomato example, it would be “what makes a tomato a tomato.”
  • Genus: the part of something that’s not unique to some essence, but is shared by others.  “A tomato” would be the species, “fruit” would be its genus.  Tomatoes are not the only fruit, but they fall in the category of fruit in general.
  • Difference: what distinguishes one species from another.  For example, Tomatoes don’t usually go in fruit salads.  Tomatoes are also noticeably nastier than other fruit.
  • Properties: the characteristics that make up a specific something.  Tomatoes have skin on the outside, and are wet, mushy, and have seeds on the inside.
  • Accident: Basically, a property something has right now, but doesn’t always have.  For instance, “The tomato is red, but it doesn’t necessarily have to be.”

To wrap this section up, there are a few things to keep in mind as we continue our discussion about logic and arguments.  

  1. First, we need to remember that each proposition/idea can be broken down into subject and predicate phrases, where the subject is the essence/thing, and the predicate is the description of the essence/thing.  
  2. Second, we keep in mind that we need to differentiate the number of things the predicate describes (universal vs particular), and also the qualities of the things we’re talking about (affirmative vs negative).  
  3. Next, we need to know what category of the subject we’re talking about, namely, whether we’re talking about the species, genus, differences, properties, or accidents of something.  

With this baseline information, we’re now ready to explore the basics of making an argument.

Syllogism:  The Art of Making an Argument

We’re going to be shifting to the topic of syllogisms.  Propositions when used as a part of an argument (not just a mere description), are referred to as “premises,’, and syllogisms are defined as “the simplest sequence of logical premises and conclusions, devised by Aristotle.” (11)  In other words, we can use propositions to make arguments and arrive at a conclusion.  Consider this example of a syllogism (12).

P1. All A is B

P2. All C is A

Conclusion: All C is B.

We can go back to our tomato example here, too.  Let’s just pretend that “A” is “tomatoes”, “B” is “fruit”, and “C” is “cherry tomatoes”.  Let’s apply that to our syllogism.

P1. All tomatoes are fruit

P2. All cherry tomatoes are tomatoes

Conclusion: All cherry tomatoes are fruit

Each syllogism has the same kind of makeup.  For example, syllogisms always have a collection of premises that are understood and agreed upon as true.  In this example, we have two premises, but you can have any number of propositions here if you’d like.  Conclusions are also important for every argument based on syllogism, because if we don’t have a conclusion, then all we’re doing is making observations.  That’s not a bad thing, mind you: we need to be willing to gain knowledge.  However, if we want to make decisions, we need to be able to learn – or, in other words, arrive at conclusions.  Just don’t forget to make sure that your premises actually support your conclusion (we’ll talk about Logical Fallacies another day).

In the introduction, I made a syllogistic argument, in a way.  It kind of looked like this:

P1. We run into problems

P2. Logic helps solve some problems

Conclusion: We may use logic to help solve some problems

These are super basic examples, but I’m sure you can see how they can be expanded to make more complex arguments.  Consider practicing looking at syllogisms in work, at church, or even in just the daily mundane statements of life.  These are literally the building blocks of learning and making decisions on a daily basis.

Let’s use an example from church history.  In the original 1830 edition of The Book of Mormon, Joseph Smith is labeled as being the “Author and proprietor of the Book of Mormon.”  Some critics have asserted that this is actually Joseph Smith admitting to having “authored” The Book of Mormon himself.  However, not only does that contradict what Joseph Smith wrote about in the next few pages, but it also ignores the important context of New York publishing laws at the time (13).  The argument against the idea that Joseph was claiming to the the “author” in the sense that he made up The Book of Mormon can be summarized in the following syllogism:

P1. Joseph needed to publish The Book of Mormon

P2. To publish The Book of Mormon, he needed to secure a copyright, which involved him labeling himself as “Author and Proprietor” according to New York laws at the time

P3. Translators for the 1824 KJV Bible, claimed to be “authors” of their work for copyright purposes (14)

Conclusion: Joseph labeled himself as the “Author and Proprietor” to publish, and secure copyright for, The Book of Mormon while clarifying throughout his life that he was merely a translator for the texts.

Now, I will caveat this discussion with a warning similar to the one I made in the last article.  With people, you can never really be sure what to expect, so it’s generally not a good idea to use universal arguments when dealing with people or people-based subjects…like history or religion.  If we believe in the concept of agency, we need to believe in the idea that people may choose to act differently than they previously have.  We can observe trends in behavior, but stereotyping and generalizing individuals or groups too much may lead to unnecessary conflict, limit your ability to work with others, and even sometimes lead you to make a wrong conclusion about how someone will act or react to a situation.  Critical thinkers should be willing to re-evaluate their arguments and should avoid hasty generalizations whenever possible.

Deductive vs Inductive Reasoning

This actually transitions rather well into the next portion of the discussion.  What we’ve discussed so far constitutes what most people refer to as “deductive reasoning,” or a system of proofs where the “premises logically entail its conclusion.” (15)  There is one other type of reasoning we should discuss, namely inductive reasoning.  Inductive reasoning works by making observations, and coming up with conclusions based on grouping together certain things/people.  Here’s an example:

P1. Most members of the church are nice
P2. Zach is a member of the church
Conclusion: Therefore, Zach is nice

There’s a bit of a difference here in this argument.  With deductive reasoning, if we assume that both P1 and P2 are true, then P3 MUST be true, while with inductive reasoning, P3 is only “likely” true (15).  You would have to get to know me personally and make observations to confirm that for yourself.   This is why, in most debates and discussions, deductive reasoning is usually stronger than inductive reasoning (more on that in a moment).  Even so, in terms of definitions, inductive reasoning is best understood as observing patterns in specific groups and making a prediction based on those patterns.  

For those of you who have studied statistics, this kind of thinking should be familiar to you.  Observational studies are very closely related to inductive reasoning.  For example, consider the following phrase:

“Every raven in a random sample of 3200 ravens is black. This strongly supports the following conclusion: All ravens are black.” (16)

Like with traditional statistics, inductive reasoning can only give you a degree of confidence as to what to expect from individuals who are part of a group.  Like I was saying before, even if you’re looking at 1,001 people, and you see a thousand people do the same thing, that makes no guarantee that the last remaining person in that group will do what everyone else does.  This is actually really important to us as critical thinkers because we will run into inductive reasoning very often, especially in the realm of politics, personality, and religion (things LDS people have to deal with often).  People are complicated, so naturally, those with more subjective ideas will have more inductive reasoning involved, even if inductive reasoning is considered to be “weaker” when compared to deductive reasoning.  Even so, there is a use for inductive reasoning.  Consider the following:

“In an informal, or inductive, argument, the conclusion may be false even if the premises are true. In other words, whether an inductive argument is good depends on something more than the form of the argument. Therefore, all inductive arguments are invalid, but this does not mean they are bad arguments. Even if an argument is invalid, its premises can increase the probability that its conclusion is true. So, the form of inductive arguments is evaluated in terms of the strength the premises confer on the conclusion, and stronger inductive arguments are preferred to weaker ones” (17)

As we can see, using both inductive and deductive reasoning may help increase the strength of your arguments.  As critical thinkers, we should make decisions based on the best evidence available, look at things from different perspectives, and use coherent arguments.  As we do so, we’ll be able to make more informed decisions and analyze what other people say in a more effective manner, ultimately progressing on our path toward fulfilling our divine destiny.

Conclusion

In conclusion, we’ve covered a lot of material today – and there’s still so much more that can be said about logic, and the things we can do with it.  I recommend that you review this article a few times and take some additional time to study the topics presented in this essay:  understanding some of the foundations behind propositions, building your own deductive arguments, and supporting your claims with inductive reasoning. Logic can help you make decisions and strengthen your communication and problem-solving skills.  I’ll end with one note of caution though, bringing us back to the beginning of the article.  I started by giving an example of a couple of people angrily shouting at each other.  While this is definitely a form of argument, I strongly advise against it.  As Latter-day Saints, we have an obligation to speak truth, but we also have an obligation to be peacemakers (18), and to avoid contending with anger (19).  How we say things can be just as important as what we actually say (20).  It’s a difficult line to walk, but as proponents of faith in Jesus Christ, it is our solemn duty to teach and do as He did.

References:

  1. https://www.fecundity.com/codex/forallx.pdf
  2. https://www.merriam-webster.com/dictionary/argument
  3. https://iep.utm.edu/aristotle/
  4. https://www.english.hawaii.edu/criticalink/archive/aristotle/life.html
  5. https://plato.stanford.edu/entries/aristotle-logic/
  6. Grayling, A. C. (2019). The History of Philosophy. New York, NY, USA: Penguin Press.
  7. https://www.bu.edu/linguistics/UG/course/lx502/_docs/lx502-predicate%20logic%201.pdf
  8. https://maritain.nd.edu/jmc/etext/logic-37.htm
  9. https://maritain.nd.edu/jmc/etext/logic-35.htm
  10. https://philosophy.lander.edu/logic/prop.html
  11. https://owl.purdue.edu/owl/general_writing/academic_writing/logic_in_argumentative_writing/using_logic.html
  12. https://www.comm.pitt.edu/reasoning
  13. https://www.josephsmithpapers.org/paper-summary/book-of-mormon-1830/1 (Compare this page with this one); See also https://www.fairlatterdaysaints.org/answers/Joseph_Smith_listed_as_author_and_proprietor_of_the_Book_of_Mormon
  14. Smith, Miriam A., and John W. Welch. “Joseph Smith: “Author and Proprietor”.” In Reexploring the Book of Mormon, edited by John W. Welch, 154-157. Provo, UT/Salt Lake City: Foundation for Ancient Research and Mormon Studies/Deseret Book, 1992.
  15. https://iep.utm.edu/deductive-inductive-arguments/
  16. https://plato.stanford.edu/entries/logic-inductive/
  17. https://iep.utm.edu/critical-thinking/
  18. https://churchofjesuschrist.org/study/general-conference/2023/04/47nelson?lang=eng
  19. 3 Nephi 11:29-30
  20. https://www.churchofjesuschrist.org/study/new-era/2013/03/to-the-point/how-do-i-deal-with-conversations-about-the-gospel; https://www.psychologytoday.com/us/blog/your-wise-brain/202109/why-the-tone-your-voice-makes-such-difference

Further Study:

 

Zachary Wright was born in American Fork, UT.  He served his mission speaking Spanish in North Carolina and the Dominican Republic.  He currently attends BYU studying psychology, but loves writing, and studying LDS theology and history.  His biggest desire is to help other people bring them closer to each other, and ultimately bring people closer to God.