Often, as I see it, individuals take a partial truth but then stretch it out of proportion turning it into an untruth. There’s no reason why cat absolutely must have the spelling “cat.” The sign “cat” is an English convention.
As the brilliant essayist Theodore Dalrymple writes in his book Life at the Bottom, throwing away the supposed “oppressive” forms of conventional language standards, based on an egalitarian worldview, will entrap a poor family into remaining poor: “Linguistic and educational relativism helps to transform a class into a caste – a caste, almost, of Untouchables.”
It’s difficult to think of a better way to destroy someone’s social, intellectual, and economic mobility. Isn’t it ironic?
Of course, language is not a static thing. It changes! And a good writer sometimes does play fast-and-lose with the standard rules.
Shakespeare’s English is not our English.
Grammar can be better or worse in a time and place, and that surely affects the quality of someone’s speech or writing. There’s a kind of underlying logic in simply understanding the subject-predicate relationship. We can definitely write incoherently!
While there are borderline disputes in “higher” grammar or spelling, there are traditional conventions that everyone accepts – and these conventions allow you and me to talk to each other.
A good vocabulary increases successful communication. It makes it more efficient and sophisticated. Picking the right word cuts down on wordiness. It is thus economical. Things read more authoritatively and thereby it psychologically adds persuasive ethos to your writings. It adds precision and depth.
How, though, do we increase our vocabulary?
Without having a sufficient size, we don’t have much to draw from. My answer is to write down unfamiliar words in a notebook. I’m admittedly not always consistent, but I have begun to do this while reading. When I see a word I don’t know, I look it up, and then write it down. It doesn’t have to be a word I don’t know, actually, just something unfamiliar or unusual. Such a word sometimes gives the air of familiarity when an expert writer places it into a flawless context, yet alone it is actually unfamiliar or unusual. So look it up and write it down.
A thesaurus is a useful tool, though it’s inadequate. Like randomly searching a dictionary, a thesaurus unlikely will help you find a word that represents a complex idea you want to convey but which you cannot simplify to a specific word. That’s why you need to build your mind’s vocabulary.
This “green-eyed logic puzzle” kind of reminds me of a logic joke I’ve seen.
Four logicians walk in a bar. The host asks the question, “Do you all want a drink?” The first logician says, “I don’t know.” The second logician says, “I don’t know.” The third logician says, “I don’t know.” And the fourth logician says, “Yes!”
The fourth logician can respond with a “Yes” because if logician one, two, or three didn’t want a drink, their answer would have been a “No.” And if the fourth logician didn’t want a drink, he could have said “No.”
(Here we have three, not four, logicians!)
The “green-eyed logic puzzle,” to be sure, is more complicated than the bar joke.
Yet when you consider two prisoners, the puzzle is not too hard. It just seems hard when you have 100 people. So, when it comes to these problems, it is always a good idea to attempt to simplify it and then try to solve it. And if you can do that, you can extrapolate and tackle the seemingly more difficult problem with its greater numbers involved.
In the easy case, since it is known that “at least one person has green eyes,” person A and person B can figure out things and leave on the second night. That’s because person A knows that if person B left the first night, that would only be because B saw that A is non-green. That didn’t happen! Ergo, person A realizes that he must have green eyes.
The same logic applies to person B. Ergo, person B realizes that he must have green eyes. As the number of people increase, the number of days increases proportionally as it takes as many days to observe as there are people so as to watch their actions, and those actions reveal needed information. With three people, it takes three nights. With n people, it takes n nights. We can see this modeled after induction by generalizing from two people to n people.
The video references David Lewis (who is famous in philosophy for his ideas about “possible worlds” in logic) and suggests that the “common knowledge” being shared to everyone at once makes a difference. It makes a difference because now everyone is keeping track of everyone else based on the “common knowledge.” In other words, the video suggests, for everyone to keep track of everyone during these days with a success rate of 100 is for the simultaneity of watching at that point when the “common knowledge” was broadcasted.
Aristotle was right when he argued that accepting contradictions as true leads to utter incoherence and madness. Contradictions lead to bad thinking. Out of a contradiction, we can “prove” the moon is made out of cheese, that black is white and white is black, and that four is not identical to four.
Logic is truly a part of the liberal arts; it’s not just mathematics. We can read better and write better when we understand logic better. There are many good reasons to learn logic!
Roughly, the “subjective” is someone’s private individual realm of feelings and thoughts. That’s why we often claim that taste is “subjective.” I like ice cream, though you might hate it.
And, roughly, the “objective” is what is publicly true for all individuals. It is an “objective” truth that one plus one equals two. Nobody can change that truth; it is independent of my subjective thoughts and your subjective thoughts.
If humans didn’t exist, one plus one would still equal two. It’s also an objective fact that the Moon orbits the Earth. That’s true today and it was true before any human existed.
What Does it Mean to be Objective?
When trying to obtain truth, we should be “objective.”
Evidence SHOULD BE Objective, NOT Subjective
We can think of having knowledge, at least as a general rule, as the merging between the “objective” and “subjective.”
Yet, in this above video, it is very briefly mentioned that we can, in some contexts, consider evidence from the subjective realm. What’s the evidence that I’m happy or sad?
For me, it is how I personally (subjectively) feel.
Someone else can, perhaps, figure out that I’m happy or sad by various signs or by trusting in me once I tell them what I feel.
But are there more areas where good evidence comes from the subjective realm? What about self-reflection on the nature of what it means to act and choose? Or what about self-evident propositions? Are some self-evident propositions true because it is “subjectively” obvious they are true (such as the Law of Contradiction)? Maybe we have innate knowledge?
Or consider spiritual experiences. If someone has one, he cannot just dismiss it. He has to ponder it. He has to consider if it truly means something or not. Maybe the experience was so strong that he thinks it provides him with evidence over the spiritual or theological realms. Could it be good evidence? Maybe, maybe not.
This Video Contains the Fallacy of Subjectivism!
While I was going through the online resources for the textbook The Art of Reasoning by David Kelley and Debby Hutchins, it happened by happy coincidence that we got to work on a problem dealing with the Fallacy of Subjectivism.
All of us should be humble to the vast amount of knowledge available. Estimate that relative to your own. What would that estimate round to? About zero percent. At most, it’s just a tiny fraction of one percent. As the saying goes: the more you know, the more you know that you don’t know.
Researching anything is an overwhelming task that can seem unending. How many thousands of books and articles have been written on World War II alone? Where does someone begin? Unless you are superhuman, choices have to be made. It’s a tricky process! We can pretend to be “independent” thinkers, but all of us rely on those who we deem expert authorities.
In more ways than one are we “social animals.” That includes how we learn. Are there not “canonical texts” that shape us and society? Are not certain authors of the distant past living with us in the present? Society is no “blank slate.”
The future depends on the present and the past. Knowledge and ideas are not universally created anew nor derive out of a single person’s head. Things take place in a historical, cultural, and communal or social setting. Further, there is conflicting, contradictory, and divisive discourse within. An individual must learn how to navigate.
That’s the first step to become good at researching.
Learning to navigate, in part, depends upon developing our skills in logic and critical thinking skills. It also depends upon finding good expert authorities to help us learn about the given topic we are researching.
For example, I’ve taken some advanced mathematics with good professors. That’s how I first learned about mathematical logic. I’ve taken Professor Gerard Casey’s traditional logic course at LibertyClassroom.com. And I’ve read many, many books on logic, philosophy, and mathematics.
I recently had the pleasure (and honor!) to have a short e-mail interview with Professor Gerard Casey. He has an excellent course on traditional logic at Liberty Classroom. I’ve gone through the course, benefited tremendously from it, and know you will too.
Casey’s Freedom’s Progress? with Veatch’s Two Logics.
Gerard Casey
Dr. Gerard Casey is Professor Emeritus at University College Dublin. He received his primary degree from University College Cork, then went on to earn an MA and PhD from the University of Notre Dame. He also holds a Bachelor of Laws (LLB) from the University of London, a Master of Laws (LLM) from University College Dublin and a Doctor of Letters (DLitt) from the National University of Ireland. His books include Libertarian Anarchy, Freedom’s Progress?, ZAP, After #MeToo, and Hidden Agender.
Amateur Logician: Dr. Casey, could you please tell us a bit about yourself and your interest in logic?
Gerard Casey: Well, my discovery of philosophy at the age of sixteen coincided with my discovery of logic. I bought a copy of E. J. Lemmon’s Beginning Logicand spent the summer of 1967 teaching it to myself. Anyone who has ever read the Lemmon book will know that it’s not the most pedagogically friendly of texts, so I had many frustrating days that summer trying to come to grips with that book, especially as I didn’t have the assistance of a teacher, and the internet awaited invention.
When I went to Notre Dame for graduate studies in Philosophy, all graduate students were required to take a course in post-elementary logic. In that course, we had to come to grips with the more advanced ideas in metalogic: e.g. the Loewenheim-Skolem theorem, decidability, consistency and (in)completeness, advanced set theory, Cantor and infinity, etc.
When I took up my first teaching post at The Catholic University of America in D.C., in 1983 I taught logic for 3 years. When I returned to Ireland in 1986, it was to take up a position at University College Dublin in the Department of Logic and Psychology. I was given the responsibility for teaching an entire First Year course in Logic, which covered Aristotelian Logic, Propositional and Predicate Logic, Modal Logic, Philosophy of Logic and Metalogic. For the philosophy of logic, I discovered Susan Haack’s Philosophies of Logicand at the same time, I developed an interest in so-called deviant logics.
Dr. Casey, I enjoyed your logic course at Liberty Classroom tremendously. Your way of presenting things has influenced the site AmateurLogician.com. How did you design your logic course at Liberty Classroom and what makes it unique?
The essential elements in logic have been around ever since Aristotle codified them, but the presentation of the material is, or has been, often presented in a form that is unnecessarily complex. In my course, I try to focus on the basics and to do so in a way that makes it easy to remember and (relatively) simple to use. I have also (I think) added some constructive items not normally found in most treatments, such as the use of the rules of the syllogism to find a valid conclusion from given premises, or a premise that, if added to a single premise and putative conclusion, would give you a valid argument.
For the average person, what would you consider the most important thing to master in logic?
It may seem obvious to say this, but the core idea in logic is that of valid inference, the notion that if certain propositions are true, another proposition must also be true—not may be true, could be true, might be true, but must be true. After that, apart obviously from mastering the syllogism, grasping the relationship between propositions on the Square of Opposition is a great help to clarity of thought, that and being familiar with the other forms of immediate inference: conversion, contraposition and obversion.
What are some good books to get started in logic?
For more on Scholastic Logic, there is Raymond McCall’s Basic Logicif you’re lucky enough to find a copy second-hand, and similarly Andrew Bachhuber’s Introduction to Logic. For modern symbolic logic, there is no shortage of introductory texts, most of them, in my estimation, overloaded with material, but pretty much all of them adequate. My preference is for a minimal rather than a maximal account.
Didn’t you once collect neo-Scholastic textbooks? They sometimes get a bad rap, but there are some truly excellent texts: Peter Coffey’s logic book and ontology book, for example.
Yes, I used to have quite a collection of neo-Scholastic books but, once I retired, I had very little space for books in my house and had to reduce my collection drastically. Most of my neo-Scholastic books had to go, including my much-loved Klubertanz! I also had most of a series of such texts produced in the UK (can’t quite remember the name of the series) but that too had to depart.
Logic belongs both in the English Department and the Mathematics Department. Why do you think the education establishment has pushed away from teaching logic?
The English Department? I’ve never known an English Department to have courses in Logic! Philosophy Departments, yes; English Departments, ? Logic is still taught in Philosophy Departments, and is (or was) often a required course. I’m not sure it still is. In its more rarified aspects, logic has found a home in Mathematics Departments and, practically, in Departments of Computer Science (Logic Gates, e.g.).
Do you have a preference for Aristotelian-Scholastic logic versus the modern mathematical logic?
Yes. It is, in my judgement, more immediately relevant for practical use. But I have a preference for the modern presentation of sentential or propositional logic as I think it is more perspicuous.
Could you please summarize Henry Veatch’s arguments about the differences between these two logics?
Veatch’s book, Two Logics, is really an essay in the Philosophy of Logic, an area of study in which Susan Haack’s Philosophies of Logicis a fascinating and challenging read. One way of characterising Veatch’s concerns would be to think of them as relating to the existential/essential implications of propositions.
Veatch believes that a universal affirmative proposition such as “All human beings are mammals”, if true, is necessarily true. In Aristotelian logic, this is an ‘A’ type proposition, and ‘A’ type propositions, if true, imply, by subalternation, the truth of the corresponding ‘I’ type propositions, in this case, ‘Some human beings are mammals’. So if “All human beings are mammals” is true, then “Some human beings are mammals” would have to be true as well.
Now, in symbolic logic, “All human beings are mammals” would be represented by (x)(Hx → Mx). In symbolic logic, from the truth tables for conditionals, a conditional is false only when its antecedent is true and its consequence false or, to make the relevant point here, a conditional is true whenever its antecedent is false! This means that in symbolic logic, if (x)(Hx →Mx) were to be true because Hx is false, it wouldn’t necessarily imply that there is in fact any human being that is a mammal!, i.e. (Ex)(Hx & Mx).
Now it could be argued that in concerning itself with existential matters, symbolic logic is engaged in a kind of category error, that the relationship between A-type and I-type propositions is an intensional matter that prescinds from the existential question altogether.
There are far too many issues to give an overall summary of all the relevant and insightful elements of Veatch’s book, but whether one agrees with him or not, completely or only in part, there can be no doubt that he is engaged in reflecting on some fundamental matters concerning the relationship of logic to the real world.
Can’t we both overstate and understate the importance of logic? While logic is often necessary, not sufficient, for us to arrive at true conclusions, we clearly need more than logic. And are there any major misconceptions people have about logic?
Yes, we can both overstate and understate the value of logic. Logic is necessary for rational discourse, but, as you suggest in your question, it is not sufficient. In addition to logic, we need rhetoric, understood in the classical sense as the art of finding the available means of persuasion. Logic is an island in a sea of rhetoric. In some ways, people need to learn logic more than ever. A knowledge of the more common fallacies, both formal and informal is helpful, is also useful.
All that said, logic is a formal codification of what is already present in our discourse and I believe it is impossible for our natural languages and any system of logic to be perfectly coincident.
Your more recent books include Hidden Agender, After #MeToo, and ZAP. What are some egregious examples of illogical thinking in today’s postmodern political culture?
The logical solecisms don’t change; just the material! Today’s postmodern culture abounds in non-sequiturs, begging the question, undistributed middles, and, most significantly, the revenge of the ad hominem! The idea that the truth or validity of what one says is inherently related to one’s race, sex or age is today the most popular form of the ad hominem.
Thank you so much, Dr. Casey!
I very much appreciate you spending some time with me and my readers.
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A Few After Thoughts:
In addition to Dr. Casey’s logic course, he has a two-part course on the history of political thought at Liberty Classroom. That was the impetus behind his massive book Freedom’s Progress?: A History of Political Thought. Though I’ve only read large scattered chunks of it, it’s extremely well-written. Dr. Casey is truly a gifted, erudite individual. The text can also be used as a self-defense weapon, given the size of the book!
For full disclosure, if you do sign up for Liberty Classroom through my link, I will earn some commission as an affiliate. I’m a student there and totally recommend it.
One thing I might have clarified better in the interview: I know logic is not taught in the English department, but I think it should be, at least in terms of “informal logic.” Consider writing an argumentative essay! It seems to me that, for example, in high school, students should ideally be learning some logic both in English and in mathematics.
Many readers likely haven’t heard of neo-Scholastic textbooks. These especially flourished during the time Pope Leo XIII wrote the 1879 encyclical Aeterni Patris calling for a revival of Thomistic philosophy and theology. I reference some of these texts as it pertains to logic here. These textbooks will help “ground” anyone in classical philosophy and traditional logic.
(For more on neo-Scholastic texts, here’s a blog post from the philosopher Edward Feser.)
I’ve also had a similar view, if I understand Dr. Casey correctly, on “existential import.” In this entry, I mention that in symbolic logic, why does the proposition “some unicorns are male” imply existence whereas “all unicorns are one-horned horses” does not imply existence? The former proposition can perfectly well be entertained without having it imply existence.
Mathematical logic has it that the conditional Φ → ψ is false only when Φ is true but ψ is false. It’s otherwise taken to be true. (To be sure, this seems puzzling! Though it preserves the consistency of mathematical logic, it leads to “paradoxes of material implication.”) I write about this, e.g., here and here.
In any case, there’s a lot of things we can explore here: Dr. Casey’s intellectual biography, what logic concerns, books on logic, immediate inference, fallacies, etc.
But I’m really grateful that Dr. Casey did this short interview. All of us can learn a lot from him. And, it is my hope, that more discover his work. Check out his X (Twitter) account.
It’s the easiest, simplest introduction to symbolic logic that I know of. It’s not only a mathematical textbook, it overlaps into the liberal arts with a strong focus on translating English propositions into the language of symbolic logic.
Also, I have replied to messages sent to me via the contact form. I fear that my personal replies were sent to the spam folder. My e-mail is georgewick.il at protonmail.com.
A benefit of studying traditional logic is that it can improve our writing skills.
Peter Kreeft, in his excellent textbook Socratic Logic, mentions this. But more than logic is required. We need to develop rhetorical skills!
An argumentative essay which happens to be beautifully written needs to be balanced with its “scientific” rigor. It shouldn’t go to either extreme. You want a lively and well-reasoned essay. A good essay needs a “personal” touch to it.
Give the essay some artistic flare. Man is an emotional animal, not only a rational one. Indeed, we are stirred on by the contrary emotions of desire and aversion. We are not Vulcans from Star Trek. It is just to get angry at injustice! But don’t substitute feelings for reason.
Heated polemics are not necessary to arguments, though.
All I’m driving at is that you want to add some of your own emotional flavor to the essay to get an emotional reaction. Cold logic usually is not enough. The syllogism you’re using might not be your own creation, but the wording of it is. Present it artfully. Appeal both to the intellect and emotions.
Aristotle talked about ethos, pathos, and logos. He knew that we appeal to an audience with more than just raw reason. Logos is only a part of the formula. We have to show them that we are competent and ethical; that’s ethos. We need to appeal to their emotions; that’s pathos.
Read great essayists! Read someone like Peter Kreeft. Study his prose with its logos, ethos, and pathos. Or read social theorist Thomas Sowell. He wastes no words. We learn by example; I know I do!
The best writers can write with subtleties, nuances, distinctions.
And this brings me to something that, for whatever reason, blew up on YouTube’s algorithm. (It has around 1,000 views! How does that happen?)
