...for the Stronger

 

In the center you have Plato on the left and Aristotle on the right

 

Nosotros nos hemos educado bajo la influencia humillante de una filosofía ideada por nuestros enemigos, si se quiere de una manera sincera, pero con el propósito de exaltar sus propios fines y anular los nuestros.

[We have been educated under the humiliating influence of a doctrine designed by our enemies, perhaps in good faith, but with the aim of exalting their own goals and nullifying ours.]

~José Vasconcelos1

Important Concepts

 

Distinguishing Deduction and Induction

As you saw in the Important Concepts, I distinguish deduction and induction thus: deduction purports to establish the certainty of the conclusion while induction establishes only that the conclusion is probable.2 So basically, deduction gives you certainty, induction gives you probabilistic conclusions. If you perform an internet search, however, this is not always what you'll find. Some websites define deduction as going from general statements to particular ones, and induction is defined as going from particular statements to general ones. I understand this way of framing the two, but this distinction isn't foolproof. For example, you can write an inductive argument that goes from general principles to particular ones, like only deduction is supposed to do:

  1. Generally speaking, criminals return to the scene of the crime.
  2. Generally speaking, fingerprints have only one likely match.
  3. Thus, since Sam was seen at the scene of the crime and his prints matched, he is likely the culprit.

I know that I really emphasized the general aspect of the premises, and I also know that those statements are debatable. But what isn't debatable is that the conclusion is not certain. It only has a high degree of probability of being true. As such, using my distinction, it is an inductive argument. But clearly we arrived at this conclusion (a particular statement about one guy) from general statements (about the general tendencies of criminals and the general accuracy of fingerprint investigations). All this to say that for this course, we'll be exclusively using the distinction established in the Important Concepts: deduction gives you certainty, induction gives you probability.

In reality, this distinction between deduction and induction is fuzzier than you might think. In fact, recently (historically speaking), Axelrod (1997: 3-4) argues that agent-based models, a new fangled computer modeling approach to solving problems in the social and biological sciences, is a third form of reasoning, neither inductive nor deductive. As you can tell, this story gets complicated, but it's a discussion that belongs in a course on Argument Theory.

In this course we will only focus on deductive reasoning, primarily because of our need to study the relationship between premises and conclusion. Truth be told, inductive logic is a whole course unto itself. In fact, it's more like a whole set of courses. I might add that inductive reasoning might be important to learn if you are pursuing a career in computer science. This is because there is a clear analogy between statistics (a form of inductive reasoning) and machine learning (see Dangeti 2017). Nonetheless, this will be one of the few times we discuss induction. What will be important to know for our purposes, at least for now, is only the basic distinction between the two forms of reasoning—nevermind that the distinction is fuzzy to start with.

Food for Thought...

 

Assessing Arguments

 

Some comments

Validity and soundness are the jargon of deduction. Induction has it's own language of assessment, which we will not cover. These concepts will be with us through the end of the course, so let's make sure we understand them. When first learning the concepts of validity and soundness students often fail to recognize that validity is a concept that is independent of truth. Validity merely means that if the premises are true, the conclusion must be true. So once you've decided that an argument is valid, a necessary first step in the assessment of arguments, then you proceed to assess each individual premise for truth. If all the premises are true, then we can further brand the argument as sound.3 If an argument has achieved this status, then a rational person would accept the conclusion.

Let's take a look at some examples. Here's an argument:

  1. Every painting ever made is in The Library of Babel.
  2. “La Persistencia de la Memoria” is a painting by Salvador Dalí.
  3. Therefore, “La Persistencia de la Memoria” is in The Library of Babel.

 

La Persistencia de la Memoria, by Salvador Dalí

At first glance, some people immediately sense something wrong about this argument, but it is important to specify what is amiss. Let's first assess for validity. If the premises are true, does the conclusion have to be true? Think about it. The answer is yes. If every painting ever is in this library and "La Persistencia de la Memoria" is a painting, then this painting should be housed in this library. So the argument is valid.

But validity is cheap. Anyone who can arrange sentences in the right way can engineer a valid argument. Soundness is what counts. Now that we've assessed the argument as valid, let's assess it for soundness. Are the premises actually true? The answer is: no. The second premise is true (see image). However, there is no such thing as the Library of Babel; it is a fiction invented by a poet. So, the argument is not sound. You are not rationally required to believe it.

Here's one more:

  1. All lawyers are liars.
  2. Jim is a lawyer.
  3. Therefore, Jim is a liar.

You try it!4

Pattern Recognition

 

Sidebar

 

While pattern recognition is useful for assessing for validity, ultimately what we are really looking for is soundness. That means that we need a method for assessing each of the premises for truth. This begs the question: how do we know if the premises in an argument are true? Attempting to answer this question might drag us into the weeds very quickly. If we try to, say, first decide what truth even is, we would need to get into a complicated discussion in the field of epistemology. Epistemology is a branch of Philosophy concerned with the nature and limits of knowledge; e.g., questions like: "What is truth?", "What is the difference between fact and opinion?", "What justifies our knowledge claims?", and "What are the limits of human knowledge?"

In this class, we will largely bypass the finer distinctions of epistemology—although the interested student can take my PHIL 101 course. Instead, we will be pragmatic and operate within a scientific worldview. In other words, we will take for granted that there are some tried and true methods for ascertaining which statements are true and which ones are not. Following the critical thinking textbook written by Jack Lyons and Barry Ward, we can say that “[t]hese seem to be the main ways we have of determining whether premises are true: perception, inference, and testimony” (Lyons and Ward 2018: 246).

Perception is probably the most straightforward way of assessing a claim for truth. You basically just check for yourself. In other words, you use direct sensory information to confirm or disconfirm some claim. Having said that, per Lyons and Ward, we actually tend to not rely on this method when assessing most claims for truth. This is because most of the claims we have to assess for truth aren't the kinds of claims that can be easily verified with just the senses. There is usually some intermediate steps between hearing the claim and putting yourself in a position to be able to directly assess the claim for truth with your senses. Moreover, these intermediate steps are usually too much of a hassle. For example, perhaps you've heard that water boils at a lower temperature in the mountains than at the beach. While you are perfect capable of performing this experiment on your own, you're probably more likely to look it up on Google than actually get direct sensory information with regards to this claim. Similarly, you've heard of the state of Alabama, but I'd wager that most of you haven't visited it. Nonetheless, you still believe it exists—not through direct sensory experience but through some other method.

You can also, if you have all the relevant information, make logical inferences in order to decide whether a given claim is either true or false. For example, here's a logic puzzle from an LSAT prep course:

A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit. Question: If the last digit of an acceptable product code is 1, it must be true that the:
(A) first digit is 2
(B) second digit is 0
(C) third digit is 3
(D) fourth digit is 4
(E) fourth digit is 0.

In case you're dying to know, the answer is (A). However, most claims that you will assess for truth will not have carefully specified constraints on them like this logic puzzle. So, even if you actually wanted to do some logic puzzles, you would likely not have all the information you need to assess a claim for truth using this method.

That leaves us only with testimony. In other words, most assessments for truth will come by way of deferring to the testimony of others who we have deemed to be competent in the topic we are dealing with. In other other words, we typically defer to experts in a given field when assessing the truth of a claim from said field. However, it's not so simple. Here's a head-scratcher: How can you spot the experts if you’re not an expert? This is, once again, very similar to a problem that Plato considered. In his dialogue called Meno, while the characters are debating the true nature of virtue, Socrates and Meno wonder if it will be possible to find what they’re looking for if they don’t really know what it is. With regards to the problem of identifying experts, we have to ask ourselves the following question: if I don’t know the answer to some query, how am I going to know whether some other person knows what he or she is talking about?

Furthermore, it may be the case that some individuals might not be recognized as experts but really do know their way around some particular domain. For example, it might be the case that some known terrorist, e.g., Ted Kaczynski, can actually answer some complicated mathematical questions, even though you wouldn't expect it. Still, even though some people who are widely thought to know actually don’t really know and some people who aren’t recognized as knowers really do know, it’s often best to go with recognized experts (Lyons and Ward 2018: 248). But watch out: you have to find experts in the relevant field. For example, an astrophysicist is an expert (in astrophysics), but she might not be ideally suited to answer questions about, for example, economics.

Last but not least, beware of the Dunning–Kruger effect. See the Cognitive Bias of the Day below.

 

 

 

 

Argument Extraction: Thrasymachus and Injustice

 

The sociological elements of science

 

Lyons And Ward

At this point we can push back against Socrates a bit. Recall that Socrates makes the point that injustice causes inner conflict in groups. He then further makes the case that inner conflict is not desirable. However, it does seem like some institutions do operate quite well with plenty of inner conflict. In fact, some institutions have mechanisms to deal with and can even thrive on conflict. The most obvious example I can think of is the institution of science. Science today is a complex institution, with various disciplines and subdisciplines, which focuses on testing and updating empirical hypotheses through data-collection and experimentation. Importantly, this is all done within a somewhat adversarial (or competitive) social institution. Scientists compete for grant money, check each other's work through attempted replications, and even attempt to falsify each other's theories. Conflict appears to be built into the system. But it works! In fact, it appears that it is because of this adversarial nature that science tends to be “self-correcting.” That is to say that over time false hypotheses, even if they were at one-time universally accepted, are eventually weeded out (see Lyons and Ward 2018: 274-75).5

Are we sure it's the adversarial element in science that makes it so successful? Intelligent people can disagree on this (see Firestein 2012 for another interesting view). However, we can at this point at least discard some philosophies of science that have fallen out of fashion. For example, some thought that science was about provability. Someone who believes in provability in science might argue that science works because successful scientific theories are ones that we can conclusively prove to be true. But...

“Consider a general claim like, ‘Negative electric charges always repel each other,’... However many test cases you observe that satisfy [this] generalization, there is an untold number that you have not observed” (Lyons and Ward 2018: 278).

In other words, it is impossible to prove with deductive certainty that, say, negative electric charges always repel each other since this would require examining all instances of electric charges interacting with each other. Clearly, this is impossible. This is obviously not a knock on science; it's just that provability in science is not how science actually works.

 

Karl Popper
Karl Popper (1902-1994).

Further, science contains many accepted theories that had (or still have, in some cases) unobserved postulates; in other words, accepted scientific theories contain claims that were not proved for a long time (e.g., genes, germs, electrons) and even cases where perhaps it cannot be proved ever (e.g., string theory).6

There's also the idea of falsifiability in science. It was Karl Popper (2002/1934) who argued that the difference between scientific claims and non-scientific claims is that science exhibits falsifiability, i.e., scientific claims could in principle be refuted via experiment, while non-scientific claims (like the claims of astrology) can typically not be falsified (thus rendering astrology a pseudoscience). This sounds great initially. It does seem like that is what is distinctive about science. But is that really how it works? First off, in practice, scientists do not immediately throw out a theory if it conflicts with data—and that’s a good thing(!). For example, in the late 1700s Uranus was discovered and scientists used it as an opportunity to test Newton’s laws of gravitation. The test failed; Uranus’ motion deviated significantly from their predictions. While Popper’s theory suggests we abandon the theory of gravitation, scientists instead hypothesized (accurately) there was another planet affecting Uranus’ orbit. They were right: it was Neptune. See? We can't toss out a hypothesis that doesn't comport to the data immediately since it might be another part of the theory that is causing the error in prediction. Popper appears to be wrong.

“Popper’s picture of science is too simple… He makes it seem that when we test a hypothesis, we only use that one hypothesis to make the prediction. So, if the prediction, is wrong, there is only one rational response: reject the hypothesis. But that’s clearly false of our example, and of scientific predictions in general. In almost every scientific prediction, there will be many premises required to deduce the prediction. So, when the prediction goes wrong, it is at least possible that the culprit is not the hypothesis we intend to test, but one of the other premises” (Lyons and Ward 2018: 280).

So these philosophies of science, although intuitive initially, appear to be incomplete. It does appear that the adversarial nature of science is a driving force behind its effectiveness. However, notice this is also a hypothesis—namely a hypothesis in the sociology of science. As such, it might get falsified eventually. But that's ok! For now at least, we can see the adversarial nature of science as a possible counterpoint to one of Socrates' assumptions.

 

 

 

 

 

Do Stuff

 

 

Executive Summary

  • The basic distinction, so far as this course goes, between deduction and induction is that deductive arguments attempt to provide full support for the conclusion, so that if the premises are true, then the conclusion must be true. Inductive arguments, on the other hand, provide probabilistic support for a conculsion; i.e., in inductive arguments, if the premises are true, then the conclusion is very like to be true.

  • We will primarily be using deductive arguments in this course. As such, we must master the jargon of deduction. An argument is valid if the premises force the conclusion on you; i.e., if the premises are true the conclusion must be true. An argument is sound if it is a. valid, and b. has true premises.

  • Thus far we can assess for validity either using the imagination method or the pattern recognition method. We will be using testimony as our method of assessing premises for truth (to check for soundness). We will primarily heed to the testimony of academics and scientists.

  • In Republic (336b-354c), Socrates engages with Thrasymachus, who attempts to show that injustice is more beneficial to the individual than being just. This will be a recurring theme in the remainder of the book.

 

 

FYI

Supplemental Material—

Advanced Material—

Related Material—

 

Footnotes

1. Translation by instructor, R.C.M. García.

2. By the way, I'm not alone in using this distinction. One of the main books I'm using in building this course is Herrick (2013) who shares my view on this distinction.

3. Another common mistake that students make is that they think arguments can only have two premises. That's usually just a simplification that we perform in introductory courses. Arguments can have as many premises as the arguer needs.

4. This argument is valid but not sound, since there are some lawyers who are non-liars, although not many.

5. A fascinating idea is the possibility that this might mean that many (all?) hypotheses which are considered fact today will very likely be found to be erroneous in the future (Laudan 1981). This is called pessimistic meta-induction. To make this idea more credible, consider what the state of physics was in the late 19th century. It appears that the famous physicist Max Planck was advised to not go into physics since it seemed like they were pretty much done. “[W]hen the great German physicist Max Planck was beginning his studies in the 1870’s, he was advised by a physics professor to choose some other subject, because everything important had already been discovered—there were just a few holes to fill in” (Lyons and Ward 2018: 283). At the same time, we shouldn't take pessimistic meta-induction further than what it really claims. In other words, we shouldn't take it to say that science is futile. The scientific method is the most robust, successful method for acquiring empirical knowledge ever—although it should be clear that it can answer only empirical questions and we can never be certain that our current empirical knowledge won't eventually be overturned by future findings.

6. As it turns out, there's an active debate about string theory. Woit (2007) argues that string theory is not science (hence, he argues that it’s “not even wrong.”) At the same time, some physicists have high hopes for string theory (see Greene 2010). For a relatively manageable introduction into this debate see Hossenfelder (2020).