Logic – 2

What do these two examples of syllogistic-style arguments have in common?

Husband: Honey, our children are hungry.  Feeding them your meatloaf would eliminate their hunger. Therefore, you should cook meatloaf.

Wife: But, honey, your second premise is faulty.  For feeding them your lasagna would also eliminate their hunger.  Therefore, you should cook tonight.

Candidate 1: Programs to help the poor are meant to decrease poverty.  But there is more poverty today than there was before these programs began.  Therefore, programs designed to fight poverty actually acccomplish the opposite.

Candidate 2: Your argument proposes a single cause for poverty.  But there might be many causes for poverty.  Thus, your argument is invalid. 

First off, both arguments consist of properly constructed syllogisms, and both are countered with effective challenges based on classic principles of logic.  Second off, they both sound completely idiotic since no human being in their right mind would actually talks this way.

These examples highlight one of the challenges with traditional logic which is designed to create a language and framework into which any argument (sound or unsound, based on reality or fantasy) can be fit.  And while it’s all well and good to know that the argument “All mermaids are female.  Gwen is a female. Therefore Gwen is a mermaid.” is fallacious (regardless of whether or not mermaids exist); here on earth mermaids don’t exist (as far as we know).  More importantly, people talk to and argue with each other using actual human language that can lose its persuasive power (not to mention its ethical underpinning) when it is boiled down to symbols and straight jacketed into “proper” logical syntax.

Now one can make the case that even the most complex arguments presented in the floweriest of language can be reworked into logical structures, and that these structures are a better basis of analysis than the original text.  But might there be a way to take a look at the actual conversations real people have with each other and place them into a framework that lets us look at them in context, without having to boil everything we say down to the question of whether A equals NOT A?

I mentioned that many new logical systems have been developed over the years and while some of them are mathematically complex and best suited for specific purposes (like the creation of computer software), some wrestle with the need to build a rigorous structure around arguments without turning interesting prose into quasi-mathematical symbols which might eliminate value found in the subtlety of the original language.

My favorite attempt to create this type of structure is the ToulminModel (developed by the British Philosophy Professor Stephen Toulmin) which proposes the existence of practical or substantial arguments (wonder why I like him?) that can be diagramed in the following manner:

In this model, the Claim is an assertion you are trying to prove, the Grounds consist of the information you bring to prove the claim and the Warrant supports your assertion that the Grounds should lead you to the Claim.

“What’s the big deal!” I hear you cry out.  Isn’t a “Claim” just a conclusion to a logical argument?  And aren’t “Grounds” just another way of describing your premises, with logic serving the role of the “Warrant” that links the two?

Actually, no, since Grounds in the case of a Toulmin argument might consist of facts (even axiomatic facts that logic requires everyone to agree to as the basis of any argument).  But they might be laws, regulations, social customers, literary references, or any other man-made (or even natural) “thing” that can provide support for the Claim. And the Warrant can make a logical connection, but it might also make an emotional or ethical appeal (all equally valid under Toulmin’s scheme).  And the fact that the Warrant requires Backing (a demonstration that the Warrant is sound and appropriate) adds an additional layer of rigor, even if this Warrant relies primarily on logic to link A (Grounds) to B (a Claim).

Toulmin also adds another nice feature: the Qualifier, that lets you present exceptions to your Claim. While qualifications can be implied in logical statements such as SOME As are NOT B, natural language cries out for us to specify which As we are talking about.  So the claim that “Freedom of speech is an unarguable good.” can be easily qualified as “Freedom of speech is an unarguable good, except in cases where it might lead to physical harm to someone else.” without diminishing the original point (or leaving us responding to an seemingly logical but actually illogical argument that “Since you don’t believe in free speech in all situations, you don’t really believe in free speech).”

Now Toulmin diagrams can get quite complex, especially once you realize that Grounds may be required to support a Warrant and that this means the Warrant can play a secondary role as another Claim (or Sub-Claim) that needs to be supported (with Grounds, Warrants and Backing) before it can be accepted and used to prove the ultimate Claim.

This might all sound a bit abstract, but as we’ll see once we start digging into actual political debates (i.e., arguments) Toulmin provides an important arrow in our quiver as we try think about the best way to think for ourselves during a Presidential election when many people would prefer that we not think at all.

Logic - 1

Let’s take a step back from faith and talk about something that we can all agree is a major component of critical thinking which is logic. 

Logic has been part of this discussion since it began.  Sometimes I talked about it as an element of an effective and successful argument (one in which conclusions follow logically from premises). I’ve also contrasted things that may or may not be a requisite for critical thinking (including imagination, emotion, and faith) to something that surely is (logic).  But what exactly do we mean when we talk of “logic?” 

The good news is that we do not need to fully answer this question and know everything about the answers in order to draw upon important logical concepts as needed as we analyze the upcoming Presidential election.  Like fallacies, logic consists of many different components and comes in many different flavors and an understanding of all of them is not required for some basic logical principles to help guide our thinking.

But we need to keep in mind that, unlike fallacies (which can be thought of as a long list of “broken” arguments, from which we are free to pick and choose which ones might be relevant for a particular argument or discussion) logic is a complete system (actually a set of systems).  In fact, fallacies are simply arguments that break the rules set up by one or more of these system.  So while we are free to use the tools of logic selectively to support a critical thinking exercise, if you want to go past the practical critical thinking project encouraged in this blog, a good first step would be a study of logic.

But what do we man when we talk about “studying logic?”  Two thousand, or one thousand or even one hundred years ago, the answer to that question was simple: studying the logical systems constructed and formalized by (surprise, surprise) Aristotle (i.e., “The Philosopher”). 

The notion that arguments can be written in specific syntax of statements such as “All A’s are B’s” “Some A’s are NOT B’s” and organized into sets of statements such as…

All A’s are B’s

All B’s are C’s;

Therefore all A’s are C’s

… (called a syllogism) is also derived from Aristotle’s formal logic which is part of “The Philosopher’s” complete logical system built into works referred to as “The Organon” (stop snickering out there).

Of course, the study of logic wasn’t set in amber 2400 years ago, but was developed, forgotten, rediscovered and supplemented over time.  The use of diagrams and illustrations (especially ones that could be reproduced using newfangled devices such as printing presses), helped create new ways of looking at logical statements and relationships that went beyond what ancient thinkers taught (or thought). 

The good news about formal logic is that one can become proficient at it by taking a single course on the subject (as I did years ago as an undergraduate), although one can dedicate one’s life to studying the topic deeply.  The bad news is that fewer and fewer people every get the chance to take such a course, despite the fact that an understanding of formal logic and rhetoric was once a requirement for being considered an educated person.

This is usually the point where some old timer chimes in about how much we’ve lost by giving up study of the classics in favor of “fad” topics such as sociology and quantum mechanics.  But this complaint misses two key points, namely:

* The reason classical subjects (like logic and Latin) are not taught today is that the explosion of knowledge brought about by the scientific revolution and modernity has created vast and exciting new topics to learn about and explore; but more importantly;

* There are other newer, heavily-mathematical, modern systems of logic (such as symbolic logic) that go way beyond what Aristotle ever dreamed of.  And in terms of sheer numbers, more people are taking classes in these modern logical systems than ever studied Aristotle’s creations (although study of these various logics – and their practical application – is more frequently referred to as “computer programming”)

These complex systems (and even large parts of the Aristotelian system) go way beyond what is needed to determine if a Presidential candidate has built his proposals on a strong logical foundation or a pile of sand. But it is worth looking at one modern logical system that is particularly relevant to something that formal and mathematical logic doesn’t always care about: normal human conversation.