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.