Logic as Theory, Not Dogma

There are many interesting remarks that arise when people are discussing areas of disagreement, perhaps especially in areas of philosophical disagreement. These include:

  • “That’s illogical!”
  • “It’s logically impossible for that to happen!”
  • “That violates the Laws of Logic™!”
  • Etc. etc.

There are a number of interesting questions that can be asked here: “What is logic? What is the relationship (if there is one) between logic and reality? What are these ‘Laws of Logic’ and why are they special?” However, let’s stick with the question of what logic itself is. This can be phrased a number of ways:

  • The study of valid argument forms
  • The study of the correct principles of reasoning or inference
  • The study of the logical consequence relationship
  • The study of what follows from some set of truths, and why it follows

And so on. One fundamental reason we want to have the correct answers about how to reason is that we want to be able to discern how to determine what else is true, given some set of known truths. And if a party makes an invalid inference, we want to be able to point out that there is a gap between what’s asserted & what is concluded.

But there’s an interesting quality to the discourse about logic. When speaking about whether or not some piece of reasoning is valid, the remarks I mentioned at the beginning seem to conceptualize logic as some concrete, unchanging thing. It seems to view logic and logical rules as something handed down, rather than as a topic that has changed over time. And this is flatly untrue.

Without getting into the discussion about Non-Classical Logics, logic has changed over time. For about 2,300(-ish) years, Aristotelian Logic was the dominant logic in Western Philosophy. However, around the end of the 19th century, logicians began to realize that Aristotelian logic was unable to account for the inferences that were being made in mathematics at the time. In order to make logical sense of the reasoning mathematicians were engaging in, the systems of logic we now call “Classical Logic” were born. Logicians like Frege intended for this new logic to form the foundation of mathematics (a program known as “Logicism”). This project, however, ended in failure thanks to the work of other logicians like Kurt Gödel and Bertrand Russell.

But there is something important to note here: Logic changed. And it didn’t change by the pure light of natural reason or some intuition about a priori truths. Rather, logicians had data which they needed to account for – the reasoning mathematicians were engaging in at the time. The new logic had a different logical consequence relation than the old one.  Some argument forms which were valid in Aristotelian Logic were no longer valid, & some previously invalid argument forms were now valid. Take the following syllogism:

  • All Bs are Cs
  • All Bs are As
  • Therefore some As are Cs

Aristotelian logic considers this a valid argument, but it is invalid when translated into Classical Logic. What I aim to get at is fairly simple. The picture of logic as this inscrutable, unquestionable entity is blatantly ahistorical. Logical systems are theories about what follows from what, and why they follow. Just as other fields construct theories to account for the relevant data, so too are logics created to ascertain what the norms of correct reasoning are. Unsurprisingly, there are many debates about the respective virtues of logical systems and the problems they purport to solve.

But what exactly should qualify as correct reasoning is a complex topic. Is there only one correct system of reasoning, one true logic (logical monism)? Or perhaps different logics are apt to different domains, so that there is no one true logic (logical pluralism)? How do we decide between logical systems in the first place? And in doing so, must we privilege a particular logic?

Irrespective of your view on these & other related philosophical problems, you must be able to account for the historical facts about how logic has developed. Otherwise you seem to be giving a baseless “just so” story, and this makes it difficult to take your view as anything other than dogma.

If you’re interested in why exactly Classical Logic superseded Aristotelian Logic, I’ve uploaded an edited part of a talk Graham Priest once gave. It outlines the history & reasons behind the shift from Aristotelian Logic to Classical Logic. I hope this is helpful!

Link: https://www.youtube.com/watch?v=f3gMR0qVjRc

http://plato.stanford.edu/entries/logic-ontology/#Log

Priest, Graham. Doubt Truth to Be a Liar. Oxford: Clarendon, 2006. Print.