Normativity of Logic and the Preface Paradox

normativity logic

I recently came across a surprising claim: that logic is normative. That is, it is in some sense wrong to deny logic. The claim isn’t surprising because it’s controversial; instead, it’s so obvious that it’s initially jarring to see it spelled out explicitly. What is controversial is the claim that followed: that logic’s normativity isn’t universal. In other words, that it is sometimes rational to accept a deductive argument as valid, accept all its premises as true, and yet still deny its conclusion. Let’s see why this might be and whether it holds up.

The Preface

A well-known paradox, the Preface, goes as follows: I assert each thing I state in this post. After all, if there were something here I did not wish to assert, I would not state it. However, I also assert that I’m wrong about at least one thing I say here. Write anything long enough, and chances are, no matter how thoroughly you check yourself, you’ll get at least one thing wrong. (This post isn’t very long, but as an amateur writing on a complex topic, the post needn’t be very long for me to feel confident that there’s at least one mistake in it.)

So far so good. Here’s the trouble. Let’s label my assertions in this post p0, p1, p2, … pn. I’m apparently asserting that each of those is true, but also denying that their conjunction – (p0 & p1 & p2 & … & pn) – is true.…

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The Münchhausen Trilemma

There are many forms of radical skepticism: skepticism of the external world, skepticism of other minds, and skepticism of rationality, to name just a few. They arrive at skepticism via different channels, some more successful than others.

Agrippan skepticism is an ancient Greek variety. It is perhaps the hardest-hitting attack on the possibility of knowledge in the history of philosophy. I don’t know of any satisfactory solution.

Epistemologists agree on this much: in order for a belief to count as knowledge, it needs to be at least a justified true belief. What does it mean for a belief to be justified? It means we have a reason for believing it. If this reason will work as justification, it must be a reason that we know.

Of course, if we know this reason, it must be a justified true belief. So what is its justification? It has to be some other reason that we know. And we’re off on a regress.

The problem can be put this way: justification can only happen in three ways:

  • Regress argument: belief A is justified by belief B, which is justified by belief C, which is justified by belief D, and so on.
  • Circular argument: belief A is justified by belief B, which is justified by belief A.
  • Dogmatic argument: belief A is axiomatic. It requires no justification.

None of these options succeed in justifying a belief. Regress arguments fail to justify because they never bottom out at some belief that is already justified.…

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Train of Thought #87

I love following trains of thought.

I was staring at a fireplace listening to music. I had the following progression of thoughts:

  1. The bass line in this song is really awesome.
  2. It’s a very active bass line. I don’t know much about music and almost nothing about good bass playing. Any active bass line is going to sound good to me.
  3. Does that mean that, since I don’t know much about music, none of my opinions about music matter?
  4. I have strong opinions about music. Favorite albums, artists, songs, instrumentalists. To someone who knows a lot about music, those opinions must seem superficial and misguided.
  5. This is true even if we agree that taste is subjective. Even among matters of subjective taste, some taste is refined and some misses all the nuances of the form. Some is based on understanding the medium and some is based on irrelevant associations.
  6. Does this mean that all of our opinions about subjects in which we are not experts are misguided?
  7. Actually, even if we’re experts, we can always assume that there’s another expert who knows the subject more, or we can imagine one in the future who will. That person’s opinion is based on more and better evidence than mine. Shouldn’t I just automatically adopt his position?
  8. Does this mean we shouldn’t believe any of our beliefs? Should we assume all our beliefs are wrong? Should we just believe what the most knowledgeable expert beliefs?

My train of thought took me to radical skepticism, as they often do.…

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