Is Logic Normative?

Many philosophers hold that logic is normative: logic tells us how we ought to reason. This video outlines some arguments for the normativity of logic.

0:00 - Introduction
3:41 - Normative consequences
10:44 - Error
17:55 - Demarcation
22:07 - Pluralism
33:52 - Logic vs the norms of belief?

-- Haack, Susan. (1996). Deviant Logic, Fuzzy Logic. Chicago: Chicago University Press.
-- Harman, Gilbert. (1986). Change in View. Cambridge, MA: MIT Press.
-- Labukt, Ivar. (2021). "Is logic distinctively normative?" Erkenntnis 86: 1025-1043.
-- Quine, W. V. O. (1951). "Two dogmas of empiricism." Philosophical Review 60(1): 20-43.
-- Russell, Gillian. (2020). "Logic isn't normative." Inquiry 63(3-4): 371-388.
-- Williamson, Timothy. (2013). Modal Logic as Metaphysics. Oxford: Oxford University Press.

[alexandersanchez]

As a mathematician stumbling on this video, to my mind, “logic” and “reasoning” are completely distinct concepts in my mind. The latter is a cognitive activity tantamount to usefully processing data about the world, and the former is a formal system—no different than a game of chess or a computer program.

In that sense, I think my initial objection to the notion of logical normativity can probably be reasonably dismissed as semantics/trivial; “logic” is just symbol-pushing and doesn’t make external claims about anything.

And, of course, “reasoning” is only a useful emergent physical phenomenon—and probably just illusory in the final empirical analysis. This doesn’t seem to be what people mean by “logic” either. (It’s just a physical phenomenon. E.G., is photosynthesis normative?)

However, I think what’s actually being asked is whether or not “the systematic philosophical study of correct/useful reasoning” makes normative claims. Framed this way, I think the answer is *obviously* yes: we need to choose what we mean by correct/useful!

As I said, this isn’t my field and I’m just an amateur. Feedback appreciated! (Please let me know all the dumb mistakes I’ve made.)

[kimwelch]

Math is a language for describing relationships (between what and what is irrelevant). What you care about in logic is the relationship between elements and propositions on those elements. Logic really says nothing about truth or falsehood outside 'true' and 'false' being elements of a proposition. Everything else is interpretation. There are an uncountable number of logical statements which are perfectly valid logical statements but for which any interpretation would be ludicrous. Math is a game whose interpretation is sometimes useful in explaining how things in the real world relate within given bounds.

[droe]

The purpose of logic is to reveal "good" vs "bad" reasoning. It cannot tell us what we should or should not believe, but it can help us think clearly and consistently. It can also not tell us what is true or not true, because the terms within logical arguments (by terms I mean the claims or premises, etc.), can be true or false. Logic is, then, a tool to guide thinking, not belief or truth.

[franciscofont]

Excellent video! This was one of the few topics that I couldn't even fathom how someone could argue that logic isn't normative, but I must say, you gave some really good arguments that changed my mind on this

[MsNathanv]

Thank you, I found this very interesting.

I was really absorbed in the preface paradox, never having encountered this before, but it seems that there is a very simple way out of this paradox, by saying "I believe P" is really a shorthand for "I believe P is *likely* ." Indeed, we may find that we accept P, Q, and P conjunction Q in some subset of our beliefs-- maybe if we assign "Triangles have three sides" and "Squares have four sides", for example-- when we have beliefs that we find *perfectly* likely.

It also seems like it would be worthwhile to examine in more detail exactly what normativity *is*, and exactly what the significance of logic (or other rules of reasoning) being normative would be. We can describe many moral precepts in ways less normative: if you kill somebody, you will go to jail; if you kill somebody, that will make other people sad. We can describe logical rules in similar ways: if you simultaneously accept P and not P, you will starve. But these descriptions don't capture the entirety of how we seem to feel about morality: when we say that lying is wrong, and that affirming the consequent is wrong, we don't really behave the same way in response to that wrongness, and it makes me think that this is a case where "wrong" is being given two different and relatively distinct meanings, more distinct than when we compare the wrongness of lying with the wrongness of pedophilia, where the difference feels like a difference in degree rather than quality.

[alst]

Great video! Thanks for your hard work putting it together!

[inoculatedcity]

this video is awesome because i’ve always just taken it for granted that logic is descriptive and had no idea that anyone thought it was normative, let alone that this was apparently the dominant view lol

[nutwit]

There's two kinds of statements: "is" statements and "ought" statements. They do not naturally interact. In order to bridge the gap between them, you must at some point introduce a moral assumption.

P, P -> Q |= Q doesn't say that an observer Ought to Believe Q, it says that P is true, that If P is true then Q is true, and therefore Q is true. To get from Is to Ought, you have to introduce the moral assumption that you Ought to value believing in true things. Without that bridging tactic, it isn't possible to have any sort of meaningful conversation about either morality or logic. Therefore, they aren't at odds with one another; they're companions.

[funnywarnerbox]

The way I understand it, logic/reason in itself is consequence and pattern-ness which everything follows, even competing logics. Individual formal logics are strict formulations which are allowed to follow the patterns of reason. This way we can more precisely study of more complex things because we can define them through this strict vigorous system. Like if one wants to study circles, there are competing views of what a circle is which makes them difficult to study. If you define a circle using geometry which is built from formal logic, you can make specific deductions (A circle is set of points of equal distance from a center, and from this you can make deductions about its area, circumference etc. You cannot do this if the object circle is not strictly defined using geometry)
So individual logics are kind of like lego blocks we use to make bigger and more complex structures. But logic itself is like the principle which allows any kind of blocks to be connected in certain ways and form these larger structures.

[martinbennett]

If logic is normative and I think the sense which includes telling us to reject inconsistency is normative, this normative aspect is an axiom that is not part of logic. It is outside the logical system but necessary for the practice of logic.

[minch]

This was so interesting! Glad I stumbled across it

[alegian]

Having some basic probability theory intuition, I found the preface paradox really interesting. It makes sense that you consider your beliefs to have a small error probability, and "rolling the dice" for every individual belief is likely to show "no error", but considering the conjunction of all beliefs, the probability of "error" is almost surely 1. Or I might just be connecting random dots :D

[elinope]

The simultaneity problem of special relativity gives a good example of logical truth leading to separate branching paths.

[ignotumperignotius]

Quite good stuff, Normativity is a gnarled thicket

[unreasonable]

The problem of belief in P1, P2 etc but not in the conjunction of P1& P2 etc goes away if you think of beliefs (at least your empirical beliefs) as Bayesian.

[yuriarin]

great video if you want to continue the series on logic paraconsistency might be a great topic

[xiutecuhtli]

These are good ideas.

I think saying "if X is true, then Y is true" like a language, is logic, and there's no "ought to" about it but there is "it doesn't follow the language" about it. and the decision to translate observations into premises and translate conclusions into assumptions is like a separate attachment to logic, and there is "ought to" about that choice, and also "ought to" about which logic language you choose for translation

[peterp-a-n]

Great video (and a very endearing ending).

[CorbinSimpson]

Category theory offers a systematic exploration of the issues you raise in the second half. Categorical logic is a complete answer to the question of when a formal system should be considered a logical system. LEM can be seen as a special axiom which is not needed for general topos theory.

[DubmanicGetFlazed]

The term "moral realist" always cracks me up ever since I first heard it. "Me? Of course I am a moral realist!!! that means my morality is the real morality. Any one who doesnt believe in my morality is a moral Fake-ist, or a moral imaginary-ist" lmao. (i know thats not the common definition but it the absurdity of the name implies something allong these lines.