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This is very interesting even to a non-philosopher - if I get time I will check out the video after work. I've been a logical monist but to be honest I have not interrogated these axioms as much as I could have. The notion of choosing logical pluralism over logical monism is enticing. Thanks.

I'm assuming the idea is that identity, non-contradiction and excluded middle remain tautologies but are less certain even if it is generally held that these are the preconditions for sensible communication.

I found it fairly clear. But here's the article from which it derives.

https://gilliankrussell.files.wordpress.com/2018/05/logicalnihilism-philissues-v3.pdf

Also, see Logical Pluralism on Stanford.

To be a law of logic, a principle must hold in complete generality
No principle holds in complete generality
____________________
There are no laws of logic.
— Gillian Russell — Banno

So this conclusion is not a law of logic. Okay.

Nothing to see here, move along.

What?

Mathematics in its entirety lacks a foundation. Yep.

Spill on aisle Real Number.

Sorry, Prof. Russell, I'm an embodied cognitivist with respect to abstract formal constructs.

Identity: ϑ ⊧ ϑ; but consider "this is the first time I have used this sentence in this paragraph, therefore this is the first time I have used this sentence in this paragraph"

I'm looking forward to the video at leisure but this leapt out for attention. Isn't it an indexical (context-dependent) utterance? The second utterance expresses a different proposition from the first - so they are not identical propositions and we would not expect identity to hold. The expression "this sentence" refers to a different sentence in the first utterance from the second.

(Just as my saying "I am Cuthbert" expresses a different proposition from someone else's saying "I am Cuthbert", which explains why the same utterance can be either true or false depending upon context.)

But there's only one sentence. Ah. Shut ma mouth. I will watch the video. I know it's all a trick, though, so I'm not going to be taken in. Not that I'm prejudiced, of course.

Yep. That's dealt with in the video, at the end. The the monster-barring response?

Fingers in ears, la-la-la. Looking forward to it but I'm supposed to be 'working from home' right now.....

Looks like a really interesting video. Only watched first 8 minutes, but sounds inspiring. I am always interested in some new or different view point on the subject or topics. Will bookmark and watch the whole lot either tonight or this weekend. Thanks for sharing. :up:

To be a law of logic, a principle must hold in complete generality
No principle holds in complete generality
____________________
There are no laws of logic. — Gillian Russell

What about if I apply the conclusion (There are no laws of logic) to Gillian Russell's argument? The argument seems to be self-refuting - it relies on the laws of logic i.e. it assumes there are laws of logic but claims there are no laws of logic. Contradiction! Gillian Russell is contradicting herself full tilt.

Logic can't be used to negate itself for to do that is to affirm itself. Contradiction!

Dealt with a few minutes into the video.

Fingers in ears, la-la-la. Looking forward to it but I'm supposed to be 'working from home' right now..... — Cuthbert

:grin: You poor bugger. Feel for you.

Have a look when you have time - and see the article cited, too. It's curious stuff. There's something going on.

Deal with a few minutes into the video. — Banno

Roger!

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Do you think Lalatos’ approach to the logical proof is consistent with the later Wittgenstein? I wonder i particularly about the notion of truth , as opposed to usefulness , with regard to logical
proof.

But what all those people (Quine, Williamson, Preist, Kleene...) have in common is they think there's one logic, and, the one they like, that's the one. — 2:10

Really? We can assume they are all monist, which I'm hoping will gloss as absolutist? I.e. not tolerant, or relativist, inasmuch as (not) regarding logics as horses for courses? [Thought I could safely use this figure without implying anything was a race, nvm.]

I can see how someone of that persuasion (far more prevalent than I knew) might survey the totality of courses and decide that the only horse suitable is Humpty Dumpty, or worse. But a pluralist (relativist? or am I unaware of a recognised distinction?) already allows such a choice for a slowest [having fewest laws] variety of horse:

[1] Tell me, do you think that a language game that assumes no logical law whatsoever deserves to be called a logic?

[2] Perhaps not, but it's moot, because either it or a game with precisely one such law will definitely be a very weakest logic. Granted, 'weak logic' has the flavour of an oxymoron, but its instances clearly have at least mathematical interest, and might include also certain poetry, music, mime etc. What's the big deal?

[1] Ah, but the trouble is, I'm assuming that: to be a law of logic, a principle must hold in complete generality. You say 'horses for courses' so you probably don't agree?

[2] Relative to the totality of courses, guilty as charged. Only an absolutist, who didn't appreciate that truth is relative to a discourse, would agree. But on a course, in a discourse, which is good enough, a principle will indeed hold in complete generality if I call it logical. That's what I mean by logical: completely general (within the discourse) in governing inference from one statement to another.

70

Someone the other day said of "The Selfish Gene" that it was most influential amongst those who had read only the title.

I wonder if that is true to some extent here, too.

I'm an embodied cognitivist with respect to abstract formal constructs. — 180 Proof

So, pretty much, am I. I don't see any prima facie contradiction between the two. Embodied cognitivism does not rule out abstract formal constructs.

The horse will win, or not. There are no other options. So binary logic is applicable.

Lakatos is known mostly as the foil for Feyerabend's anarchic method. So the obvious choice would be to address Feyerabend's criticism of Lakatos' strategy to this instance. That might be what you have in mind, but we might make it explicit. I don't think Feyerabend addressed the Euler example directly -I checked the indexes of both Against Method and Science in a free society and found no mention.

But these would be odd bedfellows, since it seems clear that Feyerabend would side with the logical nihilists against both logical monism and Russell.

My suspicion is that Feyerabend would treat binary logic as a natural interpretation, as so closely connected with the craft of logic as "to need a special effort to realise their existence and to determine their content" (Ch 6 of Against Method).

We are left with the critique found in Chapter 16, that Lakatos' method is disguised anarchy. On this account lemma incorporation and monster barring are equally valid, the choice being arbitrary - at best an aesthetic or moral preference.

Curiously Russell has another published article arguing that logic is not normative. Unfortunatly I have not been able to access it.

So Logical Nihilism has me returning to what I had taken as pretty much settled; that scientific progress does not result from a more or less algorithmic method - induction, falsification and so one - but is instead the result of certain sorts of liberal social interaction - of moral and aesthetic choice.

And this is why the article is worthy of consideration. It's ramifications are broad.

You had me up to the conclusion. Perhaps there is no perfect source of knowledge; which so happens to include logic. It doesn't mean logic is an unreliable tool, because that would require logic.

So Logical Nihilism has me returning to what I had taken as pretty much settled; that scientific progress does not result from a more or less algorithmic method - induction, falsification and so one - but is instead the result of certain sorts of liberal social interaction - of moral and aesthetic choice. — Banno

Seems to be your work. I wasn't going to suppose being worthy of certiorari.

And elimination: ϑ & ϒ ⊧ ϑ; But consider "ϑ is true only if it is part of a conjunction". — Banno

No one addressed this; I think it quite funny. So I'll spell it out.

1. This sentence is true only if it is not part of a compound sentence

2. Snow is white

therefore, since 1) stands alone, and snow is indeed white, both premises are true. So by &-introduction:

3. This sentence is true only if it is not part of a compound sentence and snow is white

...which is false, since "This sentence is true only if it is not part of a compound sentence" now occurs in a compound sentence. (A compound sentence is formed by adding two independent clauses together using a conjunction.

This is a variant on SOLO from p.9.

So who will bar the monster, and who will befriend him?

TO whom is this addressed, and to which conclusion?

Edited to taste.

Watching an adroit logician play with this stuff is like watching an talented musician; they know the rules, but break them intentionally in order to keep it interesting.

Watching an adroit logician play with this stuff is like watching an talented musician; they know the rules, but break them intentionally in order to keep it interesting. — Banno

Not unlike jazz improv.

Yep, except I'm not keen on jazz. Too many words.

Edit: Taking that further, jazz can be cleverness that hides ugliness. I suppose on that account Russell' s work might be seen as clever but ugly. Perhaps that is what the objection is.

, @180 Proof Starting at 16:41

"Arguments can be good in all kinds of ways even when they are not logically valid".

But also, "If someone gives you a classically valid argument for the view that there are no valid arguments, that ought to be seriously worrying to someone who accepts classical logic".

...and then the discussion of modus ponens. How confident are you that there are no counter instances? But note, from the article, that logical nihilism is not the view that there are no logical truths; it is the view that there are always counter instances:

if all it took to be a logical nihilist was commitment to the view that there are no logical truths, then some logicians who would not regard themselves as nihilists—and don’t seem to deserve the title—would get counted as such. For example, Strong Kleene logic is a logic on which there are no logical truths, though modus ponens and disjunctive syllogism both hold.7 It seems wrong to classify Strong Kleene logicians as logical nihilists.

2 Towards logical nihilism
Russell invents what we might call a ladder of interpretation, starting with a single interpretation, then two, three, and presumably so on.

On a single interpretation, "T", the fallacy assuming the consequent is true. Sot he only way to avoid AC being a logical law is to widen the interpretation to include "F"...

AC looks like a logical law because the interpretation is limited.

Russell asks why we should not apply this reasoning to the law of excluded middle. Why not similarly conclude that it only looks like a logical law because we arbitrarily limit the interpretations to "T" or "F"?

Expanding the "library of interpretations" provides similar counterexamples for various other supposed logical laws.

First off, a confession - I haven't had time to watch the video so what I'm about to say might change after.

Starting at 16:41

"Arguments can be good in all kinds of ways even when they are not logically valid". — Banno

What's Gillian Russell's citeria of a good argument? Whatever it is, it doesn't seem to be about validity and if not, how does she know the conclusion is true given some premises are?

Her issue seems to be with deductive logic (validity above) but then she isn't saying anything we already don't know - there are cogent inductive arguments that aren't deductively valid - the conclusion is probable but not necessary.

1. 99.99% of Indians are mathematcian = M
2. Y is an Indian = I
Ergo,
3. Y is a mathematician = Y

In modus ponens (the sticking point insofar as the OP is concerned) form the inductive argument looks like:

4. If (M & I) then Y
5. M & I
Ergo,
6. Y

As you can see, statement 4 even if it isn't completely true, it's truer than false. Let's just say you would bet big on it.

However, 6 doesn't follow deductively from 4 and 5 i.e. it's invalid but still, and notably, the argument is good.

I haven't had time to watch the video so what I'm about to say might change after. — TheMadFool

Do that, then. Or read the article.