. It's not my job to immediately anticipate what is confusing you about the subject — TonesInDeepFreeze

I'm not saying it is. In fact I am saying it isn't. If it was, you wouldn't be too good at it. Still grateful for the clue though.

you wouldn't be too good at it — Olivier5

I certainly don't claim to be especially skilled in seeing into the minds of people who are ill-informed about the subject to know how they came to their misconceptions. Sometimes, though, I do sense at which point they got off track. And I did so soon enough with you too.

clue — Olivier5

It was not just a clue. It was a clear, concise, and precise statement.

I'm curious to see though whether you're going to continue with snide, petty, ill-premised misgivings against the person who gave you correct information.

by not subsuming LEM within an LEM/LNC combo, we can take out LNC to get paraconsistent logics — TonesInDeepFreeze

I suppose this is the main advantage of dissociating the two.

Coming back to the topic at hand, I do have a question after all: has anyone tried to build a bridge based on paraconsistent logic then, and if yes, what does the bridge look like?

What do you mean by a "bridge"?

I suppose this is the main advantage of dissociating the two. — Olivier5

Also, to be able to get intuitionisitic logic.

I mean a permanent or semi-permanent man-made structure for the purpose of allowing folks to pass over a river (usually) or another obstacle, by walking or driving a vehicle on the structure. A variety of design types are known, but I am not aware of the existence of any paraconsistent bridge. This would tend to prove that Turing was onto something.

Also, to be able to get intuitionisitic logic. — TonesInDeepFreeze

What's intuitionistic about the 'inclusive or' in LEM? Can a door be both open and not open at the same time? Can a man be alive and not be alive at the same time?

take out LNC to get paraconsistent logics — TonesInDeepFreeze

I need to correct that. Usually, paraconsistent logic is attained by not having EFQ. Taking out LNC would be something different. Nevertheless, I still think it is the case than having LNC and LEM as different principles bears upon paraconsistent logic though in a more involved way than I incorrectly stated.

I mistakenly thought you meant 'bridge' in the sense of a connection between the two logic principles.

I have no idea about paraconsistent logic used in engineering. However, the Stanford article I suggested does talk about paraconsistent logic used in computing and especially for databases.

What's intuitionistic about the 'inclusive or' in LEM? — Olivier5

I don't think it's particularly intuitionistic. Rather, it's that LEM (which is with inclusive-or) is eschewed in intuitionistic logic, while intuitionistic logic does accept LNC, so having LEM and LNC as different principles makes it convenient to describe intuitionistic logic relative to classical logic.

A bit confusing now... It seems to me that you just said that paraconsistent logics exclude the LNC, then you backtracked. But if the backtracked version is the correct one, they become irrelevant to this discussion.

Yes, I corrected myself. It's more complicated than I suggested. Indeed, you can see for yourself at the Stanford article. But it's still the case that paraconsistent logics do allow theorems of the form P & ~P.

Life is too short, and I tend to find SEP unreliable.

One way of formulating the hard problem is to ask: if we had a complete, canonical, objective, physicalist account of the natural world, including all the physical facts of the brain and the organism, would it conceptually or logically entail the subjective facts of consciousness? If this account would not entail these facts, then consciousness must be an additional, non-natural property of the world. — Joshs

Thanks for providing these quotes Josh. For the sake of simplicity I'll just address the parts that seem salient to me one at a time.

If we had "a complete, canonical, objective, physicalist account of the natural world" would that not be a subjective fact of consciousness? Or would you say it is an objective fact of consciousness? I see a problem with the 'subjective' or the 'objective' there; why not just ask whether it would entail the facts of consciousness. If it were compete then I would say it would, it would have to in order to count as complete.

It's not clear what Thompson has in mind with "the subjective facts of consciousness", and it's also not clear why they should be referred to as subjective rather than objective.

Fair enough, although you make it sound as if Wittgenstein wanted to invite as many contradictions as possible. If there are contradictions to be discovered in mathematics, I just don't see how their discovery could do anything to change. or motivate a change, in the current working practice of structural engineering calculation. But I have to admit that I'm no mathematician by any stretch.

@Banno

I believe math is, inter alia, a language.

Going by what Israeli-born historian Yuval Noah Harari says in his book Sapiens, the written word was created to handle mathematical information (accounting, inventorying) - partial scripts they're called. Only later did people expand written language to full scripts, ones capable of recording any and all conversations (poetry to prose).

I believe math is, inter alia, a language. — TheMadFool

Good, but not sure of the inter alia...

What else is it?

My inclination is to treat maths as a grammar; misusing "grammar" in a familiar way.

That is, maths is a way of talking, a set of language rules. Hence the spoons example that I have repeated several times but which does not seem to have drawn comment.

That there are five spoons on the table is a way of talking about the stuff on the table.

Any mooted inconsistency in mathematics will not change the number of spoons on the table.

The history of division, especially in Egypt, seems to fit the historical model you suggest, where an enacted solution, a procedure, became encapsulated into a formal calculation. One onion each until there weren't enough to go around, then a half onion each, then a quarter, and so on until there was not enough left to argue about. This became the basis for the quite clever method of doubling for multiplication and division used in Egypt.

One objection might come from those who think 0.99...<>1; dare I mention it? There is a point at which some folk fail to see the process 9/10+9/100+9/1000... become the very same as 1; This lack of insight is the very source of many an internet troll-fest. It's an adult version of subsitising, of looking at a group of objects and realising how many there are. Someone might characterise this as a move from a process to a thing; but I think that argument weak.

I tend to find SEP unreliable. — Olivier5

:wink:

Doubtless this is because you find it so often at odds with your own views.

One wonders why.

Life is too short, and I tend to find SEP unreliable. — Olivier5

What an absurd proposition. :eyes:

doubtless you are aware of the following, but for ...
Paraconsistent logic drops

A, ~A ⊢ B

- the explosion or ex contradictione quodlibet by introducing a third truth value. A consequence of that is that (A & ~A) is allowed, but that it is not assigned either T or F, but N.

Paraconsistent logic does not allow contradictions; it does not allow (A & ~A) to be true.

Dialetheism assigns truth to (A & ~A). That's a different fish.

Good, but not sure of the inter alia...

What else is it? — Banno

:chin: You have a point. Mathematics, I wanted to say, is abstractions but so are the words in natural language. Yet, very thought-provoking, is it not?, that mathematics seems to be universal; that is to say it doesn't seem to be culturally/geographically constrained. Everyone everywhere, it appears, hit upon the idea of numbers & shapes - there are numerous mutually unintelligible natural languages but math stands out as one language that everybody understands (trade, money, engineering). This to the extent that scientists, mainly astronomers, are under the impression that the safest bet in re communicating with aliens is to use math. Is there something we're missing here?

1/10+1/100+1/1000... become the very same as 1 — Banno

$\frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+...= 1$

Thanks for spotting my error.

So folk become puzzled as to why it should turn out that 2 is so useful for Fijians as well as for Europeans. All languages use nouns, too, but this does not lead to puzzlement. Some ways of talking are better than others.

Adopting an argument from Davidson, what would a community look like in which 2+2=3? What utterances or behaviours of theirs would convince us that they thought this? How could they be seen to bring two groups of two together and get 3? How could they behave as if that were what happened? Perhaps they pretend that the fourth item has disappeared; but what would that look like to us - a ritual?

So folk become puzzled as to why it should turn out that 2 is so useful for Fijians as well as for Europeans. All languages use nouns, too, but this does not lead to puzzlement. Some ways of talking are better than others. — Banno

Indeed, it puzzles me. A certain aspect of reality (quantity) is discovered all over the world almost simultaneously, accepted, fast & furious, by everyone. There are non-mathematical entities of course that too enjoy a similar status e.g. morality, variations don't detract from the overall universality of the notion of right and wrong. That's intriguing as hell.

Adopting an argument from Davidson, what would a community look like in which 2+2=3? What utterances or behaviours of theirs would convince us that they thought this? How could they be seen to bring two groups of two together and get 3? How could they behave as if that were what happened? Perhaps they pretend that the fourth item has disappeared; but what would that look like to us - a ritual? — Banno

Couldn't parse that to respond sensibly.

There is a point at which some folk fail to see the process 9/10+9/100+9/1000... become the very same as 1 — Banno

Yeah, it approaches 1, but it never quite does become 1, though, does it?

The inability to see that " 9/10+9/100+9/1000... " is another way of writing "1" is a measure of someone's lack of capacity to do maths.

So let's not go down that burrow.

has anyone tried to build a bridge based on paraconsistent logic then, and if yes, what does the bridge look like? — Olivier5

The inability to see that " 9/10+9/100+9/1000... " is another way of writing "1" is a measure of someone's lack of capacity to do maths.

So let's not go down that burrow. — Banno

Are you going to make a cogent argument as to how a series that is approaching 1 and could do so forever without actually reaching it is the "very same as 1", or are you going to throw around snide comments instead? ( Note; I'm not denying that for mathematical purposes it may be good enough to count that series as equivalent to 1, but the logic says that no matter how many fractions sequentially decreased tenfold you add, you will never actually get there.

Couldn't parse that to respond sensibly. — TheMadFool

Fair enough. It needs expansion. But I don't have the inclination to write an essay now.

A certain aspect of reality (quantity) is discovered all over the world — TheMadFool

I think that's not what happens. Rather, a certain way of talking about the world is found in many places. There are, after all, languages without much by way of number. Would you say that the folk who speak them have failed to notice an aspect of reality, or would you say that they have no use for a particular process, a certain way of speaking?

Exactly!

Are you going to make a cogent argument as to how a series that is approaching one and could do so forever without actually reaching it is the "very same as I" — Janus

No, partly because I don't wish to derail my own thread, and partly because there are plenty of places you can find these using Google.

I'm not being snide. It is a genuine issue amongst mathematics teachers. See the Wiki article on 0.99... It's on a par with kids who are not able to see three dots as three.

Folk who think 0.99...<>1 have missed a vital aspect of mathematics.

The interesting thing about that Escher image is that unlike orthographic projections, that would be impossible to construct, this building with its stairways looks like it would be possible to construct; it just defies gravity.