What if “If And Only If” was removed as a construct?

What if “If And Only If” was removed as a construct?

I don’t know. That’s why I ask questions — to find out!

https://en.wikipedia.org/wiki/If_and_only_if
It’s interesting reading if you haven’t read it already.

It’s a very strong connective.. and I think it’s sometimes too commonly used inappropriately.

Basically it sets up a bi-directional condition of

https://en.wikipedia.org/wiki/Necessity_and_sufficiency

I know I know. I much prefer causality. Binary logic can be so confining but it works great with electronic circuits.

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Well the first establishes an “if” and the second fixes the “if” to an absolute.


I found a chart. I think I was connecting the concepts together in my head.

To me, “if and only if” requires two things to be absolutely connected, it is similar in strength to exclusiveness of the XOR. In both cases, there’s absolutely no leeway at all.

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But what if it’s never actually true but only partially so under certain limited conditions?

I think all circuits can be constructed with either NAND or NOR circuits. “Not And” and “Not Or”. The “Exclusive OR” circuit is actually kind of complicated.
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I wasn’t portraying as entirely arbitrary. Rather, it’s a pragmatic and useful construct that isn’t necessary. It simplifies, yes, but not necessary.
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I’m not great at binary math or truth tables. But I can watch animations of water pipes and things demonstrating them. Then they make more sense to me.

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Yes. That’s something I wasn’t 100% sure about until nd I puzzled it out above [you already knew it but we had to do it the hard way :) ] –
If and only if and XOR (Exclusive OR) are identical in results.

You’ll do fine in it. I only know it from a computer science POV – and even there ,,just through experience not through classes. You know it through philosophy which is far stronger from a theoretical understanding I believe.

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I’m just implying that most categories that are “if and only if”d (or XOR’d) are poorly constructed exclusive biconditional relationships.

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I think it’s great you’re expanding into areas that you’re unfamiliar with. I think it makes a person stronger. You’ll tie in concepts you’re comfortable with with the concepts as presented in the textbook and before you know it, you’ll be teaching it in a way that is comfortable for you and pragmatic for the students. In short, I have no doubt you’ll do great.

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You have to add more conditions Josh. That’s the thing. There’s a lot of assumptions built into the statement that are unspoken and assumed.

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Indeed. It’s powerful, I don’t take that away from it, but I honestly can’t wait until more extensive and complicated logics fill our computer circuits. They’ll do amazing things, even more than they do today.

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There’s more variables than are stated. it’s not being obtuse but rather being complete.

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For some circumstances, a male XOR female. or, “A person is a male if and only if the person is not a female”.

In other circumstances, that’s absurd to even state.

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Indeed. I prefer more expansive things. Combinatronics I think it’s called. How you can take two things, combine them in a myriad of ways that they combine even further until you end up with more than you could possibly imagine in a very short amount time/effort/space.

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If you ever do computer programming, and if you have you’ll remember – you have to specify everything properly. You can take shortcuts of course. But someone breaks your program because one of your shortcuts didn’t anticipate their usage, it’s not their fault for using your program wrong. It’s the programmers fault for not anticipating. Is that fair? No. But that’s how it is.

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Variables is what I meant to say, not conditions.

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Then it could be defined several other ways.

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If a needle is removed from a compass, do we stop saying “This is a compass”? It’s still a compass. But is it a working compass? No.

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It doesn’t though. You take the needle out of a compass and say “This is a compass”. That’s not a lie. It’s still a compass.

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In both cases you can say truthfully, “This is a compass”. You need a better example.

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woah – that statement might need some unpacking (further describing) for me to understand it fully. I think you said a lot in there that I need to hear more about

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I’m in the “shoulda-coulda-woulda” been a teacher category. Probably middle school gifted kids. But life takes you in different directions, so I do the same kind of stuff online with anybody who comes along. I don’t have to deal with internal school politics so that’s a bonus but a paycheck would be nice

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You’re implying (not stating overtly) then, that if something does not fulfill its implied purpose, a word describing it cannot be used honestly?

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I understand the point you were making but I didn’t think it was a good example because it’s too easily overturned. Perhaps the same can be said of my OP but yours is a weaker case. I’ll explain:

Usage of language. A gun is still a gun if the firing mechanism is removed.

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From a usage standpoint, it is a gun that does not fire. But if I hand it to you, show it to you in a case, talk about it in every other circumstance than using it, it will still be referred to as a gun.

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The entire notion of truth? No. But the biconditional notion of “necessary and sufficient” applying with full material equivalence? Yes.

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You can have negation without exclusivity.

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Are you referring to a state where the Truth being arrived it is only considered Truth “if and only if” I use the definition that includes “necessary and sufficient” as its definition?

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The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true or simultaneously false

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I don’t think you have to throw the whole kit and kaboodle out Mark Cidade just because 0.999999 <=> 1. Is it 1? Yes and no. Pragmatism saves the day.

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I’m restrained in my answer for truth by the conditions applied by the rules of logic yes?

My answer will only be valid if and only if I follow these conditions yes?

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Assertion and belief (assent) is all that’s required for know if something is true.

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In that construct, yes. But in reality – how we actually do things – 0.9999999999999999 is usually enough to = 1. We build upon that “as if true” because it’s the best we can do.

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You can if you like. I’ll read it as “Peter gave up because he saw where he might not be entirely correct, therefore leaving graciously is the best option”

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That’s nice for the game of logic but real world uses non-monotonic logic How often do we actually have enough data to base our conclusions upon? Not often at all.

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Not at all. It just doesn’t fit your if and only if conditions.

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Some of the better models of brain processing involve sparsely populated data. Far more empty spaces than filled. The math works better, the conclusions are more human-like but it takes far more processing power.

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The truth is arrived at when someone says “I have arrived at the truth”. Then if somebody else agrees or multiple people agree or computers are programmed to agree, well, you see where it’s going.

Unfortunately, it really is as simple as that for truth. The system you’re using is fantastic and very very pragmatic but it’s a system that is ultimately of rhetoric. “Does it convince?”

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Now you’re being dramatic again. Pointing out limitations does not require abandonment.

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I like the ideas of math and logic but not math and logic itself. Too maze-like and too many weird symbols to remember.

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For many people that is absolutely true. Sad? Yes. But true? Yes.

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I’ve been entirely honest. If I was joking and it appeared to be dishonesty, then I apologize.

I asked “What if if and only if was removed as a construct?”

Through these discussions, I’m finding out.

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For one thing, removing “if and only if” makes it difficult for Peter to win an argument.

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There needs to be a human being at the programming desk, yes. Neural networks approximate things but if they’re approximating in a way different from how we wish, problems can occur.

Thankfully, fancy and straightforward logic _WORKS_ most of the time for most things in most situations.

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“if and only if” I follow the system you’re working within am I allowed to define truth.

Otherwise, I will be unable to show it to you because you will not look at anything that is not behaving as things do in the system you’re working within. It is irrelevent, invisible, unimportant, superfluous, etc. Closed Universe. It may be a complete universe but it is a completely closed universe.

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IFF isn’t required for all systems of logic. Some second order logics for example don’t need it at all. Simply assert.

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I’m speaking of (Whatif) + (IFF) was removed as a construct.

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You’re asserting it as truth. Proving my point.

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sufficiency and necessity establish relationships.

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It has strong bivalance. I think three = are used for IIF.

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IFF produces the inverse truth table to XOR. XNOR is identical to IFF.
[not a red herring but background materials]

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You can construct OR and NOT from NAND or NOR gates. No IFFs needed.

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All binary logic circuits can be built out of NAND or NOR gates. [or combinations].

This blew my mind when I first learned it. Still blows my mind when considering it.

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If you consider NAND or NOR gates like Venn diagrams though, it makes sense. It establishes SOME basic relationship between them: areas that overlap for sure.

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Same. It’s a “mindblown” moment though when it ‘clicks in’.

So hang on: you’re saying without IFF you can’t have a NOT?

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I’d have to check. An XOR is equivalent to a IFF just inverted. But I don’t remember the difference between OR and XOR.

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But XOR wouldn’t exist without IFF and IFF wouldn’t exist without XOR because they’re the same just inverted.

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But the not isn’t fundamental to a circuit. “NAND” AND ‘NOR” are more fundamental.

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wait… I might be wrong about that… now my mind is switching to telegraph wires and lightbulbs..

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Well… wait.. binary, there’d have to be a fundamental. “open” “not open”.
Maybe there’s the IFF right at the root.

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But the IFF is in the description of the circuit not the circuit itself in that case.

“This circuit will close if and only if the telegraph switch is pressed down to make a connection and if and only if there is battery power attached and if and only if the battery isn’t dead and if and only if there is something to push it down and if and only if the Universe is around… and.

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Well even with THAT… does a circuit close IF AND ONLY IF the mechanism for closure does the closing?

Nope. There’s other conditions which can close a circuit so that it functions.

Logicians make terrible engineers because they’re focused on the circuitry and not the conditions within which the circuitry is used.

There’s a FANTASTIC site of NASA problems that occurred (some deadly) when circuit designers were so focused on the logic of the circuit they didn’t consider conditions where circuits can entirely change behavior.

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‘ve never been comfortable with IFFs (or XOR for that matter). I’m fine with assertions and allowing variables to be temporarily equivalent or exclusively one OR the other for a moment or two… but only as a convenience not as a state of being.

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I guess at the bottom of it all, I just don’t like material equivalence . Pick a realm and I’ll tell you what I don’t like about something being considered materially equivalent. [I’ll sound absurd doing so but yes, I’d find a rant about it somehow]

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Don’t like it. You know what one of my fascinations is? Boundaries. Been a fascination for a lifetime.

I have yet to find a boundary that doesn’t have a multitude of layers of some kind. Even those layers aren’t exclusively “not” each other but have some interfacing as well.

My mind brings it all the way down to Pauli Exclusion… then I get mad at Pauli for asserting it without proof… and then I come back up to more visible levels.

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Yet you had people like Wheeler who thought that perhaps faster than c was possible. [i don’t remember why now]. I think of e=mc2 as a nice guideline to work with but I still suspect there’s some wiggle room.

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I’m probably a … what’s that word physicalist? something like that – at heart – but yet I love the abstract as well. Eh I’m all over the place.

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Well, depends on zoom level though. That’s the part that gets me and keeps me going. At a far off zoom, my table is 6′ long and 3’wide. Tape measure says so. Math works.

But with a finer tape measure, things start getting stranger and stranger.

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For a pragmatic level though, I’m fine with what we use. But even in cases of theoretical physics for example: these measurements are under highly constrained and controlled lab conditions. It’s the “if and only if” situation again.

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Say a particular color is wavelength of 455nm or whatever. Where is that true? Lab conditions. It’s a standard, like the meter bar in Paris. The instruments are calibrated to it, so that’s what they’ll always read.

But hop over to the real world and you get “conditions”. Those conditions change received light. It’s no longer 455nm or whatever unless you are very strict about how you read that light and even then it’s likely to have a bit of a range to take into account surrounding color temperature and such. Amazing stuff to me.

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I’d never want these systems or methods to stop and be abandoned. Rather I enjoy exploring their points of failure.

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All we have is messy conditions though. That’s the fun thing about certain types of science. They create ARTIFICIAL conditions to get results which they then apply to the NATURAL world.

Doesn’t mean they’re wrong. But I get a kick out of “Science book says [x] but my situation says [y]. How can that be?” and that’s when you realize labs are few and far between.

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I give the sciences a hard time *because* we depend on them so much. They don’t get a “get out of jail free” card from me. They’re too important to just let them do what they do without scrutiny.

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Yeah, the pragmatics of it. I love the pragmatics of it. What gets my goat is when people forget (and they do!) that the sciences are fundamentally messy and pragmatic and subject to revision. What I see a lot of is people who kneel at the altar of science (which usually means theoretical physics, one of the *least* “sciencey” of the sciences generally) and becoming advocates instead of adopting a scientific mindset themselves.

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I’m the same way with logics. If you apply logic only when it’s suitable and then get annoyed and start using sarcasm or emotional outburst _instead of_ continuing to apply logic even when it doesn’t fit the purpose you set out for initially, then that to me, is a failure to apply logic. Oh Feynmann – I’ll read this now. Been a while since I’ve seen/read something of his and I love his style.

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Good read. I read it slowly because I didn’t want to miss anything. He’s like gold to me and very few are.

Love the rat experiment and it’s true. People look straight for the answer they want and of course they find a way to prove it, but they won’t think to seek out the unexpected.

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I like finding out where I’m wrong. Otherwise I’m just a know-it-all and learn nothing — the irony of having knowledge but being unwilling to acquire more baffles me. I learned a lot tonight and I always do. I don’t always admit it I don’t always say thank you. I don’t always say “hey this is where I was wrong – THANK YOU for pointing it out”, but I try. But even when I don’t, I make mental notes and try to improve. There’s always room for it.

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