[logic] inclusive and exclusive disjunction

[Anne B]

learnlogictheeasyway.com

Lesson 2.1.2 discusses Inclusive Disjunction and Exclusive Disjunction.

I had heard the terms before and knew what they meant. But I didn’t realize until now that in English we usually use the same word for both and we expect people to know which one is meant by the context.

The course gives a good example for an exclusive disjunction: a mother saying to a kid “You can have ice cream or cake.” The mother is giving permission for the kid to have one or the other but not both. She is forbidding her kid to have both ice cream and cake. The kid is expected to know this.

[Anne B]

I want to try looking at sentences with “or” in them to see how easy it is to tell whether “or” is meant as inclusive or exclusive and to get an idea of how often and in what contexts each meaning is used.

I took the sentences with “or” from this essay:

http://curi.us/2235-discussions-should-use-sources

If you want to try doing this yourself before reading what I wrote, search for “or” on that page.



> People think you should debate or explain stuff yourself, not cite books or articles.

First “or”: inclusive. If people think you should debate or explain stuff yourself, they’d also be okay with you both debating and explaining stuff yourself.

Second “or”: inclusive. If people think you shouldn’t cite books and you shouldn’t cite articles, they’re also going to think you shouldn’t do both.

> But the truth doesn’t depend on what ideas are in my head or what I remember.

Inclusive.

> Even most of what Rand, Mises or Reisman said about it wasn’t new.


Inclusive. There could be something that two of them both said, and this sentence would apply to that something.

> Then when you debate someone, your idea is a book or article that you can cite.

Exclusive. A cite couldn’t be both a book and an article.

> So it’s just like citing a Mises book, it’s pointing at the existing literature and trying to figure out what the discussion tree looks like, what is answered and unanswered, refuted or not, etc.

Exclusive. Something can’t be both refuted and not refuted.

> • Citing stuff you don’t understand or haven’t read.

Inclusive.

> • Judging cites by the author’s name or what his conclusion is.

Inclusive.

> There’s a ton of socialist literature and a socialist is a good person to help guide me to the best stuff and also, simultaneously, to the key stuff to criticize (or cite criticism of) to change his mind.

Inclusive.

> If you’re just trying to practice explaining stuff, not actually trying to reach a conclusion in the field, then using little or no literature can make sense.

Exclusive. “little” and “no” can’t both be the case at the same time.

> This is especially true for complicated, established fields like economics or philosophy.

Inclusive.

> It’s less true for a very new field like AGI, but even then you shouldn’t be e.g. reinventing algorithms, data structures, or programming languages – there’s lots of existing stuff that’s worth using (even an imperfect programming language is generally far better than trying to make a new one).

Inclusive.

> Yeah maybe if you reinvent 100,000 points from scratch there will be a big chunk there someone could use and combine with some existing knowledge, but if that’s what’s going to happen you might as well do that yourself (develop in, from day 1, as an improvement on some existing knowledge – as something that can be added to some existing knowledge and/or some changes to some existing ideas with problems – rather than ignoring existing knowledge and leaving it to someone else to convert your work to be relevant to other ideas humanity has).

Inclusive. Is “and/or” a way of saying “inclusive or”?

> Then you’re trying to outcompete thousands or millions of people’s cooperative efforts by yourself.

Inclusive.


From these examples, it seems that “or” is inclusive unless both things are not possible. However, this wouldn’t work for the ice cream and cake example in the logic course. It would be possible for the child to eat both ice cream and cake, but that’s not what the mother is saying.

How about sentences where “either” is used with “or”? I’m going to make that a separate post.

[Anne B]

My intuition is that “either…or” specifies an exclusive “or”. After looking at some definitions, I am not sure if my inuition is correct.

https://www.macmillandictionary.com/dictionary/british/either-or-or

> used for showing two or more possibilities or choices
> You must answer either yes or no.
> You can contact us either by phone, by email, or by letter.
> When there’s a crisis, they either do nothing or do something totallyuseless.


https://dictionary.cambridge.org/us/grammar/british-grammar/either-or

> Either… or… connects two choices:
>
> I’ve saved some money to buy either [choice 1]a DVD player or [choice 2]an MP3 player.

https://www.thefreedictionary.com/either+...+or

> either ... or
> 1. used in positive statements
> You use either and or when you are mentioning two alternatives and you want to show that no other alternatives arepossible. You put either in front of the first alternative and or in front of the second one.
> Recruits are interviewed by either Mrs Darby or Mr Beaufort.
> He must have thought that I was either stupid or rude.
> I was expecting you either today or tomorrow.
> People either leave or are promoted.
> Either she goes or I go.

https://www.ldoceonline.com/dictionary/either-or

> either ... or
> a) used to begin a list of two or more possibilities
> You add either one or two cloves of garlic.
> She’s the kind of person you either love or hate.
> b) used to say that if one thing does not happen then something else will have to
> It’s your choice! Either she leaves or I will!
> £75 seems a lot to pay for a starter motor, but it’s either that or a new car!
> c) an either-or situation a situation in which you cannot avoid having to make a decision or choice

“decision” means to pick only one thing. “choice” usually means to pick only one thing, but not always. “possibility” could mean to pick only one thing or that you have the option of picking more than one thing. The examples given in the definitions are mostly exclusive “or” situations but not all of them are.

So overall I still think “either…or” implies an exclusive disjunction but maybe not always?


How about “either-or” or “either/or”? I think they are both considered to describe an exclusive “or” situation.

https://dictionary.cambridge.org/us/dictionary/english/either-or

> either-or

> used to refer to a situation in which there is a choice between two different plans of action, but both together are not possible:

https://www.lexico.com/en/definition/either%2For

> An unavoidable choice between alternatives.
> ‘an either/or situation’

[Elliot Temple]

On Nov 9, 2019, at 4:11 AM, Anne B <anne...@gmail.com> wrote:

> On Nov 9, 2019, at 4:30 AM, Anne B <anne...@gmail.com> wrote:
>
>> learnlogictheeasyway.com
>>
>> Lesson 2.1.2 discusses Inclusive Disjunction and Exclusive Disjunction.
>>
>> I had heard the terms before and knew what they meant. But I didn’t realize until now that in English we usually use the same word for both and we expect people to know which one is meant by the context.

yeah

>> This is especially true for complicated, established fields like economics or philosophy.
>
> Inclusive.

For this usage, note that one could write “and” instead of “or”. It’s a close call on which word to use. Doesn’t make much difference.

>> Yeah maybe if you reinvent 100,000 points from scratch there will be a big chunk there someone could use and combine with some existing knowledge, but if that’s what’s going to happen you might as well do that yourself (develop in, from day 1, as an improvement on some existing knowledge – as something that can be added to some existing knowledge and/or some changes to some existing ideas with problems – rather than ignoring existing knowledge and leaving it to someone else to convert your work to be relevant to other ideas humanity has).
>
> Inclusive. Is “and/or” a way of saying “inclusive or”?

Yes. Exclusive “or” is more common in English overall, or is a default in certain kinds of sentences, or something. So needing to say and/or (for both) is reasonably common but needing to specify xor (exclusive or) doesn’t come up much IME.

It’s the other way in logic and programming: “or" is inclusive and there's “xor" for exclusive.


Elliot Temple
www.curi.us

[Alisa Zinov'yevna Rosenbaum]

On Sat, Nov 09, 2019 at 07:11:21AM -0500, Anne B wrote:

> On Nov 9, 2019, at 4:30 AM, Anne B <anne...@gmail.com> wrote:

>> Then when you debate someone, your idea is a book or article that you can cite.
>
> Exclusive. A cite couldn’t be both a book and an article.

Consider this propositional logic formula:

X \/ ~X

Is that disjunction (\/) exclusive?

[Anne B]

I say no but I haven’t researched it.

[Alisa Zinov'yevna Rosenbaum]

On Thu, Nov 14, 2019 at 02:34:34PM -0500, Anne B wrote:

> On Nov 14, 2019, at 9:38 AM, Alisa Zinov'yevna Rosenbaum wrote:

>> On Sat, Nov 09, 2019 at 07:11:21AM -0500, Anne B wrote:

>>> On Nov 9, 2019, at 4:30 AM, Anne B wrote:

>>> http://curi.us/2235-discussions-should-use-sources

>>>> Then when you debate someone, your idea is a book or article that you can cite.
>>>
>>> Exclusive. A cite couldn’t be both a book and an article.
>>
>> Consider this propositional logic formula:
>>
>> X \/ ~X
>>
>> Is that disjunction (\/) exclusive?
>
> I say no but I haven’t researched it.

Why not? It can't be the case that both X and ~X are true. IIUC, that's essentially the reason you concluded that the "or" in the phrase "book or article" was exclusive.

[anonymous FI]

On Nov 9, 2019, at 4:11 AM, Anne B <anne...@gmail.com> wrote:

> On Nov 9, 2019, at 4:30 AM, Anne B <anne...@gmail.com> wrote:
>
>> learnlogictheeasyway.com
>>
>> Lesson 2.1.2 discusses Inclusive Disjunction and Exclusive
>> Disjunction.
>>
>> I had heard the terms before and knew what they meant. But I didn’t
>> realize until now that in English we usually use the same word for
>> both and we expect people to know which one is meant by the context.
>>
>> The course gives a good example for an exclusive disjunction: a
>> mother saying to a kid “You can have ice cream or cake.” The
>> mother is giving permission for the kid to have one or the other but
>> not both. She is forbidding her kid to have both ice cream and cake.
>> The kid is expected to know this.
>
> I want to try looking at sentences with “or” in them to see how
> easy it is to tell whether “or” is meant as inclusive or exclusive
> and to get an idea of how often and in what contexts each meaning is
> used.
>
> I took the sentences with “or” from this essay:
>
> http://curi.us/2235-discussions-should-use-sources
>
> If you want to try doing this yourself before reading what I wrote,
> search for “or” on that page.

>> Then when you debate someone, your idea is a book or article that you
>> can cite.
>
> Exclusive. A cite couldn’t be both a book and an article.

The "or" doesn't provide alternative types of cites. You don't
understand the sentence grammar. The part about cites is a modifier
tacked on at the end which could be removed without changing the use of
"or".

[Anne B]

Ah, good point. The relevant part is “your idea is a book or article”. In that case, I think it’s an inclusive “or”. Someone could write up an idea as both a book and an article. There’s no reason to think the writer is saying it has to be one or the other.

[Anne B]

In propositional logic, I read things literally. In English, I take into account context and real-world knowledge. I can’t really say why though.

[Alisa Zinov'yevna Rosenbaum]

I dropped a quote level and omitted a quote attribution my 06:38:10AM reply [Alisa638] to Anne B.

On Thu, Nov 14, 2019 at 06:38:10AM -0800, Alisa Zinov'yevna Rosenbaum wrote:

> On Sat, Nov 09, 2019 at 07:11:21AM -0500, Anne B wrote:

That attribution line shouldn't be there. I didn't quote anything from Anne B's 07:11:21AM post [Anne711]. Instead, I should have replied to Anne B's 4:30 AM post [Anne430], which I introduced in the line below:

>> On Nov 9, 2019, at 4:30 AM, Anne B <anne...@gmail.com> wrote:

>>> http://curi.us/2235-discussions-should-use-sources

The above line was in Anne B's 4:30 AM post, but not in my 06:38:10AM reply. Leaving out that attribution and dropping a quote level (see below) made it look like Anne B wrote the following line, when, in fact, it was written by Elliot Temple.

>>> Then when you debate someone, your idea is a book or article that you can cite.

That line was part of Anne B's 4:30 AM post. However, she *quoted* it there, so it should have been preceded by an extra level of quoting in my 06:38:10AM reply.

I don't know how that mistake happened. The line was properly quoted in Anne B's 4:30 AM post, and my email software automatically adds an extra quote level when I reply. Maybe I inadvertently deleted a quote level.

Conclusions: I guess I need to be more careful when trimming extra text to make sure I don't delete a quote attribution.

[Alisa638] https://groups.google.com/d/msg/fallible-ideas/B0Tpvgb1jVE/lJy_Og31BAAJ

[Anne430] https://groups.google.com/d/msg/fallible-ideas/B0Tpvgb1jVE/RZhmiwGKBgAJ

[Anne711] https://groups.google.com/d/msg/fallible-ideas/B0Tpvgb1jVE/4yRxj3aLBgAJ

[Alisa Zinov'yevna Rosenbaum]

On Thu, Nov 14, 2019 at 02:34:34PM -0500, Anne B wrote:

> On Nov 14, 2019, at 9:38 AM, Alisa Zinov'yevna Rosenbaum wrote:

>> Consider this propositional logic formula:
>>
>> X \/ ~X
>>
>> Is that disjunction (\/) exclusive?

> I say no but I haven’t researched it.

I suggest you research it, if you want to learn propositional logic. You cannot reliably understand disjunction in propositional logic nor use it correctly unless you know whether or not it is exclusive.

[Anne B]

Instead of my last paragraph, I should have written:

In propositional logic, there are different symbols for inclusive disjunction and exclusive disjunction. So I read each symbol as what it is. In English, the word “or” can mean either inclusive or exclusive disjunction, so I look at context to try to figure out which.

[Alisa Zinov'yevna Rosenbaum]

On Thu, Nov 14, 2019 at 03:57:44PM -0500, Anne B wrote:

> In propositional logic, there are different symbols for inclusive disjunction and exclusive disjunction.

What symbol does learnlogictheeasyway.com use for exclusive disjunction?

[Alisa Zinov'yevna Rosenbaum]

On Sat, Nov 09, 2019 at 07:11:21AM -0500, Anne B wrote:

> I want to try looking at sentences with “or” in them to see how easy it is to tell whether “or” is meant as inclusive or exclusive and to get an idea of how often and in what contexts each meaning is used.
>
> I took the sentences with “or” from this essay:

> http://curi.us/2235-discussions-should-use-sources

>> If you’re just trying to practice explaining stuff, not actually trying to reach a conclusion in the field, then using little or no literature can make sense.

> Exclusive. “little” and “no” can’t both be the case at the same time.

Just because X and Y are in fact exclusive doesn't mean that someone who writes "X or Y" intends the "or" to be exclusive.

Here, I don't think that "or" was exclusive. I think it was an inclusive "or".

My test for inclusive vs exclusive "or" is: does the author care whether the options are in fact exclusive? In the quoted sentence above, I don't think the author cares.

Suppose the author had written instead: "using fewer than 10 cites or even no cites can make sense". Since 0 cites is fewer than 10, the two options are not exclusive in the alternate version. I think that the alternate version has essentially the same meaning as the original, so I conclude that the "or" in the original version is not exclusive either.

In contrast, when a waiter says, "You can have mashed potatoes or fries with your steak," he is following a policy that says that a patron can normally order one or the other as a side dish, but not both. Thus, the waiter cares about the two options being exclusive, and the "or" is therefore exclusive.

[Anne B]

I like your test better than mine.

[Anne B]

x∨

[Alisa Zinov'yevna Rosenbaum]

On Thu, Nov 14, 2019 at 12:30:10PM -0800, Alisa Zinov'yevna Rosenbaum wrote:

> I dropped a quote level and omitted a quote attribution my 06:38:10AM reply [Alisa638] to Anne B.

> On Nov 9, 2019, at 4:30 AM, Anne B <anne...@gmail.com> wrote [Anne430] :

>> http://curi.us/2235-discussions-should-use-sources

>>> Then when you debate someone, your idea is a book or article that you can cite.
>
> That line was part of Anne B's 4:30 AM post. However, she *quoted* it there, so it should have been preceded by an extra level of quoting in my 06:38:10AM reply.
>
> I don't know how that mistake happened. The line was properly quoted in Anne B's 4:30 AM post, and my email software automatically adds an extra quote level when I reply. Maybe I inadvertently deleted a quote level.

One thing that could help me figure out what went wrong in cases like this is to record a screencast for every post I make. This would let me review the screencast later, even a long time after I made the post, to see what I was doing when I made the mistake.

Making and keeping screencasts reminds me of how NASA kept detailed records of each mission during Apollo. If something went wrong, they could review their records of the spacecraft telemetry and other stuff to figure out what caused the problem.

[Elliot Temple]

That’s part of how people improve at video games. E.g. Overwatch players and speedrunners record their gameplay and review it later, especially after things go wrong.

Elliot Temple
www.fallibleideas.com

[Alisa Zinov'yevna Rosenbaum]

On Fri, Nov 15, 2019 at 04:51:44AM -0500, Anne B wrote:

> On Nov 14, 2019, at 4:34 PM, Alisa Zinov'yevna Rosenbaum wrote:

>> On Thu, Nov 14, 2019 at 03:57:44PM -0500, Anne B wrote:

>>> In propositional logic, there are different symbols for inclusive disjunction and exclusive disjunction.
>>
>> What symbol does learnlogictheeasyway.com use for exclusive disjunction?
>
> x∨

That didn't come out clearly. Is it like a "v" with an "x" through it?

The two common symbols for "exclusive or" at Wikipedia are "⊕" and "⊻" ( https://en.wikipedia.org/wiki/List_of_logic_symbols ).

IMO, the simplest, easiest-to-understand symbol for "exclusive or" is "≠" (not equal). For some reason, though, very few texts use it. Anyone know why?

[anonymous FI]

On Nov 16, 2019, at 1:39 PM, Alisa Zinov'yevna Rosenbaum

People don't conceptually connect inequality and xor. They're taught
separately and they are mostly separate concepts because inequality
works with stuff other than true/false or 1/0 inputs.

If you compare notequal and xor in programming languages like ruby
you'll find many differences. And actually that xor works on integers
but does something different than notequal.

The ruby symbol for xor, btw, is ^

[Anne B]

On Nov 16, 2019, at 4:39 PM, Alisa Zinov'yevna Rosenbaum <petrogradp...@gmail.com> wrote:

> On Fri, Nov 15, 2019 at 04:51:44AM -0500, Anne B wrote:
>
>> On Nov 14, 2019, at 4:34 PM, Alisa Zinov'yevna Rosenbaum wrote:
>
>>> On Thu, Nov 14, 2019 at 03:57:44PM -0500, Anne B wrote:
>
>>>> In propositional logic, there are different symbols for inclusive disjunction and exclusive disjunction.
>>>
>>> What symbol does learnlogictheeasyway.com use for exclusive disjunction?
>>
>> x∨
>
> That didn't come out clearly. Is it like a "v" with an "x" through it?

It’s a “v” with an “x” in front of it.

> The two common symbols for "exclusive or" at Wikipedia are "⊕" and "⊻" ( https://en.wikipedia.org/wiki/List_of_logic_symbols ).

I like “⊻” because it looks like “∨”, and we use the word “or” or the word “disjunction” in saying both.

In general, I want to use the most common symbols and terminology for things, which are not always the ones used by a particular author that I’m studying.

I’m saving that wikipedia list of logic symbols to copy and paste from. So far I’ve only found some logic symbols that I can type directly on a Mac.

[Alisa Zinov'yevna Rosenbaum]

On Mon, Nov 18, 2019 at 06:42:58AM -0500, Anne B wrote:
> On Nov 16, 2019, at 4:39 PM, Alisa Zinov'yevna Rosenbaum <petrogradp...@gmail.com> wrote:
>
>> On Fri, Nov 15, 2019 at 04:51:44AM -0500, Anne B wrote:
>>
>>> On Nov 14, 2019, at 4:34 PM, Alisa Zinov'yevna Rosenbaum wrote:
>>
>>>> On Thu, Nov 14, 2019 at 03:57:44PM -0500, Anne B wrote:
>>
>>>>> In propositional logic, there are different symbols for inclusive disjunction and exclusive disjunction.
>>>>
>>>> What symbol does learnlogictheeasyway.com use for exclusive disjunction?
>>>
>>> x∨
>>
>> That didn't come out clearly. Is it like a "v" with an "x" through it?
>
> It’s a “v” with an “x” in front of it.

Weird. Usually, math books try to use a single character to represent a single operation.

>> The two common symbols for "exclusive or" at Wikipedia are "⊕" and "⊻" ( https://en.wikipedia.org/wiki/List_of_logic_symbols ).
>
> I like “⊻” because it looks like “∨”, and we use the word “or” or the word “disjunction” in saying both.
>
> In general, I want to use the most common symbols and terminology for things, which are not always the ones used by a particular author that I’m studying.

Not-equals ("≠") is the most common symbol that has the logical meaning of exclusive-or when applied to true/false values.

[Anne B]

Here:

https://groups.google.com/d/msgid/fallible-ideas/20191116213922.n2c7ojbx7d2dm2pm%40MacBook.local

you (Alisa) wrote:

> IMO, the simplest, easiest-to-understand symbol for "exclusive or" is "≠" (not equal). For some reason, though, very few texts use it. Anyone know why?

You said both that it’s the most common symbol and that very few texts use it. Were you talking about different contexts?

[Alisa Zinov'yevna Rosenbaum]

No. Not-equals ("≠") has the same truth table as exclusive-or. And yet, for some reason (anon gave a plausible explanation in https://groups.google.com/d/msg/fallible-ideas/B0Tpvgb1jVE/ebUDqp7SBAAJ ), most people aren't aware of this equivalence, so they use relatively uncommon symbols for exclusive-or like "⊕" and "⊻".

[Alisa Zinov'yevna Rosenbaum]

On Fri, Nov 15, 2019 at 09:55:45PM -0800, Elliot Temple wrote:

> On Nov 15, 2019, at 8:23 PM, Alisa Zinov'yevna Rosenbaum wrote:

>> On Thu, Nov 14, 2019 at 12:30:10PM -0800, Alisa Zinov'yevna Rosenbaum wrote:

>>> I don't know how that mistake happened. The line was properly quoted in Anne B's 4:30 AM post, and my email software automatically adds an extra quote level when I reply. Maybe I inadvertently deleted a quote level.

>> One thing that could help me figure out what went wrong in cases like this is to record a screencast for every post I make. This would let me review the screencast later, even a long time after I made the post, to see what I was doing when I made the mistake.

> That’s part of how people improve at video games. E.g. Overwatch players and speedrunners record their gameplay and review it later, especially after things go wrong.

I've started using a program called asciinema to make screencasts of my terminal when I compose FI posts. I expect these screencasts will help me be able to look back later to see how I made particular mistakes in my posts.

Here are some screencasts I've shared at asciinema.org: https://asciinema.org/~petrogradphilos

Unfortunately, the asciinema.org screencast player doesn't (yet?) let you adjust the playback speed dynamically, like you can with YouTube, but you can change it by appending "?speed=X" to the URL ( e.g., https://asciinema.org/a/282250?speed=4 ) and re-loading.