site banner
felipec  unbelief  2yr ago (felipec.substack.com)   3612 thread views

2+2 = not what you think

felipec.substack.com

Changing someone's mind is very difficult, that's why I like puzzles most people get wrong: to try to open their mind. Challenging the claim that 2+2 is unequivocally 4 is one of my favorites to get people to reconsider what they think is true with 100% certainty.

-34
Top Bottom Old Controversial Comments
Jump in the discussion.

No email address required.

Either way 2+2=0 can be true.

Only because 4=0. So 2+2=4 is true, and the central claim of your substack post is wrong.

Correct?

No. Some basic mistakes:

  • Isomorphy requires preservation of structure, in our case the structure of respective additions. This is not the case: Addition in {0,1,2,3} works different than in ℤ/4ℤ.

  • We don't say an element in a structure is isomorphic to one in another.

  • (ℤ/4ℤ)*is an entirely different structure. For starters, it contains only 3 elements. (The * signifies we're excluding the 0.)

Only because 4=0.

So 2+2=4=0="not what you think". Therefore the claim of my post is true.

But 0 is what we think, because 0 is 4. You're just changing the representation. It's like saying "You think 2+2 is '4', but it's actually 'four'".

Also, the claim in your post was

So there you have it: 2+2 is not necessarily 4.

which is wrong whether or not 2+2=0 can be true.

But 0 is what we think, because 0 is 4.

Nobody thinks that 0 is 4.

Nevertheless it is the case. We think 4, 4 is 0, therefore "0=not what you think" isn't true.

"You" are less than 0.0001% of the population, so virtually nobody.

Did you just claim less than 0.0001% of people think 2+2=4?

4 is what everyone thinks, 0 is merely a different representation of the same object. So people are giving the correct answer, you're just insisting on a different formulation.

Did you just claim less than 0.0001% of people think 2+2=4?

No. That less than 0.0001% of people think 2+2=0?

Then explain how that's supposed to be a response to my point, please.

My point being that in Z/4Z, 2+2=0 and 2+2=4 are the same statement. Ergo, 2+2=0 is merely another way to write down what we think. We might not literally think it, but we are thinking an equivalent statement.

More comments

What is this place?

This website is a place for people who want to move past shady thinking and test their ideas in a court of people who don't all share the same biases. Our goal is to optimize for light, not heat; this is a group effort, and all commentators are asked to do their part.

The weekly Culture War threads host the most controversial topics and are the most visible aspect of The Motte. However, many other topics are appropriate here. We encourage people to post anything related to science, politics, or philosophy; if in doubt, post!

Check out The Vault for an archive of old quality posts. You are encouraged to crosspost these elsewhere.


Why are you called The Motte?

A motte is a stone keep on a raised earthwork common in early medieval fortifications. More pertinently, it's an element in a rhetorical move called a "Motte-and-Bailey", originally identified by philosopher Nicholas Shackel. It describes the tendency in discourse for people to move from a controversial but high value claim to a defensible but less exciting one upon any resistance to the former. He likens this to the medieval fortification, where a desirable land (the bailey) is abandoned when in danger for the more easily defended motte. In Shackel's words, "The Motte represents the defensible but undesired propositions to which one retreats when hard pressed."

On The Motte, always attempt to remain inside your defensible territory, even if you are not being pressed.


New post guidelines

If you're posting something that isn't related to the culture war, we encourage you to post a thread for it. A submission statement is highly appreciated, but isn't necessary for text posts or links to largely-text posts such as blogs or news articles; if we're unsure of the value of your post, we might remove it until you add a submission statement. A submission statement is required for non-text sources (videos, podcasts, images).

Culture war posts go in the culture war thread; all links must either include a submission statement or significant commentary. Bare links without those will be removed.

If in doubt, please post it!


Rules


Recommended Posts And Communities

Recommended Realtime Chats