LMD Async Tutoring

[LMD]

I’m wondering if most of these errors come from mistaking the cells/columns under consideration, and not from mistakes in the use of operations. One clue was that I didn’t have trouble finding these errors by re-doing the operations again? I could test that by hiding the columns I don’t need for the next operation.

^ That error is consistent with looking at (x, y) columns not (and(x, y), x) colums.

^ That error could either be from using xnor, or from using xor on (x,y) instead of (not(x), y).

@Elliot

Also, as a minor note, please use equality instead of xnor in general. They have the same truth table but equality is a more commonly used and intuitive concept.

Okay I’ll look into this.

[Elliot]

@LMD

I’m wondering if most of these errors come from mistaking the cells/columns under consideration, and not from mistakes in the use of operations.

Yeah I wondered if you were doing the last column based on the first 2 but you weren’t always.

[LMD]

@LMD

@Elliot

Also, as a minor note, please use equality instead of xnor in general. They have the same truth table but equality is a more commonly used and intuitive concept.

Okay I’ll look into this.

Okay I see why now. An XNOR gate outputs true if and only if both inputs are the same. So an XNOR gate can test the equality of the inputs.

It seems there are some overlapping fields that use boolean algebra (math, digital circuit design, logic, computer programming; obviously all extremely related.) Each interprets the boolean concepts slightly differently depending on their respective problems. Like xnor seems almost exclusively used in digital circuit design. Maybe because it’s more of a literal description of what the circuit is: a negated xor gate. The equality operation is like one level of abstraction above that, and more useful for most purposes. This is mainly me getting down some thoughts.

[LMD]

@Elliot

@LMD

So p⇒q outputs q if p is true. That makes sense. But if p is false it outputs true. I don’t know a way for this to make sense to me.

I can explain if needed but let’s start here:

Try making some example English sentences with IF/THEN or IMPLIES and then evaluating what the sentences mean in each scenario (each scenario = each potential truth table row). Don’t use variables.

My statement:

If there is cold weather, then I wear a jacket.

Okay what does this sentence mean?

Okay so maybe on one hand there is the truth of the statement, and on the other, the truth of the components of the statement. Maybe this reflects the two inputs and the one output?

1. So what is the truth status of the whole statement, if there is cold weather, and I am wearing a jacket? It is true or at least not contradicted by the facts.

2. What is the truth status of the whole statement if there is not cold weather, and I am wearing a jacket? It’s not contradicted by the facts. I could wear a jacket all the time, whether or not there is cold weather.

3. What is the truth status of the whole statement if there is cold weather, and I am not wearing a jacket? It is false. If the statement were true, I would be found wearing a jacket when there is cold weather.

4. What is the truth status of the whole statement if there is not cold weather, and I am not wearing a jacket? It is not contradicted by those facts. It’s consistent with the statement being true the same way that 2. is consistent with the facts.

Is this the right way to look at it? Looking at the p=>q operation as testing the truth status of a statement p=>q against the actual observed values of p and q? Like testing the truth of an empirical theory, by testing it?

[Elliot]

That’s OK. Try another IF/THEN and a couple IMPLIES, then try to write a conclusion about how they work in English and whether they correspond to logic.

[LMD]

Okay, this is what I’ve had time for for now:

If/Then

If we have more points when the game ends, then we win the game.

What is the truth of that sentence if we do have more points when the game ends but we didn’t win the game? The statement is contradicted.

If we do have more points when the game ends and we do win the game? The statement is not contradicted.

If we don’t have more points when the game ends and we lose the game? The statement is not contradicted.

If we don’t have more points when the game ends but we do win the game? The statement is not contradicted. (Like the other team could violate some rule that ends the game and forfeits the game to us? Like they cheat and so we win by default. This outcome doesn’t contradict our statement.)

The best I can say here is that one of the scenarios contradicts the sentence and the other three don’t.

Implies:

Finding something funny implies that I laugh

If I do find something funny and then I laugh then the statement is not contracted.
If I do find something funny and then I don’t laugh the statement is contradicted.
If I do not find something funny and then I don’t laugh the statement is not contradicted.
If I do not find something funny and I do laugh the statement is not contradicted (I might also laugh when e.g I’m nervous or being social)

[LMD]

My general finding is that this way I can’t say more than if they contradict or not. But they fit the pattern of the truth table. One is false out of four and it’s the one where the antecedent is true but the consequent false.

[Elliot]

Suppose I say “if you serve bacon, i’ll eat it” and then you take a shower, serve carrots, or do anything else besides serve bacon. My statement isn’t refuted, as you’ve noticed (“not contracted”). This relates to CF’s idea that not having any refutation/criticism/error is the best status an idea can have. It’s error, not positive proof, that we should seek. But this interpretation of logic is also the mainstream view not just the CF view.

You can interpret my statement like: “if you serve bacon, i’ll eat it, otherwise I have no comment on what I’ll do”

Or: “if you serve bacon, i’ll eat it; if you do not serve bacon, then I may do anything”

Or: If you serve bacon, I’ll eat it; if you serve carrots, I’m undecided; if you serve potato, I haven’t planned ahead; if you serve peas, we’ll see; if you go to Disneyland, who knows; if you fly to Mars, I haven’t committed myself to anything"

With conditional statements, we’re making a claim about a particular scenario. We aren’t making any claim about other scenarios. In other words, when P is false, we aren’t making any claim about what Q is, so Q may be anything (true or false). We’ve only put any limitation on the case where P is true.

For “Being over age 30 implies being over age 20” is true in standard English if, whenever someone is over age 30 they are always over age 20. The implication part has to always be right. And if it is, then the statement is considered correct. That’s all you need to know to conclude that P really does imply Q. You don’t have to know anything about the ~P scenario because what Q is in that case isn’t relevant to whether the statement is correct. We evaluate it just by checking that the first part being true implies the second part being true. (BTW the word “implies” is often used informally in which case the implication only has to be mostly right, usually right, a good hint, or something like that.)

[LMD]

Suppose I say “if you serve bacon, i’ll eat it” and then you take a shower, serve carrots, or do anything else besides serve bacon. My statement isn’t refuted, as you’ve noticed (“not contracted”). This relates to CF’s idea that not having any refutation/criticism/error is the best status an idea can have. It’s error, not positive proof, that we should seek. But this interpretation of logic is also the mainstream view not just the CF view.

Yeah okay cool. I didn’t expect to find this idea here.

(BTW the word “implies” is often used informally in which case the implication only has to be mostly right, usually right, a good hint, or something like that.)

Yeah I learned this recently (last 1-2 years). I thought people were just being sloppy with their language because they used ‘imply’ where there isn’t a logical implication. When I finally looked it up in the dictionary I was wrong that that’s what ‘imply’ always means. I think I changed my idea of what imply meant to the logical one sometime while reading Popper instead of seeing it as just one of the meanings.

Alright I think this is clearing up my confusion. I still have another problem though. In the context of a conditional operation, if I interpret a ‘true’ output as a ‘non-contradiction’ and a ‘false’ one as ‘contradiction’, it seems like this is a different meaning of true/false for a conditional operations than the other operations I’ve done so far. Am I wrong that this is a different interpretation or perhaps wrong that having different interpretations of what true and false mean for different operations matters?

[Elliot]

Conditional statements are extremely common in English. They don’t just use IF/THEN or IMPLIES. For example, what if I say “Red cars are cool.” then see a gray car? I haven’t made any claim about the gray car because it didn’t fit the condition. This is the same scenario you’re concerned about which has been caused by a simple adjective. It’s similar to if I said “If a car is red, then it’s cool.”

What if I say cars are cool but see a thing other than a car? The word “car” specifies the type of object. It limits my statement to only some objects and not others. It’s also a restriction on applicability, kind of similar to using an adjective.

More comments later probably. Feel free to continue with the math/logic stuff without fully resolving this first.

[Elliot]

In general, people want something along the lines of direct evidence/confirmation not just non-contradiction. This is partially a misconception about epistemology but partially just reasonable. If someone claims all red cars are cool, you should observe at least one red car (preferably dozens), and check that it really is cool, before believing them. You should also think critically about the claim in other ways.

If someone says X implies Y and you don’t get to check any case where X is true, then you generally shouldn’t be very convinced. But for evaluating logical expressions, you have to just take the information that’s given and see if it fits the claim or not.

Read the logic claims about implication like this: “If X is true then Y is true; if X is false, then Y is true or false”. Maybe this wording will solve the issue for you. With this wording, and the condition that you have to evaluate it with the information given (no seeking out more evidence and no using other types of critical thinking), then if the information is “X is false and Y is false” then you’ll have to conclude that the statement is correct in this case.

[Elliot]

Off topic assignment but let’s try a close reading and analysis to see how you do:

https://www.reddit.com/r/AITAH/comments/1djuriw/aitah_for_breaking_up_with_my_girlfriend_when_she/

Read the original post only. Do not read any comments for now.

Write analysis and your conclusion.

15-60min

[LMD]

Okay. From here:

AITAH for breaking up with my girlfriend when she tested me?

When I was 16 years old my girlfriend broke up with me. I was pathetic and begged her to change her mind. I thought I was in love and couldn’t be without her. I was an idiot.

At 16, the OP got dumped and begged his girlfriend to change her mind. OP thinks doing this was pathetic. OP thinks they were an idiot to think they couldn’t be without her.

I’m 25 now and I have promised myself I will never do that again.

OP has promised themselves that they wouldn’t do the begging breakup thing again. It’s not clear when they made this promise. Was it shortly after the first breakup, or now that they’re 25? Or some time in between?

I have had several relationships and a few hook ups. And when they end I am sad but not weak.

So the OP perhaps views their behaviour when dumped at 16 as ‘weak’. When their other relationships/hookups have ended they haven’t behaved ‘weak’ like they did when they were 16. This maybe indicates they started to change their behaviour between 16 and 25.

I had been with my girlfriend for a year and a half. We met at a social function for people in our line of work. We hit it off and started seeing each other more often then made it exclusive.

This is the girlfriend that is mentioned in the title question of the post. They didn’t necessarily work together, but were in the same line of work. They got along and eventually developed an exclusive relationship.

Recently we have been talking about moving in together. Our city is expensive and we thought we could save some money. Her apartment is bigger than mine but I own mine so we were working stuff out.

They were considering moving in together. OP owns an apartment.

Last weekend out of nowhere she says that we are moving too fast. Okay no problem we didn’t make any plans that can’t be undone yet.

Moving in together is a big step. It would be normal for someone considering this to be apprehensive. It was before they had made any significant plans yet so it was a good time to bring it up. ‘Moving too fast’ presumably means that it should slow down cos big decisions are being made too quickly.

Nope she said that she wanted to break up because she wasn’t sure I was all in.

Her thinking they are moving too fast seems to imply that OP is more ready than her to make a big change. Then she says she wants to break up because she’s not sure OP is ‘all in’? It sounds like OP is ready to make a big change in the relationship, so weird to be accused of being not being ‘all in’?

I said okay. Then she freaked out. Apparently it was a test to see if I would fight for her.

I think you would probably try to talk about the problems if you were interested in the relationship. I don’t think the choice is only between begging someone to stay and being passive and saying ‘okay’. But if true, the way she has tried to find this out from OP is dishonest. Maybe she wasn’t sure OP would be honest about the relationship if she brought it up in a conversation? That he’d be passive? He might view more of his emotions as ‘weak’ and so not be honest about them.

I’ve run out of time here at ~60mins

My conclusion about who the asshole is is that I don’t know.

---

I basically don’t have any practise doing this at all. And I kinda wasn’t sure what to do. My approach was to roughly to write down what I thought the important parts seemed to be and what the point was, and some thoughts.

[Elliot]

@LMD

I basically don’t have any practise doing this at all. And I kinda wasn’t sure what to do. My approach was to roughly to write down what I thought the important parts seemed to be and what the point was, and some thoughts.

That’s OK. Most of your comments were OK. Tips for next time:

For writing, start with a summary paragraph before going into details. That way readers (and you) have some overall picture to fit the details into. Then focus on relevant details (like pick out quotes that illustrate your claims or which refute alternative viewpoints).

For reading, read the whole thing quickly and try to get a general understanding before going into details. Details can help clarify specific points. If you’re stuck on the big picture, you can start with details that seem potentially relevant (often this means going by what sort of details are typically relevant for similar scenarios, since you don’t clearly know what’s relevant yet) and they may give you clues.

[LMD]

@Elliot

For reading, read the whole thing quickly and try to get a general understanding before going into details.

Okay cool. I definitely didn’t do this. I went sentence by sentence.

@Elliot

For writing, start with a summary paragraph before going into details.

Yup okay. Sounds good.

Would you share some links for what you consider high quality text analysis?

[LMD]

@Elliot

Conditional statements are extremely common in English. They don’t just use IF/THEN or IMPLIES. For example, what if I say “Red cars are cool.” then see a gray car? I haven’t made any claim about the gray car because it didn’t fit the condition.

Yeah cool. This also makes sense with the way of thinking about implication as sets that I encountered today when reading more about this. In this case ‘red cars’ are a subset of ‘cool things’, and ‘red cars’ are a subset of ‘cars’ (like ‘grey cars’ are). But we don’t know anything about the relationship of the sets ‘cars’ and ‘cool things’ except that the subset ‘red cars’ is common to both. So ‘grey cars’ could fall inside or outside the set of ‘cool things’ and be consistent with the claim ‘red cars are cool’. It helps me in this case to think of overlapping 2D shapes like a venn diagram.

@Elliot

Read the logic claims about implication like this: “If X is true then Y is true; if X is false, then Y is true or false”. Maybe this wording will solve the issue for you. With this wording, and the condition that you have to evaluate it with the information given (no seeking out more evidence and no using other types of critical thinking), then if the information is “X is false and Y is false” then you’ll have to conclude that the statement is correct in this case.

Yup great I think I understand now.

[LMD]

Okay from Eternity’s thread:

@Elliot

Next you need the concept of defining logic operators in terms of other operators.

For example:

nand(x,y) = ?

Answer only using the following operators: not, and, or.

Max 30min.

Okay I timed out at ~30mins without a satisfactory answer. I thought this would be easier than it was.

I made some truth tables to help me out. The things I tried didn’t work. I was kind of just trying things out to see if I got any clues. But beyond guessing and checking I didn’t have any promising ideas on how to solve it.

This works but I’m not happy with it:

not(and(x,y))

[Elliot]

@LMD

This works but I’m not happy with it:

not(and(x,y))

Why are you not happy with it?

[LMD]

I think partly it was because I see nand as being shorthand for ‘not and’, not being a different operation.

from my notes:

NAND - Symbol ~^

• NOT and AND. Negation of AND
• Negates its output. (Is it the same as negating the inputs?)
• False if
  • both inputs are true
• True if
  • either input is true
  • neither input is true
  • any input is false

Like it seemed like a cheeky non-answer. I was trying to make something with ‘or’ work but couldn’t. After I replied I read Eternity’s answer and some posts that followed it and it seems that I also had some of the same issue with trying to read into the question.

[Elliot]

@LMD

Like it seemed like a cheeky non-answer. I was trying to make something with ‘or’ work but couldn’t.

I think it’s a correct answer.

Do you like this one better?

or(not(and(x, y)), not(and(x, y)))