What the fuck, this is wrong, right? This is from stanford

A google search reveals that some Toyota models are assembled in Kentucky.

Go figure.

The first guy already told you. The -conclusion- is correct, despite the -logic- being wrong.

The conclusion and premises can be all be true even if the logic is faulty.

ok i think i see now, thanks guys

>Go figure
Who would have thought that shipping whole cars across the Pacific is more expensive than building them on site?

Intro to logic was fun. It's the one class I took where I felt I had actually learned something, instead of being fed some professors opinion.

did you take it online or as a student there?

As a student. The class had some loser psych nerds and Fedora type kids, but it was a general ed course so it wasn't packed with them. When you get into the long complicated word problems only using symbols, that's where it becomes fun. It was like math, but piecing together bits of another language.

First premise should be all cars are Toyotas.

Happens to be correct does not mean necessarily correct

>I'd need some proof
>bcoz I can't into Google

See
It was done.

Logic pro here.

Because some Toyotas are made in America

The Toyota circle should also be intersecting the Made in America circle. That's the point.

But that doesn't follow as a necessity, only as a possibility.

Yeah I'm pretty sure this is an invalid argument.

Like this:

P1. (x)(Tx ⊃ Cx)
P2. (∃x)(Cx * Ax)
C3. [ ∴ (∃x)(Tx * Ax)
4. Asm: ~(∃x)(Tx * Ax) {negation of C3}
5. ∴(x)~(Tx * Ax) {The negation of 4}
6. ∴(Ca * Aa) {Existential elimination P2}
7. ∴Ca {from 6}
8. ∴Aa {from 6}
9. ∴~(Ta * Aa) {Universal elimination 5}
10. ∴~Ta {From 9 and 8}
11. ∴(Ta ⊃ Ca) {Universal elimination step 1}
12. asm: Tb {for a counterexample to C3}
13. ∴(Tb ⊃ Cb) {Univ elim 1}
14. ∴Cb {12 and 13}
15. ∴~(Tb * Ab) {Univ elim 5}
16. ∴~Ab

From here you cannot derive a contradiction as far as I can tell but you have found a counterexample.

To make it more clear the counterexample is: Cb, ~Ab, Tb and Ca, Aa, ~Ta.

In english: Suppose one car is a toyota and not made in america and some other car is not a toyota but is made in america.

Idk I probably fucked up in that because I'm tired and my quantificational logic is rusty. Maybe your prof means in terms of syllogistic logic or some other system, or possibly they did this on purpose to show you some of the problems with whatever logical system you are currently working with. It could also just be a typo. It's worth asking them about it.

>Toyota ⊆ Cars
>StuffMadeInAmerica ∩ Cars ≠ {}
>∴ Toyota ∩ StuffMadeInAmerica ≠ {}

Wrong. Let Toyota ∩ StuffMadeInAmerica = {} and Cars = Toyota ∪ StuffMadeInAmerica. First 2 hold while the third doesn't. QED

usatoday.com/story/money/cars/2016/06/29/survey-top-made--usa-cars-toyota-honda/86510052/

The exercise is trying to tell you that you can have invalid reasoning but accidentally arrive at the correct conclusion.

Wrong. Let StuffMadeInAmerica = {}. First 2 don't hold. QED

this is the best answer in this thread

If the sets being empty breaks stuff, then the sets are not empty. Haven't you ever read a math book.

Delete this

showed you why it's an invalid argument. If the premises are both true, the conclusion does not necessarily have to be true.
However, as pointed out, some Toyotas are made in America. Which is why the professor stated the conclusion is correct.
is right in that the professor was trying to show how an argument can be invalid but still have a correct conclusion.

The X can either be in the middle, on the Toyotas' side or the Cars' side without Toyotas. Without more clues we can't be sure which it is.

hey OP, use venn diagrams. You will be enlightened.

because faulty logic sometimes leads to conclusions that happen to be correct (some toyotas are made in america)
are you sure stanford is for you buddy?

The confusion here is due to sloppy use of the word "are" and inconsistencies in how sets and members of sets are addressed.

The "y" in "All x are y" is the set of cars
The "y" in "Some y are z" is referring to specific members in the set of cars
So when you just carelessly substitute "cars" for "y" you actually mean two different things

If you rewrite it in a more consistent (but more unwieldy) manner

All x are y = "All members of x are also members of y"
Some y are z = "Some members of y are members of z"
etc.

Then you get a clearer picture of what they tried (but failed) to say. Maybe they address this in some earlier slides?

Most courses want you to give a correct answer. This example is telling you that they don't care if your answer is correct, all they are about is if your logic is valid.

Valid logic can lead to incorrect conclusions, and correct conclusions can be derived from invalid logic. The goal of a into to logic class is to teach you how to determine the validity of the logic, not the correctness of its answers.

>implying not every human with acces to internet have acces to their material

stay in your basement and stay offline pleb

Right. So Stanford was not for you, you’re just watching their slides. Pretty much proves my point

>most courses want you to give the correct answer
Ever heard of showing your work?

>Valid logic can lead to incorrect conclusions
only if your premises are incorrect

It's invalid but happens to be true. This is to distinguish validity from soundness from the truth value.

Wrong.

Valid logic applied to false premises can be valid, but unsound.

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