Logic 101 (#30): Hypothetical Syllogism

[@PunmasterSTP]

Hypothetical? More like “Hype? Nah, it’s real!” Another great video, as always.

[@TheBlackAVClub]

This is a good description of logic. thanks so much

[@Derry123456]

Can you have a hypothetical syllogism that doesent include An r? For example is this a hypothetical syllogism? If my cat is alive then it will breathe ?
Or can r be the same as p? If my cat is alive then it will be breathe therefor if my cat breathes then it is alive?
Is this sill a hypothetical syllogism

[@hdauven8434]

@@Derry123456 No it is not. The whole idea of hypothetical syllogism is that if P => Q => R are true, you are allowed to skip Q and reason that P will logically lead to the conclusion that P => R. P => Q => R with hypothetical syllogism does not lead to P = R either.
The argument you're putting forth here looks more like a bi-conditional.
A = alive, B = breath
A => B, B => A
The fallacy form of this is called circular reasoning.
Correct me if I'm wrong though.

[@mcferfer6151]

@@hdauven8434 Not circular reasoning, but affirming the consequent

[@Derry123456]

Can you have a hypothetical syllogism that doesent include An r? For example is this a hypothetical syllogism? If my cat is alive then it will breathe ?
Or can r be the same as p? If my cat is alive then it will be breathe therefor if my cat breathes then it is alive?
Is this sill a hypothetical syllogism

[@SHUBHAMGI]

Derry123456 no , it will not be hypothetical syllogism cause it's a one way function.
Understand it by an example of hashing function which is one way implication , you can't revert it.

[@accountbertolini7652]

What trips me is that [P=>(Q=>R)] [Q=>(P=>R)
In an example, it doesn't make much sense:
I am in Texas.
Texas is in America.
America is in the West.
[T=>(A=>W)]
However, [A=>(T=>W)] doesn't work as well. Being in America doesn't necessarily mean being in Texas.
Is it something with the parenthesis?

[@MardakVol]

[P=>(Q=>R)] [Q=>(P=>R) is different than the subject of this video, which is:
1. P => Q
2. Q => R
Therefore, P => R
For your problem with Texas, the way I would interpret those statements are like this:
[T=>(A=>W)] Being in Texas implies that (being in America implies that you are in the West.)
[A=>(T=>W)] Being in America implies that (being in Texas implies that you are in the West.)
Of course written this way these statements make no sense. Whether or not you are in Texas shouldn't affect if America is in the West or not.
Instead, I'd write your statements like this:
1. T (I am in Texas.)
2. T => A (Texas is in America.)
3. A => W (America is in the West.)
Through hypothetical syllogism, we can add the statement T => W (Texas is in the west) and through Modus Ponens we can conclude W (You are in the West).

[@ekoi1995]

so if A=>B; B=>C; C=>D; D=>next letter ... previous letter => Z;
can A=>Z?

[@PunmasterSTP]

Yes. As far as I know, you can just keep stringing them together.

[@ekoi1995]

@@PunmasterSTP would that be considered a slippery slope? also i think most people are also leaning to the butterfly effect

[@PunmasterSTP]

@@ekoi1995 I think that's a great observation, and I think it could be. If you're a politician or someone who doesn't think critically about the assumptions they are making, stringing together too many implications can end up with something nonsensical.
I like to think of it as a hall with mirrors on both sides. The reflections seem okay for awhile, but invariably they start to get distorted. However, in a strictly logical, conceptual or academic sense, I think stringing them together is fine for the purposes of example problems. 😃