for your example. shouldn't it be "the food does not have chicken, therefore it is beef" because p= chicken, q=beef, not chicken therefore beef in order to support ~p, therefore q?
"Something happens," temporally, between 1. and 2. so that 1. is negated, right? My question: What happens between 1. and 2.? (I'm not trying to be argumentative.)
That's one of the many forms of material implication. p v q says that at least one of those must be true, so if not p is true then q must be true. Put differently, ~p -> q.
William Spaniel ohhh ok. so assuming at least one of p and q are true. after determining that p is false which means ~p is true, then q must be the one true. when looking at a truth table, we must look at where both ~p and q are true. which shows that (~p v q) (~p--> q) correct?
I don't see the logic on these three points as a whole. If 2 is right then it is not part of 1, ie The food has Beef Taking into account the 2 would be true then 1 has to be rectified and say: 1 The food has Chicken 2. The food does not have Beef 3. Therefore, it has Chicken I listen to the rest of the video and I was getting a headache, what a way to complicate an argument. I will give you an example of how silly the argument is: Say in a restaurant a waiter shows a menu with a choice of two items on the chosen food then after the order has been placed, the waiter comes and says that one of the items is not there: The client would argue why it says in the menu something that they don't have (Your point 2) The logical approach is to rectify point 1. (remove what it does not have) so point 1 reflects a true statement.
+Oscar Alvarez To clarify disjunctive syllogism using your example (and for anyone else who reads this in the future): C: Chicken is available B: Beef is available CvB: Either chicken or beef (or both) are available C^B: Chicken and beef are both available Let's suppose the menu lists Chicken (C) then also lists Beef (B), we can combine these (using conjunction rule) to form C^B. The problem is that disjunctive syllogism requires a premise of the form PvQ, as opposed to P^Q as the menu example infers. Now, if the waiter verbally informed the clients that chicken OR beef is definitely available, then comes back 5 minutes later and says there is no beef available, the client has no argument. . Therefore if the waiter comes back and says there is no beef, then you can conclude that chicken is now the only available option remaining. That's why this rule is also referred to as "elimination".
daekist Ok, I get that but you are talking about two areas, the menu and the food (on the plate) On the printed menu it may have a choice of several sets of items but when you say the "food" it is actually the end result and that would imply a selective choice either by the waiter or yourself. Your MP is the food. So the food could have chicken or beef. "Now, if the waiter verbally informed the clients that chicken OR beef is definitely available, then comes back 5 minutes later and says there is no beef available, the client has no argument." This statement is actually wrong because as it goes I have worked on a restaurant and if one of my waiters says that there is a set of items then they ARE available. If after the order has been placed and the waiter comes back after 5 minutes saying that one of them is no longer available then the first premise is wrong and the premise should have been modified to say, today we have chicken but not beef. Basically you are missing mp2 (known) with MP1 (no fact find). They waiter lied or did not get the facts right in the first place. "That's why this rule is also referred to as "elimination". Your elimination concept is vague to say the least, it depends on the premise and could have different connotations. In the CSI world, eliminating suspects is confirming that they were NEVER there in the first place and on the food I could say to the waiter, eliminate the vegetables (I don't like them) It is subject to interpretations!!!
+Oscar Alvarez A waiter saying "I know for a fact that we have chicken AND beef" is not the same as him saying "I know for a fact that we have chicken OR beef". The truth tables for AND / OR are very different so the two above statements could never be used interchangeably (they are not logically equivalent). In real life, if a waiter says a list of items are available, the OR connective would not be used. If the items were listed, we would use AND to join them. However, if the waiter specifically said "we have chicken OR beef", this is different than simply listing the available items. When both items are available, the waiter can interchangeably say "we have chicken OR beef" or say "we have chicken AND beef" since OR only requires at least one item to be available. When only one item is available, the waiter can't say "chicken AND beef are available" since and requires both to be available. Thus the statements are not interchangeable anymore, but your argument implies they are still interchangeable statements. The scenario you seem to have the most issues with is: If the waiter says "chicken OR beef is available" when only chicken is available, he is correct. This statement is 100% true although it may be confusing to the clients. Let us carry this one step higher to make it clearer. Suppose the restaurant ran out of all meat and the manager told the cook to buy chicken OR beef IF the grocery store is still open. The store was open. By modus ponens, we can deduce that since the store was open, the cook bought chicken OR beef (we don't know exactly which one he bought). Now the waiter says to the client "we have chicken OR beef" without knowing exactly which meat was bought. Everything so far is valid and builds upon previously established premises. You might argue that the waiter should not have told the client anything without finding out which one was bought first, but that's now an issue of logistics rather than logic. The logic is sound. You're right about the ambiguity in the term "elimination" though, so no point debating that any further.
daekist Correct about the "elimination" I would just say that the propositional logic of DS is sound if it has only valid forms. 1 Black or White 2 not White Therefore Black 1 Yes or No 2 Not Yes Therefore NO Well, nothing strange here so it only begs the soundness of the content of the premise. I think we can agree on that.
I started to like the video in the first 10 seconds. Great people explain topics in simple but fun way.
This was great. Super helpful. Thank you!
for your example. shouldn't it be "the food does not have chicken, therefore it is beef" because p= chicken, q=beef, not chicken therefore beef in order to support ~p, therefore q?
Hello, great video! Is there a way to prove disjunctive syllogism formally, using the '11 axioms'?
thanks for explaining this so well, really cleared things up :)
This explanation is amazing. :)
Thanks!
"Something happens," temporally, between 1. and 2. so that 1. is negated, right? My question: What happens between 1. and 2.? (I'm not trying to be argumentative.)
Can a correctly formulated argument have contradictory premises in syllogistic logic???
How about i change it into p or q, and not q, then p. Is it same? Hope anyone can reply this thanks in advance!!!
amazing! What was i doing when i was taking this course!
What is the formal proof of DS?
Please come out with more soon!
Sorry, I'm actually teaching civil war IRL, so I have to prioritize that. I will finish these eventually.
William Spaniel
Thank you, they are really awesome videos!
why is the third row ~p --> q? i thought material implication was supposed to be ~p OR q?
That's one of the many forms of material implication. p v q says that at least one of those must be true, so if not p is true then q must be true. Put differently, ~p -> q.
William Spaniel ohhh ok. so assuming at least one of p and q are true. after determining that p is false which means ~p is true, then q must be the one true. when looking at a truth table, we must look at where both ~p and q are true. which shows that (~p v q) (~p--> q) correct?
FYI: Your example syllogism (the chicken and the beef) does not match the P & Q formula next to it.
It was P or Q.
That isn't an ampersand
Thankyouuu
Thanks!
question... can I do the distuntive syllogism with modus tollens too?
like:
~P v q
~p
therefore ~q
No. The or is not an exclusive or so you cannot make the inference that ~q is true.
Syllogism? More like silly-gism, because William dumping all this knowledge on us for free on CZcams is crazy!
1:11 Damn, these videos are so good, but it annoyed the heck out of me that he wrote both the sentences on line 2 and the conclusion wrong 😅
I took another look and I think what William wrote is correct. What seemed off about them?
is this a valid form?
I believe so. Why would it not be?
I don't see the logic on these three points as a whole.
If 2 is right then it is not part of 1, ie The food has Beef
Taking into account the 2 would be true then 1 has to be rectified and say:
1 The food has Chicken
2. The food does not have Beef
3. Therefore, it has Chicken
I listen to the rest of the video and I was getting a headache, what a way to complicate an argument.
I will give you an example of how silly the argument is:
Say in a restaurant a waiter shows a menu with a choice of two items on the chosen food then after the order has been placed, the waiter comes and says that one of the items is not there:
The client would argue why it says in the menu something that they don't have (Your point 2)
The logical approach is to rectify point 1. (remove what it does not have) so point 1 reflects a true statement.
+Oscar Alvarez To clarify disjunctive syllogism using your example (and for anyone else who reads this in the future):
C: Chicken is available
B: Beef is available
CvB: Either chicken or beef (or both) are available
C^B: Chicken and beef are both available
Let's suppose the menu lists Chicken (C) then also lists Beef (B), we can combine these (using conjunction rule) to form C^B. The problem is that disjunctive syllogism requires a premise of the form PvQ, as opposed to P^Q as the menu example infers.
Now, if the waiter verbally informed the clients that chicken OR beef is definitely available, then comes back 5 minutes later and says there is no beef available, the client has no argument. . Therefore if the waiter comes back and says there is no beef, then you can conclude that chicken is now the only available option remaining. That's why this rule is also referred to as "elimination".
daekist
Ok, I get that but you are talking about two areas, the menu and the food (on the plate)
On the printed menu it may have a choice of several sets of items but when you say the "food" it is actually the end result and that would imply a selective choice either by the waiter or yourself.
Your MP is the food.
So the food could have chicken or beef.
"Now, if the waiter verbally informed the clients that chicken OR beef is definitely available, then comes back 5 minutes later and says there is no beef available, the client has no argument."
This statement is actually wrong because as it goes I have worked on a restaurant and if one of my waiters says that there is a set of items then they ARE available. If after the order has been placed and the waiter comes back after 5 minutes saying that one of them is no longer available then the first premise is wrong and the premise should have been modified to say, today we have chicken but not beef. Basically you are missing mp2 (known) with MP1 (no fact find).
They waiter lied or did not get the facts right in the first place.
"That's why this rule is also referred to as "elimination".
Your elimination concept is vague to say the least, it depends on the premise and could have different connotations. In the CSI world, eliminating suspects is confirming that they were NEVER there in the first place and on the food I could say to the waiter, eliminate the vegetables (I don't like them)
It is subject to interpretations!!!
+Oscar Alvarez A waiter saying "I know for a fact that we have chicken AND beef" is not the same as him saying "I know for a fact that we have chicken OR beef". The truth tables for AND / OR are very different so the two above statements could never be used interchangeably (they are not logically equivalent).
In real life, if a waiter says a list of items are available, the OR connective would not be used. If the items were listed, we would use AND to join them. However, if the waiter specifically said "we have chicken OR beef", this is different than simply listing the available items.
When both items are available, the waiter can interchangeably say "we have chicken OR beef" or say "we have chicken AND beef" since OR only requires at least one item to be available.
When only one item is available, the waiter can't say "chicken AND beef are available" since and requires both to be available. Thus the statements are not interchangeable anymore, but your argument implies they are still interchangeable statements.
The scenario you seem to have the most issues with is: If the waiter says "chicken OR beef is available" when only chicken is available, he is correct. This statement is 100% true although it may be confusing to the clients.
Let us carry this one step higher to make it clearer. Suppose the restaurant ran out of all meat and the manager told the cook to buy chicken OR beef IF the grocery store is still open. The store was open. By modus ponens, we can deduce that since the store was open, the cook bought chicken OR beef (we don't know exactly which one he bought). Now the waiter says to the client "we have chicken OR beef" without knowing exactly which meat was bought. Everything so far is valid and builds upon previously established premises. You might argue that the waiter should not have told the client anything without finding out which one was bought first, but that's now an issue of logistics rather than logic. The logic is sound.
You're right about the ambiguity in the term "elimination" though, so no point debating that any further.
daekist
Correct about the "elimination"
I would just say that the propositional logic of DS is sound if it has only valid forms.
1 Black or White
2 not White
Therefore Black
1 Yes or No
2 Not Yes
Therefore NO
Well, nothing strange here so it only begs the soundness of the content of the premise.
I think we can agree on that.