Critical Thinking - 28 - Categorical Logic - Categorical Syllogisms

[@natashabenkendorf9008]

I have really enjoyed your videos on formal categorical logic. You make a difficult subject attainable. Any chance that the propositional logic videos are still coming? I would love to hear you break down that difficult subject further then you had a chance to in an earlier video.

[@allandidonato]

I am so sorry I haven’t put them out yet. I filmed them over a year ago but have been so swamped by other projects and the classes I’ve been teaching that I haven’t been able to get back to KZbin content. After I finish what I am working on now I promise I will begin to edit the next logic video. But I am so glad you found my videos helpful so far.

[@Syllogist]

Comment-3: Example Rule 4 (11:52). Algebraic calculation: x - war, y - meant to be fun, z - government action. 1. No war is meant to be fun (x’y) 2. No government action is meant to be fun (z’y) - - - Calculation: ((x’y)*(z’y))/Y = (x’yz’)/Y = x’z’ = z’x’ - - - 3. Yours: No war is a government action [ERROR INTERPRETATION] 3. VALID: No war AS NO government action (z’x’) [AS «meant to be fun»] - TRUE CONCLUSION.

[@Syllogist]

Comment-5a: Example Rule 4 (12:43). Algebraic calculation: x - Peter (loves), y - Mary Lane, z - Harry (loves). 1. Peter (loves) Mary Lane (xy) 2. Harry (loves) a Peter (loves?) (zx) - - - Calculation: ((xy)*(zx))/X = (xyz)/X = yz = zy - - - 3. 3. Yours: Harry loves Mary Lane - [ERROR INTERPRETATION because term «Peter (loves)» not equivalence to term «Peter». It is 4-th term on this syllogism]. MORE CORRECT CALCULATION: Comment-5b: Example Rule 4 (12:43). Algebraic calculation: x - Peter, y - Mary Lane, z - Harry, w= loves. 1. Peter (loves) Mary Lane (xw->y = (xw)’+y = x’+w’+y) 2. Harry (loves) a Peter (zw->x = (zw)’+x = z’+w’+x) - - - Calculation: ((x’+w’+y)*(z’+w’+x))/WX = ((y)*(z’))/WX = yz’ = z’y - - - 3. VALID: No Harry [loves as Peter] Mary Lane. (z’[WX]y) Where is problem? No problems! BECAUSE ABSOLUTLY ANY SYLLOGISM (as logic conclusion) CAN CALCULATE INTO ALGEBRAIC FORM (with right INTERPRETATION this terms!] :-)

[@Syllogist]

Comment-4: Example Rule 4 (12:24). Algebraic calculation: x - puppy (Beagle?), y - bird, z - dog. 1. No puppy is a bird (x’y) 2. No dog is a bird (z’y) - - - Calculation: ((x’y)*(z’y))/Y = (x’yz’)/Y = x’z’ = z’x’ - - - 3. VALID: NO dog AND NO puppy (z’x’) [AS «a bird»] - TRUE CONCLUSION.

[@Syllogist]

Comment-2: Example Rule 3 (10:35). Algebraic calculation: x - dogs , y - mammals, z - cats. 1. All dogs are mammals (xy) 2. No cats are dogs (z’x) - - - Calculation: ((xy)*(z’x))/X = (xyz’)/X = yz’ = z’y - - - 3. Yours: No cats are mammals [ERROR INTERPRETATION] 3. VALID: THERE IS no cats WHICH mammals (z’y) [meaning SO AS a dogs] - TRUE CONCLUSION. [«THERE IS… WHICH… SO AS…» - in volume for this 3 syllogism’s terms it’s - right! - This is yours RULE 1 (6:31)]

[@Syllogist]

You wrote that «Just take the claim that "some dogs are mammals". It does not imply that "some dogs are not mammals" - the assumption goes beyond the claim itself… Sorry, but then why do we still say "Some dogs" and not "All dogs"? Doesn't the word "Some" imply only a part of the full scope of the concept of "Dogs", meaning only "mammals" of them? How, then, to designate that part of the NON-"Some dogs" that makes up the complete set of "All dogs"?

[@allandidonato]

It sounds like it would imply only part, but that’s not how the quantifier works. It is “at least some” while possibly “all”.

[@Syllogist]

@@allandidonato Do you write: "possibly «all»", "It sounds like", "at least some"??? Weird… Are you talking about probability theory or logic? The basis of logic is the evaluation of "False" or "True", and not "Everything is Possible". If "All" and "Some" can change places at any time, then what kind of logic can we talk about?

[@allandidonato]

@@Syllogist All and Some cannot be used interchangeably I all cases, but All implies Some, and a denial of Some implies a denial of All. So we are still dealing with truth claims (of a categorical nature NOT moral logic here),

[@Syllogist]

@@allandidonato Your: " All implies Some, and a denial of Some implies a denial of All" is completely illogical. Classical logic cannot one-sidedly operate exclusively with QUALITATIVE categories of concepts in which "All women" and "Some women" are still "women", that is, equivalent concepts. Which, of course, from the qualitative side, yes, that's right. But! The problem is that the concepts of "All" and "Some" do NOT reflect QUALITATIVE, but rather QUANTITATIVE characteristics of objects of thinking! Such a purely qualitative approach is only partially suitable even when describing quantifiers. Read more about this here: 07-12. THE RULE OF NEGATION-CONFIRMATION OF QUANTIFIERS (diagrams and formulas) / LOGICAL SPECIAL OPERATION-4: kzbin.info/www/bejne/hWPGl4N9pLJ2b6c And here is the formula you mentioned (zy + zy') = z*1 [Some y + Some Non-y = It's ALL Y] has already been tested many times by me and always gives the correct conclusion of the syllogism when calculating syllogisms.

[@Syllogist]

SO FAR ABSOLUTLY ANY SYLLOGISM (as logic conclusion) CAN CALCULATE AS ALGEBRAIC FORM… I find in your good and interest clip some mistakes… Comment-1: Example (1:30). Algebraic calculation: x - logicians , y - people who embrace contradiction, z - teachers. 1. No logicians are people who embrace contradiction (x’y) 2. Some teachers are people who embrace contradiction (zy+zy’) - - - Calculation: ((x’y)*(zy+zy’))/Y = (x’yz)/Y = x’z = zx’ - - - 3. Yours: (Therefore,) some teachers are not logicians [(zx’+zx) - Why? ERROR!] 3. VALID: THERE IS teachers WHO not logicians (zx’) - TRUE CONCLUSION

[@allandidonato]

This comment just came up in my email. I love how you are engaging with the examples, very interesting interpretation. Algebra is a form of deduction, but it isn't exactly the same as categorical logic. Where I see your error is in your translation of number 2. "Some teachers are people who embrace contradiction" cannot be translated "(zy+zy'). In categorical logic a particular affirmative can express any amount of the subject, up to the entire class. So, there is no reason to assume that "some teachers are people who embrace contradiction" implies that "some teachers are NOT people who embrace contradiction". The proposition does not give us that information. All we know is that some are. It is possible that some don't embrace contradiction, but we don't know for sure. Just take the claim that "some dogs are mammals". It does not imply that "some dogs are not mammals" - that assumption goes beyond the claim itself.