Critical Thinking - 28 - Categorical Logic - Categorical Syllogisms

This episode puts it all together as we construct categorical arguments and test them for validity.

[natashabenkendorf]

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.

[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-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-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-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"?

[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