So I was pushing with it with the example I gave on deductive reasoning earlier. But there was a point to this – that it does have much to do with the type of subjects and predicates you choose. Here are some mixed examples from here with my commentary:
- All numbers ending in 0 or 5 are divisible by 5. The number 35 ends with a 5, so it must be divisible by 5.
Here we have an abstract system which is completely based on artificial rules. But also will this work in, say, base-6? Why do we assume base-10?
- All birds have feathers. All robins are birds. Therefore, robins have feathers.
Built into the definition of birds is feather. So we have a tautology.
- It’s dangerous to drive on icy streets. The streets are icy now, so it would be dangerous to drive on the streets.
Judgment and a matter of degrees, the kind of tires you may have and who is driving or a combination of these.
- All cats have a keen sense of smell. Fluffy is a cat, so Fluffy has a keen sense of smell.
A matter of degrees.
- Cacti are plants, and all plants perform photosynthesis. Therefore, cacti perform photosynthesis.
Part of the definition of plant so a tautology again.
- Red meat has iron in it, and beef is red meat. Therefore, beef has iron in it.
- Acute angles are less than 90 degrees. This angle is 40 degrees, so it must be an acute angle.
Self defining term.
- All noble gases are stable. Helium is a noble gas, so helium is stable.
- Elephants have cells in their bodies, and all cells have DNA. Therefore, elephants have DNA.
The major premise is reversed with the minor one.
- All horses have manes. The Arabian is a horse; therefore, Arabians have manes.
This is an unusual case with naked foal syndrome but mutations may occur for better or worse. The question remains does a mane define a horse?
Admittedly, this is not the best page for examples. The point though is formal logic is highly restrictive in its use and content. It also says much about language as a medium for communicating truth, particularly when tautological definitions are used. Mathematics seems a better medium but then it is formed upon an abstract system not apply in reality. For this attempts have been made with set theory.
I do not mind enumerative and eliminative induction methods, and probability in the shape of abduction. It only needs to be stated from the outset. Rigour is possible with these if used carefully.
I have yet to touch upon apoha, Saussurean system of difference, fuzzy logic or even prototype theory as a methodologies, but I will.