Flaws in English

Two examples can show why English language might not be a very good one, at least in terms of logic.

Example 1 (Transitivity)

Logic says:
Premise 1 A>=B
Premise 2 B>=C
Conclusion A>=C

where >= can be interpreted as a Math operator (A is greater than or equal to C), or the preference relation in Economics (A is preferred to C), or anything that has this property, transitivity.

Let's see what happens if we apply this to English:
Premise 1 Having a house is better than having a car.
Premise 2 Having a car is better than having a dog.
Conclusion Having a house is better than having a dog.

Good! But...

Premise 1 Winning $1 is better than nothing.
Premise 2 Nothing is better than winning $100000.
Conclusion Winning $1 is better than winning $100000.

Premises 1 and 2 are correct in English, but the conclusion is obviously not true.


Example 2 (Implication)

Logic says:
A => B is true when
1. A is true and B is true, or
2. A is false and B is true, or
3. A is false and B is false.

where => is the logical operator "imply" (A implies B). In English it is translated to "If A, then B," e.g. "If he is your dad, then he is a male"; "If 18 is divisible by 6, then 18 is divisible by 3"; "If it rains, then I will bring an umbrella."

So far so good. Let's see how it can be problematic:

All of the following are true logically (reason stated in parentheses):
1. If I have $1 billion now, then I will give you $500 million. (Because I don't have $1 billion now)
2. If I have a dog now, then my dog has 5 legs. (Because I don't have a dog now)
3. If I am a male, then Bill Gates is a billionaire. (Because both parts are true, although they are not related)

(Bertrand Russell once publicly stated that if 1=2, then he was God. This is in the same spirit as 1.)

They all make no sense in English. Apparently, the translation of => into "if then" is not a good one. (Actually "imply" isn't a good name for it either.) There is no place in English for this fundamental logic operator.