# Thread: If a = b, then 1 = 2

1. Originally Posted by steve_bank
Originally Posted by Speakpigeon
Originally Posted by steve_bank
I'd call it non sequiter. Premis and conclusion not connected logically.

If it is raining cats are dogs.
This isn't anything like an explanation.

You are repeating the commonplace answer as if it was any explanation.

EB
if a=b then 1=2.
if it is raining then the gas tank is full
fido is a dog therefore the cow jumped over the moon
fido is a dog therefore sasha is a cat

non sequitur. No connection between premise and conclusion. That is my explanation. I believe non sequitur is just a formal way of saying nonsense.

As a logician have you Carol's, also a logician, Jaberwoky?
The conditional is more akin to a premise than it is to an argument. While an argument may be fallacious, the worst a premise might be is false.

P1: if a=b, then 1=2
P2: a=b
Therefore, C: 1=2

That’s logical and a valid argument. In fact, I might go as far as saying that because it’s valid, it’s logical. The error isn’t in form but in falsity. While it might be true that the antecedent is true, the consequent is false. Since the conditional is not error free, i’d submit that the proposition is false, but that says nothing as to the validity of the argument.

2. if a=b then 1=2.

.For a valid argument conclusion must follow from premise. 1=2 does not follow from a=b. The argument is nonsense. I'd say it is non sequitur.

fido is a dog therefore sasha is a cat. Both statements may be true but the argument is invalid. Sasha is a cat does not follow from fido is a dog. Non sequitur.

3. Originally Posted by steve_bank
if a=b then 1=2.

.For a valid argument conclusion must follow from premise. 1=2 does not follow from a=b. The argument is nonsense. I'd say it is non sequitur.

fido is a dog therefore sasha is a cat. Both statements may be true but the argument is invalid. Sasha is a cat does not follow from fido is a dog. Non sequitur.
I don’t see an argument. What I see is a statement.

4. I see a conditional argument. If a then b. a is premise and b conclusion, a and be can be true or false. Either way I see the statement as nonsense for reasons stated.

If it is raining then I will carry an umbrella.

5. Originally Posted by steve_bank
I see a conditional argument. If a then b. a is premise and b conclusion, a and be can be true or false. Either way I see the statement as nonsense for reasons stated.

If it is raining then I will carry an umbrella.
I see something that is a conditional, but what I see is not an argument. It’s a statement, a conditional statement. ‘a’ is not a premise. It’s an antecedent. ‘b’ is not a conclusion; it’s a consequent.

It’s a conditional statement with an antecedent and consequent. It’s not an argument with a premise and conclusion.

Argument, no.
Statement, yes.

6. To me it is semantics. I am used to referring to any logical expression including formal and Boolean logic an an argument.

if a then b. logical expression and argument being synonymous.

Every logical argument or expression should reduce to some form of formal logic.

if a then not b.

a logical true or false
b logical true or false

truth table
a b
f t
t f

b = !a Boolean

if it is sunshine I will not take an umbrella.

If a then not b

A true sunny false not sunny
B true umbrella false no umbrella.

If a=b then 1=2. Nonsense, I don’t think you can make a truth table and hence no formal valid expression. That is my test for validity.

7. Originally Posted by fast
Originally Posted by Speakpigeon
Are you able to explain what would be illogical in the implication:

If a = b, then 1 = 2
EB
I don’t think faulty and logical is inconsistent.
A false conclusion is inconsistent with a valid argument and true premises, so yes, they can be.

But true, a false conclusion doesn't imply the argument is not valid.

Originally Posted by fast
The logic makes sense. If P, then Q. Revealing that Q is obviously false doesn’t alter the logic.
It doesn't alter the logic but it doesn't make the argument valid either.

Also, there are cases when a false conclusion implies that the argument is not valid.

Anyway, for now, you are not really answering the question.

Or are you saying that if a = b, then 1 = 2?
EB

8. Originally Posted by Speakpigeon
Are you able to explain what would be illogical in the implication:

If a = b, then 1 = 2