- #1
phoenixthoth
- 1,605
- 2
Given: my bedroom has no door.
Statement 1: My bedroom door is open.
Statement 2: My bedroom door is closed.
[Definition: closed is equivalent to not open. So statement 2 is the negation of statement 1.]
Now when I evaluate the truthfulness of statements 1 and 2...
We can translate this to a more formal logical setting by introducing the unary predicate O standing for openness and constant d, which means my bedroom door.
In this setting, statement 1 is Od and statement 2 is -Od [where - is a negation symbol]. I'm trying to figure out the truthfulness of the two statements Od and -Od.
This is where I get stuck because I suspect that BOTH Od and -Od are vacuously true as the set of all possible states of the door, which would usually have two elements in it, open and not open, is empty.
Since -Od is true, albeit vacuously, that means --Od is false. Since --Od is equivalent to Od, Od is false. And therefore, Od is true and false.
What is the flaw with my reasoning? This smells to me like the "proof" that 1=2...
Statement 1: My bedroom door is open.
Statement 2: My bedroom door is closed.
[Definition: closed is equivalent to not open. So statement 2 is the negation of statement 1.]
Now when I evaluate the truthfulness of statements 1 and 2...
We can translate this to a more formal logical setting by introducing the unary predicate O standing for openness and constant d, which means my bedroom door.
In this setting, statement 1 is Od and statement 2 is -Od [where - is a negation symbol]. I'm trying to figure out the truthfulness of the two statements Od and -Od.
This is where I get stuck because I suspect that BOTH Od and -Od are vacuously true as the set of all possible states of the door, which would usually have two elements in it, open and not open, is empty.
Since -Od is true, albeit vacuously, that means --Od is false. Since --Od is equivalent to Od, Od is false. And therefore, Od is true and false.
What is the flaw with my reasoning? This smells to me like the "proof" that 1=2...