'Provable', 'falsifiable' and logic

[RamblingOnwards]

Okay, here's an appeal to all the logic gurus out there. I think I have a handle on the terms 'provable' and 'falsifiable', but is the use of these terms complete? That is, are there statements that don't fit into the following categories?

1. Provable and falsifiable:
"My chair is red"
"My mother's name is Marigold"

2. Provable but not falsifiable:
"I sometimes wear green socks"
"Black swans exist"

3. Falsifiable but not provable:
"I never wear green socks"
"This rock keeps away tigers"

4. Neither falsifiable nor provable:
"Undetectable fairies live in my garden"

- A provable statement that is proved is true.
- A falsifiable statement that is falsified is false.
- A provable (but not falsifiable) statement that has not been proved is assumed to be false.
- A falsifiable (but not provable) statement that has not been falsified is assumed to be true.
- A statement that is neither falsifiable nor provable is assumed to be a waste of everyone's time.

What am I missing out?

 

[Jaggy Bunnet]

So we must assume that your rock does indeed keep away tigers until such time as it is proved that it does not?

 

[MRC_Hans]

*snip*

- A provable statement that is proved is true.
- A falsifiable statement that is falsified is false.
- A provable (but not falsifiable) statement that has not been proved is assumed to be false or unknown .
- A falsifiable (but not provable) statement that has not been falsified is assumed to be true. No, false or unknown unless evidence has been presented.
- A statement that is neither falsifiable nor provable is assumed to be a waste of everyone's time.YEP!

Edited to add: The tiger claim is not a good example, as it is provable, if tigers are available.

Hans

 

[RamblingOnwards]

Firstly, my trusty rock:

You're both right, my assumptions had an assumption of its own - that tests have in fact been carried out.

If you set me down with my rock in cage full of hungry tigers and they don't eat me, well, there could be a hundred reasons unrelated to my rock. If they do eat me then we know my rock didn't work. If I never go near tigers, the fact is simply untested and therefore unknown.

- A falsifiable (but not provable) statement that has not been falsified is assumed to be true. No, false or unknown unless evidence has been presented.

How about 'no man-eating socks exist' or 'no two snow flakes are the same'? By evidence do you mean testing, or do you mean underlying facts (that have been proven/disproven) that make the particular statement likely/unlikely?

 

[Jaggy Bunnet]

So we must assume that your rock does indeed keep away tigers until such time as it is proved that it does not?

All rocks have some tiger deterring properties, if thrown accurately enough.