cooltodd109 wrote:Socrates famously said that the only thing we can know is that we know nothing.
Can we truly know anything? Do we really know nothing?
If we do know something, how can we be sure that we aren't mistaken?
Socrates was an ironist. Don't take that statement literally.
-- Updated May 3rd, 2012, 10:47 am to add the following --
Logically, an argument can be valid even though the conclusion does not agree with experience. The premises of any logical argument don't have to conform to experience for a conclusion to be valid. In fact, they CAN conform to experience, be logically valid, and still yield a conclusion that doesn't agree with experience.
1. All living cats respond to stimuli 2. I respond to stimuli 3. Therefore, I'm a living cat.
Sure, it's incomplete, but it's logically valid?
No, it's not logically valid. In the first premise, what you're saying is:
For all x, if x is a living cat, then x responds to stimuli.
This says nothing about whether or not anything else responds to stimuli. It just says that if you're a living cat, you respond to stimuli, and there is not a cat that doesn't respond to stimuli. So clearly your conclusion does not follow.
-- Updated May 3rd, 2012, 10:55 am to add the following --
HexHammer wrote:Fiveredapples #42
Surely you are kidding. In the middle ages true knowledge was that the earth was flat and it was the center of the universe, it was even written in the holy book, therefore it was unquestionable.
Indeed you are very shard, but I don't agree with your logic in most of your posts.
To have knowledge of a proposition, the proposition must be true. The proposition 'The earth is flat' is not true, therefore, it's cognitively meaningless to say you have knowledge of it. Secondly, I don't see how its being written in a holy book makes a difference. For instance, imagine if in a holy book it was written that nothing exists. Would it follow then that nothing exists? Clearly not. Again, one of the conditions of knowledge is that the proposition must be true.
-- Updated May 3rd, 2012, 11:11 am to add the following --
Fiveredapples wrote:Conclusions are neither valid or invalid. Conclusions are either true or false, or follow from the premises or don't.
Actually, you've got it backwards. In logic, it's irrelevant as to whether or not the conclusions are true. Logic concerns itself only with validity. So, conclusions are not true or false, but either valid or invalid. For instance, if you say
(1) All Greeks are men, Socrates is a Greek, Therefore Socrates is a man.
You do not presuppose that there are such things as Greeks. Or else (2) would be true and you would have to ontologically commit yourself to the existence of fire breathing dragons
(2) All dragons breathe flame, x is a dragon, therefore x breathes flame.
When we say "All A's are B's", were' saying (x)(x is an A → x is a B). The '(x)' does not commit us to saying there really are A's, unlike saying (∃x)(x is an A & x is a B).