LoneBear wrote:For example, if I assert that: "given all fleeps are gorps and all smurfies are gorps, then all fleeps are smurfies." Is the assertion true or false, and why?
I think it is both true and false. Smurfies
, fleeps and gorps are the same (true), but different (false) because they have their own individual definitions. Also I dont know what fleeps and gorps would translate to in my language
But I guess it is something to do with that cartoon which I am not so familiar with, just a random memories of it.
While the statement itself may be true or false, I think LoneBear was referring specifically to the logic behind it. Smurfies
, gorps, and fleeps don't really mean anything at all so there isn't really a translation issue.
And his assertion is logically false. You cannot infer that all fleeps are smurfies
given that all fleeps are gorps and all smurfies
are gorps. The set of gorps may include all fleeps and smurfies
and could also include many other things. Within the set of gorps, there may not be any overlap between the fleeps and smurfies
though there could be as well and even a full and even full overlap is possible. Note again that what is possible is not the same as what can be inferred logically from the statements.
LoneBear's statement is a simple syllogism (a set of 3 statements which has 2 premises each with 2 terms with one shared and a logical conclusion containing a term from each premise). The broad idea is that most statements can be reduced to syllogism and if done accurately, then correct reasoning may be the result. The idea is that if the premises are true and the syllogism is logically valid, then the conclusion is also true. Here is a good summary of syllogisms (http://www.wikihow.com/Understand-Syllogisms
). It includes some diagrams which may make things easier to understand.
LoneBear's syllogism has 3 All forms of statements. However, in the premises, the predicate in one premise must be the subject in the other in order for this to be valid. For example, this would work:
All fleeps are gorps.
All gorps are smurfies
Therefore, all fleeps are smurfies
This is a valid syllogism of the AAA type. Assuming that the premises are true, then the conclusion will also be true.