SAINT GOAT!
Some very provocative arguments in support of the theory that everything is a GOAT. It is difficult to find an argument that will lend even the slightest doubt to these proofs. Truly humbling...
goatism.org
Goatism Proved by Logic!
Introduction to Propositional Logic
In Propositional Logic every statement is either true or false. There is no third way. For example, the proposition "It is raining outside" is either true or not true. Furthermore, if a statement is false then it's opposite is true. So, if "It is raining outside" is a false statement, then it's opposite "It is not raining outside" must be true.
The Logical Proof
The proposition "Everything is a Goat" is either true or not true.
If it is false, then it's opposite must be true.
The opposite of "everything" is "nothing", which give us the proposition "Nothing is a Goat".*
Now, this statement is clearly false, for goats certainly exist - we have all seen them. This means that it's opposite must be true.
Therefore, "Everything is a Goat" must be a true statement.
*Sophists may argue that we should negate the object rather than the subject of this sentence; but this simply gives us the statement "Everything is not a Goat" which is logically identical to "Nothing is a Goat".
goatism.org
Further Logical Proof!
World wide goatist research continues apace. John Berry in the USA has created the following marvellous proof:
Inductive Proof
Inductive proof: Everything is a goat.
1) Base case: Consider a set of elements consisting of one goat. That goat is a goat, so all elements in this set are goats.
2) Inductive hypothesis: If any set of k elements are all goats, then any set of k+1 elements are all goats.
Proof of inductive hypothesis: Let S be any set of k+1 goats. Number them 1 to k+1, by any selection method you like.
Now remove goat #1. The remaining set of goats 2 to k+1 is a set of k goats. So by assumption, they are all goats.
Now put back goat #1 and remove goat #k+1. Again, the remaining set of k goats (#1 to #k) are goats.
Now since there was an overlap between the two sets (for example, goat #2 was in both sets), and in each set all the goats are goats, then all the goats in the larger set of k+1 must also be goats.
We have proven by induction that any set of things, of whatever size, consists of goats. So everything is a goat.
Further great work from the United States in this great proof from James Drier:
The Drier Conditional
Consider the sentence (G):
(G) If G is true, then everything is a goat.
We can demonstrate that (G) is in fact true, by Conditional Proof:
1 SUPPOSE that G is true.
2 Therefore, "If G is true, then everything is a goat" is true. (Substitution)
3 Therefore, if G is true, then everything is a goat. (Disquotation)
4 Therefore, everything is a goat. (From 1 and 3)
On the supposition that G is true, we have proved that everything is a goat. So we have proved that *if* G is true, then everything is a goat, QED.
This completes the proof of the important lemma, that if G is true, then everything is a goat. We now proceed to the desired conclusion.
5 If G is true, then everything is a goat. (proved above by conditional proof)
6 "If G is true, then everything is a goat" is true (by Quotation)
7 G is true. (substitution)
8 Everything is a goat. (From 5 and 7)
Some will find the conclusion obvious, but it is nice to have an absolute proof. |
