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Question

How would you perform this Fitch Proof without the use of Taut Con?

13.29 Vx (Small (x) Cube (x)) Ex-Cube(x) 3x Small (x Cube(x

Solution

xx solve xxxx xxxxx xxx a xxxxxx of xxxxxxx xxxxxx yxx'xx need xx implement.

xxxxxxxxx yxxxxx x derivation xx ¬(A(AB))A¬A.

xxxxxx x, xxxxx assuming ¬(xx)

we xxxx xxxxxxxxxxy xx assume x. An xxxxxxxxxxx xx -xxxxx gives x contradiction.

xxxxxx x, xx'xx first xxxx to xxxx xxxxxxxx xxxx 3 xx hand, xxx'x xxxxxx xx 2. xxxxxx ¬(CD). xxxxxxxxxxy xxxxxx ¬x. Further xxxxxxxxxxy assume x. xxxxx xxxxxxxx D xy trick x, xxxxxxxxxxx xxxxx gives xx. We xxx xxxx x contradiction, xxxxxxxxx ¬¬C.

xxxxxxy xxxxxx x, the xxxxxxxy is xx 'xxxxxxx xxx innocent': xxxxx assuming x xxx ¬x, further xxxxxxxxxxy assume x. xxxx yxx can xxxxxx C¬C. xxxxx xxxx xxxxx of x contradiction xxxxx xxxxxx xxxx an xxxxxxxxxx of x yxx xxx infer ¬x.

So xxx xxx x, if xxxxx is x   xxxxx x then xxxx x.

xxxx xxxxx xxxxx, if x is xxx x xxxx then xxxxx x

xxxxxxxxxx xxy xxxxxxxxxxx is xxxxx above xx xxxx xxxxx is x cube.

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