[The material on Trees under Howson is probably more current than this. These notes will be updated, though (Nov 2011)]
This section of the tutorials and
A.Hausman, H.Kahane, P.Tidman [2007], Logic and Philosophy
would work well together.
6/21/07 10 Software
You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'. [Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]
You will need to use the correct logical symbols. Here they are
F ∴ F & G ∼ & ∨ ⊃ ≡ ∃ ∴ (or use the palette to produce them)
2/5/08
If a derivation contains a line of the form
n (<variable>)<scope> <any justification>
then a line of the form
<<scope>[<term>/<variable>]> 'n UI'
may be added to the derivation, provided that <variable> is free for <term> in the <scope> ie that the substitution [<term>/<variable>] is legitimate .
11/9/2007 10Software
The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).
Let us start with an Interpretation
Interpretation 1
Universe= {a,b}
F={a}
2/5/08
Hausman[2007] Logic and Philosophy Chapter 10
[The core of what follows is from Leblanc and Wisdom [1972] p.117 and f.]
10 Software
Hausman[2007] Logic and Philosophy Chapter 10
Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.
2/5/08 10Software
Hausman[2007] Logic and Philosophy Chapter 9
Existential Instantiation permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective.
The circumstance that Existential Instantiation gets invoked looks like this.
2/5/08 10Software
Hausman[2007] Logic and Philosophy Chapter 9
There is a rule for adding a Existential Quantifier. This permits the step illustrated by the following proof fragments.
5 Fa 6 (∃x)Fx 5 EG