bergmann

Some Notes on the Exercise Files

8/1/26

The program, widgets, or Notes, should be accompanied by a suitable textbook, such as:

M.Bergmann, J.Moor, J.Nelson, The Logic Book
A.Hausman, H.Kahane, P.Tidman, Logic and Philosophy 
W.Hodges, Logic
C.Howson, Logic with Trees 
R.C.Jeffrey, Formal Logic: Its Scope and Limits
H.Leblanc and W.Wisdom, Deductive Logic
B.Mates, Elementary Logic
M.D.Resnick, Elementary Logic

8/10/26

Example of a difficult derivation

6/1/09 need to check

Roll your own derivations

2013

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)

12/14/20

Tutorial 25 Exercises d

4/24/06

1/12/20

You now have the tools to appraise arguments to the level of detail offered by predicate logic.

Let us run through how these might be used with a long and difficult example.

Consider the argument

12/25/13

Skill to be acquired:

To understand how the various restrictions on the quantificational rules work to exclude certain kinds of invalid inferences

Reading

Bergmann[2004] The Logic Book Section 10.1

The Tutorial

The Rule of Universal Elimination UE

If a derivation contains a line of the form

n (∀<variable>)<scope> <any justification>

then a line of the form

<<scope>[<constant>/<variable>]> 'n ∀E'

1/12/20

The Tutorial

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}