Book contents
- Frontmatter
- Contents
- Preface
- 1 Overview
- 2 Logical connectives and truth-tables
- 3 Conditional
- 4 Conjunction
- 5 Conditional proof
- 6 Solutions to selected exercises, I
- 7 Negation
- 8 Disjunction
- 9 Biconditional
- 10 Solutions to selected exercises, II
- 11 Derived rules
- 12 Truth-trees
- 13 Logical reflections
- 14 Logic and paradoxes
- Glossary
- Further reading
- References
- Index
4 - Conjunction
- Frontmatter
- Contents
- Preface
- 1 Overview
- 2 Logical connectives and truth-tables
- 3 Conditional
- 4 Conjunction
- 5 Conditional proof
- 6 Solutions to selected exercises, I
- 7 Negation
- 8 Disjunction
- 9 Biconditional
- 10 Solutions to selected exercises, II
- 11 Derived rules
- 12 Truth-trees
- 13 Logical reflections
- 14 Logic and paradoxes
- Glossary
- Further reading
- References
- Index
Summary
OVERVIEW
We now move on to our second connective: and (&). We make a few observations about translating from English into our symbolic language. Note that we are only concerned with those occurrences of ‘and’ that connect whole sentences. Thus, for example, ‘I would like a gin and tonic’ is not a conjunction in our sense. (See the Williams sisters example below.) We then outline the two inference rules governing &, and construct some proofs using those inference rules together with the →O rule.
CONJUNCTIONS
In the simplest case, a complex English sentence such as:
(1) Piers was a CONSERVATIVE and Bruin was a MARXIST
would be represented in our symbolic notation as:
(1a) C & M
Variants on ‘and’
However, English contains many words other than ‘and’ that we shall also render as &. Thus:
Piers was a CONSERVATIVE but Bruin was a MARXIST
Piers was a CONSERVATIVE however Bruin was a MARXIST
Piers was a CONSERVATIVE moreover Bruin was a MARXIST
Piers was a CONSERVATIVE although Bruin was a MARXIST
Piers was a CONSERVATIVE yet Bruin was a MARXIST
Piers was a CONSERVATIVE even though Bruin was a MARXIST
Piers was a CONSERVATIVE nevertheless Bruin was a MARXIST
are all rendered:
C & M.
Some nuances of meaning are ignored
(i) It is true that ‘but’, ‘although’ and so on do not mean exactly the same as ‘and’. If I say ‘she was poor but honest’, I convey to my hearer the thought that poor people are not normally honest. But saying ‘she was poor and honest’ has no such consequence. Despite these differences, we assume here that the logical or inferential properties of ‘but’, ‘although’ and so on are the same as those of ‘and’, and this is why ‘but’, ‘although’ and so on get translated as ‘&’.
- Type
- Chapter
- Information
- Elementary Logic , pp. 35 - 46Publisher: Acumen PublishingPrint publication year: 2012