1. Department of English Language and Literature
Major: English Language and Literature
Semantics Session 7
“Logic”
Dr. Badriya Al Mamari
Academic year 2021/2022
2. Logic
• Logic is a word that means many things to different people.
Many everyday uses of the words logic and logical could be
replaced by expressions such as reasonable.
• Logic deals with meanings in a language system, not with actual
behaviour (partial) of any sort.
• Logic deals most centrally with Propositions. The terms ‘logic’
and ‘logical’ do not apply directly to Utterances (which are
instances of behaviour).
3. • There is an important connection between logic and rational
action, but it is wrong to equate the two because logic is just
one contributing factor in rational behaviour.
• Rational behaviour involves:
(a) goals
(b) assumptions and knowledge about existing states of affairs
(c) calculations, based on these assumptions and knowledge,
leading to ways of achieving the goals
4. *Example of rational behaviour:
1.Goal: to alleviate my hunger
2.Assumptions and knowledge: Hunger is alleviated by eating
food.
-Cheese is food.
-There is a piece of cheese in front of me.
-I am able to eat this piece of cheese
3.(Rational) action: eating the cheese
5. • Comment on the example:
Eating the piece of cheese in such circumstances is an example
of entirely rational behaviour. But the use of the word logic
here restricts the logic to the ‘calculations’ aspect of this
behaviour. The goals, assumptions, knowledge, and final action
are in no way logical or illogical, in our sense.
6. • Example of Arithmetical facts:
• ‘Arithmetical fact’ does not mean just fact involving numbers
in some way, but rather fact arising from the system of rules
defining addition, subtraction, multiplication, and division.
• A similarity between arithmetic and logic is the unthinkability
of alternatives.
Example: 2+ 2 # 5 is unthinkable.
• This is an arithmetical contradiction.
8. Activity: Mark each sentence for contradiction (C)
or for analytic (A) as appropriate:
• (1) John is here and John is not here. (C)
• (2) Either John is here or John is not here.
• (3) If John is here, John is here.
• (4) If everyone is here, no one isn’t here.
• (5) If someone is here, then no one is here.
9. • Words such as and, or, and not are not predicates and
cannot be used as referring expressions. Logic calls such
words connectives.
• The main purpose of the connectives and and or is to
‘connect’ individual propositions with other propositions.
• The kind of meaning that is involved is structural.
• It deals with the whole structures of propositions and how
they are related to each other, rather than with individual
items within propositions, such as names and predicates.
10. Grammatical forms VS Logical forms
• Some pairs of sentences with similar or identical grammatical
forms may sometimes have different logical forms.
• Example:
-Sarah and Oliver worked morally.
-Sarah and Oliver worked together.
• In order to state rules of calculation, or ‘rules of inference’,
completely systematically, these rules have to work on
representations of the logical form of sentences, rather than
on the grammatical forms of the sentences themselves
11. Grammatical forms VS Logical forms
Example 1 Example 2 Logical / non-logical
A plant normally gives off
oxygen
A rose is a plant therefore
A rose normally gives off
oxygen
A plant suddenly fell off the
window-sill.
A rose is a plant therefore.
A rose suddenly fell off the
window-sill
a generic sentence (G)
an equative sentence
(E),
pairs of sentences with
similar or identical
grammatical forms
may sometimes have
different logical forms
12. • Summary:
learning to translate ordinary language sentences into
appropriate logical formulae is a very good exercise to develop
precise thinking about the meanings of sentences, even though
the logical form of a sentence does not express every aspect of
meaning of that sentence
13. logically valid(V) VS invalid (I) conclusions
Example 1.:
• If John bought that house, he must have got a loan from the bank.
• He did buy that house, so therefore he did get a loan from the bank.
Example 2:
• If John bought that house, he must have got a loan from the bank.
• He did buy the house, so therefore he didn’t get a loan from the bank.
• Example 3:
• No one is answering the phone at Gary’s house, so he must be at home,
because whenever Gary’s at home, he never answers the phone.
14. • Logic deals with meanings in a language system (i.e. with
propositions, etc.), not with actual behaviour, although
logical calculations are an ingredient of any rational
behaviour.
• A system for describing logical thinking contains a notation
for representing propositions unambiguously and rules of
inference defining how propositions go together to make up
valid arguments.
• Because logic deals with such very basic aspects of thought
and reasoning, it can sometimes seem as if it is ‘stating the
obvious’.
15. References:
Hurford, J. R., Heasley, B., & Smith, M. B. (2007). Semantics: a
coursebook. Cambridge university press. (pp. 141 -151
