What Is Logic?
It is the study of correct reasoning.
The main building blocks of
reasoning are ARGUMENTS.
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Arguments
An argument is a set of
propositions (sentences
that can be either true or
false), in which one –
called the “CONCLUSION”
– is set up to be supported
by, or to follow from, the
others – called the
“PREMISES”.
• The premises are said to
give evidence for, or to
lead to, the conclusion.
Premise
Premise
Premise
CONCLUSION
Premise
CONCLUSION
Premise
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Premise Indicators
Conclusion Indicators
after all
may be inferred from
accordingly
ergo
as (noncomparative)
owing to
as a result
we may conclude
consequently
we may infer
as indicated by
seeing that
demonstrates that
whence
as shown by
since (non-temporal)
entails that
wherefore
assuming that
hence
which means that
because (non-causal)
implies that
which proves that
considering that
it follows that
which shows that
follows from
it must be that
for the reason that
it can’t be that
for
necessarily
for one thing
so
given that
therefore
in that
thus
inasmuch as
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• The conclusion claims to
follow from the premises
with CERTAINTY.
• The conclusion follows from
the premises with various
degrees of PROBABILITY.
• Can be either VALID (correct)
or INVALID (incorrect) –
there’s no middle ground!
• Can have varying degrees of
STRENGTH or WEAKNESS –
it’s a sliding scale.
• Information about the state
of affairs in the world MAY
affect its strength, which
depends on its CONTENT
(what it talks about).
• The state of affairs in the
world does NOT influence its
validity, which depends only
on the internal STRUCTURE
of the argument.
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Examples of deductive arguments
• Fish are not mammals, but dolphins are. So, no
dolphins are fish.
• Dogs are smarter than cats, since it is easier to
train them.
• If she were still interested in me, she would have
called, but she didn’t.
Examples of inductive arguments
• I’ve never met a golden retriever with a nasty
disposition. I bet there aren’t any.
• When blue jays are breeding, they become
aggressive. Consequently, scrub jays, which are
very similar to blue jays, can also be expected to
be aggressive when they’re breeding.
• That cat is used to dogs. Probably she won’t be
upset if you bring home a new dog for a pet.
VALIDITY and TRUTH
• A VALID argument is an
argument which CANNOT have
all true premises and false
conclusion. An INVALID
argument CAN (but does not
necessarily) have all true
premises and false conclusion.
T
T
• Remember, only DEDUCTIVE
arguments can be valid or
invalid.
T
F
• Validity depends on the
STRUCTURE (FORM) of the
argument, not on the truth of
its components (with the
exception noted above).
• If a FORM is found to be
valid/invalid, ALL ARGUMENTS
of that form will be
valid/invalid.
Valid form:
Invalid form:
All A are B; all B are C.
So, all A are C
If A, then B; B. So, A
All narwhals are
whales; all whales are
mammals. So, all
narwhals are mammals.
SOUND ARGUMENT
If you are in Ottawa,
you are in Ontario; you
are in Ontario. So, you
are in Ottawa.
X
If you are in Toronto,
you are in Ontario; you
are in Ontario. So, you
are in Toronto.
F
T
All whales are birds ;all If you are in Ottawa,
birds are mammals. So, you are in Toronto; you
all whales are mammals are in Toronto. So, you
are in Ottawa.
F
F
All whales are birds; all
birds are penguins. So,
all whales are penguins.
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If you are in Toronto,
you are in Alberta; you
are in Alberta. So, you
are in Toronto.
• Arguments: made up of premises and a
conclusion. Can be deductive (valid/invalid) or
inductive (various strengths).
• Validity: depends on the form of the argument,
not the truth of the components, EXCEPT:
It is impossible for a valid argument to have all true
premises and a false conclusion.
True Premises
False Premises
True Conclusion
Valid or Invalid
If valid, it is also SOUND
Valid or Invalid
False Conclusion
Invalid
Valid or Invalid
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Exercises – True or False?
F • An argument with all true premises and a true conclusion
must be valid.
F • If an argument has a false conclusion, it must be invalid.
T • If an argument has false premises and a false conclusion, it
could still be valid.
F • All unsound arguments are invalid.
T • All invalid arguments are unsound.
F • If an argument has at least one false premise, its
conclusion cannot be true.
T • A valid argument with a false conclusion must have at least
one false premise.
F • An invalid argument must have all true premises and a
false conclusion.
T • An argument with all true premises and a false conclusion
must be invalid.
F • An argument with all true premises and a true conclusion
must be sound.
F • If an argument is valid, its conclusion must be true.
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