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Chapter 1 – What follows from what? - Coggle Diagram
Chapter 1 – What follows from what?
Inference
A conclusion reached on the basis of evidence and reasoning.
:check::check:
Rome is the capital of Italy, and this plane lands in Rome; so the plane lands in Italy.
:check::red_cross:
Moscow is the capital of the USA; so you can't go to Moscow without going to the USA.
Logic is concerned not with whether the premisses of an inference are true or false, but whether the conclusion follows from the premisses. If an inference is true or false, that's somebody else's business (in this case, the geographer's).
Logicians call an inference where the conclusion really does follow from the premisses
valid
. So the central aim of logic is to understand
validity
.
It is common to distinguish between
two different kinds of validity
.
If the burglar had broken in through the kitchen window, there would be footprints outside; but there are no footprints; so the burglar didn't break in through the kitchen window.
If the premisses are true, so must the conclusion be. Or, to put it another way, the premisses couldn't be true without the conclusion also being true. Logicians call an inference of this kind
deductively valid
.
To say that the premisses can't be true without the conclusion being true is to say that in all
situations
in which all the premisses are true, so is the conclusion.
:old_key: To know an inference is deductively valid is to know that there are no situations in which the premisses are true and the conclusion is not.
A valid inference is one where the conclusion follows from the premiss(es).
A deductively valid inference is one for which there is no situation in which all the premises are true, but the conclusion is not.
Deduction
:
a systematic method of deriving conclusions that cannot be false when the premises are true, esp one amenable to formalization and study by the science of logic
Storm clouds are gathering; so there will be rain.
The premiss clearly gives a good reason for the conclusion, but it is not completely conclusive. After all, a change of wind can sometimes take the clouds in a different direction. So the inference is not deductively valid. Inferences like this are usually said to be
inductively valid
.
Induction
:
a process of reasoning, used esp in science, by which a general conclusion is drawn from a set of premises, based mainly on experience or experimental evidence.
The conclusion goes beyond the information contained in the premises, and does not follow necessarily from them.
Thus an inductive argument may be
highly probable
, yet lead from true premises to a false conclusion
Storm clouds are gathering; so the burglar didn't break in through the kitchen window.
The premisses seem to provide no kind of reason for the conclusion at all. It is
invalid
—both deductively and inductively.
The claims before
'so'
—logicians call them
premisses
— are giving reasons.
The claims after
'so'
—logicians call them
conclusions
—are what the reasons are supposed to be reasons for.