the Canons.

At the risk of some pedantry, we may exhibit the process as follows
(_cf._ Prof. Ray's _Logic_: Appendix D):

Whatever relation of events has certain marks is a case of causation;

The relation A: _p_ has some or all of these marks (as shown
by observation and by the conformity of instances to such or
such a Canon):

Therefore, the relation A: _p_ is a case of causation. Now, the
parenthesis, "as shown by the conformity, etc.," is an adscititious
member of an Epicheirema, which may be stated, as a Prosyllogism, thus:

If an instance, etc. (Canon of Difference);

The instances A B C B C are of the kind required:
_p q r' q r_

Therefore, A, present where _p_ occurs and absent where it
does not occur, is an indispensable antecedent of _p_.

Such is the bare Logic of Induction: so that, strictly speaking,
observation or experiment is no part of the logic, but a means of
applying the logic to actual, that is, not merely symbolical,
propositions. The Formal Logic of Induction is essentially deductive;
and it has been much questioned whether any transition from the formal
to the material conditions of proof is possible. As long as we are
content to illustrate the Canons with symbols, such as A and _p_, all
goes well; but can we in any actual investigation show that the relevant
facts or 'instances' correspond with those symbols?

In the first place, as Dr. Venn shows, natural phenomena want the
distinctness and capability of isolation that belong to symbols.
Secondly, the observing whether instances conform to a Canon, must
always be subject at last to the limits of our faculties. How can we
ascertain exact equality, immediate sequence? The Canon of Difference,
in its experimental application, is usually considered the most cogent
sort of proof: yet when can the two sequent instances, before and after
the introduction of a certain agent, be said to differ in nothing else?
Are not earth and stars always changing position; is not every molecule
in the room and apparatus always oscillating? It is true that our senses
are now aided by elaborate instruments; but the construction of these
depends on scientific theories, which again depend on experiments.

It is right to touch upon this well-known sceptical topic; but to insist
much upon it is not a sign of good sense. The works of Herschel,
Whewell, and Jevons should be consulted for the various methods of
correc