If it is not trivial that it is a tautology,
then you can do the calculation of the truth table step by step
:
((P => Q) <=> (non P => non Q) ) is a tautology if its truth table gives a full column of 1 (column 4 here)
P Q ((P => Q) <=> (non P => non Q) )
0 0 1 1 1 1 1
0 1 1 1 0 1 1
1 0 0 1 1 0 0
1 1 1 1 0 1 0
If one takes your sentence
P = "It doesn't go up"
Q = "it goes down"
If you want to refer to statistical inference hypothesis the formulation
is very different from simplist formulation like the one of a tautology.
In statistical inference one defines a null Hypothesis H0 against
an hypothesis H1 where H1 is NOT the negation of H0 but an ALTERNATIVE hypothesis to H0.
At the end you claim that the quote does require some insight into the way the
market works - which you didn't mention at the beginning.
All right but if you pretend that at each step the market will chose between up or down
well this is just random walk which is worthless since at step 2,3,4 it can be down again
after being up at time t so that you will be down. If you pretend that you will let
the market decide if it will goes up or down by managing a stop-loss you are talking about
trading strategy using a blind approach of market that is to say not much knowledge of market.
One can decide to use any kind of strategy that will work or not - that is not the question here -
but don't pretend that it induce deep Knowledge of how market works or worst pretend
that one cannot have more deeper knowledge and use it.
then you can do the calculation of the truth table step by step
:((P => Q) <=> (non P => non Q) ) is a tautology if its truth table gives a full column of 1 (column 4 here)
P Q ((P => Q) <=> (non P => non Q) )
0 0 1 1 1 1 1
0 1 1 1 0 1 1
1 0 0 1 1 0 0
1 1 1 1 0 1 0
If one takes your sentence
P = "It doesn't go up"
Q = "it goes down"
If you want to refer to statistical inference hypothesis the formulation
is very different from simplist formulation like the one of a tautology.
In statistical inference one defines a null Hypothesis H0 against
an hypothesis H1 where H1 is NOT the negation of H0 but an ALTERNATIVE hypothesis to H0.
At the end you claim that the quote does require some insight into the way the
market works - which you didn't mention at the beginning.
All right but if you pretend that at each step the market will chose between up or down
well this is just random walk which is worthless since at step 2,3,4 it can be down again
after being up at time t so that you will be down. If you pretend that you will let
the market decide if it will goes up or down by managing a stop-loss you are talking about
trading strategy using a blind approach of market that is to say not much knowledge of market.
One can decide to use any kind of strategy that will work or not - that is not the question here -
but don't pretend that it induce deep Knowledge of how market works or worst pretend
that one cannot have more deeper knowledge and use it.
