Post by Eugene 2.0 on Aug 21, 2020 8:31:58 GMT
Generalisation in logic really works, and, however, it must have some flaws.
To claim P is a general form is to say "for all P". But no P's are just P's. No individuals exist as free individuals. Metaphysically they need to have at least one relation to appear. So, P's are connected with some X's. This fact can be named as "p". (Respectively, Q's = q, R's = r...)
To claim about P's is to claim about p, and also it claim about that this P contains in each set. Also, such a set may contain different combinations of various different individuals. Thus, along with P there are Q's, R's... and so on.
As we consider that Q's, R's and the rest are indeed q, r,... then, all the P exists along with Q, R... in p, q, r... in different connections. So, P, Q, R... are p, q, r... all together are various combinations of complex propositions.
As p, q, r... implies p iff p, q, r... is conjunction. Also, another types of relations are also possible to claim it. Let's check it:
p→p
p&q→p
p&q&r&...→p
pvq→p
pvqvrv...→p
In last two premises p is implied only when either p is True, or, when p is True, but q is False or qvrv... are False altogether. However, as soon as we no longer interested in False premises we just can ignore it, or such a form (complex disjunction) is helpful to be able to falsify the premise. Each way is not impossible, and we don't need to worry about it much.
All the others relations in logic can be reduced to conjunction and disjunction.
Now, what about implying the rest? As we take P's as what is in each set, we have to be able to imply the rest.
p&q&r&...→q&r&...
pvqvrv...→qvrv... (taking into account the notes above)
The main question is:
by assuming something general are we assuming everything else?
To claim P is a general form is to say "for all P". But no P's are just P's. No individuals exist as free individuals. Metaphysically they need to have at least one relation to appear. So, P's are connected with some X's. This fact can be named as "p". (Respectively, Q's = q, R's = r...)
To claim about P's is to claim about p, and also it claim about that this P contains in each set. Also, such a set may contain different combinations of various different individuals. Thus, along with P there are Q's, R's... and so on.
As we consider that Q's, R's and the rest are indeed q, r,... then, all the P exists along with Q, R... in p, q, r... in different connections. So, P, Q, R... are p, q, r... all together are various combinations of complex propositions.
As p, q, r... implies p iff p, q, r... is conjunction. Also, another types of relations are also possible to claim it. Let's check it:
p→p
p&q→p
p&q&r&...→p
pvq→p
pvqvrv...→p
In last two premises p is implied only when either p is True, or, when p is True, but q is False or qvrv... are False altogether. However, as soon as we no longer interested in False premises we just can ignore it, or such a form (complex disjunction) is helpful to be able to falsify the premise. Each way is not impossible, and we don't need to worry about it much.
All the others relations in logic can be reduced to conjunction and disjunction.
Now, what about implying the rest? As we take P's as what is in each set, we have to be able to imply the rest.
p&q&r&...→q&r&...
pvqvrv...→qvrv... (taking into account the notes above)
The main question is:
by assuming something general are we assuming everything else?
