The law of sufficient reason is the fourth and last law of formal logic. Historically, it is also the latest, and this is no coincidence. For comparison, you can notice that the three previous laws were formulated by Aristotle in the 4th century BC.
Until the 18th century, due to its specificity, this law was not applied in classical logic. The reason for this historical delay is the following fact.
The law was introduced into the logical paradigm by Leibniz, who at the same time allowed some inaccuracy in relation to logic itself.
Leibniz described the need for substantiation as applied to mathematics, implying only purely formal, theoretical statements by evidence. However, he extended the requirement of formal provability to all nature, which is impossible to agree with.
By denying the very possibility of extensive evidence, i.e., evidence through empirical experience, Leibniz narrowed the range of applicability of the law.
On the other hand, the law of sufficient reason is a factual demonstration that all things in the world have cause and effect, all things are connected with each other, nothing disappears without a trace and does not appear on its own.
In this interpretation, the law was discovered by Democritus as early as 5-4 centuries BC. The phenomenon of complete interconnection and interdependence within the world order subsequently received the name "determinism".
The law of sufficient reason means that thought or judgment alone cannot be considered either true or false. In order to make it possible to assert truth or falsity, one must have at its disposal some rigorous proof.
A special procedure is recognized as evidence by which it can be established whether a thought corresponds to reality.
For example, the statement “Today is sunny” can be considered quite true if you look out of the window and, trusting the senses, make sure the judgment is correct.
However, such provisions are momentary and do not exhaust all cases of evidence.
A more complicated procedure for revealing the truth is such proof in which appeal to the senses is impossible. For example, an event has already taken place in the past or will take place in the future tense.
The judgment on sunny weather would sound in these cases: “It was sunny yesterday,” “It will be sunny tomorrow.”
In the first case, the evidence base exists, since you can rely on your own memory.
In the second case, the judgment is unproven, and therefore can not be considered either true or false. Regarding the weather for tomorrow, only a forecast, an assumption is possible. Probability based evidence is false.
When trying to justify the falsity or truth of thoughts and judgments, it is necessary first of all to turn to experiment, measurement, observation, research - i.e. comprehend things in their substantial aspect.
On the other hand, if the experiment reveals theoretical knowledge, which, by virtue of its generalization and proof, can be considered true, then it is possible to check judgments for truth by comparing them with theory. The law of sufficient reason in logic not only allows such an opportunity, but also allows you to treat it as a conceptually important action. In this case, it is necessary to trace the formal connection, the coincidence in form between the judgment and its theoretical evidence.
On a formal basis, it is possible to recognize in general all thoughts as related to each other, since they were all formulated. However, the principle of sufficient reason does not allow us to dwell on this step. The recognition of all thoughts as belonging to a common evidence base when empirical verification is impossible, will not provide either confirmation or refutation of the fact that they are proved. Therefore, it is impossible to verify whether they are true or false.