The foundations of logic, both modern and classical, are studied in higher education in the first courses. To learn wisdom and answer important questions of the subject "Fundamentals of Mathematical Logic" is the primary task of the student.
All scientific research is based on logical laws.
Naturally, the basis of logical analysis is the definition of truth, but it is also true that man perceives truth as a state of clarity.
Logical analysis is similar to therapy - it gives us the opportunity, at least for a while, to lose the obsessive state of misunderstanding and the vagueness of what other people write or say. We learn the basics of logic in order to further understand and demonstrate to others the significance of analysis in the “cure” of problems arising in constant communication and often resulting from the confusion and darkness of our speech. There is no desire in logic to infinitely teach everyone to think correctly and speak beautifully, but what is in her power is to develop the skill of attentive attitude to the uncertainty and ambiguity of those terms that we use daily. If the foundations of the algebra of logic cannot teach us to think and think mathematically, then at least they will help us to consistently and accurately express our own thoughts. No matter how complicated the apparatus of modern mathematical logic is, its ultimate goal is to analyze communication between people in its intellectual aspect.
To achieve the goal that you set for yourself, to learn the basics of logic can only be done in practice - in the process of comprehending all your own difficulties that appear as a result of the process of “speaking out thoughts”. In this regard, it should be noted that solving problems is by no means a panacea in the process of learning the basics of mathematical logic.
For those who nevertheless (despite all that is said a little above) want to understand the essence of the process of expressing thoughts and learn the basics of logic, we can advise you to always adhere to these rules:
1. Always remember that the development of the theoretical part as well as practical solutions to problems make sense only in the context of "growing one's own understanding." This means that both mechanical memorization of the theory and an algorithmized approach to solving problems are equally forbidden. Often an erroneous decision is much more significant in terms of personal growth than the correct, but not entirely thought out result.
2. All exercises must be performed consistently and exclusively from the beginning. It makes no sense to try to solve the problem from the next section without assimilating the previous material.
3. It is easiest to understand the essence of all logical operations, techniques and rules in the process of solving problems. The more solved problems you have in your arsenal, the better you learn the basics of logic.
4. It is also useful to know the following: no matter how many logical tasks you solve in the process of cognition, you will not achieve an automatic understanding of all logical problems, if they are not accompanied by your own mental activity that seeks expression.
5. Finally, you should pay attention to such a rule, which has not lost its relevance to this day, which was proposed by L. Carroll: “If possible, find a“ brilliant ”friend with whom it will be easier for you ... to discuss the difficulties that arise. Verbal discussion is an ideal way to resolve all the most difficult issues. When something is baffling (it doesn’t matter, in logic or in another area), I discuss this problem out loud, even if I am completely alone. You can explain everything to yourself clearly! In addition, explaining to himself the solution to the problem, the person shows amazing patience. ”