Why Despite Advanced Logic and Mathematics, People Struggle with Correct Inferences?

The question of why, despite the incredible advances in fields such as logic and mathematics, people still frequently fail to think correctly and make accurate inferences, raises an interesting paradox. This is not a failure of logic or mathematics; it is a problem of humanity's lack of critical thinking—skill which can be cultivated and developed.

The Parallels: Sports and Modern Life

The analogy often drawn, similar to questioning why athletes continue to improve yet children remain overweight, is apt. In today's modern society, social and economic specializations enable individuals to be more skilled in narrower domains, even as they become less productive or capable in broader contexts. Just as we used to grow crops, now we primarily serve coffee or manipulate spreadsheets. This shift reflects a broader convergence towards a society where false or artificial constructs reign.

Brilliant astrophysicists and groundbreaking theorems, while awe-inspiring, have little impact on our everyday reality. References from the virtual world, derived from artificial realities, do not provide tangible advancements in our true world. Consequently, the logical and critical thinking skills we should be developing are being overshadowed by the pseudo-logic prevalent in media and the internet.

The Role of Information and Media

Our logical and critical thinking abilities are increasingly shaped by the vast amounts of information we consume from media and the internet. While we develop some logical skills from handling this information, the thinking involved is often non-productive and lacks rigor. This is frequently not about understanding the truth but about winning arguments and defeating opponents, regardless of the correctness of our positions.

A Logical Analysis of the Problem

To address the original question more methodically, let's break it down using logical reasoning:

Why if P does not imply Q happens?

The reason is there is no implication connecting P to Q. Perhaps we should delve even deeper:

Suppose Px “knows advanced logic” and Qx is “makes correct inferences.” The question then is:

Why if there exist people x such that Px is true, is it not the case that for all people y Qy?

Even the implication Px Qx is not strong enough to guarantee this is correct. Here's an example model:

Charlie: knows advanced logic, false; makes correct inferences, true Donald: knows advanced logic, false; makes correct inferences, false Edgar: knows advanced logic, false; makes correct inferences, true

In this model, Px Qx holds true. However, it is evident that there are individuals (e.g., Edgar) who do not make correct inferences despite not knowing advanced logic. Therefore, even if a perfect reasoning scheme exists, not everyone is trained in it, suggesting:

“Not knowing logic does not prevent people from making inferences anyway.”

Furthermore, the implication Px Qx is questionable as well, and the original poster's assumption might be flawed. Perhaps a better question to ask would be:

Why, if you studied logic, did you ask a question that presupposes an implication that does not hold?

Resolving this introspective question may provide clarity to the original issue.

Conclusion

While advanced logic and mathematics can undoubtedly help in making accurate inferences, the lack of critical thinking skills can overshadow these benefits. Developing a robust, critical thinking mindset is essential for proper logical reasoning and informed decision-making. This skill is not innate but can be learned and honed. Recognizing the limitations of pseudo-logic and the importance of genuine critical thinking will help move us towards a society that values accurate reasoning and effective problem-solving.