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The connection between logic and philosophy has been debated by logicians and philosophers since the two subjects were first identified. Some people believe that logic is a kind of philosophy, while others believe that logic is a tool used in philosophy. This is a problematic question, because many people are under the impression that logic provides access to objective truth. Logic is often applied outside of philosophy, but whether it is considered philosophy in these other fields is largely a matter of opinion.
In order to understand the connection between logic and philosophy, it is important to first understand what each study entails. Logic is the study of reasoning, whereas philosophy is better characterized as a study of general problems. Both of these disciplines involve using reasoning, but the rules of reasoning in logic are sometimes independent from the rules of reasoning in philosophy. Likewise, whereas logic often has specific forms concerning what is and is not a valid conclusion, philosophy is more open.
Given these differences, the connection between philosophy and logic would seem to be one of reliance. Philosophy relies on logic in order for its claims to be true, but it does not rely on any specific system of logic in particular. Without reasoning, there cannot be valid solutions to problems faced by philosophy.
Even so, it could be said that the relationship between logic and philosophy is actually the reverse. Logical systems might be said to depend on philosophical solutions, because logic has been conceived of in many different ways. This understanding of the connection is perhaps less common but no less true. In essence, the science known as logic is a philosophical solution to the problem of reasoning.
It is also possible to conceive of the connection between logic and philosophy in a historical sense, looking at the many philosophers who have pondered this problem. Aristotle, Kant, and Hegel all considered logic in their times. In this case, philosophy is related to logic through historical proximity, and both sciences affect each other.
Both logic and philosophy are exercises in thought, and both depend on individual reasoning for their success. While logic does not usually concern itself with the meanings of its conclusions, philosophy seeks to solve problems using logical processes. This perhaps is the biggest difference between logic and philosophy: While logic looks at the process, philosophy desires the conclusion. Even so, these two disciplines are deeply intertwined and cannot be easily separated.
The study of logic can employ formulas, such as A therefore B if not C, to arrive at a definitive answer. It seems this would give weight to the theory mentioned in the article that logic is a tool used in philosophy, as well as in quantifying the way we view the world.
In this sense, logic can be viewed as concrete, while philosophy is very personal - based on our individual beliefs and observations of the world around us.