Logic world history definition9/20/2023 And that is pretty appealing to me.Īnyway, Bolzano’s analysis of logical consequence is a great step in the direction of constructing modern formal logic. Different rules will give you a different story when it comes to what’s valid and what’s not. Bolzano is really interesting here, because he says that it’s entirely a matter of convention. Now, it’s still very much an open question as to what you are allowed to change, and what you should keep fixed when you’re testing an argument. The premises are true but the conclusion is false on a Friday for example. This works sometimes but not all the time. Note that the closely related shapeĭoesn’t work, and we can see that it doesn’t work by looking at an example: Therefore Sally is putting her life at risk. If Sally is joining the army, she is putting her life at risk. Is valid because we will never step from truth to falsity no matter how we change the subject matter. If Sally is coming to the party, Jim will be happy. This is what Bolzano was trying to supply.)Īnyway, he argued that you can tell that an argument from premises to a conclusion is logically valid if and only if it never proceeds from truth to falsity no matter how you change the non-logical vocabulary in the argument. You can really only do this if you have a good understanding of how reasoning works. The 1800s involved mathematicians painstakingly going over old reasoning step-by-step to see if (and how) the reasoning worked, and to see where it might go wrong. (This was important for his project of understanding mathematics, and making it clearer, because mathematicians were getting into knots considering infinite numbers, infinitesimal numbers, and many other seemingly paradoxical things. He was the first philosopher to give a precise analysis of logical consequence in terms we would recognise today. But for my money (and in my discipline) Bolzano was worth much more than this. He’s probably best known for what he has done in mathematics: the precise definition of continuity when it comes to real-valued functions. Bernhard Bolzano (1781-1848)īolzano was a philosopher, mathematician and logician who had important things to contribute in each of these fields. “Great Moments in Logic” published online, 2004.
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