The logic of infinity is not only related to epistemology. Self-evident truths break any regression of “Why?” questions. You can start from certain premises with known truth values. Chains of reasoning can be grounded in a bedrock foundation: logical necessity. While it’s true that an infinite regress is a logical error, not all propositions are contingent truths.
Of course, if you follow my work, you know I strongly disagree.
No non-contingently true premise exists, therefore we cannot know anything at all. Many skeptical philosophers have profoundly concluded: therefore, all knowledge is without foundation. There’s no reason to believe any proposition in an infinite chain – because there’s no real justification to be found, by definition. Thus, by logical necessity, any argument which falls into an infinite regress is foundationless. If you ever end up with a non-contingently true premise, you’re not dealing with an infinite regress. If we were to ask, “ Ultimately, what is conclusion Z justified by?”, the only logically consistent answer is to say, “Nothing”. It will never work, no matter how many zeros you add together.Įvery proposition is contingent – contingent on other contingencies. It’s like adding up an infinite amount of 0’s to try to get 1. It’s a chain of empty vessels regardless of how many there are, you’ll logically never end up with justification for a single proposition. The error is similar to the Liar’s Paradox you never end up with a concrete proposition to evaluate as true or false.īy definition of what we mean by “infinity”, no proposition contains a truth value by itself. If each link in the chain is true, then we can trust the conclusion (assuming the reasoning is sound).īut when we interject infinity into the chain, we’re presented with a problem: we’re never given a reason to believe any proposition in the first place – i.e. If there’s a falsehood anywhere in the chain, it poisons every conclusion which follows. Each proposition is like an empty vessel, dependent on the truth-value of the premise before it. This means, each proposition in the chain – without exception – is contingent on its preceding premises. If proposition X is false, we’ve no reason to believe proposition Y is true.Īnd of course, the same is true of proposition X. We’ve only one reason to believe it’s true: if, and only if, its justifying premise – proposition X – is true. If proposition Y is false, then we’ve no reason to believe conclusion Z is true. We’ve only one reason to believe it’s true: if, and only if, its justifying premise – proposition Y – is true. That might not seem intuitive, so I’ll explain.Įxamine conclusion Z. If this chain of reasoning has no end, then we’ve no reason to believe proposition Z or any other proposition in the chain is true. For every proposition, Joe can respond, “And what’s your justification for that?” Joe: “And what’s your justification for proposition X?”Īnd so on, ad infinitum. Joe: “And what’s your justification for proposition Y?” Joe: “What’s your justification for proposition Z?” One logical error which is commonly misunderstood, and often outright defended, is the infinite regress. The clearer you think, the clearer you see the world, the clearer you see the errors in other people’s reasoning – which tend to be numerous, repeated, and sometimes aggressive. On the one hand, it’s essential to understand logical errors.
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