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In logic, you start with premises to obtain conclusions. But how do you know that the premises themselves are true?

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    There have to be a couple of dozen variations of this question already on the site, but the search facilities are so bad that I've given up on trying to find one. Feb 6 at 20:39
  • In general, premises don't need to be true. For instance, imagine I say: "When it's a sunny sunday, I go to the swimming pool." You can see this as a theorem, with premise "It's a sunny sunday" and conclusion "I go to the swimming pool". This theorem is true, and useful if you're interested in my sunday activities. Nevertheless, the premise is false today, since today is tuesday.
    – Stef
    Feb 6 at 22:21
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    Premises in an argument are just propositions. Asking how we know a premise is true is like asking how do we know any proposition is true? That is the subject matter of epistemology. The main ways are perception, memory, inference, testimony, reasoning.
    – Bumble
    Feb 6 at 22:33
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    There's plenty more to say than this, but my 2 cents worth would be: The same way we know conclusions are true Mar 10 at 9:13

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There is only the bad message. In short words: Logic does not provide a way to prove the premises. Logic cannot create new true statements beyond the premises. Instead, logic “milks” the premises to see what they contain.

The premises of a formal theory are named axioms. Axioms should be consistent with each other and with the rest of the statements, and they should be useful to derive what one expects to be true. But axioms cannot be proved, necessarily.

In former times, one thought that axioms were evident statements, true by intuition, and axioms would not need a proof. But evidence is a subjective property like certainty is. Evidence is not an objective property like truth is.

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  • But this leaves us paralyzed what would be the use of trying to milk premises if we don't know even if they are true or not and if we rely on axioms doesn't this mean anyone can set any axiom he wants a Christian might set the axiom that Christianity is absolutely true and then reason from that? Feb 7 at 18:47
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    @NeoGranicen You are right. And this axiom is indeed the basis of Christian religion: Jesus is the Word of God. - But the example also shows, that not everybody agrees to accept this statement as an axiom of his own worldview. The choice of axioms is not universally unique.
    – Jo Wehler
    Feb 7 at 19:02
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    does this suggest that there is no objective truth? Feb 7 at 19:05
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    @NeoGranicen Bad news: Yes, there is no objective truth. Good news: We do not need objective truth. We live on the basis of confirmed hypotheses.
    – Jo Wehler
    Feb 7 at 19:09
  • So if we want the nearest thing to true premises how can we do so? maybe empirical evidence would help but what other valid methods can we use? and how is a hypothesis confirmed and if it confirmed by observations cant it be that the next observation can destroy the whole hypothesis? Feb 7 at 19:14
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Bumble said in the comments:

Premises in an argument are just propositions. Asking how we know a premise is true is like asking how do we know any proposition is true? That is the subject matter of epistemology. The main ways are perception, memory, inference, testimony, reasoning.

This is the best response. Premises are just propositions, so any way in which one can show a proposition to be true suffices. Robert Audi would have a slightly different answer than our local logical expert: perception, memory, consciousness, reason (which includes inference), and testimony. Epistemologists frequently seize on what might be called brute facts that arise from immediate and spontaneous apprehension. If you glance out your windows and smell a fire, and see the fire, and the heat of the fire affects you, and you see firefighters running about dousing the fire with water, and then in the following argument:

P1. The house next door is on fire.
P2. The fire department has arrived and seems well trained and equipped.
C. Therefore, the fire will soon be extinguished.

The truth of the first premise might be taken as a brute fact. Or, you might not be sure of what you're seeing so you talk to the firefighters. Or, you may bring in a forensic specialist to collect evidence and testify. Or you may watch a video form your doorbell camera a week later to refresh your memory.

What's important to understand is that all premises are just logical propositions, so how they are true is covered by the standard epistemological toolbox including the various theories of truth. Now, often, we use a chain of reasoning so that that the premise of argument two is the conclusion of argument one. Euclid's Elements is historically significant because this sort of chain of reasoning is systematic, effective, and thorough. Here, we can be sure that theorem is constructed on top of theorem, and the whole system of premises and conclusions rests on several axioms. (Five, the parallel postulate being the interesting one). Such reasoning is considered foundationalist.

So, ultimately, premises are just propositions, and they are proved in accordance with one's theory of evidence.. In chained reasoning, they are generally the products of prior inference. And ultimately, the question of how reason is constructed across multiple arguments is of great philosophical interest to which the terms Agrippan tropes and Münchhausen trilemma.

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In general, premises don't need to be true.

For instance, imagine I say:

When it's a sunny sunday, I go to the swimming pool."

You can see this as a theorem, with premise "It's a sunny sunday" and conclusion "I go to the swimming pool".

This theorem is true, and useful if you're interested in my sunday activities. Nevertheless, the premise is false today, since today is tuesday.

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  • but when you are trying to reach truth you need to be sure the premises you are reasoning from are true I'm not talking here about if the argument is valid or not I'm talking about how to reach true conclusion that we know came from true premises? Feb 7 at 18:50
  • @NeoGranicen Yes. If you know that P is true and that P => Q is true, then you can conclude that Q is true.
    – Stef
    Feb 8 at 10:19
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We can’t know that the premises are true — rather, we assume that they are true for the purpose of the exercise.

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    I'm not downvoting, but if premises are conclusions from other arguments, then we can know they are true. That's why in mathematics, we can use a theorem as a starting point for a lemma or corollary, or additional theories.
    – J D
    Mar 8 at 15:22
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As many others have pointed out, there is no way to prove that the premises of any argument are true. The choice of our premises cannot be made 'rigorously', they are accepted on faith, if we truly believe them, or else chosen 'for the sake of argument' if we are considering a hypothetical.

It is possible, however, to show that certain premises are self-contradictory. This can lead to the rejection or modification of premises, and is always a step towards the truth. When we are dealing with hypotheticals, we expect this to happen, but when we are dealing with dearly-held beliefs, it's quite the shock!

The first category is, in my mind, much more important, especially if we are talking about premises that define our values. Our notions of what is 'right' and 'wrong' can be shown to be contradictory, or to lead to undesirable outcomes even by their own standards, but they cannot themselves be 'proven' correct.

Ultimately, our premises are chosen by intuition. We just have to make our best guess. Hopefully we can correct for our own biases and filter out the noise of current intellectual fashion. Unfortunately, we have no way of escaping our ignorance. There's always going to be something that we don't know we don't know. If you are of a materialist persuasion, this basically means we only stumble on the truth by accident. If you believe we have souls, you can be more hopeful: there may be a divine element in us that guides us towards truth.

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