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I'm pretty new to logic. I recently purchased "A Concise Introduction to Logic" by Patrick Hurley based on reviews. So far I'm liking the book. I'm really focusing hard on the first chapter to get a good foundation, and I have a concern: if premises must also be a valid conclusion with valid premises, can we ground truth on anything?

Using an example from the book:

All film stars are celebrities.
Halle Berry is a film star.
Therefore, Halle Berry is a celebrity.

So, I'm thinking of two scenarios about how the premises are considered. The first is a matter of definition. By the way we define "film stars" and "celebrities" the state of being verb "are" simply draws our attention to the state condition that "A" is "B".

The other scenario I envision is where each premise must also be a valid conclusion:

Someone known by many people in the public is a celebrity.
Film stars are known by many people in the public.
Therefore, all film stars are celebrities.

My concern is that it would lead to an infinite series of arguments and we would just end up talking in circles about nothing.

People in the public watch films.
By watching films, one knows the actors.
People in the public know the actors in films.

Do we eventually say that we are satisfied that the premise of a conclusion can stand on its own, or do we really just not continue this exercise infinitely because we would rather do something else with our time?

  • The question is incomplete: need always should be followed by for. In order for an argument be meaningful, indeed. Just to be a correct deductive conclusion - no. – rus9384 Aug 2 '18 at 17:47
  • Indeed, no. en.m.wikipedia.org/wiki/Münchhausen_trilemma – CriglCragl Aug 3 '18 at 8:42
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    The question seems to conflate validity with truth. In logic, "truth" is not such a useful concept. Your conclusions are only as true as your premises, and then only if your logic is perfect. Thus, an easy way to disprove something is to disprove a premise. But the contrapositive (you can prove something by proving its premises) is normally impossible. Thus, while logic is a tool of Philosophy, you need more than logic to get at truth. (Basically, I just explained why I only took one course in the Philosophy department.) – Jeffiekins Aug 3 '18 at 18:29
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Short answer : NO.

Arguments are either valid or not.

Premises and conclusions are sentences, and thus they are either true or false.

See Valid argument :

In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. [see also Hurley, page 44]


Regarding the issue about "grounding" discussed in the text, we have to note that the definition does not say nothing about the way we have to use in order to establish the truth of the premises.

The example from the book you are quoting is an instance of the valid "schema" :

All As are Bs;

HB is an A.

Therefore HB is a B.

How we know that "All As are Bs" ?

It can be a "linguistic convention" : "every unmarried man is a bachelor".

It can be a natural fact or law or it can be an inductive generalization : "all ravens are black".

But all this is not relevant for the validity of the argument : logic is not Theory of Knowledge.


Related : Aristotle and knowledge :

Aristotle argued that knowing does not necessitate an infinite regress because some knowledge does not depend on demonstration:

Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. [Posterior Analytics I.3 72b1–15]

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    Does the same hold true for the soundness of the argument? (TIL: I did not use the strict logical definition of validity) – NonSecwitter Aug 3 '18 at 16:47
  • Re-reading this, I think the answer to my follow up question is that an argument can be sound without using a formal argument to prove the truth of the premises. I could use a formal argument, or I could base truth on knowledge in the ways you mention. – NonSecwitter Aug 3 '18 at 18:32
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Validity in logic is a somewhat tricky notion to understand as it is different – though only subtly – from related, pre-theoretic notions. For instance, not every valid argument is ‘convincing’ or ‘useful’ in a pre-theoretic sense, nor is every ‘convincing’ or ‘useful’ argument valid. (See examples below.)

To address your question more directly, suppose that φ is a premise in some (valid) argument. Then we can easily find a second valid argument of which φ is the conclusion: ‘φ, therefore φ’ would be an example. This is valid (because the conclusion is true if the premise is), but of course it’s not very useful or informative. So, in that sense, the answer to your question is yes: the premises of every (valid) argument are themselves conclusions of a valid argument.

I realise this doesn’t address your concern about an infinite regress; but bear in mind that, for an argument to be valid, its premises and conclusion need not be true! The following is an example:

P1: Trump is a Democrat.
P2: All Democrats live in Texas.
C: Trump lives in Texas.

This is a valid argument (of the same form as your film star argument), but neither the premises nor the conclusion are true. It’s nevertheless valid because, if the premises are true, the conclusion must be true, also. A lot of (introductory) logic is concerned with spelling out this sense of ‘must’, but that’s beyond the scope of my answer. (Note though that it doesn't involve special definitions for 'film star' or 'celebrity'.)

Validity is different from soundness: an argument is sound if, in addition to being valid, it has only true premises (and hence a true conclusion). Every sound argument is valid, but not every valid argument is sound. An argument could have true premises and a true conclusion, but still fail to be sound – because it fails to be valid. (E.g.: ‘Trump is a Republican. Thus, London is in England’.) If φ is true, ‘φ, therefore φ’ is sound. Hence if φ is a premise in a sound argument, it will also be the conclusion of a sound argument.

7

Do we eventually say that we are satisfied that the premise of a conclusion can stand on its own, or do we really just not continue this exercise infinitely because we would rather do something else with our time?

I think there are two ways in which this can be understood. Your question isn't one about logic, because logic doesn't say anything about the premises or where they come from. Instead, it's either a question of epistemology or a practical issue of how to make philosophical arguments.

The epistemological issue

The idea is this: if we depend on some premises in order to reach conclusions, how are we justified in taking these premises? So, it's an issue of the structure of knowledge. This question goes all the way back to Ancient Greece to Pyrrhonian scepticism. The basic idea is called Agrippa's Trilemma or Münchhausen Trilemma. Wikipedia will do here.

The article already mentions foundationalists and coherentists. Foundationalists (about justification) believe that we can in fact go back after every premise all the way until we get some sort of basic truth. Some "modest" foundationalists will make a weaker claim, but we can take out of it that this is how we can structure justification.

Then there are coherentists. Those generally believe that justification is holistic, so that we can't go back to basic truths, but that instead a good justification belongs to a non-contradictory net. In the trilemma, this is kind of the circular solution.

Those are the basic two directions. Apart from that, other theories try to combine the two, circumvent the problem, or try to get rid of the need for justification. There's also infinitism, which thinks that there are justificatory chains (just like foundationalism) that just, well, don't come to an end.

The practical issue

I'll keep this short, mainly because there aren't any set positions for this. (Although there's another epistemological issue related to this, but I'll bracket that.)

I believe this very much depends on the claim that we're making and what we want to achieve with our argument. If we want to think about issues for ourselves, then simply using what we're already holding as plausible can be just fine. If we want to join the discussion about an issue then we should be clear about our starting points and not be too far off from the discourse. If we want to specifically convince someone then we should go back until we think that there's a consensus about the starting point (or until we are okay with with dissent).

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This known as the ”infinite regress” problem in Epistemology.

The regress argument (also known as the diallelus (Latin) or diallelon, from Greek di allelon "through or by means of one another") is a problem in epistemology and, in general, a problem in any situation where a statement has to be justified.

According to this argument, any proposition requires a justification. However, any justification itself requires support. This means that any proposition whatsoever can be endlessly (infinitely) questioned.

Source: Wikipedia

There are numerous counter-positions that argue different definitions and requirements to address this issue; Foundationalism, Coherentism, Infinitism and Skepticism. These are discussed in the above article.

A good example of Infinitism is the World Turtle proverb.

A father and son are discussing the world. The father explains:

*- “We build our houses on the earth, the earth rests on an elephant, the elephant on a tortoise.”

*- “And what does the tortoise rest on?”

*- “Another, larger tortoise. My boy, it’s tortoises all the way down.”

Johann Gottlieb Fichte, in pondering the infinite recursive issue, refers to this concept on this exact philosophical question:

"If there is not to be any (system of human knowledge dependent upon an absolute first principle) two cases are only possible. Either there is no immediate certainty at all, and then our knowledge forms many series or one infinite series, wherein each theorem is derived from a higher one, and this again from a higher one, et., etc. We build our houses on the earth, the earth rests on an elephant, the elephant on a tortoise, the tortoise again--who knows on what?-- and so on ad infinitum. True, if our knowledge is thus constituted, we can not alter it; but neither have we, then, any firm knowledge. We may have gone back to a certain link of our series, and have found every thing firm up to this link; but who can guarantee us that, if we go further back, we may not find it ungrounded, and shall thus have to abandon it? Our certainty is only assumed, and we can never be sure of it for a single following day."

Fichte, J. G. (1794). Ueber den Begriff der Wissenschaftslehre oder der sogenannten Philosophie (Concerning the Conception of the Science of Knowledge Generally) (A. E. Kroeger, Trans.).

Source: Wikipedia

  • This relates to the answer provided by Mark H. – PV22 Aug 4 '18 at 17:53
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I am not sure whether I fully understand your question. You ask about valid premises and conclusions, but a "valid conclusion" or "valid premise" is comparable to an "ambitious number", inasmuch none of these expressions really makes sense.

Premises and conclusions may be true or false, but may not be valid. There is no such thing as a valid conclusion, neither is there a valid premise.

"valid" in logical parlance is exclusively an attribute of arguments. As you know, an argument is a compound of one or more premises, and one conclusion.

Conversely, an argument cannot be true or false. It can only be valid or invalid. Its validity does not depend on the truth of its parts. An argument can be valid even if none of its parts are true.

Is it possible that you confuse "true" with "valid", and "valid" with "sound"?

  • Yea, I used the vulgar vernacular sense of valid without realizing it :P – NonSecwitter Aug 3 '18 at 17:06
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If I understand you correctly, your concern is basically: "how can we ever say that an argument is sound, given that that would require us to figure out that the premises are true .. which would seem to require a sound argument to demonstrate their truth ... and hence we obtain an infinite regress?"

Or, to put it more simply: "How can we stop a 3 year old from endlessly repeating "But why?""

One answer is that there are plenty of things we can use as 'ultimate' or 'basic' premises:

  1. Observations: if you and I observe that my shirt is red, then we can use that as a starting premise ... no need to construct an argument to argue that my shirt is red

  2. Definitions/Axioms If we define a square to have four corners, then we can use that as a basic premise: a square has four corners. Especially in mathematics we often use axioms: statements we simply assume to be true, just so we can explore some 'world'

  3. Concensus/Common knowledge: While certain truth is very nice, in practice we realize the problems with actually obtaining it. So, in practice, we often will accept any premises we all 'agree to'. For exmaple, many thousands of years ago we all believed the earth was flat ... and so it was perfectly acceptable to start an argument with 'The earth is flat'.

Of course, I could just say that 'facts' are what can be used as 'starting' premises ... but facts typically come in one of these three forms.

0

No. You could, for example, introduce the premise P & ~P and conclude by contradiction that ~[P & ~P].

protected by Philip Klöcking Aug 3 '18 at 14:03

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