8

I am beginning to read the book titled forallx An Introduction to Formal Logic by P.D. Magnus. This is an open source book. On page 4 Magnus states:

enter image description here

In this open source book found here: https://math.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Claassen_and_Ikeda)/05%3A_Logic/5.01%3A_Logic_Statements the author states that opinions don’t count as sentences because one person might consider it true while another might consider it false. enter image description here This author wouldn’t consider “Rhubarb is tasty.” as a sentence. So which definition is correct to use? Thank you!

6
  • 2
    Do you mean a statement?
    – g s
    Commented Dec 18, 2023 at 2:54
  • Yes. In the first book they used the word ‘sentence’ and in the other they used the word ‘statement’. I figured they were talking about the same thing.
    – Dr. J
    Commented Dec 18, 2023 at 2:56
  • The second text sounds too dogmatic, I would say. But see about Jörgensen’s dilemma for the debate. Commented Dec 18, 2023 at 2:57
  • I’ll read up on this! Thank you for your response!
    – Dr. J
    Commented Dec 18, 2023 at 4:27
  • 1
    no "Rhubarb is tasty.” can be considered a sentence: we can assume "other alternatives" irrelevant, and it has (..can have... individually differing) "boolean value".
    – xerx593
    Commented Dec 18, 2023 at 11:46

5 Answers 5

17

Magnus is correct. Lippman seems to be suffering from the very confusion that Magnus warns about (apparently Lippman is a mathematician rather than a philosopher or logician). Logic is all about form. A series of sentences like

(1) Every living thing is beautiful.

(2) A hagfish is a living thing.

(3) Therefore a hagfish is beautiful.

is a valid argument regardless of whether the premises are true or not, and regardless of whether it is even possible for the premises to be true or not. Here is another valid argument:

(4) All borogroves are slithy.

(5) Nothing slithy is vorpal.

(6) therefore, no borogrove is vorpal.

The reason these arguments are valid is because they have a valid form. Lippman seems to think that logic is about making sound arguments--arguments where the premises are true and the form is valid--but that is not what the study of logic is, at least not in the modern sense.

One way you can tell that Lippman is wrong is because validity is preserved through substitution of names. So if this is valid,

(7) The house is red.

(8) All red things are blue.

(9) The house is blue.

(and it is valid), then so is the same argument substituting red for beautiful in all occurrences:

(7') The house is beautiful.

(8') All beautiful things are blue.

(9) The house is blue.

5
  • Thank you for your response! This makes sense. When you say “regardless of whether it is even possible for the premises to be true or not” what do you mean by this? Could you explain this further because I have some confusion? From reading the text from Magnus he said that a sentence has to be either true or false. So wouldn’t the premises have to either be true or false? Thank you!
    – Dr. J
    Commented Dec 18, 2023 at 4:27
  • I'm referring to Lippman's claim that an opinion isn't true or false. Magnus may have been a bit cavalier in saying that statements have to be true or false. They only have to have the form of true or false sentences. That's what my example of borogroves was intended to illustrate. Commented Dec 18, 2023 at 4:31
  • Ok makes sense. Maybe I misinterpreted what Magnus was meaning. When you say that statements have to have the form of true or false sentences all your meaning is that the sentence ‘can’ be true or false? For example in your example, the premise “All borogroves are slithy.” can be true or it can be false. Whereas something like “Why is the sky blue?” can’t be true or false because it’s a question.
    – Dr. J
    Commented Dec 18, 2023 at 4:36
  • 1
    Upvotes for Jabberwocky. Commented Dec 18, 2023 at 11:50
  • 1
    NB in the original Jabberwocky it was "borogoves" that were mimsy (no "r" after the "g").
    – psmears
    Commented Dec 19, 2023 at 11:56
9

Magnus and David Gudeman are right, but Lippman has correctly alerted to a place where errors can sneak in, so I thought it worth adding an explanation of what I suspect was bugging Lippman about opinions.

If the statements mean exactly what the words mean in that sentence structure and nothing else, then they're fine.

However, if you interpret statements which are usually taken to imply prepositional phrases the way that they are generally meant in common language, then you can make an argument which is fallacious or which has a false premise seem like it it is a valid argument with a reasonable premise. Since statements of opinion routinely omit an implied prepositional phrase ("to me"), they're prone to this sort of abuse or error. The problem, however, is not the opinion. It's the implied preposition.

Consider:

  • The dog is outside.

  • That which is outside is not inside.

  • Therefore, the dog is not inside of the fence.

Something seems wrong about this, but it's not obvious what until you explicitly add the prepositional phrases that your experience with English fills in subconsciously.

  • The dog is outside of the house.

  • That which is outside of a boundary is not inside of that boundary.

  • Therefore, the dog is not inside of the fence.

Obviously this is a blatant non-sequitur, while

  • The dog is outside of everything: the house, the fence, the city, the country, the atmosphere, the solar system, etc, etc.

  • That which is outside of a boundary is not inside of that boundary.

  • Therefore, the dog is not inside of the fence.

is valid but has a blatantly false premise.

Similarly

  • Rhubarb is tasty [to me - true]/[to everyone - false]

  • That which is tasty [to a person] is liked [by that person]

  • Therefore, Lippman likes rhubarb.

Which is fallacious if we take "to me", and valid but has a false premise if we take "to everyone".

7
  • Thank you! This makes sense. One part that I wanted to ask for clarification was when you stated “If the statements mean exactly what the words mean in that sentence structure and nothing else, then they're fine”. Could you explain this further? Thank you!
    – Dr. J
    Commented Dec 18, 2023 at 16:03
  • @Dr.J I meant basically "if no prepositional phrase is implied, or if the specific prepositional phrase is implied by the word itself, not by context". For an example of the first, "God is good" nearly always implies moral goodness with no implied prepositional phrase, while "Right here is good" implies "satisfactory [to my aesthetic sensibilities or for my practical purposes]". For the second, off the top of my head a naked "next" as in "David is next" always implies "next in the queue", so omitting the preposition is safe.
    – g s
    Commented Dec 18, 2023 at 16:27
  • I see. So then would the example Magnus provided be considered a statement? Since we could use “to me” or “to everyone” as you pointed out.
    – Dr. J
    Commented Dec 18, 2023 at 19:08
  • @Dr.J since Bumble kindly wrote an extended extension to my extension which answers that, I shall pass the buck on to Bumble!
    – g s
    Commented Dec 18, 2023 at 21:17
  • 1
    Typo: "non sequitOr" should be "non sequitUr"
    – psmears
    Commented Dec 19, 2023 at 11:56
4

I was reluctant to add an answer to this question, because I agree both with David Gudeman's answer and also with the answer from g.s. that acts as a rider to it. But a couple of further points are relevant.

One of the reasons many philosophers distinguish between a sentence and a proposition is to avoid the ambiguities that may arise when sentences are uttered by different people. A simple example of this occurs when resolving indexicals. Suppose Alice says, "It is raining where I am right now", and Bob says, "It is not raining where I am right now". These utterances are not contradictory because they contain the indexicals 'I' and 'now'. It would be possible to turn these into sentences with specific places and times and then there would be no contradiction. We can describe this situation by saying that while Alice and Bob have uttered the same sentence, they have expressed different propositions.

Now suppose Alice says, "Rhubarb is tasty" and Bob says, "Rhubarb is not tasty". We may resolve the apparent contradiction by saying that Alice is expressing the proposition that Alice finds rhubarb tasty, while Bob is expressing the proposition that Bob does not find rhubarb tasty. The sentences, "Rhubarb is tasty" and "Rhubarb is not tasty" are contradictory in formal logic, but the propositions they express are not, when uttered by different people.

Incidentally, in this example, Alice and Bob are still disagreeing with one another, even though they are not actually contradicting each other. Each is performing a speech act: Alice is affirming the tastiness of rhubarb, and Bob is denying it. These speech acts conflict, but not all conflict is contradiction.

Apart from the issue of opinion, Lippman commits a howler by saying, "the truth of a statement is established beyond ANY doubt by a well-reasoned argument". Good grief. What world is he living in? In the world I live in, nothing, or almost nothing, is established beyond any doubt. He is making the elementary error of confusing logic with epistemology. Logic is in the business of telling you what follows from what. It is not directly concerned with whether a proposition is true.

2
  • Ok I think I get the idea. So in the example Magnus provides he states “Rhubarb is tasty.” is a sentence. This can be true or false so it is a sentence. However the sentence “Rhubarb is not tasty.” contradicts “Rhubarb is tasty. However without specifying Alice or Bob they are ambiguous. But they are still sentences because they “can” be true or false? Am I understanding this correctly?
    – Dr. J
    Commented Dec 18, 2023 at 23:46
  • Yes. "Rhubarb is tasty" and "Rhubarb is not tasty" can be considered contradictory sentences in formal logic. So one is true, one is false. Logic is not concerned with what reasons you might have for believing a sentence to be true, or whether it is a matter of opinion, an established fact or just a hypothesis. But the same sentence when uttered by different people on different occasions may express different propositions. Unfortunately, the word 'proposition' is itself used in many different ways by philosophers.
    – Bumble
    Commented Dec 19, 2023 at 0:51
2
  1. I consider Magnus‘ definition of a “sentence” to be problematic.

    If “Rhubarb is tasty” is declared as an opinion-based statement and if it qualifies as a “sentence”, then also the negation “Rhubarb is not tasty” is a sentence.

    As a consequence, the truth-value of a sentence does not depend only on the sentence itself, but it depends also on the speaker of the sentence. That’s no longer the basic approach of logic.

    Hence I do not accept Magnus’ definition of “sentence” and vote for Lippman’s definition which conforms to the usual approach of logic.

  2. Note: If Magnus changes “Rhubarb is tasty” to “Jack says that Rhubarb is tasty” then he obtains a sentence also in the sense of Lippman. And possibly that’s what Magnus wants to use as input for his logic.

2
  • 1
    As David Guderman's answer says, the definition Magnus is using is the formal definition in logic. "Rhubarb is tasty" can be a premise or conclusion in a syllogism, and so it is a sentence under the formal definition. The individual words/phrases are essentially variables and operators, and their meaning is irrelevant; this is why David points out that the validity of a syllogism is preserved through substitition of names. "Rhubarb is tasty" is thus equivalent in meaning (from this perspective) to "Grazinkto is sprooff", or anything else of the form "A is B".
    – Idran
    Commented Dec 18, 2023 at 16:20
  • 1
    @JustinHilyard See plato.stanford.edu/entries/truth/#TruBea section 2.1 stating that sentences are truth-bearers. The OP's question is about "sentences", they are more than just arbitrary variables.
    – Jo Wehler
    Commented Dec 18, 2023 at 18:05
0

As a tangent, things get interesting if you consider that Lippman may be trying to push a logical positivist agenda. Perhaps Lippman considers 'proposition' and 'statement' to be synonymous. If you look at it like this, then a statement like 'Rhubarb is tasty' is not literally significant/cognitively meaningful (from Ayer's criteria in Language, Truth, and Logic), it is more or less the same as a statement like 'borogrove vorpal vorpal borogrove'. 'Rhubarb is tasty' doesn't count as a statement or proposition in this case. The language of logic depends not only on connectives, but also other things (propositions in the case of propositional logic or variables, names, etc for predicate logic). Like Bumble says, "the truth of a statement is established beyond ANY doubt by a well-reasoned argument" is a bad sentence, ignore it.

There's a bit of philosophy of language for you.

1
  • Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center.
    – Community Bot
    Commented Dec 20, 2023 at 9:12

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .