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I often see the word "assertion" in books of philosophy of language or logic. They may list a sentence like

Snow is white.

Then somewhere in the context, they may write "assertion of the sentence". I'm confused about the meaning of the word "assertion". In the following sentences, which is equivalent to which?

  1. Snow is white.
  2. "Snow is white" is true.
  3. assert snow is white
  4. assert "Snow is white" is true
  5. think/believe snow is white
  6. think/believe "Snow is white" is true
  7. say "Snow is white"

Based on my understandings of the other answers, I give some thoughts(not necessarily true) on my question. A sentence listed on a single line is an assertion like

Snow is white

But when describing the assertion somewhere in the context, we cannot write "Snow is white" is ... because that is describing a sentence not an assertion. We cannot either write Snow is white is ... because it is not correct in syntax. It seems the only way to repeat the assertion in context is the assertion that snow is white(or the assertion of "Snow is white") is .... That is why the word "assertion" frequently occurs in context.

So, 1,2,3,4 in the question are equivalent to each other(1,2 are equivalent according to Tarski's T-Scheme, as are 3,4). Assert is stronger than think/believe which are stronger than say.

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    Snow is not white but it is white, don't be confused. If it is books of philosophy of language, it can be semantic like 6 think/believe "Snow is white" is true. If it is logic, it needs context, "snow is white" is not enough. Or you can add (why) snow is white or (if) snow is white, or else relevant. Jan 31, 2023 at 15:23
  • Or modern fashionable (highly likely) snow is white. Jan 31, 2023 at 16:05
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    According to the deflationary theory of truth, they're all more or less equivalent to each other, and that's it, there is no further notion of truth aside from this semantic word game.
    – Kevin
    Feb 1, 2023 at 7:09
  • Same here. Assertion = "valid affirmation" seems to solve most of my own issues. Regarding your cases, they are not much related to the main question, the meaning, except its linguistic usage in different contexts: 1. assertion; 2. assertion that 1 belongs to the system "truth"; 3. Imperative asking to assert 1; 4. equivalent to 2 using 3; 5. Imperative using thinking; 6. equivalent to 2 using 5; 7. Imperative verbally stating 1.
    – RodolfoAP
    Feb 1, 2023 at 8:30
  • What about: """Snow is white" is true." is true." is true.
    – Stef
    Feb 1, 2023 at 16:49

7 Answers 7

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A very rough approach is the following: humans use sentences, i.e. expressions made of words (spoken or written) in many contexts, i.e. speech acts.

See Assertion: "Asserting is the act of claiming that something is the case. [...] We make assertions to share information, coordinate our actions, defend arguments, and communicate our beliefs and desires."

When we use a sentence to express "facts" of the world, we say that the sentence expresses a proposition.

See also Facts and States of Affairs as well as Proposition.

Recently, the old philosophical term "judgement" (see e.g. Brentano’s Theory of Judgement) has been revived so that assertion and judgement are strictly linked.

The speech act of assertion is the linguistic counterpart to the notion of judgement: acknowledging the truth of a thought or proposition.

See Per Martin-Löf, Truth of a Proposition Evidence of a Judgment, Synthese (1987) as well as Intuitionistic Type Theory.

And see Maria van der Schaar (editor), Judgement and the Epistemic Foundation of Logic (Springer, 2012) as well as Giuseppe Primiero, Information and knowledge: A constructive type-theoretical approach (2008, Springer).

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    So, is '"Snow is green" is false' an assertion or not?
    – William
    Jan 31, 2023 at 15:56
  • You are narrowing down the narrative. You assume from the proposition of "human did the rule". So you making something like : snow is white cuz it is a human said. Who is a human? Im not, or not only a human. Jan 31, 2023 at 15:57
  • @William - yes, because it expresses a true "fact", because snow is not green. Jan 31, 2023 at 15:57
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    +1 While the Logical Atomists maintained that assertions necessarily are truth-conditional utterances that mirror facts in the state of affairs, this is a presumption of the correspondent theory of truth. According to other theories, assertoric force can occur in other ways such as characterizing the truth conditions regarding the coherence of truth values among propositions.
    – J D
    Jan 31, 2023 at 16:58
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    What remains correct though is that an assertion is a speech act, and so it differs from a sentence or proposition, whether or not we adhere to the correspondence theory of truth. One can assert a falsehood, so an assertion does not have to be true.
    – Bumble
    Jan 31, 2023 at 17:43
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An assertion in philosophy is simply a claim of some sort, usually of the form NOUN VERB PROPERTY, such as 'Snow is white', 'Insects have six legs', 'beauty is in the eye of the beholder' or 'Marco Ocram writes the world's funniest books'. Assertions, therefore, purport to be true, but they can be false or untestable etc.

In the example you give...

'Snow is white' is an assertion, as is '"Snow is white" is true', but the phrase 'assert snow is white' seems to be an instruction.

As well as describing an explicit claim, such as the phrase 'Snow is white', the word assertion can be used to refer to the claim in terms of its meaning rather than referring to the statement per se. In the example you gave, the distinction is unclear and potentially confusing, since the straightforward meaning of the phrase 'snow is white' is snow is white, so the meaning and the phrase are easily mistaken for each other. However, if you take a phrase such as 'Most people don't like swimming in the sea because it is full of sharks' you might consider that it contains two assertions, one being that the sea is full of sharks and the other being that the shark infestation deters swimmers. There I am using the word 'assertions' to refer to the implications conveyed by the statement rather than to the statement itself.

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    'Bob swims' is an assertion which lacks a PROPERTY. Thus, intransitive verbs assert as well as transitive ones.
    – J D
    Jan 31, 2023 at 16:55
  • @JD indeed, that is quite correct, thank you. Jan 31, 2023 at 17:20
  • If 'Snow is white' is an assertion, the "assert" in "assert snow is white" seems redundant.
    – William
    Feb 1, 2023 at 14:20
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    "Snow is white" is not an assertion in all contexts. In the context "If snow is white then coal is black", it is not an assertion. Assertion is an action that is done with a proposition, it is not simply another word for "proposition". Feb 1, 2023 at 14:46
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A proposition is a sentence that is either true or false. Assertion is one of the things you can do with a proposition. To assert a proposition is to say or write it with the intention of claiming that it is true. Not all uses of a proposition are assertions. You can, for example merely mention a proposition (not use it) by putting it in quotes or putting it by itself on a page as in

Snow is white.

Here the proposition is not being asserted but merely exhibited. I'm not claiming that it is true. You can also use a proposition without asserting it. For example if I wrote "If snow is white then roses are read." (without the quotes of course) then I'd be using the proposition "snow is white" hypothetically, not asserting it. Similarly, I could say, "Is it the case that snow is white?" where I am not asserting it, but asking it. Or I could deny the proposition by saying "It is not the case that snow is white."

In none of the above examples am I asserting the proposition because I am not claiming that it is true. An assertion is not the proposition itself; rather it is an action that I take, an attitude I express towards a proposition. In English, in normal conversation, one asserts a proposition merely by saying or writing it as in "Snow is white", but it is the action intended by saying or writing it that makes it an assertion, not the text itself.

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  • Your differentiating a sentence without assertion from the same sentence but with assertion has insight.
    – William
    Feb 1, 2023 at 14:10
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When people talk, they say things that might be true or false. In fancy philosophical terminology, an assertion is simply a proposition which is an abstraction of sentences with truth conditions with the intent to communicate to others. "The house is on fire" is an assertion because it may or may not be true. "Is the house on fire" is neither true nor false, but is asking after the truth condition.

Assertions, therefore are distinguished from other sorts of utterances that don't have truth values. "Bob swims" is an assertion because it may be he doesn't know how or doesn't at the moment. But "Ouch, yikes, what the?!?" Is an utterance that isn't true at all. In English grammar, assertions are generally called declarative sentences. Other types of sentences such as exclamations, imperatives, and interrogatives don't have truth value, that is, they aren't true or false.

A few more distinctions can be drawn to help give context. "Bob swims" and "Bob schwimmt" are sentences or utterances, but they express the same idea, that is they are used in the same way. Thus, there is 'Bob swims' the sentence, and 'Bob swims' the proposition or idea. According to pragmatists, an assertion is a proposition which is viewed as a proposition AND an action. In this context, the terms assertive or assertoric force are sometimes used to make clear that 'assertion' is being used as a speech act.

Lastly, when you talk about thinking or believing propositions, you are in the realm of propositional attitudes. Thus "I believe 'Snow is white'" is a propositional attitude because it asserts two things, "I believe X" and X. The first proposition is called the attitude towards the second.

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Just to add to the above, one interesting distinction in your 7 situations is between 3 and 7, and to see that, consider the perspective of a polylinguist. One can assert that snow is white without using the English language expression to do so; one can assert that snow is white by speaking the German expression “Schnee ist weiß”.

Of course this piggybacks on a significant work of linguistic labour in determining that these two sentences in different languages mean the same, and in particular that the Anglophone translation is capable of making these kind of schematic interpretations, since as we’re using it, “assert” is an English word, and the propositions we take the speaker to be asserting are themselves construed in an English home language.

But one can say sentences in many languages, even if we try to use assertion to capture the common thread of what is being communicated in the utterance of those sentences.

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  • So, your point is "assert sentence1" is equivalent to "assert sentence2" provided that sentence1 represents the same proposition as sentence2.
    – William
    Feb 1, 2023 at 14:13
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In math and software engineering, assertion is a statement that must be true for all talking downstream to be valid. If the assertion is not correct, the talking downstream is not relevant, unusable, not possible to apply, like:

assert volume > 0

Assertions are important in understanding the described or programmed algorithm and its limitations.

It may be something similar here. Assertions are checked for correctness and usually the program is stopped immediately if they do not hold.

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An assertion is simply a claim that is made without any justification. For example:

Peter is goes running every day last week

Whilst:

Peter goes running every day last week as ever morning last week I saw him running through my window.

More specifically, an assertion offers an alleged fact without supplying the justification or evidence for that fact.

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