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Can there exist a "self-evident" statement? That is, can there exist a statement that offers sufficient substantiation for itself?

For example, a statement can be constructed

This statement is true.

Can such a statement be categorized as self-evident since it attempts to argue its own validity? Moreover, can another example be constructed where the proposition and its justification are expressed in one statement?

A is true because B, which is a logical justification for A, is true.

Will this statement constitute as an example of self-evident statement?

If such a "self-evident" statement can exist, is it rationally justified to doubt the statement?

Lastly, what are some examples of "self-evident" truths? Many people argue that our existence is self-evident. According to the definitions that you may provide above, will such an example constitute as self-evident?

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  • Technically, "this statement is true" isnt valid logic, because it references itself.Your 2nd example involves two statements that reference each other, ultimately the same thing.If you accept Set Theory, the only "self-evident" statements are ones we accept as axioms (although, as Godel noted, they may end up contradicting each other). You could argue statements like A or (not A) (or other tautologies) are self-evident (for any statement A), but that's arguably just because of how we define logic. And, of course, things like the Declaration's preamble are only metaphorically self-evident.
    – user935
    Aug 14, 2018 at 19:28
  • Addendum: just because ("A" or "not A") is true doesn't mean either A or not A is provable (truth and provability aren't identical, alas).
    – user935
    Aug 14, 2018 at 19:30
  • I made an edit hopefully to clarify the question. You may roll it back as I assume you are aware. Aug 14, 2018 at 21:46
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    "This statement is true" is known as the Truth teller sentence, and is usual seen not as self-evident but as undecidable, see Ross's answer. In typical use Self-evidence refers not to self-justification but to some kind of intuitive support, as in "lines intersect at a point" or "I think therefore I am"
    – Conifold
    Aug 14, 2018 at 21:51
  • If you accept ZF set theory is consistent, any theorem proven by it is technically "self-evident" since it's mathematically equivalent to the set of axioms. My latest guess at what self-evident "really" means is provability. You are looking for P such that "P is provably true, because P is true". There are definitely statements in ZF that don't have that property (ie, they are true but unprovable), but I think ZF requires "P is true" come from "P is provably true", not vice versa.
    – user935
    Aug 18, 2018 at 16:08

3 Answers 3

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One can find many self-evident statements. Let "P" be any statement that one can assign a truth-value to, that is, that one can assign either "true" or "false" in a truth-functional logic.

Now "P" is clearly not self-evident, but "P v ¬P", that is, "P" or not "P" is self-evident in that truth-functional logic.

Since "P" was arbitrary, this generates many self-evident statements.

For a reference see forall x: Calgary Remis, section 15.6 on "Disjunction", pp 112-116.

Now consider the questions:

Will this statement constitute as an example of self-evident statement?

Given an appropriate "P", "P v ¬P" should be self-evident in a truth-functional logic.

If such a "self-evident" statement can exist, is it rationally justified to doubt the statement?

One can rationalize most anything. So it is possible to doubt this self-evident statement. One could move from a truth-functional logic to some other kind of logic.

Lastly, what are some examples of "self-evident" truths? Many people argue that our existence is self-evident. According to the definitions that you may provide above, will such an example constitute as self-evident?

Let "P" be "I am alive". Then "P v ¬P" would be "I am alive or it is not the case that I am alive". I think that would be self-evident in a truth-functional logic.


Reference

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

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  • Can you answer, if the statement P: " I exist" is self-evident? Aug 14, 2018 at 21:44
  • That statement would not be based on the pattern I provided, however, it might be considered self-evident using some reasoning like Descartes' "I think therefore I am". However, I hear there are people who doubt even that. Aug 14, 2018 at 21:48
  • If to understand a statement one needs to learn what a "truth-functional logic" is it can hardly be called "self-evident". And if we take "P or not P" in the intuitive sense then I am not so sure either since even some mathematicians (intuitionists) consider it generally false. Maybe "P is P" would work better.
    – Conifold
    Aug 14, 2018 at 22:02
  • @Conifold "P is P" might work although I am sure someone will find a way to doubt it as well. A truth-functional logic is a classic logic with the law of excluded middle where sentences take on the value of either "true" or "false" with nothing inbetween. It is the logic that works with truth tables. Aug 14, 2018 at 22:55
  • Aristotle, who first explicitly stated P or not P, did not know "classical logic", neither did Kant. It is a 19th century creation after much effort, not exactly self-evident. Aristotle also rejected P or not P with respect to the future contingents, as in the tomorrow's sea battle example. That's a general problem, "self-evident" is either false or needs too many caveats to be evident, P is P was denied by Hegel.
    – Conifold
    Aug 14, 2018 at 23:11
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Self-evidence In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof...

"This sentence is comprised of words." is proved to be true entirely on the basis of the meaning of the terms: {sentence}, {comprised}, and {words} combined together to form the compositional meaning of the whole sentence.

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  • This sounds correct... Just some further note worth pointing out: self-evidence in epistemology is nothing but tautology in logic which can give no additional information besides their meaning. However, for a thorough logical empiricist such as Quine as expressed by his Two Dogmas of Empiricism, even self-evident synonym is synthetic (bachelors is an unmarried man), it needs some posterior experience to know its meaning, otherwise it's meaningless. Apr 25, 2021 at 3:03
  • @DoubleKnot I am acutely aware of Quine. I wonder if he would disagree that sentences are comprised of words are purely analytic. Perhaps we can divide the analytic / synthetic distinction such that all meanings that can be expressed using language are analytic. All meanings that require sensory stimulus (or memory of sensory stimulus) are synthetic. It might be that most knowledge requires at least a little of both.
    – polcott
    Apr 25, 2021 at 3:13
  • Surely Quine would disagree with your clear-cut demarcation as he emphasized such demarcation is a metaphysical article of faith, just as an open set of the real line, no matter how small it still contains both rationals and irrationals... So for him such effort is not useful at all (Frege had similar thought as expressed in his Sense and Reference discussion). Even "x(t)=x(t)" is not that self-evident for instructed only computers without any conscious experience.So under such POV, epistemology inevitably needs consciousness to circularly interpret itself if we can claim we know something... Apr 25, 2021 at 4:35
  • @DoubleKnot analytic expressions are the aspects of meaning that can be expressed as relations between words. When Rudolf Carnap expressed that bachelors are unmarried in his Meaning Postulates (1952) he meant that the otherwise totally meaningless term "Bachelor" does not have the property of the otherwise totally meaningless term "Married". This fits into Gödel's view "theory of simple types" such that a knowledge ontology can be defined: en.wikipedia.org/wiki/Ontology_(information_science)
    – polcott
    Dec 28, 2021 at 21:56
  • Description logic (DL) is usually the decidable two-variable fragment of FOL as ontological knowledge representation language commonly used in Web Semantics AI world. And your Gödel's view about simple type theory later evolves to the popular NFU as a foundation of math having more expressive power than ZF and still popular today within set-theorists circle. Church reformulated it to his own version and becomes a foundation of computation. So none has dealt with analytic/synthetic issue or addressed Quine concern about no such distinction really exists, it's only epistemic convenience for mind Dec 28, 2021 at 22:40
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No. 'Self evident' is an illusion, sustainable only because of implicit familiarity with context. It's a bad concept, outdated in philosophy, and it shouldn't be relied on or appealed to.

Euclid's axioms were taken to be self-evident foundational statements. It turns out bot only were there other sets of axioms, but Euclid's do not describe our particular universe, because of curved spacetime.

Arguably the strongest candidate for 'self evident' is Descartes' cogito. But that cannot survive addressing the Private Language argument.

The liar paradox of This statement is false shows to the problematic slipperiness of your first example.

The Law of the excluded middle is not the only option, and needs careful thought about non-contradiction (Russell's paradox) and exclusion as failure (in programming).

Self identity is not immune to challenge and context. Consider a framework like anatta, non-essence in the context of dependent arising. Or causality understood as concerning narrative groupings in a conceptual overlay (Is the idea of a causal chain physical (or even scientific)?), making any narrative grouping subject to reframing in a different narrative and salience landscape which groups different phenomena.

I would look to Nancy Cartwright's 'How The Laws Of Physics Lie' to understand how deductive truths only work within frameworks of assumptions and approximations, so given those there can be provable truths, sometimes obvious or 'self evident' seeming ones, but they in fact rely on an implicit abstraction of reality, ie something outside of the self that is evidencing, and remain open to challenge by looking at the validity of those assumptions and approximations.

It should be considered purely poetic language.

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