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In the following link (http://www.importanceofphilosophy.com/Metaphysics_ExistenceExists.html) the authors are basically arguing that there exists some truth that we cannot disprove by any other statement. For example, we cannot give an example of an argument against existence since we would contradict ourselves.

I want to ask the following: If we are not able to disprove a statement without creating a contradiction like in the previous example, what does it mean for a statement? Does it mean that we can be certain of it? Isn't it just an argument from ignorance to say that we are certain of it?

Also, according to the article in the link, they are calling such a statement an axiom. Does it mean that an axiom is a statement that we cannot disprove (if not, what do we then call such a statement that we cannot disprove)? If such a definition of an axiom could be right, couldn't we also say then that an axiom is a statement which is unthinkable for a person to not be the case? Please give me some relevance to this. I'm a bit lost here.

  • The concept of "absolute truth" is tricky (and probably meaningless) : every argument (and thus every conclusion that we may assert as TRUE) needs a "context", i.e. a set of premises, rules, definition that we have tio agree on as meaningful and "sound" in order to share and understand the argument. Obviously, we can "change context" and discuss the premises and rules themselves (and this is probably the main business of philosiophy) but we cannot step out of every context and hope to continue the "dialogue". – Mauro ALLEGRANZA Sep 18 at 12:20
  • " an axiom is a statement which is unthinkable for a person to not be the case ?" No; an axiom is an assumption that - in a specific context (like e.g. a Mathematical or scientific theory - we assume as TRUE in order to develop our argument/theory. – Mauro ALLEGRANZA Sep 18 at 12:22
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    "Is there anything we can be certain of?" Probably not; you can see e.g. L.Wittgenstein, On Certainty as well as SEP's entry on Certainty. – Mauro ALLEGRANZA Sep 18 at 12:23
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    If we can prove that negation of a statement implies a contradiction then it is thereby proved. But pragmatic contradiction is not a real contradiction. One can not truthfully utter "I am dead" without creating a contradiction, but they may, nonetheless, be dead. If we simply can not disprove a statement it may be true, or undecidable, or not even truth-apt. – Conifold Sep 18 at 13:01
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    @TKN I feel you've hit on the core issue. We must prove the negation implies a contradiction and cannot assume it. This is indeed Aristotle's instructions for dialectical logic, embodied in the Rule for Contradictory Pairs. Yet it is not easy to prove this where it is not tautologically true and it is usually impossible, Some philosophies deny the truth of all positive statements about Reality along with their negations, and logic cannot defeat this position. , – PeterJ Sep 21 at 12:23
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If we are not able to disprove a statement without creating a contradiction like in the previous example, what does it mean for a statement? Does it mean that we can be certain of it? Isn't it just an argument from ignorance to say that we are certain of it?

Let's step back, take off our glasses of objectivity, and ask, what exactly are truth, proof, certainty, and evidence?

This is a high-level philosophy question which depends on your worldview. I'm going to answer from the perspective of a moderately naturalized epistemology, since epistemology is the area in philosophy that addresses these sorts of issues. I'm also going to invoke the language of Stephen Toulmin that he used in his method.

A statement in logic is generally understood as a syntactical expression of a proposition, and it is not the statement per se you are interested in, but the proposition which addresses the semantics and logics of the concepts. When we consider issues like veracity and modality of a proposition, we can generally do within three separate ways: questions of correspondence, coherence, and pragmatism. To complicate matters, the question of evidence (like invoking warrant, backing, and rebuttals) and proof are also complicated, and are very much domain specific.

Also, there are many types of belief where proof and evidence aren't even required, such as revealed religion, in which adherents are certain, that is to say have no doubt (see Hoffer's True Believer) and don't feel the need to reason. Another example are cranks and crackpots in technical fields such as physics, who often claim that fundamental truths are wrong, and they have "proven" it despite the entire field of experts examining and rejecting their conclusions. Even experts in a field may have complicated and sophisticated claims regarding their hypotheses that may disagree, and are certain of it; they often are champions of entire schools of thinkers who argue points back and forth!

If you're looking for satisfaction, look to evolutionary psychology which argues that if you accept evolution as true, then one can see the brain as sort of an engine of inference which works with modality to select from competing propositions to make decisions (studied by axiology). Those decisions have survival value. Is there a lion crouched and hungry in the bushes? Two men may argue, and having the correct answer is essentially determined by who, if anyone, gets eaten. Compare this to two philosophers who argue over what it "means" for there to "exist" a lions in the bush. Both are likely to go home and get a good night's sleep.

What does it "mean" to be certain without proof? It all depends on the context.

  • Thank you very much for your very good answer! You seem very knowledgeable therefore I would really like to ask you a question if you will which I cannot find an answer to. Lets say that I want to write a book about physics. In this book I would argue some obvious or well accepted things like 'speed of light is ...' or that space is expanding etc. But I want my book to do not have any implicit axioms based on which I argue these things. I would like to say explicitly in the beginning of the book all the axioms that I suppose are true in this book and based on which I will argue other things. – TKN Oct 20 at 9:10
  • For example, one of these axioms would be that I suppose in this book that objective physical reality exists (meaning that the physical reality is not just some picture in my brain in the vat skeptical hypotheses.). The reason for this is to make clear to any person reading this book, that all the things I argue here are not necessarily true without accepting these axioms. – TKN Oct 20 at 9:10
  • My question is: How do philosophers call this effort to make all implicit axioms explicit in a propositions? How do philosophers call these implicit axioms which are also common in every everyday speech? How would you call a propositions which use a lot of implicit axioms and therefore these propositions seem not very believable? – TKN Oct 20 at 9:11
  • (this problem of statements with implicit axioms, which are unknown to me, are everywhere around me, in every book etc, and I have really a difficulty to understand people because all of this.. Most of the people I know seem to me that they do not even realize the existence of implicit axioms based on which they are arguing something. They do not even realize for example that objective physical reality is not necessarily true and that they take it as granted, just believe in it without even realizing it.) – TKN Oct 20 at 9:11
  • So, when one is doing any domain-specific argumentation, say in physics, one has implicit assumptions. The philosophical term for those implicit assumptions is metaphysical presuppositions. If you argue that "physical reality exists" then you are engaged in declaring an ontological presupposition since you are declaring a concept as real and existing, that is using "existential quantification". Ontology is the study of what exists, and one's list of things that exist are one's "ontological commitment". en.wikipedia.org/wiki/Ontological_commitment – J D Oct 20 at 11:56
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Rather than asserting an answer it might be best to focus on what Jeff Landauer and Joseph Rowlands are claiming on their Importance of Philosophy site that the OP references and base an answer on what they have written.

They define an axiom as follows:

An axiom is an irreducible primary. It doesn't rest upon anything in order to be valid, and it cannot be proven by any "more basic" premises. A true axiom can not be refuted because the act of trying to refute it requires that very axiom as a premise. An attempt to contradict an axiom can only end in a contradiction.

As clarification, they claim that an axiom is not an arbitrary statement such as one of Euclid's postulates that one accepts to start a deductive theory. They have only three axioms:

  1. Existence Exists. "[T]here is something, as opposed to nothing."
  2. Law of Identity. "Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is."
  3. Consciousness. "Descartes argued that consciousness is axiomatic because you cannot logically deny your minds existence at the same time as using your mind to do the denying."

Here are the questions that I will try to answer based on assuming what Landauer and Rowlands are saying is true.

Does it mean that we can be certain of something rather than nothing?

By the Consciousness and Existence Exists axioms we can be certain we are conscious and we exist.

Also according to the article in the link they are calling such a statement an axiom. Does it mean that an axiom is a statement that we cannot disprove (if not, how do we than call such a statement we cannot disprove?)? If such a definition of an axiom could be right, couldn't we also say then that an axiom is a statement which is unthinkable for a person to not be the case?

We cannot disprove such an axiom because an "attempt to contradict an axiom can only end in a contradiction". It would appear that such an axiom is "unthinkable for a person to not be the case".

If we are not able to disprove a statement without creating a contradiction like in the previous example, does it mean that such a statement is the absolute truth?

The authors call these axioms irreducible primaries. They do not rest on anything to be valid. They cannot be refuted. Such axioms could be called absolute truths.

These answers depend on accepting what Landauer and Rowlands claim which may be true and which sounds plausible enough although there may be others who disagree with them. Disagreements are not disastrous. They are ways to understand reality better.


Landauer, J., Rowlands, J. Retrieved on September 18, 2019 from Importance of Philosophy at http://www.importanceofphilosophy.com/

  • How does a "argument from ignorance" fit in these statements which are pragmatic contradiction? Can we say that though we are not able to disprove such a statement without creating a contradiction now it doesn't mean that we will never be able to do so? Is this possibility real or is this possibility somehow ruled out by own nature of such a statement? – TKN Sep 19 at 10:42
  • @TKN Not being able to disprove something without deriving a contraction would not an argument from ignorance. We should not be able to prove false statements. What they are saying is that "existence exists" cannot be denied without leading to contradiction, so it must be true. Also, arguments from ignorance need not be fallacious, but I don't think this is an argument from ignorance. A fallacious argument from ignorance would go something like this: (1) We don't know that person is a witch. (2) But misfortunes have occurred. (3) Burn the witch just in case. – Frank Hubeny Sep 19 at 11:54
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You could perhaps look into so-called transcendental arguments, which have the form you seem to be interested in.

In a transcendental argument you argue (against an opponent) for a substantial claim, using as premise a trivial claim that the opponent does not dispute. A popular example is arguing for the reality of the external world against a skeptic, using as premise the mere fact that the skeptic is able to formulate its skeptical doubt.

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