Yes, you read the title correctly and it’s not clickbait, there are good reasons to believe all of these things although they are all different from each other, but all of them are quite tame views. Hopefully, reading this article will make you think of these views in a good light (or at least not think of them as nonsense). I know, for me, it was fun to see how I used to think of these things as utter gibberish, but I am now quite sympathetic to them. We will start in order, but you can choose what poison you want to drink first from the table of contents

So, the first installment of this absurd article, huh? There are no laws of logic, now on its face this claim seems plainly absurd and untenable both intuitively and logically. However, this is much more defensible (as with the other topics of this article are) than you may think

Russell's argument for nihilism goes like this:

Before we go into the argument, Russell first explains her terms. A "law of logic" is a simple statement of logical consequence of the form Γ ⊨ Φ. Logical nihilism is the view that no such statement is true; the extension of the logical consequence relation is empty

Okay so now on the two premises, starting with the Generality Principle: "To be a law of logic, a principle must hold in complete generality"

This is less controversial and usually intuitive for monists but what is meant by complete generality? We say a principle has complete generality just in case it holds under every possible interpretation of the non-logical vocabulary.

That is, for a law of logic to be genuinely logical, it must be:

That is all quite non-controversial so far, Logic abstracts away from the content of given terms. Consider:

All X are Y
Z is an X
Therefore, Z is Y

This works identically whether we're discussing:

Philosophers (All Greeks are mortal / Socrates is Greek / Therefore Socrates is mortal)

Chemistry (All acids have pH < 7 / Hydrochloric acid is an acid / Therefore it has pH < 7)

Fiction (All unicorns have horns / Sparkle is a unicorn / Therefore Sparkle has horns)

Or say we had a tautology “Mars is dry or not dry” (P v -P) the statement would compute as true even if “Mars” referred to my bottle of cologne and “dry” referred to the property of being a prime number

In this case though for complete generality Russell makes a point that this involves an absolutely unrestricted universal quantifier over interpretations. Essentially that a law of logic must be true in every interpretation without exception or restriction (which is typically what people think traditional laws to be e.g. LNC, LEM, etc.) and this is a problem

This is what the second premise aims to show with the interpretations view as logical consequence is defined (following Tarski) as truth-preservation under all possible interpretations of the non-logical vocabulary. Russell's argument is that for any proposed law Γ ⊨ Φ one can find a "sufficiently rich library of interpretations" that furnishes a counterexample. The argument proceeds by presenting "monsters" (counterexamples) that defeat progressively weaker and more fundamental logical laws (For the sake of brevity I am only going to show some examples but not exhaust all of the available counterexamples and arguments Russell gives)

Defeating Classical Logic: Its laws, like the Law of Excluded Middle, hold only if we assume just 'True' and 'False' as interpretations. The Law of Excluded Middle fails if we enrich our interpretations to include "gaps" (e.g., a "Neither" value, N, as well as a “Both” value B) as in Strong Kleene logic. This can arise from things like dialetheism, vagueness, presupposition failure, paradoxes etc. This is more straightforward and many responses that can be put in response to the law of noncontradiction can also be used against LEM they are kind of companions in guilt so we will keep this short and the literature there is extensive anyway.

Now for Identity, Φ ⊨ Φ This is the rule asserting that any sentence entails itself, usually taken to be the most fundamental inference rule of all. For what it is worth she treats this principle as a minimal, uncontroversial law of logic. If anything deserves the title “law of logic,” it is that a statement entails itself.

But she shows that even this most basic law fails if we adopt the criterion of complete generality. In classical model theory, identity holds because interpretations assign stable truth-values to each atomic formula, and compositionality ensures that the value of a sentence does not depend on its syntactic location.

However, Russell presents linguistic “monsters”-SOLO and PREM-where:

An atomic sentence’s truth-value depends on its syntactic role, or on whether it appears as a premise vs. as a conclusion, or on whether it is embedded vs. standalone.

This means that:

If so:

Φ ⊭ Φ

in complete generality because there exist legitimate interpretations where the identity of meaning is broken by context.

If you still hold your grievances, then we can survey the options here. First, though let’s look at conjunction introduction and what Russell calls SOLO where SOLO cases involve expressions whose truth-values change simply by being embedded.

A SOLO-like sentence:

Consequence:
Let Φ be a SOLO-like atom.

Then:

Φ ⊢Φ

fails under complete generality.

On the other hand, PREM cases show that the role of a sentence (premise vs. assertion) affects its truth-value, Russell cites PREM to demonstrate that some sentences have “premise-sensitive” semantics.

Example (simplified illustration inspired by PREM-style cases):

Thus:

Identity again fails. Russell posits a sentence 'PREM' that is true when it is a premise and false when it is a conclusion. The argument 'PREM' ⊢ 'PREM' fails, as the premise is true and the conclusion is false^.

Defeating Strong Kleene (MP, DS): The same jazz here, principles like Modus Ponens and Disjunctive Syllogism fail if we further enrich interpretations to include "gluts" from paraconsistent semantics (e.g., a "Both" value, B) that can motivated by paradoxes like the liar

Since no principle, not even Identity, survives this progressive enrichment of "all interpretations," the second premise of the nihilist's argument ("No principles hold in complete generality") is true. Therefore, there are no laws of logic. Russell also deftly notes this view is not self-defeating: a nihilist can use truth-preserving steps in their own reasoning without being committed to the universal generality of those steps as logical laws.

Russell's paper is a beautifully sophisticated dialectic. It does not, as a cursory reading might suggest, advocate for logical nihilism actually. Instead, she does three things:

It’s nothing to fear, just progress that seems needs to be made. Russell, simply put, is just trying to give us a better way to think about logic. The “complete generality” requirement is too strong. It does not reflect how real languages work and it makes the very concept of a “logical law” collapse into nihilism. (Maybe the logic part may have been clickbait a little)

The second installment of our absurd article, is a view that I take to be very defensible and quite persuasive despite the backlash it gets, this “truth-relativism” (otherwise called alethic relativism) is easily one of the best contenders between truth theories

What Relativism is NOT:

Before we actually speak of relativism, from my experience, it is more important that we talk about what relativism is not to avoid the common misunderstandings that seem to steer people away from the position.

To start, relativism is NOT subjectivism. Relativism by itself does not entail that believing that P means that P is true and it also does not entail that for any proposition P, there is a stance in which P is assigned any truth value. (Different relativists may say different things about this point). This is one that is repeated over and over again but is understandable given some notions of relativism that people are familiar with (e.g. Cultural relativism, agent-relativism). Alas it is still wrong and not what relativism is

Relativism does NOT need a thesis of plentitude such that for every proposition there is some perspective from which that proposition is true

Relativism is NOT the view that all views are equal.

(Now note that “Perspective” is meant to be a catch-all term here used in a very broad sense, it can be replaced with many things like conceptual schemes, frameworks, standpoints, paradigms etc. There are different ways to define perspective that can be drawn)

Going through the thesis the dependence (D) clause is simply stating that you can assign truth value to a belief only from a given perspective (or framework, scheme, standpoint, etc). So the truth of propositions is relative to perspectives and there are no truths simpliciter, i.e. no truth-values independent of all frameworks. Also, crucially, NNS is not equal validity, which is a ranking of perspectives (ranking them as equal). NNS on the other hand is saying there is no neutral way to privilege certain perspectives above others, such that whenever you judge/assign truth-value to a perspective, you do so from within a given perspective 

No Neutrality
As far as NNS goes, it actually seems rather intuitive that it is impossible to find a truly neutral or objective standard or some sort of meta-justification/meta-truth assignment to judge between systems of belief. The truth-conditions will always be framework relative and any justification and truth-value you offer for your own system will necessarily start from principles and assumptions within that system. As the SEP article put it:

“The relativistically inclined find further support for their position in the contention that there is no meta-justification of our evaluative or normative systems, that all justifications have to start and end somewhere… and that there are no higher-order or meta-level standards available for adjudicating clashes between systems in a non-question begging way… there is no neutral or objective starting ground for any of our beliefs”

A nice way of putting it would be through Macfarlane’s context of assessment (CA), although he only defended relativism at local levels. We will take his context of assessment and say what we’ve been saying through different words so it’s more clear. So no proposition has a truth-value independent of a Context of Assessment (or framework, perspective, etc).

Therefore, the CA parameter is always present, even if it looks different across domains:

Now those are just examples and not necessarily exhaustive of all of the contexts of assessment a particular domain could be using or if those are the assessments particular domains are using at all

Do also note that if one were to present some truth that somehow all frameworks agreed it would not make that truth framework-independent or CA-independent by itself

Underdetermination
If one so desired they could also use a supporting argument that empirical evidence (e.g. "data") is never sufficient on its own to prove a single scientific theory is true. For any given set of data points, it is always possible to draw multiple, incompatible theories that all perfectly account for that data. Because the evidence "underdetermines" the theory, the choice between rival theories cannot be made on the basis of evidence alone. Thus pointed back into the direction of relativism when it comes to the truth of theories (e.g. one may propose theoretical virtues for the truth-values of theories— there is also more to say on empirical evidence later on). Another line of thought that can be paired with this is that of context-dependence such that beliefs get their truth-value (and are largely influenced) relative to epistemic systems and the like (e.g. socio-cultural determinants of human beliefs). Do note that this is more about justification.

For an example of a position of relativism, consider Marletta’s Truth Value Ascription Relativism (TVAR) from semantic incommensurability. If semantic incommensurability is true then the paper would hold a sort of argument by analogy where a paradigm's core laws function like a Wittgensteinian "grammar" or a Kantian a priori structure. A grammar (like the rules of chess) or a system of measurement (like the metric system) defines the possibility of making meaningful statements

Consider the analogy of the standard meter bar in Paris. A statement like "This table is one meter long" can be tested and found to be true or false by comparing it to the standard meter. But what about the standard meter bar itself? The question, "Is the standard meter bar one meter long?" is meaningless. It is not true or false; it is the standard that defines the length "one meter". In application, a paradigm's fundamental laws (like Newton's F=ma) function in the same way. 

They are not empirical statements to be proven true or false; they are "grammatical" rules that define what 'force' and 'mass' mean within that system. Therefore, paradigms themselves are "neither true nor false".

This leads to the paper's central claim. The relativism implied by Kuhn is TVAR (Truth-Value Attributions Relativism). It states that a proposition that is a candidate for being true-or-false in one lexicon may be meaningless or nonsensical (i.e., not a candidate for a truth value) in another.

The defense for this is that evaluating any statement requires two steps. (1) Status Evaluation: Is this statement a meaningful candidate for a truth-value attribution?. This step depends entirely on the lexicon/paradigm. (2) Justification: If it is a candidate, we use logic and evidence to determine its specific truth value (true or false). A statement like "Newtonian mass is conserved" is true in the Newtonian lexicon. However, trying to import a statement from a different lexicon (e.g., "Aristotle's 'natural motion' is caused by 'Newtonian force'") doesn't produce a falsehood; it produces nonsense. It "would build contradictions about observable phenomena into language itself" as stated by Marletta. This view is perfectly compatible with truth being objective, absolute, and universal within a given lexical structure. The relativism here is about the availability of propositions to be evaluated in the first place.

Now this was just an example of a form of alethic relativism and not necessarily what I will be pushing here (which is Natalie Ashton’s rendition– although the two do blend together quite well and make a strong case together). To me, relativism almost seems trivially true, so much so that most theories of truth can be argued to entail relativism and that any candidate neutral/absolute truth can be argued to be dependent on particular perspectives (frameworks, schemes, etc). As well as that it explains many things better than competing theories of truth (like future contingents for example). That is just a general gist though for an intuitive idea of relativism. Now I will quickly survey some common objections that I see to relativism that do not quite do the job 

Relativism is self-defeating:
(a): What about the statement that “all truths are relative” is that not an absolute statement?

(b): If relativism is only relatively true then that means it can be relatively false and therefore contradicts itself

(c): If absolutism is relatively true then that also refutes relativism

Correspondence and empirical truths refute relativism:
Now this is a response I think is just as common, and I honestly take it that these two things are the same refutation whereby empirical claims correspond to the world. But there are many ways one can respond to this, one such is Kane B’s response: correspondence claims that P is true just in case P corresponds to the facts. i.e. P bears a special kind of "matching" relation to the facts. But what is this matching relation supposed to be? According to a relativist, a person compares what they take to be the proposition with what they take to be some aspect of the world, and they judge that they share the relevant features, where what counts as the relevant features is determined by the person in question.

What exactly it could be for a proposition to match the world, independently of anybody's judgment about it, is much more obscure and queer. A serious problem for traditional correspondence theory is that there are a variety of relations that propositions can bear to the facts. So if P bears a truth-making relation to the facts, then ~P must bear a falsity-making relation to the facts. If I can map P to the facts, I must be able to map ~P to the facts (because I can ~P to P via the negation function). This is actually quite a popular problem with correspondence (and more generally using states of affairs which much can be said on– so much so in fact that I am going to choose to keep it brief for the paper), now the correspondence theorist might reject negative facts. Then maybe “Not-P” is true because P fails to correspond to a fact.

“It’s true that snow is not white” because “snow is white” fails to correspond to any state of affairs.

But now correspondence theory stops explaining truth and starts explaining falsity. It defines truth in terms of non-correspondence, and this is circular, since we’re trying to say what truth is, not what falsehood is.

Even worse: this makes the truth of “Not-P” depend on the absence of a fact corresponding to P, which is not itself a correspondence relation. The world doesn’t positively contain “non-whiteness of snow” it simply lacks “whiteness of snow.” So, correspondence becomes asymmetric. So: what relation counts as the correspondence relation? Again, the relativist can just appeal to the judgment of the person, etc. , comparing the proposition and the world. This is only a small excerpt of what could be said against correspondence and there are much more things that can be posited

Let us sum it all up to avoid any misunderstanding, relativism claims that the truth of any proposition is relative to some framework where a “framework” could mean (a) conceptual scheme, language, epistemic system, paradigm, parameters, etc. So, we obtain

Thus, there are no framework-independent/neutral (absolute) truths. Truth is indexed to systems of evaluation, etc.

Consider TVAR and conceptual schemes: Different linguistic and conceptual frameworks carve up reality differently. For instance: what counts as "water" depends on linguistic and chemical frameworks.

What is true in one system may not even be formulable, let alone true, in another. Any statement about the world will involve some lexicon or classification scheme. I don't think that there is any good way of making sense of the idea that such classification schemes 

When I say, “It’s true that snow is white” What counts as “snow”? (linguistic/conceptual), what counts as “white”? (perceptual/physical norms), what counts as “true”? (semantic conventions). This is one such example of trying to show how truth-value may be relativized to frameworks

We have obtained from Macfarlane and Marletta that any statement about the world will involve some lexicon or classification scheme and that these classification schemes arguably do not "carve nature's joints", Truth is relative to the schemes that we construct.

When we look at other theories of truth, most of them are perfectly compatible with relativism to the point it gives so much credence to relativism (e.g. deflationary theory of truth, coherence theory).  Your current beliefs about truth, likely already entail relativism, most of you I would argue do not believe there are truths free of any context of assessment, perspectives, etc. So, I rest the case for relativism

Alas the final installment of our seemingly absurd article, this view I actually expect the most people to agree with as the family of positions it comes from (deflationism) has become quite popular as of recent. I will be drawing upon the brilliant Graham Seth Moore’s work for this, which you can find here: Graham Moore

“Facts" are not real, distinct entities in the world's furniture; they are a "useful fiction" of language whose sole purpose is to allow us to express generalizations.

The word "fact" serves a purely logical and linguistic role. Its main job is to help us express a "plurality (perhaps infinitely many) of sentences, without having to express each one." This works via a "syntactical trick":

This allows you to make "shorthand" statements. Instead of asserting the infinite list:

...you can just say, "I am talking about all of the facts about Graham". According to Moore, this is the entire purpose of fact-talk.

The metaphysical consequence of this linguistic thesis is quite attractive, insofar as fact-talk does not increase our ontology.

When you say, "There is a cat on the mat," you are, at the very least, ontologically committed to two things: a cat and a mat. When you add, "It is a fact that there is a cat on the mat," you have not added a "third entity" (the fact) to your world. You are still only committed to the cat and the mat.

Facts, therefore, are not real "denizens of the world". They are a "harmless myth" or a "fictitious assertion" that we "project... from true sentences" for the sole purpose of generalization.

Now Moore is not a traditional truth-deflationist; in fact, he finds that view "implausible” (That is where I must beg to differ). He argues that the "nominalizing-for-the-sake-of-generalizing" role is a better fit for the "fact" operator than the "is true" predicate as it is expressively more powerful than truth-deflationism

Truth-deflationism is limited. Since "truth is a property of representations" (like sentences or propositions), you can only generalize over things we have already managed to represent in language or thought

Fact-deflationism has no such limit. It can generalize over all properties, including those we have no words for or have never conceived of

When you say, "All of the facts about Graham," you are including properties of Graham that may be un-representable in English. When you say, "All of the truths about Graham," you are, by definition, only talking about the represented ones. This makes fact deflationism a much more robust tool for doing metaphysics, as it allows us to talk about all of reality, not just the parts of it we've managed to describe.

Wow, what an absurd article you just read through in its entirety, you must be a fairly absurd person, and I appreciate that. So yes, there are no laws of logic, all truth is relative, and “facts” don’t exist… hopefully what was written was convincing of those things. In fact, I am not even necessarily committed to all of these positions myself although I find them all coherent nonetheless

If, after this thorough exegesis, you still find yourself believing that this article is "self-defeating," "incoherent," or "utter gibberish," I can only say this:

From my perspective, this article is a masterpiece of unassailable reason and logical rigor and that is a fact.