Illogical.

Words alone are not enough.

I first met Kathleen Stock in Brighton on 16th July 2018. In our brief encounter, I recall mentioning that simple predicate logic was all that was needed to get us out of the gender mess. Dr Stock probably thought I was hopelessly naïve, mansplaining, an idiot, or all three of the above. Now, I mention this meeting for two reasons, the first is that our heroic philosopher has (as I was in the midst of writing this article) just expressed some frustration with the process of the Supreme Court in its deliberations over the meaning of the word woman.

Dr Stock’s reaction to the call for a flowchart on X

https://x.com/Docstockk/status/1861757995891224787

Yes, a flowchart would be helpful.

The second reason is that I, too, had become a little antsy with our learned Lords and Ladies holding sway over the highest court in the land. Specifically, the judges’ collective inability to apply basic rules of logic to the problem they were charged with resolving was, as when I first wrestled with it in 2018, turning me into a gibbering imbecile.

In the six years since I made the bold claim that all we needed was logic, I have learned a great deal. When I first resolved to join in with sorting out the gender mess, I assumed everyone could see what I could see - especially those on the side opposing self-identification of gender identities. This was hopelessly naïve. We all come to this with wildly different experiences, different educations, different ways of seeing the world. My background includes a first career as a software engineer. Back in the days when computer programs were often written at machine level, expected to be correct, and debugging was a very costly exercise, a great deal of importance was placed on logical correctness. Consequently, computer engineers of the 1980s were taught Boolean logic, mathematic (to manipulate binary arrays) and electronic (to understand chip design) as well as predicate logic (to write correct programs).

We were told philosophers learned logic, too. So of course, Professor Stock would know what I was wittering on about, right? Probably not. Logic is the study of correct reasoning, but it is a surprisingly broad field. There are formal and informal methods. Informal logic is associated with logical fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal, almost mathematical, language. Our shared understanding of logic was likely less than the shared medical understanding of a chiropodist and a dentist.

Anyway, back to the Supreme Court, where our judges seemed to be learning the hard way that they need a crash course in logic. Their often clumsy interjections had already reminded me of my wild claim that logic was the answer. In the six years since, computer science has advanced such that today’s artificial intelligence software, in the form of Large Language Models, can perform useful tasks that would hitherto have forced me to blow the dust off old textbooks and do some hardcore revision. And so I was minded to ask ChatGPT to perform the following:

The response is reproduced at the end of this article.

What drew me from turning my curiosity, and idle ChatGPT query, into this article was a combination of Kathleen Stock’s post on X - wasn’t that a coincidence? And prior musing on the nature of logic as used in these three differing professions.

While formal logic is the realm of the computer scientist, and philosophers might employ some predicate logic but are more likely to pursue the informal logical analysis, lawyers, if they use any logic at all, will almost always do so from the informal toolkit. One easy way to comprehend these differences is to consider the differences between Verbal Reasoning and Non-Verbal Reasoning you might have encountered in school (or in getting a child into a selective school).

Logic becomes a part of one. If obliged to use it regularly, it becomes internalised. After a while there is no need to show workings, you can just see the correct answer in the mind’s eye. This is a skill that is less prevalent now than it once was, we live in an era when feelings are considered to be at least as important as facts. Logic does not work on feelings, its raw materials are hard facts. Computer programming has been lifted far away from the machine. What of philosophy and law?

Of course, the law is as much about rhetoric and precedent as it is about demonstrable proofs. And it might be assumed by the profession that maybe the criminal law might benefit from more logic - “my client cannot be in two places at once, your honour” - than other branches. I would disagree.

The evidence from the last two days is that highly paid arbiters, presumed to be at the pinnacle of their realm, are struggling with both the black-and-white of formal logic and the inferences one can draw if versed in the informal variety.

In fact, there is often merit in performing a more formal logical analysis of what might be usually considered an informal exercise. One such technique is the “decision tree”. These are useful, and often called flowcharts, for determining what decisions are required and how to make them. This particular decision tree only partially addresses the specific question raised in court today in that it points to the women in question having access to the standard treatment under the Equality Act.

Testing for discrimination when gender reassignment is involved.

The judge asked “if a natal man has GRC as a woman who do not present as women then they may not be discriminated against if the employer is discriminating against women, does that affect the women being able to identify a comparator, then can they bring a discrimination claim?”. To which the barrister’s response was “can I look at that over lunch? I think I need a flowchart to work it out.” [ per

Open Justice with Tribunal Tweets

]

In that example, it would seem that there is positive discrimination in favour of the man because he is a man and thus the women are being discriminated against on the basis of sex. Nevertheless, the law would benefit from more flowcharts!

We might also surmise that had the government of 2004 applied a little logic when considering the Gender Recognition Bill, we might never have acquired such a poor Act.

Both formal and informal logic should be expected of senior lawyers and of legislators. Formal logic for abstraction, informal logic for rhetoric and real-world problem-solving.

Computer engineers and philosophers are quite correct in expecting more from those making and interpreting law.

The Fundamentals of Logic should be part of any course to qualify those aspiring to legislate or to judge.

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ChatGPT Response to “use predicate logic to disprove gender identity ideology”

Here is the response to the challenge (a key to symbols used is provided at the end) :

Gender identity ideology asserts that an individual's subjective experience of gender is the definitive criterion for determining their "gender" or legal/biological sex. Using predicate logic, this ideology can be challenged by demonstrating internal contradictions or conflicts with established facts. Below is a structured disproof using predicate logic principles.

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1. Core Proposition of Gender Identity Ideology

• Claim: Gender identity is self-defined and supersedes biological sex.

  • Symbolically: ∀x (GI(x) → SD(x)), where GI(x) represents the proposition "x's gender identity is valid," and SD(x) represents "x’s self-declaration is sufficient for determining gender."

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2. The Principle of Non-Contradiction

• In classical logic, a proposition cannot simultaneously be true and false:

  • ¬(P ∧ ¬P).

• If gender identity ideology leads to contradictions when applied consistently, it cannot be a valid framework.

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3. Disproof Through Contradiction

Argument 1: Biological Facts vs. Self-Declaration

• Biological Reality:

  • Biological sex is determined by observable traits such as chromosomes (XX, XY), reproductive anatomy, and gametes. Let B(x) = "x is biologically male or female."

  • B(x) is immutable: ∀x (B(x) → ¬C(x)), where C(x) represents "x can change biological sex."

• Gender Identity Ideology:

  • GI(x) asserts that self-declaration alone (SD(x)) determines gender, irrespective of biological sex. Thus: ∃x (SD(x) ∧ ¬B(x)).

• Contradiction:

  • If SD(x) determines gender, then B(x) is irrelevant. However, physical reality (chromosomes, reproductive functions) consistently asserts ¬C(x), contradicting GI(x).

Argument 2: Gender Identity Is Non-Falsifiable

• Falsifiability Requirement:

  • A valid scientific proposition must be testable and falsifiable: ∀P (¬T(P) → ¬V(P)), where T(P) represents "P is testable," and V(P) represents "P is valid."

• Self-Declaration as the Criterion:

  • GI(x) asserts ∀x (SD(x) → GI(x)). However, SD(x) is entirely subjective and lacks external validation, making it unfalsifiable.

• Result:

  • If gender identity cannot be falsified, it violates the basic principles of scientific and logical reasoning.

Argument 3: Logical Conflicts with Legal and Biological Frameworks

• Scenario: Legal and medical contexts rely on biological sex (B(x)) for safety, fairness, and functionality. For instance:

  • In sports: ∃x (GI(x) → Adv(x)), where Adv(x) represents "x gains an unfair advantage."

  • In prisons: ∃x (GI(x) ∧ Risk(x)), where Risk(x) represents "x poses a safety risk in sex-segregated spaces."

• Contradiction:

  • If GI(x) allows ∃x (SD(x) ∧ ¬B(x)), it undermines frameworks built on B(x), leading to conflicts in law, safety, and fairness.

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4. Predicate Logic Summary

1. ∀x (B(x) → ¬C(x)): Biological sex cannot change.

2. GI(x) → SD(x): Gender identity ideology hinges on self-declaration.

3. ∃x (SD(x) ∧ ¬B(x)): Gender identity contradicts immutable biological sex.

4. ¬T(GI(x)) → ¬V(GI(x)): If gender identity is unfalsifiable, it lacks logical validity.

5. GI(x) ∧ Legal/Medical Frameworks: Leads to contradictions in fairness, safety, and policy.

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5. Conclusion

Gender identity ideology relies on subjective, unfalsifiable claims that conflict with biological and logical frameworks. Using predicate logic, we see that this ideology violates the principle of non-contradiction, fails the test of scientific validity, and leads to inconsistencies in critical societal domains like law and medicine. Thus, it is logically untenable as a framework for determining sex or gender.

Symbols and Their Meanings

1. ∀ (Universal Quantifier)

   • Meaning: "For all" or "for every."

   • Usage: Indicates that the statement applies to all elements in a given domain.

     • Example: ∀x (B(x) → ¬C(x)) means "For every individual x, if x is biologically male or female, then x cannot change biological sex."

2. ∃ (Existential Quantifier)

   • Meaning: "There exists."

   • Usage: Indicates that the statement applies to at least one element in the domain.

     • Example: ∃x (SD(x) ∧ ¬B(x)) means "There exists at least one individual x whose self-declaration conflicts with their biological sex."

3. → (Logical Implication)

   • Meaning: "If...then..."

   • Usage: Represents a conditional relationship where if the first statement is true, the second must also be true.

     • Example: GI(x) → SD(x) means "If x has a valid gender identity, then it is based on self-declaration."

4. ¬ (Negation)

   • Meaning: "Not" or "It is not the case that."

   • Usage: Negates the truth of a statement.

     • Example: ¬(P ∧ ¬P) means "It is not the case that both P and not P are true."

5. ∧ (Logical Conjunction)

   • Meaning: "And."

   • Usage: Combines two statements such that both must be true for the conjunction to be true.

     • Example: SD(x) ∧ ¬B(x) means "Self-declaration of gender and the absence of alignment with biological sex."

6. ∨ (Logical Disjunction) (Not explicitly used in the original text but relevant for predicate logic)

   • Meaning: "Or."

   • Usage: Combines two statements such that at least one of them must be true.

     • Example: P ∨ Q means "Either P or Q is true, or both."

7. T(P) (Testability Predicate)

   • Meaning: Indicates that a proposition P is testable.

   • Usage: Used to evaluate whether a statement or theory can be empirically verified.

     • Example: ¬T(GI(x)) → ¬V(GI(x)) means "If gender identity is not testable, then it is not valid."

8. V(P) (Validity Predicate)

   • Meaning: Indicates that a proposition P is valid.

   • Usage: Used to assess the logical or empirical truth of a statement.

     • Example: ¬V(P) means "Proposition P is not valid."

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Key to Variables

1. x: Represents an individual or subject within the domain (e.g., a person).

2. P: Represents a proposition or statement.

3. B(x): Indicates that x has a specific biological attribute (e.g., male or female).

4. SD(x): Indicates that x has made a self-declaration of gender identity.

5. GI(x): Represents that x’s gender identity is considered valid.

6. C(x): Indicates that x can change their biological sex.