NEXUS METHODS WORKSHOP · THREE PUBLISHED WORLDS
What does a test really tell us?
A logical counterexample, a simplified signal threshold and an AI classification score may look like answers. They answer different questions. Work through the original published models side by side and explain which conclusions each actually supports.
No account, external API, real-world personal measurements or grading. The neuron units and classifier observations are fictional teaching examples, not medical or AI-product predictions.
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01 · PHILOSOPHY & REASONING
Can an inference fail even when its conclusion sounds convincing?
Classical propositional validity asks if any assignment makes every premise true and the conclusion false. It does not check whether the premises describe the real world.
Worked example — affirming the consequent: invalid. 1 truth-table assignment(s) make both premises true and the conclusion false.
Why the counterexample matters
Knowing that Q is true does not tell us whether P caused or implied it, even when “if P then Q” is true. Compare with modus ponens, where affirming P does entail Q if the conditional premise holds.
Source-linked study: Deductive Arguments: Validity and Soundness · Deductive Validity Lab
02 · LIFE, BODY & MIND
What can a simplified threshold demonstrate?
This invented arithmetic model subtracts inhibition from excitation and compares the result with four arbitrary units. It illustrates a threshold rule, not actual membrane voltage or biological neural signalling.
Worked example — 6 − 2 = 4 units. Threshold 4 reached: illustrative signal.
Why a toy signal is not a clinical prediction
A number in invented units cannot reveal an actual neuron’s timing, ion channels or electrical properties. Use this result to discuss the meaning of a model boundary, not a person’s health.
Source-linked study: How Neurons Send Signals · Neuron Threshold Sandbox
03 · TECHNOLOGY & AI EVALUATION
When one threshold changes, which errors change?
The original classifier Lab uses twelve invented labelled observations. A chosen threshold classifies an observation as positive when its invented score reaches that value. Count the mistakes instead of trusting a single percentage.
Worked example — threshold 60: TP 4, FP 2, TN 4, FN 2. Precision 66.7%, recall 66.7%.
What if precision is undefined?
At a threshold where the model predicts no positive cases, there are no predicted positives from which to calculate precision. Undefined is not a perfect result. The scores are not from a real AI deployment.
Source-linked study: Evaluating AI Models Beyond Accuracy · Classifier Trade-offs Lab
Compare the three answers
At the initial settings: the inference fails a deductive validity test; the invented neuron model reaches its threshold; and the fictional classifier has both false positives and false negatives. These observations answer three different questions.
| Method | What it evaluates | What the result cannot prove |
|---|---|---|
| Logic | Whether premises logically entail a conclusion within a stated form | That the premises describe true facts |
| Toy neuron threshold | Whether invented inputs cross a specified arithmetic boundary | Any individual biological signal or medical finding |
| Fictional classifier | Error counts and precision/recall for twelve invented observations | Real model performance, safety or fairness |
Reflect before moving on
- What counts as a counterexample in logic—and how is that different from a false positive in classification?
- What did moving a threshold change? Which factual assumptions remained unchanged?
- What additional evidence would you need before using any of these examples to make a real-world claim?
Read a possible synthesis
Each model supplies a bounded answer: formal entailment, an abstract arithmetic outcome or error counts for fictional cases. A correct internal computation does not, by itself, validate the assumptions or show that a model generalizes beyond its input. Look at its sources, definitions and intended use before claiming more.
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