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Wittgenstein's ladder

Wittgenstein's ladder is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Wittgenstein's ladder rather than just read about it. In short: In philosophy, Wittgenstein's ladder is a metaphor set out by Ludwig Wittgenstein about learning. In what may be a deliberate reference to Søren Kierkegaard's Concluding Unscientific Postscript to Philosophical Fragments, and using a metaphor by Sextus Empiricus in the second or third century CE, the penultimate proposition of the Tractatus Logico-Philosophicus (translated from the original German) reads: 6.54 Meine…

Key takeaways

  • Wittgenstein's ladder belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Wittgenstein's ladder to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Wittgenstein's ladder from memory before moving on to harder problems.

Reference excerpt

In philosophy, Wittgenstein's ladder is a metaphor set out by Ludwig Wittgenstein about learning. In what may be a deliberate reference to Søren Kierkegaard's Concluding Unscientific Postscript to Philosophical Fragments, and using a metaphor by Sextus Empiricus in the second or third century CE, the penultimate proposition of the Tractatus Logico-Philosophicus (translated from the original German) reads: 6.54

Meine Sätze erläutern dadurch, dass sie der, welcher mich versteht, am Ende als unsinnig erkennt, wenn er durch sie – auf ihnen – über sie hinausgestiegen ist. (Er muss sozusagen die Leiter wegwerfen, nachdem er auf ihr hinaufgestiegen ist.)Er muss diese Sätze überwinden, dann sieht er die Welt richtig. [My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright.]

This passage suggests that, if a reader understands Wittgenstein's aims in the text, then those propositions the reader would have just read would be recognized as nonsense. From Proposition 6.4 to 6.54, the Tractatus shifts its focus from primarily logical considerations to what may be considered more traditionally philosophical topics (God, ethics, meta-ethics, death, the will) and, less traditionally along with these, the mystical. The philosophy presented in the Tractatus attempts to demonstrate just what the limits of language are—and what it is to run up against them. Among what can be said for Wittgenstein are the propositions of natural science, and to the nonsensical, or unsayable, those subjects associated with philosophy traditionally—ethics and metaphysics, for instance. The penultimate proposition of the Tractatus, proposition 6.54, states that once one understands the propositions of the Tractatus, one will recognize that they are nonsensical (unsinnig), and that they must be thrown away. Proposition 6.54, then, presents a difficult interpretative problem. If the so-called picture theory of language is correct, and it is impossible to represent logical form, then the theory, by trying to say something about how language and the world must be for there to be meaning, is self-undermining. This is to say that the picture theory of language itself requires that something be said about the logical form sentences must share with reality for meaning to be possible. This requires doing precisely what the picture theory of language precludes. It would appear, then, that the metaphysics and the philosophy of language endorsed by the Tractatus give rise to a paradox: for the Tractatus to be true, it will necessarily have to be nonsense by self-application; but for this self-application to render the propositions of the Tractatus nonsense (in the Tractarian sense), then the Tractatus must be true. Other philosophers before Wittgenstein, including Sextus Empiricus, Fritz Mauthner, Zhuang Zhou, and Arthur Schopenhauer, had used similar metaphors. In his notes of 1930, Wittgenstein returns to the image of a ladder with a different perspective:

Ich könnte sagen: Wenn der Ort zu dem ich gelangen will nur auf einer Leiter zu ersteigen wäre, ich gäbe es auf dahin zu gelangen. Denn dort wo, ich wirklich hin muß, dort muß ich eigentlich schon sein.Was auf einer Leiter erreichbar ist interessiert mich nicht. [I might say: if the place I want to reach could only be climbed up to by a ladder, I would give up trying to get there. For the place to which I really have to go is one that I must actually be at already. Anything that can be reached with a ladder does not interest me.]

See also Kōan – Short instructive text in some Buddhist practices Lie-to-children – Teaching a complex subject via simpler models Neurath's boat – Philosophical analogy about knowledge

References

Worked examples

Example 1 — a first encounter with Wittgenstein's ladder

Start with the simplest possible case. Write down what Wittgenstein's ladder claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Wittgenstein's ladder before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Wittgenstein's ladder ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Wittgenstein's ladder

In research
Wittgenstein's ladder appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Wittgenstein's ladder in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Wittgenstein's ladder is common in secondary-school and first-year university syllabi. It links to neighbouring topics Analytic philosophy, Ladders, Linguistics stubs, so understanding it makes those chapters shorter.
In everyday life
Look for Wittgenstein's ladder outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Wittgenstein's ladder in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Wittgenstein's ladder means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Wittgenstein's ladder out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Wittgenstein's ladder in simple terms?

In philosophy, Wittgenstein's ladder is a metaphor set out by Ludwig Wittgenstein about learning. In what may be a deliberate reference to Søren Kierkegaard's Concluding Unscientific Postscript to Philosophical Fragments, and using a metaphor by Sextus Empiricus in the second or third century CE, t…

Why does Wittgenstein's ladder matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Wittgenstein's ladder?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Wittgenstein's ladder.

Tags

  • Analytic philosophy
  • Ladders
  • Linguistics stubs
  • Ludwig Wittgenstein
  • Philosophical analogies
  • Philosophy of education
  • Philosophy stubs

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