Notes · PhilosophyUK · A-Levels

The limits of knowledge

This topic examines philosophical scepticism — its difference from ordinary doubt, and the distinction between local and global scepticism — through Descartes' three waves of doubt, which drive towards global doubt about the external world. It then reconstructs Descartes' own response, the cogito and the rebuilding of knowledge via God, and evaluates it against the Cartesian circle and rival empiricist and reliabilist responses.

5 sections~23 min reading time2 competenciesLevel Foundation 1 · Standard 2 · Advanced 2

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Exam profile

AO1 · Demonstrate knowledge and understanding of philosophical scepticism, Descartes' sceptical arguments and the main responses to themAO2 · Analyse and evaluate whether global scepticism can be answered and whether Descartes' reconstruction escapes the Cartesian circle, reaching a justified conclusion

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basic level

At AS-Level, explain the difference between philosophical scepticism and ordinary doubt, state the three waves of doubt, and give the cogito as Descartes' response.

higher level

At full A-Level, reconstruct the sceptical arguments and the cogito as explicit arguments, run the Cartesian-circle objection in full, and evaluate empiricist and reliabilist responses to global scepticism.

Depth

Text

Contents · 5 sections

The limits of knowledge

Philosophical scepticism: local and global doubt#

FoundationAQA 7172 3.1 Epistemology — The limits of knowledgeDfE GCE Philosophy subject content

Local and global scepticism

Fig. 1Local scepticism doubts one area; global scepticism attacks a source on which most beliefs rest.

Philosophical scepticism must be distinguished carefully from ordinary, everyday doubt (sometimes called 'normal incredulity'). Ordinary doubt is doubt for which we have a specific, local reason — I doubt this banknote is genuine because it feels odd, I doubt the witness because she has a motive to lie — and it is resolved by ordinary means, such as checking or getting better evidence. Philosophical scepticism, by contrast, doubts whole classes of belief on general grounds, without any particular reason to think a given belief is false, and it cannot be settled by ordinary checking because the sceptical scenarios are designed to be undetectable from within experience. The sceptic does not claim we are wrong; the sceptic claims we cannot rule out that we are wrong, and so do not have knowledge.

The philosophical sceptic typically exploits the gap between our evidence and the truth of our beliefs. If knowledge requires that our justification rule out all possibilities of error, and if there are error-possibilities (dreams, deceiving demons, brains in vats) that our evidence cannot rule out — because they would produce exactly the same experiences — then we lack knowledge. The argument does not need to show that any sceptical scenario is actual; it needs only to show that we cannot know it is not, since a possibility we cannot exclude is a possibility that, if knowledge requires certainty, defeats the knowledge claim. This is why scepticism is a challenge about the STANDARDS for knowledge, not a set of first-order claims about the world.

Scepticism comes in two scopes. Local scepticism doubts a specific area or source of belief while leaving others intact — one might be sceptical about knowledge of the future, or of other minds, or of moral truths, while confidently claiming knowledge of one's present experience. Global scepticism doubts (almost) all our beliefs at once, typically by attacking a source on which nearly everything rests: if all my beliefs about the external world depend on sense experience, and sense experience as a whole can be doubted, then knowledge of the external world collapses globally. Descartes' project is to push doubt to the global limit deliberately, in order to find whatever, if anything, survives it.

It is important to see that Descartes is a METHODOLOGICAL sceptic, not a sceptic by conviction. He wields doubt as a tool: by provisionally treating as false anything that can be doubted, he hopes to sweep away all merely probable opinion and reach a foundation of absolutely certain, indubitable beliefs on which to rebuild knowledge securely (his 'method of doubt' in the First Meditation). The aim is anti-sceptical — to defeat scepticism by finding an unshakeable foundation — but the method requires taking scepticism to its most radical extreme first. The three 'waves of doubt' of the next section are the successive stages by which he drives doubt from the local to the global.

Worked example

Diagnosing a doubt

Classify each as ordinary doubt, local scepticism or global scepticism: (a) doubting a receipt is genuine; (b) doubting we can ever know the future; (c) doubting there is any external world.

Assess (a)
There is a specific reason and it is checkable — ordinary doubt, resolvable by ordinary means.
Assess (b)
A whole area (future-directed belief) is doubted on general grounds while other knowledge stands — local scepticism.
Assess (c)
The very existence of the external world, on which nearly all belief rests, is doubted — global scepticism.
Note the method
Descartes deploys (c) methodologically, to find what survives radical doubt.

Result: (a) ordinary doubt, (b) local scepticism, (c) global scepticism; only (c) is the radical, source-attacking doubt Descartes uses to seek an indubitable foundation.

Typical mistakes

Treating the sceptic as claiming our beliefs ARE false; the claim is that we cannot rule out error, so we lack knowledge, whether or not the beliefs are true.
Presenting Descartes as a genuine sceptic; his doubt is a method for reaching certainty, not a settled scepticism.

Active revision

Explain the difference between philosophical scepticism and ordinary doubt, and between local and global scepticism. (5-mark AO1 response)

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for philosophy (Department for Education)

Descartes' three waves of doubt#

StandardAQA 7172 3.1 Epistemology — The limits of knowledgeDfE GCE Philosophy subject content

The three waves of doubt

Fig. 2Doubt escalates from marginal perceptions to all external-world beliefs to mathematics itself.

In the First Meditation Descartes advances doubt in three escalating 'waves', each casting doubt over a wider class of beliefs than the last. The first wave is the argument from illusion, or the unreliability of the senses: the senses sometimes deceive us — a square tower looks round from afar, a straight oar looks bent in water — and 'it is prudent never to trust completely those who have deceived us even once'. But Descartes immediately limits this wave: it undermines only distant or marginal perceptions, not the vivid, close-up conviction that I am sitting here by the fire holding this paper. Sensory illusion alone does not reach the everyday perceptual beliefs at the core of our knowledge, so a stronger argument is needed.

The second wave is the dreaming argument, which does reach those core beliefs. When I dream, I often have experiences as vivid and coherent as waking ones, and I take them at the time to be real; yet they are not. Crucially, 'there are no certain marks by which the state of waking can be distinguished from sleep' — nothing internal to my present experience guarantees I am not now dreaming. So for all I can tell from the inside, my conviction that I am sitting by the fire could be a dream: any particular external-world belief might be a dream-belief. This generalises doubt to the whole of my perceptual knowledge of the external world, since no perceptual experience carries a certificate of its own veridicality. Descartes notes, though, that even in dreams certain simple and general truths — of arithmetic and geometry, that 2 + 3 = 5, that a square has four sides — seem to remain true, so the dreaming argument does not touch mathematics.

The third wave is the evil demon (malicious deceiver) argument, designed to doubt even these. Descartes supposes 'some malicious demon of the utmost power and cunning' who devotes all his energies to deceiving him — not only about the external world (making it seem there is earth, sky and bodies when there are none) but even about the simplest matters, so that perhaps he goes wrong every time he adds two and three or counts the sides of a square. Since I cannot rule out such a deceiver, I cannot be certain even of what seems most rationally self-evident; the demon extends doubt from the a posteriori to the a priori, from the external world to mathematics and logic themselves. At the end of the First Meditation, doubt is therefore global: nothing at all has yet survived.

The three waves form a deliberate crescendo of scope: illusion doubts marginal perceptions; dreaming doubts all external-world beliefs; the demon doubts even mathematics and reason. Reconstructed as an argument, the sceptical strategy is a modus tollens: if I knew that p (say, that I have hands), I could rule out every possibility incompatible with p (that I am dreaming, deceived); but I cannot rule out those possibilities; therefore I do not know that p. In symbols the conditional is

K \rightarrow R

and the sceptic asserts

\neg R

, concluding

\neg K

. The power of the arguments lies in the undetectability of the scenarios: each is constructed so that it would produce experiences exactly like the ones I have, so no experience can tell against it — which is why ordinary checking is powerless and only a response at the level of standards can help.

Worked example

Reconstructing the dreaming argument

Set out the dreaming argument as an explicit argument and identify its key premise.

P1
Dream experiences can be subjectively indistinguishable from waking experiences.
P2
There is no internal mark that certifies a present experience as waking rather than dreaming.
P3
So for any external-world belief based on present experience, I cannot rule out that it is a mere dream-belief.
C
Therefore I cannot be certain of any external-world belief, so (if knowledge requires certainty) I do not know it.

Result: The argument's load-bearing premise is P2 — the absence of a mark of waking; a response must either supply such a mark or deny that knowledge requires ruling out the dream possibility (reliabilism).

Typical mistakes

Saying the dreaming argument shows we ARE dreaming; it shows only that we cannot rule out dreaming, which is enough to defeat certainty.
Claiming the evil demon is meant to be believed in; it is a device to test whether even a priori truths can be doubted, not a metaphysical hypothesis Descartes accepts.

Active revision

Outline Descartes' three waves of doubt and explain how each extends the scope of the previous one. (12-mark AO1 response)

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for philosophy (Department for Education)

The cogito as a foundation#

StandardAQA 7172 3.1 Epistemology — The limits of knowledgeDfE GCE Philosophy subject content

The cogito

Fig. 3Doubting is a kind of thinking, and thinking requires a thinker, so 'I exist' cannot be doubted.

At the start of the Second Meditation Descartes finds the one thing the demon cannot make him doubt: his own existence as a thinking thing. However powerful the deceiver, 'he will never bring it about that I am nothing so long as I think that I am something'; the very act of doubting, being deceived, or thinking presupposes a thinker. 'I am, I exist' is 'necessarily true each time it is put forward by me or conceived in my mind'. This is the cogito ('I think, therefore I am', in the Discourse formulation): an indubitable foundation that survives all three waves of doubt, because even a global deceiver needs a mind to deceive.

The cogito is best understood not as a syllogism ('everything that thinks exists; I think; so I exist') but as a first-person intuition whose certainty is grasped in the very performing of it. Its self-verifying character is the key: the proposition 'I exist' cannot be false when I entertain it, because entertaining it is itself a thinking, and thinking requires a thinker. This makes it immune to the demon: the demon can make me wrong about mathematics and the external world, but cannot make me wrong that I exist while I am thinking, since deceiving me is itself a way of ensuring there is a me to deceive. The cogito thus meets Descartes' own standard for a foundation — it is clearly and distinctly perceived and cannot be doubted.

From the cogito Descartes extracts more than bare existence. Reflecting on WHAT he is, he argues that he can doubt he has a body (the demon might fake that) but cannot doubt that he thinks, so his essence, so far as he can be certain of it, is to be 'a thing that thinks' (res cogitans) — a mind whose nature is thought and which does not depend on any material thing for its being known. He also derives his criterion of truth by generalising from the case: what makes the cogito certain is that it is perceived clearly and distinctly, so 'I can lay it down as a general rule that whatever I perceive very clearly and distinctly is true'. This clear-and-distinct-ideas criterion is the engine of the reconstruction that follows.

Even the cogito, however, has been challenged, and a strong answer notes the limits of what it secures. Bertrand Russell and Georg Lichtenberg argued that Descartes is entitled only to 'there is thinking going on', not to 'I think': the 'I', a persisting substantial self, is smuggled in, whereas all that is strictly indubitable is the occurrence of a thought, not an enduring thinker who owns it. Hume's bundle theory of the self reinforces this: introspection reveals only a bundle of perceptions, never a self over and above them. Moreover, the cogito secures only the present existence of thinking; it does not by itself establish that I persist through time, that I have a body, or that anything external exists. So the foundation, though genuinely indubitable, is extremely thin — which is exactly why Descartes needs the further, and far more contested, proofs of God to rebuild the rest of knowledge.

Worked example

Assessing the 'I' in the cogito

Evaluate the objection that the cogito establishes only 'there is thinking', not 'I think'.

The objection
Russell/Lichtenberg: the indubitable datum is the occurrence of a thought; positing an enduring 'I' who owns it goes beyond what is certain.
Hume's support
Introspection finds only a bundle of perceptions, never a persisting self, so the substantial 'I' is not given.
A Cartesian reply
A thought must be someone's; an unowned thought is unintelligible, so 'I' is not an addition but part of what thinking is.
Weigh
Even granting a subject of the present thought, nothing yet shows it persists or is a soul; so the cogito secures a momentary thinker at most.

Result: The cogito secures present thinking and (arguably) a present subject, but not a persisting, substantial self; the foundation is indubitable yet very thin, which is why the reconstruction leans so heavily on God.

Typical mistakes

Presenting the cogito as a syllogism vulnerable to doubting the major premise; its force is as a self-verifying performance, certain each time it is thought.
Overstating what the cogito proves; it secures present thinking/existence only, not a body, a persisting self, or the external world.

Active revision

'The cogito gives Descartes a secure foundation for knowledge.' Assess this claim. (25-mark essay)

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for philosophy (Department for Education)

Rebuilding knowledge: God and the external world#

AdvancedAQA 7172 3.1 Epistemology — The limits of knowledgeDfE GCE Philosophy subject content

The reconstruction of knowledge

Fig. 4From the cogito, via God's existence and non-deception, Descartes rebuilds trust in reason and the senses.

Having secured the cogito and the clear-and-distinct-ideas criterion, Descartes must escape the 'egocentric predicament' — locked inside his own mind, certain only of his present thinking — and rebuild knowledge of God and the external world. His bridge is God. In the Third Meditation he argues for God's existence, first by the trademark (or causal) argument: I have an idea of God as an infinite, perfect being; by the causal principle, there must be at least as much reality in the cause of this idea as in the idea itself; but I, a finite, imperfect being, cannot be the cause of an idea of infinite perfection; so the idea must have been caused by an actually existing infinite, perfect being — God, who has stamped this idea in me like a craftsman's trademark on his work.

God then does the essential epistemic work. Because God is supremely perfect, God is no deceiver — deception is a defect, incompatible with perfection. So God would not create me with a faculty of clear and distinct perception that systematically leads me astray. This validates the criterion: whatever I perceive clearly and distinctly is true, because a non-deceiving God guarantees it. With this guarantee Descartes can dismiss the evil demon (a non-deceiving God would not permit such wholesale deception) and reinstate mathematics and logic. He then argues (Sixth Meditation) that my vivid, involuntary sensory ideas of bodies must be caused by external material things, since God has given me a strong inclination to believe this and no faculty for detecting any other source; a non-deceiving God would not implant so strong and uncorrectable an inclination if it were false. So the external world is restored — its existence underwritten, once again, by divine veracity.

The reconstruction has an elegant architecture: cogito to God (via the trademark argument) to the reliability of clear and distinct ideas to mathematics and the external world. Everything after the cogito hangs on the proofs of God, because it is God's non-deceiving nature that licenses trust in reason and the senses. This makes the structure only as strong as its weakest link, and the weakest links are precisely the proofs of God and the causal and clear-and-distinct principles they employ — principles that the demon was supposed to have called into doubt. That tension is the opening for the famous objection considered next.

The reconstruction is vulnerable at several points even before the circle. The trademark argument assumes a scholastic causal principle ('there must be as much reality in the cause as in the effect') that Hume and later empiricists reject, and assumes I have a genuine, positive idea of infinite perfection rather than a merely negative idea of 'not-finite'. The move to the external world assumes that a good God would not permit a strong false inclination, which is contestable (we have other strong inclinations that mislead us). And the whole edifice presupposes that the certainty of the cogito can be extended, by long chains of clear-and-distinct reasoning, to remote conclusions — yet the demon's original threat was precisely that even apparently clear reasoning might be corrupted. So the reconstruction is far more fragile than the foundation, and most philosophers judge that Descartes does not, in the end, earn his way back to the external world from within the egocentric predicament.

Worked example

Reconstructing the trademark argument

Set out Descartes' trademark argument for God's existence as explicit premises.

P1
I have an idea of God as an infinite, supremely perfect being.
P2
By the causal principle, a cause must have at least as much reality as its effect (including the 'objective' reality of an idea).
P3
I, a finite imperfect being, do not have enough reality to be the cause of an idea of infinite perfection.
C
So the idea must be caused by an actually existing infinite perfect being — God, whose 'trademark' the idea is.

Result: The argument is valid but rests on the contested scholastic causal principle and on my having a genuinely positive idea of infinity; deny either and the reconstruction loses its bridge from the cogito to God.

Typical mistakes

Skipping the role of God; for Descartes the external world is known only because a non-deceiving God guarantees clear and distinct perception — the senses are not trusted directly.
Confusing the trademark argument (from the idea of God within me) with the ontological argument (from the concept of God); Descartes gives both, but they are distinct.

Active revision

'Descartes successfully rebuilds knowledge of the external world.' Discuss. (25-mark essay)

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for philosophy (Department for Education)

The Cartesian circle and other responses#

AdvancedAQA 7172 3.1 Epistemology — The limits of knowledgeDfE GCE Philosophy subject content

The Cartesian circle

Fig. 5Clear and distinct ideas are used to prove God, and God is used to validate clear and distinct ideas.

The most famous objection to Descartes' reconstruction is the Cartesian circle, pressed by Antoine Arnauld in the Fourth Objections. Descartes uses the clear and distinct perception of certain premises to prove that God exists and is no deceiver; but he then uses God's non-deception to guarantee that clear and distinct perceptions are true. This is circular: the reliability of clear and distinct ideas is used to establish God, and God is used to establish the reliability of clear and distinct ideas. If, before proving God, I cannot trust clear and distinct reasoning (because the demon might corrupt even that), then I cannot trust the clear and distinct reasoning by which I prove God; but if I can trust it, I do not need God to underwrite it. Either way the proof fails to do its job.

Descartes' defenders offer replies. One distinguishes between current clear and distinct perceptions, which are irresistibly certain WHILE held, and the memory of past demonstrations, which the demon might make me misremember; on this reading God is needed only to guarantee the reliability of remembered reasoning across time, not the self-evidence of present intuition, so there is no circle at the level of what is presently perceived. Another reply holds that the cogito and the axioms are psychologically indubitable in the moment, and God's role is to convert this subjective certainty into objective, stable knowledge (scientia). Whether these rescue Descartes is disputed: critics respond that even present clear and distinct perceptions were supposed to fall under the demon's doubt, so appealing to them before validating them re-opens the circle.

Because Descartes' own response is widely thought to fail, other responses to scepticism become important. Empiricist responses, developed in the perception topic, hold that the external world need not be proved with Cartesian certainty but can be established as the best explanation of the coherence and involuntariness of our experience (Locke's causal argument; Russell's inference to the best explanation). This concedes that global scepticism cannot be refuted with certainty but denies that certainty is required for knowledge: the external-world hypothesis is far more reasonable than the sceptical alternatives, and reasonableness is enough. The sceptic replies that a dream or demon could produce equally coherent experience, so the inference is only probable — but the empiricist bites this bullet, holding that probable knowledge is still knowledge.

The most direct anti-sceptical strategy rejects the sceptic's key assumption that knowledge requires certainty or the ruling-out of every error-possibility. Reliabilism holds that knowledge is true belief produced by a reliable process; if my perceptual faculties are in fact reliable, then I know there is a table before me, whether or not I can PROVE to the sceptic that I am not dreaming. On this externalist view the demand to answer the sceptic from within, with certainty, is simply the wrong standard — I can know without knowing that I know, and without being able to exclude undetectable error. G. E. Moore's 'here is one hand' makes a kindred point: the claim that I have hands is more certain than any premise of the sceptical argument, so it is more reasonable to reject a sceptical premise than to accept the sceptical conclusion. A balanced judgement is that global scepticism cannot be refuted on its own terms (with certainty, from within), so Descartes' foundationalist reply fails; but that scepticism relies on an over-demanding conception of knowledge, and once knowledge is understood as reliable or best-explanatory true belief rather than as certainty, the sceptical challenge, though never conclusively silenced, loses its power to show we know nothing.

Worked example

Model 25-mark plan: can global scepticism be answered?

Plan an essay defending a judgement on whether global scepticism can be answered.

Thesis
Global scepticism cannot be refuted on its own (certainty-from-within) terms, but it rests on an over-demanding standard, so reliabilism dissolves it.
AO1
Explain the waves of doubt, the cogito, and Descartes' God-based reconstruction.
Descartes fails
The Cartesian circle shows the reconstruction cannot validate reason without presupposing it; the foundationalist answer collapses.
Better responses
The empiricist best-explanation reply (knowledge without certainty) and reliabilism/Moore (reject the certainty standard) address the sceptic differently.
Judgement
Conclude that if knowledge requires certainty, the sceptic wins; but that standard is unmotivated, and on a reliabilist account we know much — so scepticism is dissolved, not refuted.

Result: A defensible judgement: Descartes does not defeat scepticism (the circle), and it cannot be refuted with certainty; but the sceptic's certainty requirement is the real target, and rejecting it (reliabilism) restores knowledge without answering the sceptic on the sceptic's own impossible terms.

Typical mistakes

Misstating the circle as merely 'assuming what you want to prove' without the two specific directions (ideas to God; God to ideas).
Assuming reliabilism REFUTES the sceptic; it rejects the sceptic's certainty standard, dissolving rather than defeating the challenge — a different and worth-noting move.

Active revision

'Global scepticism cannot be answered.' Is this claim true? Defend your answer. (25-mark essay)

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for philosophy (Department for Education)

References & sources

Sources

Department for Education

GCE AS and A level subject content for philosophy

The limits of knowledge

5 sections~23 min reading time2 competenciesLevel Foundation 1 · Standard 2 · Advanced 2

The limits of knowledge

Key points

Diagnosing a doubt

Key points

Reconstructing the dreaming argument

Key points

Assessing the 'I' in the cogito

Key points

Reconstructing the trademark argument

Key points

Model 25-mark plan: can global scepticism be answered?

Sources

The limits of knowledge

Key points

Diagnosing a doubt

Key points

Reconstructing the dreaming argument

Key points

Assessing the 'I' in the cogito

Key points

Reconstructing the trademark argument

Key points

Model 25-mark plan: can global scepticism be answered?

Sources