The Paradox of the Stone and the Euthyphro Dilemma | AQA A-Level Philosophy

Oct 15

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AQA A-Level Philosophy | Free Revision Notes

Estimated study time: 35 minutes

exam-style questions section

The Paradox of the Stone and the Euthyphro Dilemma A-Level Philosophy revision examines two challenges to the coherence of the traditional concept of God. The paradox of the stone questions whether omnipotence can be consistently understood, while Plato's Euthyphro dilemma asks how God's will relates to moral goodness. AQA specifically identifies both as arguments concerning the possible incoherence of God. These debates build directly on the meaning of God's attributes [Divine Attributes] and show why precise definitions matter in philosophical argument.

Learning Objectives 🎯

By the end of this revision page, you should be able to:

Explain the paradox of the stone and why it challenges omnipotence.
Distinguish different interpretations of omnipotence.
Explain both horns of Plato's Euthyphro dilemma when applied to a monotheistic God.
Analyse how the Euthyphro dilemma affects God's omnipotence and supreme goodness.
Distinguish a challenge to a divine attribute from a proof that the whole concept of God is incoherent.
Evaluate whether the paradox of the stone or the Euthyphro dilemma successfully establishes incoherence.

Revision Notes 📚

Why are these arguments important?

AQA describes God as traditionally omniscient, omnipotent and supremely good or omnibenevolent. It then explicitly requires consideration of arguments that challenge whether this concept is coherent, including:

the paradox of the stone
the Euthyphro dilemma
the compatibility of omniscience with free human beings.

The last of these is explored separately in divine foreknowledge and freedom [Omniscience and Human Freedom].

The first two focus particularly on God's power and goodness.

The underlying philosophical question is:

Can the attributes traditionally assigned to God be understood without contradiction?

That is different from asking whether God actually exists. An argument may challenge the coherence of the concept before the question of existence is considered.

Omnipotence

Before considering the paradox of the stone, you need a precise definition of omnipotence.

AQA defines an omnipotent God as all-powerful, but recognises two possible interpretations:

God has the power to do anything.
God has the power to do anything that is logically possible.

These definitions look similar, but the difference is crucial.

We can represent them as:

O1=God can do anythingO_1 = \text{God can do anything}

and:

O2=God can do anything logically possibleO_2 = \text{God can do anything logically possible}

The paradox of the stone puts pressure particularly on the first, unrestricted interpretation.

Why logical possibility matters

A logically possible state of affairs is one that does not involve a contradiction.

For example, asking whether a being can perform an action only makes sense if the description represents a possible action.

So when omnipotence is defined as:

power to do anything logically possible\text{power to do anything logically possible}

a defender of omnipotence can argue that an inability to bring about a contradiction does not represent a genuine lack of power.

This distinction becomes the central issue in the paradox.

The paradox of the stone

AQA presents the paradox as a challenge to the coherence of omnipotence.

The question is:

Can God create a stone so heavy that God cannot lift it?

The problem appears whichever answer is given.

If God can create the stone

Suppose the answer is yes.

God creates a stone that God cannot lift.

Then:

There is something God cannot do: lift the stone.\text{There is something God cannot do: lift the stone.}

If omnipotence means having unlimited power, this appears to show that God is not omnipotent.

If God cannot create the stone

Now suppose the answer is no.

Then:

There is something God cannot do: create the stone.\text{There is something God cannot do: create the stone.}

Again, it seems that God's power has a limit.

AQA therefore presents the problem as follows: if God can create the stone, God cannot lift it; if God cannot create the stone, there is something God cannot create. Either way, a limitation seems to have been identified.

The structure of the paradox

The reasoning can be represented simply:

An omnipotent being can do anything.
Either God can create an unliftable stone or God cannot.
If God can create it, God cannot lift it.
If God cannot create it, God cannot create something.
In either case, there is something God cannot do.
Therefore, God is not omnipotent.

The argument is designed to show a tension within the concept of unrestricted omnipotence.

Why is it called a paradox?

AQA describes a paradox as a case where apparently acceptable premises seem to generate a logically unacceptable conclusion. A paradox may be answered by rejecting a premise, identifying faulty reasoning or accepting the surprising conclusion.

That is important here.

The stone paradox does not have to be accepted immediately as proving that omnipotence is impossible. One possible strategy is to challenge how omnipotence has been defined.

Response: omnipotence and logical possibility

The most important response supported by the supplied AQA material comes from the alternative interpretation of omnipotence:

God can do anything that is logically possible.

Consider the proposed task:

Create a stone that an omnipotent being cannot lift.

If God is omnipotent, the description requires both:

God is able to lift anything logically liftable\text{God is able to lift anything logically liftable}

and:

there exists something God cannot lift\text{there exists something God cannot lift}

The defender can argue that the task itself contains the problem.

The stone would have to be:

liftable by an omnipotent being and not liftable by that omnipotent being\text{liftable by an omnipotent being and not liftable by that omnipotent being}

The issue may therefore concern a contradictory description, rather than a genuine task that an all-powerful being fails to perform.

Does this limit God's power?

A critic might reply:

If God cannot perform this task, there is still something God cannot do.

But the defender can distinguish:

a possible task that God lacks the power to perform
a description that does not specify a logically possible task at all.

If omnipotence means the power to do everything logically possible, then failure to realise a contradiction would not count against omnipotence.

This creates the key evaluative issue:

Does restricting omnipotence to logical possibility weaken omnipotence, or does it simply clarify what genuine power involves?

A strong exam answer should address this rather than simply saying that "God cannot do logically impossible things".

Does the paradox prove God is incoherent?

Not automatically.

The paradox clearly creates a problem for the unrestricted definition:

omnipotence=ability to do absolutely anything\text{omnipotence} = \text{ability to do absolutely anything}

But AQA explicitly recognises another definition:

omnipotence=ability to do anything logically possible\text{omnipotence} = \text{ability to do anything logically possible}

So an important evaluation is that the success of the paradox depends partly on which analysis of omnipotence is accepted.

If the restricted definition is coherent, the paradox may show that the first definition is defective without showing that the concept of an omnipotent God is itself impossible.

This illustrates a major philosophical skill: an objection may defeat one formulation of a position without defeating every possible formulation.

Plato's Euthyphro dilemma

The second major issue concerns God's relationship with moral goodness.

AQA explains that Plato's original Euthyphro concerns piety or holiness and what is loved by the gods. When adapted to monotheism, the dilemma concerns the relationship between God and moral goodness.

The question becomes:

Does God will or command what is morally good because it is good, or is something morally good because God wills or commands it?

These are the two horns of the dilemma.

Understanding a dilemma

A philosophical dilemma gives two alternatives where each appears to create an unwanted consequence.

Here the alternatives are:

Horn 1

God commands an action because it is morally good.\text{God commands an action because it is morally good.}

Horn 2

An action is morally good because God commands it.\text{An action is morally good because God commands it.}

AQA explains that neither option appears desirable for the classical theist.

First horn: God commands what is good because it is good

Suppose:

God commands morally good actions because they are already morally good.

This means their goodness does not depend upon God's command.

The order of explanation is:

action is good→God commands it\text{action is good} \rightarrow \text{God commands it}

God recognises or responds to goodness rather than creating goodness by willing it.

The problem: goodness appears independent of God

AQA identifies the consequence directly: the essence of moral goodness is located outside God's will.

God does not determine what goodness is.

Instead, something is good independently and God wills it because it is good.

This threatens a conception in which God is the ultimate source of moral goodness.

The problem for omnipotence

AQA also states that this horn challenges God's omnipotence.

Why?

If moral goodness exists independently of God's will, then God cannot simply make the moral standard different by willing differently.

There appears to be something God's will does not determine.

The first horn therefore creates tension between:

God as omnipotent
goodness existing independently of God's will.

This links directly back to omnipotence [Divine Attributes].

Second horn: something is good because God commands it

Now take the other possibility:

An action is morally good because God wills or commands it.

The order of explanation becomes:

God commands the action→the action is good\text{God commands the action} \rightarrow \text{the action is good}

On this interpretation, God's will determines moral goodness.

This avoids placing the standard of goodness independently of God.

However, it produces a different problem.

The problem: moral goodness becomes arbitrary

AQA identifies the problem with this horn as the threat that moral goodness becomes arbitrary.

If goodness depends entirely upon what God wills, there appears to be no independent moral standard explaining why one divine command is good rather than another.

The worry can be represented as:

Whatever God wills=morally good\text{Whatever God wills} = \text{morally good}

If so, goodness appears determined simply by God's will.

This threatens the idea that God's supreme goodness has meaningful moral content independent of whatever God happens to will.

The two horns compared

Horn	Claim	Problem identified by AQA
1. God commands the good because it is good	Goodness is prior to God's command	Goodness exists outside God's will and God's omnipotence is challenged
2. The good is good because God commands it	God's command determines goodness	Moral goodness appears arbitrary

The strength of the dilemma comes from the fact that either answer appears to threaten part of the traditional concept of God.

The Euthyphro dilemma and omnipotence

The first horn raises a direct issue for God's power.

If God commands goodness because it is independently good, then:

God’s will does not determine moral goodness\text{God's will does not determine moral goodness}

This can be interpreted as a limitation upon divine power.

The question becomes:

Can God genuinely be omnipotent if there is a moral standard independent of God's will?

This connects the dilemma directly with the debate about divine attributes [Divine Attributes].

However, careful evaluation is needed. A limitation only threatens omnipotence if omnipotence requires God's power to determine moral truths.

The provided AQA material identifies the challenge but does not supply a detailed resolution.

The Euthyphro dilemma and supreme goodness

The second horn generates a different problem.

If:

goodness depends entirely on God’s command\text{goodness depends entirely on God's command}

then saying:

"God commands what is good"

risks becoming difficult to distinguish from:

"God commands what God commands."

The central issue identified in the AQA material is arbitrariness.

If there is no standard beyond divine willing, it becomes harder to explain goodness independently of God's will.

This matters because God is traditionally understood as supremely good or omnibenevolent.

A concept of goodness that is simply fixed by whatever God wills may therefore appear to weaken the significance of saying that God is good.

Does Euthyphro prove that God is incoherent?

The dilemma certainly creates philosophical pressure.

If the first horn is accepted:

goodness is independent of God's will
God's omnipotence appears threatened.

If the second horn is accepted:

goodness depends upon God's will
morality threatens to become arbitrary.

However, this should not immediately be treated as a decisive proof of contradiction.

For the dilemma to establish that the concept of God is incoherent, it would need to show that:

the two horns exhaust the possible relationships between God and goodness, and
both alternatives are genuinely incompatible with the traditional concept of God.

The supplied AQA material identifies the two problematic horns but does not provide an additional specified solution to the dilemma. It would therefore be inappropriate here to introduce a further theological theory and present it as specification content.

A careful conclusion is that the Euthyphro dilemma places significant pressure on the relationship between divine omnipotence and supreme goodness, but whether it proves outright incoherence depends upon whether its assumptions and alternatives can be defended.

Paradox of the stone and Euthyphro compared

The two arguments challenge different parts of the concept of God.

	Paradox of the Stone	Euthyphro Dilemma
Main attribute challenged	Omnipotence	Omnipotence and supreme goodness
Central question	Can God create something God cannot lift?	Does God command goodness because it is good, or is it good because God commands it?
Problem	Either answer appears to place a limit on divine power	One horn places goodness outside God's will, the other makes goodness arbitrary
Important response/issue	Define omnipotence in terms of logical possibility	Assess whether either horn is compatible with the traditional attributes
What must be evaluated?	Whether the task describes a genuine logical possibility	Whether the two alternatives establish a genuine inconsistency

Both arguments therefore illustrate the importance of conceptual analysis.

They do not merely ask what attributes God has. They ask whether those attributes can be defined and combined consistently.

Which argument creates the stronger coherence challenge?

The specification requires students to analyse and evaluate, so simply describing both arguments is not enough.

The paradox of the stone can be challenged fairly directly using AQA's alternative definition of omnipotence:

God can do anything logically possible\text{God can do anything logically possible}

If creating an unliftable stone for an omnipotent being involves a contradiction, the paradox may depend upon an unreasonable understanding of omnipotence.

The Euthyphro dilemma is structurally different.

Neither horn involves the same obvious appeal to a logically contradictory task. Instead, each produces a consequence that appears problematic for the traditional conception of God.

This means that the two arguments should not be treated as identical forms of challenge.

A useful evaluation framework

When evaluating either argument, ask four questions:

What exactly is being challenged?Is it omnipotence, supreme goodness or the whole concept of God?
What definition is being assumed?The paradox of the stone changes significantly depending on how omnipotence is defined.
Does the argument establish a contradiction?A difficult implication is not automatically a logical inconsistency.
Could the concept be reformulated without losing the original attribute?For omnipotence, AQA's logical-possibility definition provides exactly this kind of move.

These questions are also useful preparation for God's omniscience and human freedom [Omniscience and Human Freedom], another AQA challenge to the coherence of the traditional concept.

Overall assessment

The paradox of the stone is strongest against an unrestricted definition according to which omnipotence means being able to do literally anything. Once omnipotence is understood as power to do anything logically possible, the defender can argue that the paradox describes an incoherent task rather than a genuine limitation.

The Euthyphro dilemma presents a different challenge. If God wills the good because it is independently good, the standard of goodness appears outside God's will and divine omnipotence is challenged. If something is good merely because God wills it, goodness threatens to become arbitrary.

Neither argument should simply be announced as proving that God is impossible. The philosophical task is to establish whether an actual contradiction follows from the traditional divine attributes.

Key Words 🔑

Key word	Student-friendly definition	How it may be used in an exam
Omnipotence	God's being all-powerful, understood as being able to do anything or anything logically possible.	Define the attribute before assessing the paradox of the stone.
Paradox of the stone	A challenge asking whether God can create a stone so heavy that God cannot lift it.	Use to analyse whether omnipotence is internally coherent.
Euthyphro dilemma	The dilemma asking whether God commands what is good because it is good, or whether it is good because God commands it.	Use when evaluating the relationship between God and moral goodness.
Arbitrary	Determined without an independent standard that explains why one option is morally good rather than another.	Use when explaining the problem created by the second horn of the Euthyphro dilemma.
Coherence	The ability of a concept or set of claims to be held consistently without contradiction.	Use when assessing whether these arguments undermine the traditional concept of God.

Hints from the Examiner Reports 💡

No lesson-specific examiner guidance was identified in the provided reports.

For AQA questions using explain, the command word requires students to write in detail, with relevant elaboration, examples, implications and connections where appropriate.

Examiner hint: When explaining either argument, do not stop after stating the question. Show exactly why each possible answer creates a problem.

Common Mistakes ⚠️

Mistake: Saying the paradox simply asks whether God can lift a heavy stone

Why this is incorrect:The weight itself is not the philosophical issue. The stone is defined as one that God cannot lift, creating the apparent conflict with omnipotence.

How to improve:Explain both possibilities: if God creates it, God cannot lift it; if God cannot create it, God's creative power appears limited.

Mistake: Ignoring the different definitions of omnipotence

Why this is incorrect:AQA explicitly allows omnipotence to mean either being able to do anything or being able to do anything logically possible.

How to improve:State the definition you are using and explain how it changes the force of the paradox.

Mistake: Claiming that inability to perform a contradiction obviously proves weakness

Why this is incorrect:That assumes without argument that a logically contradictory description represents a genuine task.

How to improve:Ask whether the proposed action is logically possible before treating failure to perform it as a restriction of power.

Mistake: Reversing the two horns of Euthyphro

Why this is incorrect:Each horn generates a different problem.

How to improve:Remember:

good first→goodness independent of God’s will\text{good first} \rightarrow \text{goodness independent of God's will}

God’s command first→risk of arbitrariness\text{God's command first} \rightarrow \text{risk of arbitrariness}

Mistake: Saying the first horn disproves God's goodness

Why this is incorrect:The specific AQA criticism is that it locates moral goodness outside God's will and challenges omnipotence.

How to improve:Identify the precise attribute threatened rather than making a broader claim than the argument establishes.

Mistake: Saying the second horn proves that God commands evil actions

Why this is incorrect:That claim is not established by the dilemma as presented in the supplied AQA material.

How to improve:Use AQA's precise criticism: the second horn threatens to make moral goodness arbitrary.

Exam-Style Questions ✍️

Question 1

Define what is meant by God's omnipotence. (3 marks)

Indicative answer:Omnipotence means that God is all-powerful. It can be understood as the power to do anything or, alternatively, the power to do anything that is logically possible.

Marking guidance:Credit an accurate definition. Recognition of the two possible interpretations provides a particularly precise response.

Question 2

What is the paradox of the stone? (3 marks)

Indicative answer:The paradox asks whether God can create a stone so heavy that God cannot lift it. If God can create it, there is something God cannot lift. If God cannot create it, there is something God cannot create. Either answer therefore appears to limit God's omnipotence.

Marking guidance:Both sides of the paradox should be stated clearly.

Question 3

Explain how defining omnipotence in terms of logical possibility can respond to the paradox of the stone. (5 marks)

Indicative answer:Omnipotence may mean the ability to do anything that is logically possible. The proposed task asks an omnipotent being to create something that an omnipotent being cannot lift. A defender can argue that this description is contradictory and therefore does not represent a genuine logically possible task. God's inability to perform it would therefore not show a limitation in God's power.

Marking guidance:The answer should explain why logical possibility changes the argument, not simply state the alternative definition.

Question 4

Explain the two horns of the Euthyphro dilemma. (5 marks)

Indicative answer:The first horn says that God commands what is morally good because it is already good. This makes goodness independent of God's will and challenges God's omnipotence. The second horn says that something is morally good because God wills or commands it. This threatens to make moral goodness arbitrary.

Marking guidance:Both horns and the problem created by each should be clearly distinguished.

Question 5

A philosopher argues:

"If God cannot make an unliftable stone, God cannot be omnipotent."

Explain one response to this argument. (5 marks)

Indicative answer:The response is that omnipotence can be understood as the ability to do anything logically possible. An unliftable stone created by an omnipotent being may involve a contradiction because an omnipotent being, by definition, cannot be overcome by the stone's weight. Therefore, failure to create such a stone need not represent a genuine limitation on God's power.

Marking guidance:A strong answer connects the response explicitly to the definition of omnipotence.

Question 6

Explain why the first horn of the Euthyphro dilemma may challenge divine omnipotence. (5 marks)

Indicative answer:The first horn holds that God commands morally good actions because they are independently good. This means the standard of moral goodness does not depend upon God's will. God therefore does not determine what goodness is, which appears to place something outside the scope of God's power and so challenges omnipotence.

Marking guidance:The response must explain the connection between independent goodness and the alleged limitation of God's power.

Question 7

Explain why the second horn of the Euthyphro dilemma threatens to make moral goodness arbitrary. (5 marks)

Indicative answer:The second horn says that actions are morally good because God commands them. This makes God's will the basis of moral goodness. There is therefore no independent moral standard explaining why God's commands are good, which creates the concern that moral goodness is determined simply by whatever God wills.

Marking guidance:The explanation should show why dependence on divine command creates the arbitrariness problem.

Question 8

Evaluate the view that the paradox of the stone shows that an omnipotent God is impossible. (25 marks)

Indicative content:

A developed answer could consider:

Omnipotence as the ability to do anything.
The structure of the paradox.
If God creates the stone, God cannot lift it.
If God cannot create it, God's creative power appears limited.
The alternative AQA definition of omnipotence as the power to do anything logically possible.
Whether an unliftable stone for an omnipotent being represents a genuine possible task.
Whether inability to bring about a contradiction should count as weakness.
Whether restricting omnipotence to logical possibility preserves the original meaning of being all-powerful.
The distinction between defeating one definition of omnipotence and showing that every concept of omnipotence is incoherent.

Marking guidance:A strong answer should analyse the definition of omnipotence at the centre of the argument, develop objections and responses, and reach a reasoned conclusion about whether a genuine contradiction has been established.

Question 9

Evaluate whether the Euthyphro dilemma shows that the traditional concept of God is incoherent. (25 marks)