Problems for Cosmological Arguments | AQA A-Level Philosophy
For Specification 7172
AQA A-Level Philosophy | Free Revision Notes
Estimated study time: 45 minutes
Problems for Cosmological Arguments A-Level Philosophy revision brings together the four objections AQA specifies for the cosmological arguments: the possibility of an infinite series, Hume's objection to the causal principle, Russell's fallacy of composition objection, and Hume and Russell's challenge to the possibility of a necessary being. These objections do not affect every cosmological argument in exactly the same way, so effective evaluation requires matching each criticism to the particular reasoning used by the Kalām, Aquinas, Descartes and Leibniz.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Explain why the possibility of an infinite series threatens some cosmological arguments.
Explain Hume's objection to the causal principle using Hume's Fork.
Explain Russell's fallacy of composition objection.
Explain Hume and Russell's objection to the possibility of a necessary being.
Apply the objections accurately to the specified cosmological arguments.
Compare and evaluate the strengths and weaknesses of the Kalām, Aquinas, Descartes and Leibniz.
Revision Notes 📚
What are cosmological arguments?
Cosmological arguments reason from the existence of the world, or some general feature of it, towards a first cause, reason or explanation.
The specified arguments use several different starting points:
Argument | Starting point | Conclusion sought |
Kalām | Temporal beginning of the universe | An uncaused first cause |
Aquinas' First Way | Change | An unchanged changer |
Aquinas' Second Way | Atemporal efficient causation | A first efficient cause |
Aquinas' Third Way | Contingent beings | An underived necessary being |
Descartes | His continuing existence | A cause of his preservation |
Leibniz | Contingency and sufficient reason | A necessary explanation |
These are all cosmological arguments, but they are not one single argument repeated six times. AQA specifies the different forms separately.
This means an objection may be devastating to one version while only indirectly challenging another.
The four specified problems
AQA requires four main issues:
the possibility of an infinite series
Hume's objection to the causal principle
Russell's objection that the argument commits the fallacy of composition
Hume and Russell's objection to the possibility of a necessary being.
A strong essay should explain what each objection actually targets rather than listing all four criticisms against every cosmological argument.
The Possibility of an Infinite Series
What is an infinite series?
An infinite series is a series without a limit or first member in the relevant direction.
Applied to cosmological arguments, the series could consist of:
causes
events
beings
dependent explanations.
The objection is simple:
If an infinite series of causes, events or beings is possible, then perhaps no first cause is required.
AQA explicitly identifies this as an objection to cosmological arguments that claim a first cause is necessary for a temporal or atemporal series.
Why does an infinite series threaten cosmological arguments?
Many cosmological arguments rely on the claim that an explanatory series cannot continue indefinitely.
They reason:
dependent causeexplained by another causeexplained by another causeeventually requires a first cause.
But if the series can continue infinitely, the move to a first member becomes questionable.
The objection therefore challenges:
Why must there be a first cause at all?
If the answer is simply that a causal series cannot be infinite, the cosmological argument must justify that claim.
The infinite-series objection and the Kalām
In The Kalām Cosmological Argument [The Kalām Cosmological Argument], the argument depends directly upon a temporal beginning.
It reasons from:
the universe began to exist
towards:
an uncaused first cause of that beginning.
The possibility that the relevant temporal series has no beginning would therefore challenge a central premise of the Kalām.
If the past series could be infinite, there would not necessarily be a first temporal event requiring the kind of first cause specified by the argument.
The objection is therefore highly relevant to the Kalām's route to God.
Infinite regress and Aquinas' First Way
In Aquinas' First and Second Ways [Aquinas' First and Second Ways], Aquinas' First Way reasons from change towards an unchanged changer.
The important series is a series of changers.
Aquinas argues that if every changer depended upon another changer without any first source, the present process of change would lack an ultimate explanatory foundation.
The infinite-series objection questions this.
Why could there not simply be:
changer explained by changer, explained by changer, without a first changer?
If such a series is possible, Aquinas needs an additional reason why an unchanged first changer must exist.
Infinite regress and Aquinas' Second Way
The Second Way is particularly important because it involves atemporal or hierarchical causation, rather than simply asking what happened first in time.
So the objection is not merely:
Perhaps the universe has existed forever.
Aquinas could accept an infinitely extended temporal past while still claiming that the present hierarchy of efficient causes requires a first sustaining cause.
The relevant objection must therefore ask:
Could the atemporal hierarchy itself be infinite?
If it could, then Aquinas' claim that a first efficient cause is necessary would be weakened.
AQA's formulation of the objection explicitly allows it to target both temporal and atemporal causal series.
Infinite regress and Aquinas' Third Way
In Aquinas' Third Way and Leibniz [Aquinas' Third Way and Leibniz], the regress concerns necessary beings whose necessity is derived from other necessary beings.
Aquinas argues that there must eventually be:
a necessary being whose necessity is not derived from another.
The infinite-series objection asks whether a series of derived necessary beings could continue indefinitely.
If it could, Aquinas would need to explain why an underived necessary being must still exist.
Infinite series and Leibniz
Leibniz's argument is slightly different.
His concern is not simply whether a series has a first member.
His principle of sufficient reason demands an adequate explanation of why contingent reality exists.
Even if the series of contingent beings were infinite, Leibniz can still ask:
Why does this entire contingent series exist rather than not?
So simply allowing an infinite series does not automatically answer Leibniz's explanatory question.
The critic would need to argue either:
that the infinite series needs no further explanation, or
that explaining every member is enough.
The second possibility connects directly with Russell's fallacy of composition objection.
Hume's Objection to the Causal Principle
What is the causal principle?
The causal principle is the claim that events have causes.
It can also be expressed more generally as the idea that what exists or occurs has a cause or explanation.
Cosmological arguments often depend upon causal principles in order to move from:
something exists or occurs
to:
there must be some cause or explanation of it.
Hume's Fork
Hume's objection can be understood through Hume's Fork.
Hume distinguishes between:
relations of ideas, known a priori and necessarily true
matters of fact, known through experience and contingently true.
Consider:
Everything that begins to exist has a cause.
Hume's objection is that this principle cannot be established in either way.
It is not a relation of ideas because denying it does not produce a contradiction.
But experience cannot establish it as a universal matter of fact either, because experience can never examine every possible case.
Therefore, the universal causal principle has not been justified in the way the cosmological argument requires.
Why is it not a relation of ideas?
A relation of ideas is necessarily true.
Its denial would involve contradiction.
But consider:
Something begins to exist without a cause.
Hume's objection is that this statement may seem strange, but it is not logically self-contradictory.
We can conceive the proposition without combining logically incompatible concepts.
Therefore:
"Everything that begins to exist has a cause"
is not established as a necessary truth merely through reasoning.
Why can't experience establish the principle universally?
We certainly experience many causal relationships.
But experience gives us particular observations.
It cannot establish:
Every event, everywhere and in every possible case, must have a cause.
No finite collection of experiences establishes an unrestricted universal claim.
So Hume's objection is not:
We never observe causes.
It is:
Our experience does not justify the universal necessity required by the causal principle.
That is a much more precise objection.
Hume and the Kalām
The objection is especially direct against the Kalām.
The Kalām's first premise states that things beginning to exist have causes.
If Hume is correct, that causal principle cannot be established as either:
a necessary relation of ideas
a universally established matter of fact.
The Kalām may still have a valid deductive structure, but if its causal premise is unjustified, the argument would not be sound.
This distinction between validity and soundness is crucial.
Hume and Aquinas
Hume's challenge can also place pressure on Aquinas because Aquinas uses principles about:
causes of change
efficient causation
causal dependence.
However, the objections must be applied precisely.
Aquinas' Second Way, for example, is not based on exactly the same temporal causal principle as the Kalām.
A student should therefore avoid writing:
"Hume disproves Aquinas because not everything has a cause."
That is too crude.
The better question is:
What causal principle does this particular Way depend upon, and has Aquinas justified it?
Hume and Descartes' continuing existence
Descartes' Argument from Continuing Existence [Descartes' Argument from Continuing Existence] depends upon the idea that continuing existence requires causal explanation or preservation.
A Humean challenge can therefore ask:
Why assume that continuing existence must have such a cause?
If that causal requirement cannot be established universally, Descartes' argument loses a central premise.
Russell's Fallacy of Composition Objection
What is the fallacy of composition?
The fallacy of composition occurs when someone assumes that because something is true of each member of a collection, it must also be true of the collection as a whole.
For example:
hydrogen is not wet
oxygen is not wet
water is composed of hydrogen and oxygen
it would be a mistake to conclude merely from this that water is not wet.
The properties of the parts do not automatically transfer to the whole.
Russell's objection to cosmological arguments
Russell argues that some cosmological arguments make exactly this kind of mistake.
They reason:
each individual being has a cause or explanation
and then move to:
therefore the collection of beings, the universe, must itself have a cause or explanation.
Russell argues that this move is not automatically justified.
AQA identifies Leibniz's argument from contingency as a particular target, while noting that the objection may also be applied to other cosmological arguments.
Applying the objection to Leibniz
Leibniz argues that contingent beings require explanations.
He then asks for a sufficient explanation of contingent reality as a whole.
Russell challenges this move.
Suppose every contingent being already has an explanation.
Why must there then be:
one additional explanation for the entire collection?
That may be a move from:
every member has an explanation
to:
the set itself must have a further explanation.
Russell claims that this may commit the fallacy of composition.
Leibniz's possible pressure point
The debate therefore concerns whether:
explaining every individual member
is sufficient to explain:
the whole contingent state of affairs.
Leibniz's principle of sufficient reason pushes towards a further explanation.
Russell challenges whether that further explanatory demand is legitimate.
So the dispute is not simply about whether individual things have explanations.
It concerns whether the whole needs an additional explanation.
Does the composition objection apply equally to every cosmological argument?
No.
It is most direct where an argument moves explicitly from features of members of the universe to a claim about the universe as a whole.
It is less obviously applicable to Descartes' argument, for example, because Descartes begins from his own individual continuing existence rather than inferring directly from all members to the whole universe.
Similarly, Aquinas' First Way begins from change rather than simply saying:
every individual thing has a cause, therefore the whole universe has a cause.
A strong essay should therefore avoid mechanically attaching Russell's objection to every cosmological argument.
Hume and Russell: The Impossibility of a Necessary Being
What is a necessary being?
A necessary being is a being that could not fail to exist.
This idea is central to:
Aquinas' Third Way
Leibniz's argument from contingency.
It also connects with some ontological arguments studied earlier.
The critic asks:
Can existence itself ever be necessary in this way?
Necessity and propositions
Hume and Russell challenge the idea that an existing thing can be necessary.
The objection is that necessity properly belongs to propositions.
A proposition is necessary when its denial is inconceivable because it entails a contradiction.
For example, if denying a claim produces a logical contradiction, then the claim may be necessary.
But consider:
God does not exist.
Hume and Russell's objection is that there is no contradiction contained simply in this denial.
The same concern applies to existence claims generally.
They therefore reject the claim that God can be established as a necessary being.
Why this threatens Aquinas' Third Way
Aquinas concludes that there must ultimately be:
a being whose necessity is not derived from anything else.
But if Hume and Russell are right that no existing being can possess necessary existence, this conclusion becomes impossible.
The objection attacks the very category Aquinas needs:
necessary being.
So even if Aquinas successfully demonstrates that contingent beings need some explanation, he would still need to show that necessary existence is a coherent property of a being.
Why this threatens Leibniz
Leibniz also concludes that the ultimate sufficient reason for contingent reality must be necessary rather than contingent.
If necessary beings are impossible, this conclusion fails too.
A critic could say:
Leibniz has moved from a demand for explanation to a kind of being that cannot exist.
The burden therefore falls on Leibniz to defend the possibility of necessary existence.
Does this objection prove that God does not exist?
No.
It attacks a particular claim:
God exists necessarily.
A successful objection would show that an argument cannot establish God as a necessary being.
It would not automatically establish:
God does not exist at all.
Again, criticism of an argument and denial of its conclusion should be kept separate.
Comparing the Four Problems
Problem | What it challenges | Especially relevant to |
Infinite series | The claim that a causal or explanatory series must have a first member | Kalām, Aquinas' Ways |
Hume on causal principle | Universal causal claims used as premises | Especially Kalām, but relevant to other causal arguments |
Fallacy of composition | Moving from explanations of members to an explanation of the whole | Especially Leibniz |
Impossibility of necessary being | The claim that a being can exist necessarily | Aquinas' Third Way and Leibniz |
This table is useful for revision because it prevents the objections becoming a generic memorised list.
Comparing the Specified Cosmological Arguments
The Kalām
The Kalām Cosmological Argument [The Kalām Cosmological Argument] begins with the temporal beginning of the universe.
Its major pressure points include:
whether a temporal series must have a beginning
whether the causal principle can be justified
whether a first cause follows from the premises
whether that cause can be identified with God.
The infinite-series and Humean causal objections are particularly direct.
Aquinas' First Way
The First Way begins from change.
Its major pressure points include:
Aquinas' account of change as actualisation of potential
whether every change requires an actual changer
whether the relevant series of changers can be infinite
whether an unchanged changer amounts to God.
The infinite-regress objection is especially important.
Aquinas' Second Way
The Second Way begins from efficient causes and uses atemporal causal dependence.
Its major pressure points include:
whether self-causation is impossible
whether a hierarchical causal series can be infinite
whether a first efficient cause is required
whether that first cause is God.
A temporal objection alone is not sufficient because Aquinas is not merely looking for the earliest event.
Aquinas' Third Way
The Third Way begins from contingent beings.
Its major pressure points include:
whether Aquinas is entitled to infer that universal contingency would mean there had once been nothing
whether derived necessity can regress indefinitely
whether an underived necessary being is possible
whether the necessary being can be identified with God.
The Hume and Russell objection to necessary existence is particularly significant here.
Descartes' argument from continuing existence
Descartes' Argument from Continuing Existence [Descartes' Argument from Continuing Existence] begins from Descartes' continued existence and the need for causal preservation.
Its pressure points include:
whether continuing existence requires an active cause
whether the causal principle is justified
whether an infinite explanatory series is possible
whether the preserving cause established has to be God.
Russell's parts-to-whole objection is less direct here because the argument does not depend upon moving from every member of the universe to the whole universe.
Leibniz's argument from sufficient reason
In Aquinas' Third Way and Leibniz [Aquinas' Third Way and Leibniz], Leibniz asks for a sufficient reason why contingent reality exists.
Its pressure points include:
whether the principle of sufficient reason is true
whether an infinite contingent series could be sufficient
whether the whole requires an explanation beyond explanations of its members
whether the argument commits the fallacy of composition
whether a necessary being is possible.
Russell's objections are therefore particularly important to Leibniz.
Do the objections defeat all cosmological arguments?
Not automatically.
One reason cosmological arguments need to be considered separately is that they use different:
starting points
causal principles
types of dependence
conclusions.
For example, showing that:
an infinite temporal past is possible
may strongly affect the Kalām, but it does not automatically answer Aquinas' argument from atemporal causation.
Likewise:
Russell's fallacy of composition objection
is especially direct against a Leibnizian move from contingent members to the whole, but less obviously targets Descartes' individual continuing existence.
Good evaluation therefore requires precision.
Which premises do the objections attack?
A useful evaluation method is to identify the exact target.
Infinite series
Attacks:
A first member of the explanatory series is necessary.
Hume's causal objection
Attacks:
The causal principle can be known as universally true.
Russell's composition objection
Attacks:
What is true of each member must also be true of the whole.
Necessary-being objection
Attacks:
A being can possess necessary existence.
These are distinct objections to distinct philosophical moves.
Validity and soundness
Many cosmological arguments are presented deductively.
This creates an important distinction.
An objection may show that:
a premise is false or unjustified.
That would threaten the soundness of the argument.
It does not necessarily show:
the conclusion fails to follow from the premises.
That would be an issue of validity.
For example, Hume's objection to the Kalām's causal principle primarily attacks whether a premise should be accepted, not whether the argument's core inference is valid.
Does failure of a cosmological argument prove there is no God?
No.
Suppose Russell successfully shows that a particular argument commits a fallacy of composition.
The correct conclusion would be:
this argument has failed to establish God.
It would not follow:
therefore God does not exist.
Similarly, showing that an infinite series is possible would challenge arguments claiming that a first cause is necessary, without proving that no first cause actually exists.
This distinction is vital in 25-mark evaluation.
Do cosmological arguments establish the full traditional God?
A further problem concerns the strength of the conclusion.
Suppose one of the arguments establishes:
a first cause
an unchanged changer
a sustaining cause
a necessary being
an ultimate explanation.
Does it follow that this being is automatically:
omnipotent
omniscient
supremely good
eternal or everlasting?
Not without further argument.
This links the cosmological arguments back to Divine Attributes [Divine Attributes].
A strong answer should distinguish:
proving that some ultimate cause or explanation exists
from:
proving that the complete traditional God exists.
Overall Comparison
The cosmological arguments share a search for an ultimate explanation, but their differences matter.
The Kalām depends heavily on temporal beginning and causation. Aquinas' First and Second Ways focus on change and sustaining causal dependence. The Third Way moves from contingency to necessity. Descartes asks what accounts for his continuing existence. Leibniz asks for a sufficient reason for contingent reality.
The four specified objections therefore attack different points. The possibility of infinite series challenges the necessity of a first member. Hume questions whether universal causal principles can be justified. Russell challenges reasoning from individual members to the universe as a whole. Hume and Russell reject the idea that an existing being can be necessary.
The most effective evaluation is therefore comparative: identify which premise an objection targets, whether the argument actually depends on that premise, and how much of the conclusion survives if the criticism succeeds.
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Infinite series | A series without a first or final limit in the relevant direction. | Use when questioning whether a first cause is necessary. |
Causal principle | The claim that events, existence or occurrences have causes or explanations. | Use when explaining Hume's objection to cosmological arguments. |
Fallacy of composition | The error of assuming that what is true of each member of a group must also be true of the group as a whole. | Use when explaining Russell's objection, especially to Leibniz. |
Necessary being | A being whose existence could not fail. | Use when discussing Aquinas' Third Way, Leibniz and Hume and Russell's objection. |
Cosmological argument | An argument from the world or its general features towards a first cause, reason or explanation. | Use when comparing the specified arguments. |
Hints from the Examiner Reports 💡
No lesson-specific examiner guidance was identified in the provided reports.
Common Mistakes ⚠️
Mistake: Applying every objection equally to every cosmological argument
Why this is incorrect:The arguments have different starting points and logical structures.
How to improve:Explain exactly which premise an objection targets before applying it.
Mistake: Saying an infinite universe automatically defeats Aquinas' Second Way
Why this is incorrect:The Second Way concerns atemporal or hierarchical causal dependence, not simply the existence of an earliest temporal event.
How to improve:Ask whether the hierarchical causal series could itself be infinite.
Mistake: Saying Hume proves that events do not have causes
Why this is incorrect:Hume's objection questions whether the universal causal principle can be justified as a necessary truth or established by experience.
How to improve:Focus on the justification for the causal principle rather than claiming Hume denies all causation.
Mistake: Describing the fallacy of composition as simply "the universe has parts"
Why this is incorrect:The fallacy concerns an invalid move from a property of the parts to the same property of the whole.
How to improve:Identify the alleged inference from each member requiring explanation to the whole universe requiring an additional explanation.
Mistake: Saying a necessary being means a being that exists forever
Why this is incorrect:Necessary existence means that the being could not fail to exist, not merely that it lasts indefinitely.
How to improve:Keep necessity separate from temporal duration.
Mistake: Concluding that a failed cosmological argument proves atheism
Why this is incorrect:Showing that an argument fails does not establish that its conclusion is false.
How to improve:State precisely what the objection establishes about the argument.
Exam-Style Questions ✍️
Question 1
Define the fallacy of composition. (3 marks)
Indicative answer:The fallacy of composition occurs when someone wrongly assumes that because a property is true of each individual member of a collection, the same property must also be true of the collection as a whole.
Marking guidance:Credit both the move from members to whole and the fact that the inference is not necessarily legitimate.
Question 2
Explain why the possibility of an infinite series creates a problem for cosmological arguments. (5 marks)
Indicative answer:Some cosmological arguments claim that a series of causes, events or dependent beings must ultimately have a first member. If an infinite series is possible, there may be no need for a first cause. The argument must therefore establish why the relevant series cannot continue indefinitely.
Marking guidance:A strong answer should explain how the objection attacks the claimed necessity of a first cause.
Question 3
Explain Hume's objection to the causal principle. (5 marks)
Indicative answer:Hume argues that the claim that everything beginning to exist has a cause is not a relation of ideas because denying it creates no contradiction. Experience also cannot establish the claim as a universal matter of fact because we cannot observe every possible case. The universal causal principle therefore lacks the justification required by cosmological arguments.
Marking guidance:Credit accurate application of both sides of Hume's Fork.
Question 4
Explain Russell's fallacy of composition objection to cosmological arguments. (5 marks)
Indicative answer:Russell argues that cosmological arguments may move illegitimately from the claim that each individual being has a cause or explanation to the claim that the whole collection of beings, the universe, must itself have a further cause or explanation. What is true of every member need not be true of the whole.
Marking guidance:The response should make the parts-to-whole inference explicit.
Question 5
Explain Hume and Russell's objection to the idea of a necessary being. (5 marks)
Indicative answer:Hume and Russell argue that necessity properly applies to propositions rather than existing things. A proposition is necessary when denying it creates a contradiction. However, denying that God exists does not appear contradictory. They therefore reject the claim that God can be established as a necessarily existing being.
Marking guidance:Credit the connection between necessity, contradiction and existence.
Question 6
Explain three problems for cosmological arguments. (12 marks)
Indicative content might include:
The possibility of an infinite series of beings, events or causes.
Why an infinite series would challenge the claim that a first cause is necessary.
Hume's objection to the causal principle.
Hume's Fork and the distinction between relations of ideas and matters of fact.
Russell's fallacy of composition objection.
Why the properties of members do not automatically transfer to the whole.
The specific relevance of composition to Leibniz.
Hume and Russell's objection to necessary beings.
The claim that necessity belongs to propositions rather than things.
The absence of contradiction in denying God's existence.
Marking guidance:A developed answer should explain how each objection affects a premise or inferential move rather than merely naming three objections.
Question 7
Evaluate whether Hume and Russell successfully undermine cosmological arguments. (25 marks)
Indicative content:
A developed answer could consider:
Hume's objection to the causal principle.
Whether universal causal claims can be justified.
The special relevance of the causal objection to The Kalām Cosmological Argument [The Kalām Cosmological Argument].
Whether Aquinas' causal principles differ sufficiently from the Kalām to resist the same criticism.
Russell's fallacy of composition objection.
Its particular relevance to Leibniz's argument from contingency.
Whether explaining each contingent being removes the need to explain the whole.
Hume and Russell's rejection of necessary beings.
Whether denying God's existence genuinely shows that necessary existence is impossible.
The distinction between rejecting a cosmological proof and disproving God.
Whether different cosmological arguments survive different objections.
A reasoned judgement about how much of the cosmological case remains if the objections succeed.
Marking guidance:The strongest responses will apply each objection selectively and accurately rather than treating "the cosmological argument" as one single argument.
Question 8
Evaluate the cosmological arguments for the existence of God. (25 marks)
Indicative content:
A developed answer could compare the full range of specified arguments:
The Kalām
Temporal causation.
The universe's beginning.
An uncaused first cause.
Hume's causal objection.
The possibility of an infinite temporal series.
Aquinas' First Way
Change and actualisation of potential.
The unchanged changer.
Whether the series of changers can be infinite.
Aquinas' Second Way
Efficient causes.
Atemporal causal dependence.
The first sustaining cause.
Whether a hierarchical regress can be infinite.
Aquinas' Third Way
Contingent and necessary beings.
Derived and underived necessity.
Whether necessary beings are possible.
Descartes
Continuing existence and preservation.
Whether continued existence requires a cause.
Whether an ultimate preserving cause must be God.
Leibniz
Contingency.
The principle of sufficient reason.
The explanation of contingent reality as a whole.
Russell's fallacy of composition objection.
The challenge to necessary beings.
Overall evaluation
Whether any infinite causal or explanatory series is possible.
Whether causal principles are sufficiently justified.
Whether moving from parts to whole is legitimate.
Whether necessary existence can belong to a being.
Whether a first cause, sustaining cause or necessary being is sufficient to establish the traditional God.
A reasoned judgement about which premises survive the specified criticisms and what the arguments collectively establish.
Marking guidance:A strong response should compare the arguments throughout, match objections precisely to the reasoning they challenge, and distinguish between establishing an ultimate explanation and establishing the full conception of God.
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