Hume VS Leibniz

What is Hume’s fork? Does Hume’s distinction succeed in overthrowing the foundations on which Leibniz’s rationalist metaphysics rest?

I will begin with an explanation of Hume’s fork. Hume’s fork is a distinction between two ways of acquiring knowledge: relations of ideas and matters of fact. This distinction ‘forks’ out bidirectionally, hence the name. I will explain both prongs of Hume’s fork below.

Relations of ideas

Relations of ideas are true by definition. 3 examples of this are:

1. A square has 4 equal sides.

2. Every mother has a child.

3. If Napoleon reigned for 10 years, then he reigned for at least 7 years.

This type of knowledge is acquired a priori. For example, I can know every mother has a child by reason alone. I do not need to look to the exterior world to conclude this statement is true. It is true by rational analysis. To put it differently, this knowledge is necessary because it has to be true by definition. Later philosophers (Kant, 1781; Ayer, 1936) often dubbed this group of knowledge analytic knowledge, because it is attained by analysis alone. Another term used is analytic a priori knowledge. Analytic a priori knowledge is formal, logical and abstract. For Hume, this is a solid basis for acquiring true knowledge.

Matters of fact

The other prong of Hume’s fork is the notion of matters of fact. This type of knowledge is true by observation. 3 related examples of this are:

1. This tabletop is shaped like a square.

2. My mother has two children.

3. Napoleon reigned from 1804 – 1814, and for another 111 days in 1815.

This type of knowledge is acquired a posteriori. For example, it is not self-evident that Napoleon ruled for ten and a bit years. To acquire this knowledge, I need to look at the exterior world to conclude this is a true statement. This would be from looking at historical documents, registries, archives, fact-checking with other historians’ dates, the internet, etc. It is true based upon external observation.

Hume dubs this ‘contingent’ knowledge because it is contingent on a host of things, including observation, repetition, verification and interpretation. Kantians and others have dubbed this category of knowledge as synthetic; it requires a synthesis of different factors, which rely on our senses and rationality; we are the ones putting the pieces together. Synthetic a posteriori knowledge is empirical, concrete and not always logical. After all, it is true that a platypus is an egg-laying mammal, even though an egg-laying mammal seems to defy logic. For Hume, synthetic a posteriori knowledge is not a solid basis for acquiring knowledge.

In short, Hume’s fork is the most fundamental idea he has on epistemology. How does this compare to Leibniz’s ideas on epistemology and metaphysics?

Predicate-in-notion

Leibniz has several ideas on epistemology and metaphysics. The cornerstone idea of Leibniz’s worldview is the predicate-in-notion (Leibniz, 1685.) This principle states that every true proposition always contains a subject and predicate i.e., a thing and a property. For Leibniz, a true proposition also contains the predicate in the subject. For example, ‘a pentagon has 5 sides’ has:

- a subject (a pentagon)

- a predicate (the property of having 5 sides.)

The predicate is also contained in the subject i.e., there are 5 sides ‘contained’ or within a pentagon. Put more casually, the predicate-in-notion describes some thing having some property.

However, describing some thing as having some property does not automatically make it true. The sentence ‘Napoleon was Chinese’ has a predicate-in-notion structure but is a false statement. Therefore, Leibniz further elaborates on his epistemology with two types of truth:

1. Truths of reason

2. Truths of fact

Truths of reason

These are truths we can reach by reason alone. They are a priori and they fulfil the principle of non-contradiction. Take the example ‘Brothers are male siblings.’ This statement is true by definition. If we deny the statement ‘Brothers are male siblings’ then we are saying ‘Brothers are not male siblings’, which is a contradiction. If we deny the statement ‘A square has 4 sides’, we are saying ‘A square does not have 4 sides’ and so on. Truths of reason cannot contradict themselves, whereas truths of fact are often contradictory as shown below. A truth of reason is also necessary i.e., it is true by definition. A truth of reason is also universal i.e., it is true in all cases. More on this point later.

Truths of fact

These are truths we reach by observation. They are a posteriori. Truths of fact do not have to fulfil the principle of non-contradiction, nor do they have to be predicates-in-notion (although they often are.) For example, the statement ‘platypuses are egg-laying mammals’ seems to be a contradiction, but it is a true statement because it has been observed to be so. Truths of fact are contingent on other truths of fact; they depend on cause and effect i.e., things that happen in the physical world. They are also contingent on our senses and our experiences. This is in contrast with truths of reason, which are necessary because they must be true by definition, by circumstance, by reason, by logic, etc. Truths of fact are also singular, in contrast to truths of reason, which are universal. Leibniz explains the distinction between singular truths and universal truths with a creative idea: possible worlds.

Distinction between singular and universal truths

Leibniz believes in God. God is omnipotent by definition, so could have made any number of worlds instead of the one we live in. He could have made a world where the sky is green, or a world where Napoleon won the Battle of Waterloo, or a world where fish have legs, etc. Put another way, there could be an infinite number of possible worlds. For Leibniz however, God is not beyond the laws of logic. For God to be perfect, God has to be logical (Leibniz, 1685.) Therefore, in any of these possible worlds, logic still has to stand. In any of these worlds, truths of reason still have to be true, even if the truths of fact are different from our world.

For example, in a world where Napoleon won at Waterloo it still remains true that a square has 4 sides. This is because Napoleon winning at Waterloo is a singular truth which is contingent on the causes and effects in this alternate world. A square having 4 sides is a universal truth which has to be necessarily true, because it is true by definition, does not depend on observation and does not depend on any laws of physics. A 4-sided square has to be true in the world of a victorious Napoleon, or any other world God could make.

Put tersely, singular truths are dependent on material reality, whereas universal truths are not. Napoleon winning is dependent on the material conditions of this alternate world, but a square having 4 sides does not depend on material conditions at all.

Before comparing Leibniz’s ideas with Hume’s fork, it is worth briefly explaining two more metaphysical ideas Leibniz postulates. I will then compare his ideas with Hume’s fork.

Principle of perfection

As mentioned before, Leibniz believes in God. His metaphysics depend on God’s existence. God is perfect by sheer logic because God is omnibenevolent. For Leibniz, this means everything God does also has to be perfect. That includes the flawed, fallen world we currently live in. God has made this world to be ‘the best of all possible worlds.’ God could have made a myriad of other possible worlds, but He chose to make this one. Why? Because this is the best of all possible worlds that is logically consistent, rationally sound and preserves free will (Leibniz, 1710.) All other possible worlds would be less perfect than the one we live in according to Leibniz.

Principle of sufficient reason

For Leibniz, every action has a cause; every event has a reason behind it. This applies to both necessary truths of reason and contingent truths of fact. Leibniz admits we frequently do not know why things are the way they are. He says:

“Our reasonings are grounded upon two great principles, that of contradiction… And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us.” (Leibniz, 1714.)

It seems Leibniz believes if God is moral, He cares and He is perfect, then there is a sufficient reason behind every event in existence, even if we finite humans cannot understand why. Another way of putting it is everything in existence is a priori knowable for God, because God can foresee every single thing that will ever happen and can know why it will happen.

Leibniz’s distinctions VS Hume’s fork

Both Leibniz and Hume make important distinctions in epistemology. Leibniz’s distinction between truths of reason and truths of fact is very similar to that of Hume’s fork: relations of ideas and matters of fact. However, both philosophers interpret this distinction very differently to each other and take their perspectives in very different directions. They also both believe legitimate knowledge is acquired in very different ways.

Does Hume’s fork overthrow Leibniz’s metaphysics? In short, if Hume is right about fundamental epistemological and metaphysical questions, then his fork does indeed undermine Leibniz. I would not say it overthrows Leibniz though, even if Hume is right about everything he postulates. There are tensions between the two philosophers though and they are worth noting to clarify the differences.

Reason for everything VS Nothing has a reason

Leibniz’s claim is at odds with Hume’s worldview. He states all of existence is cause and effect, with God being the first cause of everything. It is like an incredibly intricate spider’s web of cause and effect, with one thing leading to another, with every single thing in existence interacting with and dependent upon everything else. Not only this, but every event has a reason behind it too.

This is at odds with Hume’s epistemology. Hume points out we can never observe or experience causation itself – we only observe what he dubs a ‘constant conjunction’ between events happening. In other words, we only actually observe effects and assume there are causes at play. For example, if I drop an apple, it will surely drop to the ground. Hume would contend that whilst it is very likely the apple will fall to the ground, there is no certainty it will. We assume the apple will fall to the ground based on our prior experiences, but this is an assumption and not an unshakable truth. There is no guarantee that something will happen in the future the same way it happened in the past. This is the origin of the infamous ‘problem of induction’ (Hume, 1748.) Hume’s argument is completely at odds with Leibniz’s argument that every event is a product of cause and effect. Hume is saying that there is no cause and effect!

The ambiguity of metaphysical claims

Hume does not even accept metaphysical claims because they are not meaningful. This is very much at odds with Leibniz who makes extremely bold metaphysical claims e.g., that we live in the best of all possible worlds. For Hume, metaphysical claims are not meaningful because they are not based on experience; Hume is an empiricist (one who believes knowledge comes from observation.) Hume also dislikes metaphysics because it makes unprovable claims. Metaphysical ideas are not even ‘relations of ideas’ for Hume because they have no basis in everyday experience. In other words, Hume’s fork rejects much of metaphysics. Hume himself says:

“Principles taken upon trust, consequences lamely deduced from them, want of coherence in the parts, and [want] of evidence in the whole, are everywhere to be met within the systems of the most eminent philosophers, and seem to have drawn disgrace upon philosophy itself.” (Hume, 1739.)

Principles ‘taken upon trust’ are not only weak arguments, but they are not even reason-based from Hume’s perspective. This is ironic considering Leibniz is considered a rationalist, a reason-based man.

How can this be the best of all possible worlds?

In my view, the notion that this world is the ‘best of all possible worlds’ is Leibniz’s biggest Achilles’ heel. Hume’s fork would reject this claim for being neither a relation of experience-based ideas, nor as matter of fact. Nor do I think Hume would ever believe this is the best of all possible worlds… he was notoriously sceptical of God’s existence, never mind this world being inherently good. Hume is not even needed to seriously critique this idea… to argue this world is the best of all worlds does away with all theodicies and much of theology. It also goes against religious scripture in my opinion i.e., the Tanakh (Old Testament), New Testament and Quran all insist God wants the world to be a better place, implying this is not the best of all possible worlds. Furthermore, it goes against human intuition and other trains of rational thought e.g., Augustine’s City of God being an ideal version of the City of Man – our world (Augustine, 426.)

Hume’s weaknesses

I have prodded Leibniz with Hume’s fork, and Hume’s fork is quite a sharp philosophical tool. Leibniz definitely has some weak points. However, Hume is not perfect either and Hume’s epistemology does have some weaknesses. One could say Hume’s fork is a bit rusty.

Hume’s claims are not based on experience

Ironically, Hume’s hyper-scepticism and rationality are not based on empiricism. At best, they are based on abstract thoughts that are interpretations of his experiences. At worst, they are not based on external factors nor rational thought at all, but mere scepticism. His whole philosophical framework is arguably built on a an anti-rational and baseless foundation of critiquing knowledge without discovering it. It is a harsh argument with some truth behind it.

If Hume is right, science is wrong

Hume’s fork does away with induction. This is because Hume believes all knowledge is based in experience (Hume, 1748.) Therefore, Hume’s fork can only legitimate empirical knowledge; knowledge we acquire from our senses. After all, empiricists believe ideas derive solely from experience. However, committed to being intellectually honest, Hume points out that we cannot rely on inductive knowledge from an empirical perspective. This is because induction is based on prior events happening again in the future, which is a position that cannot be proven by prior experience, or anything for that matter. It is like the example of dropping an apple; we only assume the apple will fall in the future because it has fallen to the floor every single time previously… but this is not proof it will fall in the future.

This is a radical position for Hume to take. It seriously undermines the scientific method, much of which is based on observation, prediction and verification, all of which are inductive methods. Science is built on the assumption that what has been observed in the past will happen again in the future. Science seems to be an incredibly powerful, reliable, repeatable and useful tool despite Hume’s criticism. To do away with induction, the foundation stone of science, seems to be extremely radical and unhelpful.

Hume’s assumption

Hume has not disproven causation – he’s assuming there is no causation. Just as causal thinkers assume causation is there, Hume and non-causal thinkers are assuming that there is no causation there. Believing in constant conjunction instead of causation is a belief - an assumption. Causation and non-causation are unverifiable ideas, and likely unfalsifiable. In Hume’s words, his principle of non-causation is a ‘principle of trust.’

God might still be there

Also, Hume has not necessarily proved Leibniz is wrong because Hume has not shown that God does not exist. Nobody can prove or disprove God’s existence, because it is another unverifiable and unfalsifiable claim. Hume’s fork would reject God as being a non-empirical idea, but that does not mean God is not there. It just means we finite mortals cannot always understand God’s ways… just because there are stars we cannot yet see, it does not mean those stars are not there. Dismissal is not disproving.

Conclusion

It seems Hume has clay feet just as Leibniz does. But to answer the question, does Hume’s fork overthrow Leibniz’s metaphysics? Hume’s fork does overthrow Leibniz, but only if Hume is right about fundamental philosophical questions, which I do not think he is. I think Hume is partially wrong, but I also think Leibniz is partially wrong! Specifically, Leibniz’s claim that this world is the best of all logically possible worlds is untenable to me, as explained above.

Hume is right only if we assume Hume is right about non-causation and the problem of induction, which I believe are two radical claims that I respectfully disagree with. Hume assumes that there is no causation, only constant conjunction. He cannot prove his claim that an apple might float upwards instead of falling downwards. It is the same logic he uses to critique rationalists who Hume argues cannot prove a dropped apple will always fall downwards. The scientific tradition is built upon the power of induction, repeated experimentation and refinement. How could doubting induction ever scratch a nick on the achievements of science?

Even if Hume is right about the problem of induction, induction is far too powerful a tool to stop using. I am philosophical pragmatist, meaning the validity or truth value of an idea depends on how useful it is. In other words, I believe ideas are tools, and induction is an extremely useful tool, even if induction extrapolates false ideas on rare occasions. Even if induction is not always the rock-solid truth, it seems to be very close to the truth a lot of the time.

Again, Hume’s claim of non-causation is an assumption and not a very helpful one. Even if there is no such thing as cause and effect, cause and effect seems to be a very useful framework in physical science, medicine, philosophy and theology. It is through the prism of cause and effect that people understand the mechanics of the universe. If one billiard ball hits a second ball on a pool table, the second ball moves because the first ball hit it (note the word cause in because.) If Hume denies cause and effect and insists on conjunction, then does that mean it is coincidence the second ball moves? Could the second ball just do something random? Things start to become very messy very quickly when one denies causation.

I think Hume is wrong on induction and causation and Leibniz is wrong on theodicy. Nevertheless, I believe Hume’s fork is compatible with God’s existence and some of Leibniz’s ideas. This means I do not believe Hume’s fork overthrows Leibniz’s metaphysics, because I think the two are somewhat compatible with one another. I also do not think Hume’s fork is crafted on a solid metaphysical basis, because its foundation for attaining knowledge is very open to question. It is worth mentioning that not all of Leibniz’s ideas are compatible with Hume’s fork, specifically the principle of sufficient reason, the principle of perfection and God’s a priori knowledge of all events. However, the predicate-in-notion principle, the principle of non-contradiction and some of his notions of God are compatible with Hume’s fork.

To conclude, I do not believe Hume’s fork overthrows Leibniz’s metaphysics because I do not think Hume is completely right, but his fork helps expose some of Leibniz’s flaws.

References

Augustine. (426) On the City of God Against the Pagans. Hippo Regius/Annaba, Algeria.

Ayer, A. J. (1936) Language, Truth and Logic. 2^nd edn. London: Penguin Books.

Hume, D. (1739) A Treatise on Human Nature. London.

Hume, D. (1748) An Enquiry Concerning Human Understanding. London.

Kant, I. (1781) Critique of Pure Reason. Königsberg/Kaliningrad.

Leibniz, G. W. (1685) Discourse on Metaphysics. France.

Leibniz, G. W. (1710) Essays of Theodicy on the Goodness of God, the Freedom of Man and the Origin of Evil. France

Leibniz, G. W. (1714) The Monadology. France.