1. Intuition and deduction thesis (rationalism)
We can gain synthetic a priori knowledge through intuition and deduction (Descartes on the existence of the self, God and the external world).

2. One final option!
Empiricists claim that all knowledge of synthetic propositions is a posteriori, while all a priori knowledge is of analytic propositions. So, anything we know that is not true by definition or logic alone, we must learn and test through the senses.
Rationalists deny this, claiming that there is some a priori knowledge of synthetic propositions.

3. According to rationalists there are two key ways in which we gain such knowledge:
The knowledge is innate (already in our minds at birth).
Rational ‘intuition’ and deduction together help us to acquire certain truths intellectually.

4. Focus on 2.
Rationalists argue that we can deduce synthetic knowledge about the world from our rational intuition a priori (without experiencing/observing the world).
Rational intuition involves discovering the truth of a claim just by thinking about it.
Descartes argued that we can establish knowledge of the existence of the self, God and physical objects through rational intuition and deduction.

5. Descartes on the Existence of the Self
After using his three waves of doubt, Descartes concluded that ‘cogito ergo sum’ – ‘I think therefore I am’ – was the only piece of knowledge he could be certain of. He thought this because, even if he doubts his own existence, he is still thinking and thus he cannot doubt that a thinking thing exists:
‘he [the evil demon] will never bring it about that I am nothing while I think I am something.’ Descartes, Meditations on First Philosophy, Meditation II.

6. Descartes on the Existence of the Self
From this truth, Descartes hope to build his system of infallible beliefs.
At this point, Descartes does not know whether or not he has a body; he can only know that he is a thinking thing:
‘a thing that doubts, understands, affirms, denies, wants, refuses, and also imagines and senses’ Descartes, Meditations on First Philosophy, Meditation II.

7. Descartes on the Existence of the Self
Descartes knows what type of thought he is engaging in; for example ‘affirming’, ‘sensing’, ‘imagining’, etc. and he cannot be wrong about this – he can’t mistakenly think he is affirming when he is actually imagining.
Descartes defines his idea of the cogito (the existence of a thinking thing) as clear and distinct.
He then argues that, whatever he can perceive clearly and distinctly is true.
Descartes defines a clear idea as: ‘ present and accessible to the attentive mind – just as we say that we see something clearly when it is present to the eye’s gaze and stimulates it with a sufficient degree of strength and accessibility.’

8. Descartes on the Existence of the Self
He defines a distinct idea as: ‘so sharply separated from all other ideas that every part of it is clear.’
For Descartes, our rational intuition is knowing that clear and distinct ideas are true.
Therefore, Descartes has shown how, through a process of rational intuition and deduction, he can know the synthetic truth that the self exists.
However, Descartes questions that, while we must consider that a clear and distinct thought is true when we consider it, how do we know that it is true when we are not focussing on it?

9. Descartes on the Existence of the Self
In order to know whether clear and distinct thoughts are true when we are not focussing on them, Descartes argued that we need to know that we are not being deceived by God or an evil demon.
Therefore, Descartes sets out to prove that we are not being deceived in order to establish the truthfulness of clear and distinct ideas and, from that, the existence of an external world.

10. Descartes on the existence of God.
Descartes offers two a priori arguments to prove the existence of God: His Trademark Argument and his Ontological argument.
Both of these arguments move from an idea of an omnipotent and perfect being to the existence of this being.
In addition to proving God’s existence, Descartes needs to show that this God would not let us be deceived.
It is a clear and distinct idea that God’s perfection is not compatible with deception.
Therefore, God would not deceive us or let us be deceived by an evil demon.

11. Descartes on the existence of the external world.
Descartes argues that he has a clear and distinct idea of what a physical object is.
He also argues that his perceptions of physical objects are involuntary and ‘much more lively and vivid’ than imagination or memory.
As his perceptions are involuntary they cannot be caused by himself (otherwise he would know about the cause of them) so they must be caused by something external to him.
As God exists and is perfect and not a deceiver, Descartes’ perception of physical objects must be caused by physical objects themselves.
Therefore, there is an external world of physical objects causing our perceptual experiences.

12. SO……
Therefore, according to Descartes, he is able to prove the existence of the self, God and an external world through a process of rational intuition and deduction rather than sensory experience.

13. Geometry
Geometry is another proposed example of how we can gain substantive knowledge of the world independently of the senses.
For example, the Greek mathematician Euclid started with a set of self-evident axioms and definitions (e.g. All right angles equal each other) and moved from these to prove a further set of propositions.
Through the careful use of reason, Euclid was able to establish a large and systematic body of truths all derived from his initial axioms and definitions.
It is argued that the truths established through reason are synthetic rather than merely analytic because they can be applied to the world (for example we are able to construct buildings and bridges using geometrical propositions).
Geometry seems to be telling us new facts about the nature of physical space, facts that have genuine application and are not just true by definition.