Seeing and hearing &c. directly (I know there is a chair in the room because I can see it)
Seeing and hearing indirectly, by testimony, photographs, books &c. (you believe I am 38 because I told you - you know what your great grandfather looked like from a photograph)
Remembering (you believe you had carrots for lunch because you can remember it)
Logic and inference (you can make new beliefs by putting old ones together logically)

     Some other means of getting knowledge you might include are:

       Scripture [a special kind of testimony, because allegedly infallible]
       Clairvoyance [a special kind of seeing and hearing directly]
       Direct communication from God [another special kind of testimony]

Which of these could deceive us?

Seeing and hearing often deceive us.
People often lie or are mistaken (nothing someone tells you is certain)
Photographs can be manipulated or just unclear.
Memory often plays tricks on us.

A philosophy or science based on these things could be wrong.

Logic cannot be wrong. There is ultimately only one logical rule - if something is p then it is not not p. For example: if I am happy, then I am not not happy.

Why can logic not be wrong? Because it is the basis of all our meaningful language and thought. If it is wrong, there is no point in saying so because there is nothing left to say so with.

"All sentences in the English language are meaningless".

If this sentence is true, it is meaningless and if it is meaningless it cannot be true.
To say "Logic is invalid" similarly destructs itself because if logic is invalid then it could be valid or invalid (because it no longer has to be one or the other), in which case the sentence is quite pointless.

Thus, a philosophy based on pure logic could not be wrong.

But normally, logic works on other propositions, that we have discovered through one of the other means. A philosophy based on this sort of logic could be wrong.

We need a philosophy based on pure logic and nothing else… Then, we can be certain of what we discover.

Descartes thought he had done this. He proved he existed by pure logic. He also proved God existed by pure logic. Finally, he proved everything else existed by equally pure logic. He had found the solid basis on which philosophy could be built. Or so he thought…

Many people damn Descartes (I do, for example). But historically he is very important. He ushered in an era of philosophical freedom, in principle, since philosophy no longer depended on Plato or the Bible or even our own eyes. He finally allowed the possibility of Europe moving out of the Dark Ages into the age of Enlightenment. He was a rationalist, who relied on reason alone.

Here is what he (thought he had) proved:

1 I exist. If I doubt whether I exist I must exist, otherwise I couldn't doubt it. That, surely, is logic.

2 God exists because
a) The concept of God is perfect and I am imperfect (I have doubts, which make me imperfect by definition). What is imperfect cannot create what is perfect, and yet I have the concept of God. Therefore, the concept of God must have been planted in me, not created by me. Only what is perfect could plant the perfect concept in me. By definition, only God is perfect. Therefore God implanted the idea of God in me. Therefore, God exists.
b) I can imagine something (God) which exists by definition (i.e., its definition includes 'existence' as a property, just as the definition of 'unicorn' includes 'having one horn' as a property. If something which existed by definition did not in fact exist, that would be a contradiction - a non-existent God would be like a four-angled triangle or a three-horned unicorn. We can't have contradictions - therefore God exists.

3 The world exists because by definition God is perfectly good and by definition he exists. If he is perfectly good he would not fool me into believing that the world existed - that would be deceiving me. Therefore, the world exists.

Descartes went further, in fact. He spoke of the 'I' which he had proved to exist as a soul and distinguished it from matter.

Some would say you cannot even be sure of logic - you just have to use it. If you wear pink spectacles, everything looks pink and you can't see it any other way. Perhaps we see the world 'logically' - through 'logical spectacles' and we can't see it any other way. But perhaps it isn't really logical…

Does it MATTER if we are certain or not? Providing we can live our life out competently, does it matter how we manage it? On planet earth, it seems, only humans worry about finding 'the truth'. Are we actually being over-optimistic in thinking we can do this and perhaps wasting our time?

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