Truths of Reasoning and Truths of Fact

“You are a king, then!” said Pilate.
Jesus answered, “You say that I am a king.  In fact, the reason I was born and came into the world is to testify to the truth.  Everyone on the side of truth listens to me.”
“What is truth?” retorted Pilate.  With this he went out again to the Jews gathered there and said, “I find no basis for a charge against him.  But it is your custom for me to release to you one prisoner at the time of the Passover. Do you want me to release ‘the king of the Jews’?”

  • John 18:37-39

Then the Lord spoke to Job out of the storm.  He said:
“Who is this that obscures my plans
    with words without knowledge?
Brace yourself like a man;
    I will question you,
    and you shall answer me.

“Where were you when I laid the earth’s foundation?
    Tell me, if you understand.
Who marked off its dimensions?  Surely you know!
    Who stretched a measuring line across it?
On what were its footings set,
    or who laid its cornerstone—
while the morning stars sang together
    and all the angels shouted for joy?

  • Job 38:1-7

“So how is it possible to progress from knowing what will happen tomorrow somewhere on the other side of the world?  For Leibniz, the answer lies in the fact that the universe is composed of individual, simple substances called ‘monads.’  Each monad is isolated from other monads, and each contains a complete representation of the whole universe in its past, present, and future states. …
“Leibniz claims that every human mind is a monad. …
“Is the temperature of the surface of Betelgeuse a truth of reasoning or a truth of fact? …
“The trouble for Leibniz is that he holds that truths of reasoning are ‘necessary’, meaning that it is impossible to contradict them, while truths of fact are ‘contingent,’ they can be denied without logical contradiction.  A mathematical truth is a necessary truth, because denying its conclusions contradicts the meanings of its own terms.  But the proposition ‘It is raining in Spain’ is contingent, because denying it does not involve a contradiction in terms – although it may still be factually incorrect.
“Moreover, Leibniz tells us that whereas no-one can reach the end of an infinite analysis, God can grasp the whole universe at once, and so for him all truths are necessary truths.  The difference between a truth of reasoning and a truth of fact, therefore, does seem to be a matter of how one comes to know it – and in that case it is difficult to see why the former should always be seen to be necessarily true, while the latter may or may not be true.”

  • Sam Atkinson (senior editor), The Philosophy Book, Big Ideas Simply Explained

Gottfried Leibniz (1646-1716) seemed to try a unification of the Empiricists (i.e. John Locke, George Berkeley, and David Hume) and the Rationalists (i. e. Rene Descartes, Benedictus Spinoza, and Immanuel Kant), but he did so from a Rationalist point of view.  Thus, facts determined by reasoning became necessary, while facts determined by observation became contingent upon observation as to whether these were even facts, or mere conjectures.

Yet, Leibniz determined that for God all facts are necessary, for God necessarily knows everything, by God’s omniscience.  Jesus said that He is the Truth.  While Pontius Pilate was trying to get the facts regarding the charges against Jesus, Jesus was arguing a philosophical argument.  When Pilate tired of the argument, saying “What is truth?”, Pilate tried to bargain with the crowd, since he found no way to see guilt in Jesus, or to argue philosophically with Jesus.  But the ultimate reason for God’s knowledge to be necessary truth is His retort to Job.  “Where were you when I created the heavens and the earth?!”  Everything is God’s and God made all things.  And yes, God knows the exact temperature on the surface of Betelgeuse, and He knows if it is raining at this moment in Spain, and the exact location of each raindrop.  He knows them as necessary truth, for who could ever contradict God?

I had a beloved professor.  While I took several engineering classes under him, he also taught a non-engineering engineering class.  That is, the class was for non-engineering majors to get an introduction of what engineering was.  He always had a pop quiz (meaning an unannounced quiz), and many of these quizzes would make Leibniz proud.  On a rainy day, he might ask the class if the sun was shining.  Although it could not be observed by the empiricists, it is a necessary truth that the sun is shining.  If the class was at night, he could ask the class the same question with the same correct answer.  The sun is shining at night, but we are shadowed by the earth and cannot see it.  Then, if it was sunny, he would ask if it was raining?  Here is where the contingent truth enters the picture.  It is probably, at one given moment or another, raining somewhere on the face of the earth.  But the proof of that truth of fact is contingent upon observation.

In other words, each class period started with a quiz to see if the students could think.  Sadly, he had a poor success rate.  I often took the quizzes along with a few others, just for fun, and when he and I both had spare time, we would sit in his office and discuss our thoughts on the subject.  He often gave me the pop quiz before he gave it to the class, just to see if I was thinking.

You see, a good engineer is not one who can make the most complex of calculations or have the books memorized, the good engineer is prepared to step away from the process for a few seconds and think it through.

At one point in my career, my boss was used as a consultant on a project where someone was converting dirt into iron, by slowly roasting it.  The pilot plant process was going well on the top surface of the soil, but not beneath the surface.  He got the group together for a brainstorming session, otherwise we were not involved.  He described what was going on.  Someone asked if the soil was an iron oxide enriched soil, which the soil was.  But then I ruined the brainstorming session by introducing truth to the discussion.  I said, “Once you create a crust of iron on the surface that blocks the atmosphere from reaching the lower layers of dirt, the reaction stops.  Besides, the reaction, overall, is endothermic.”  He told me the process was exothermic and stormed from the room.

The others turned to me, and I explained that to turn raw iron ore into iron, it was a three-step process.  Each reaction step needed contact with the atmosphere, usually the carbon monoxide in the furnace gases.  I had already done the research for a different process, one that worked.  Of the three reaction steps, one was slightly exothermic (releasing heat that could further the reaction), but the other two reaction steps were endothermic (absorbing heat from other processes in order to have a reaction at all).  Since all the heat was generated from above the pile of dirt, the heat could not penetrate to the lower layer of dirt until a point when the iron formed on the top prevented the atmosphere from reaching the lower layer.

What the process needed was a stirring action or a rotating drum drier (tumbling action), but because the boss included the fire that created the carbon monoxide in his thinking, he could never see the problem with the process.  He got angry and cut off further discussion.  Thus, the pilot plant failed.  The failure was not that the process could not work, but it did not work as designed due to a lack of thinking.

Yet, thinking was the usual process of the Rationalists, those who only saw existence in rational thought.  The Empiricists also thought about the existence of something, but they had to see it, touch it, smell it… sense it.  Leibniz tried, from his Rationalist background, to create a bridge between the two schools of thought.

Whether he was successful or not, his rational conclusion regarding God is important.  God created the heavens and the earth, but God remains engaged in the goings on of the earth.  Thus, God knows everything.  God knows down to the fraction of a degree how hot every stars’ surface is, not just Betelgeuse.  And since God knows without anyone being able to contradict God, God’s knowledge is necessary truth.

Indeed, when Thomas asked about where Jesus was going, Jesus answered, “I am the way and the truth and the life.  No one comes to the Father except through me. (John 14:6)

If you like these Tuesday morning essays about philosophy and other “heavy topics,” but you think you missed a few, you can use this LINK. I have set up a page off the home page for links to these Tuesday morning posts. I will continue to modify the page as I add more.

Soli Deo Gloria.  Only to God be the Glory.

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