I'm going to comment on this post:
There is much talk about logic today. It is obviously used significantly in discussions with philosophers and mathematicians. It has also been a tool of some (particularly presuppositional) apologists to argue for God. They insist that atheists cannot account for logic since it is immaterial and universal. Since logic undeniably exists, then something else immaterial and “universal” must also exist to account for it, namely God.
There's a lot more to the argument than: since universal, immaterial logic undeniably exists, then something else immaterial and “universal” must also exist to account for it, namely God.
This understanding of logic is taught as if it is some ephemeral abstract notion or set of principles of reason that “exists” only in the mind with no basis in physical reality.
The position is that logic primarily or fundamentally subsists in the infinite and timeless mind of God. God's mind is the exemplar. Logic has its "basis" in God's mind. However, math and logic are exemplified in time and space.
That is, according to this argumentation physical reality cannot account for the principles of logic. Nothing could be further from the truth. The principles of logic, such as the principles of identity, excluded middle, and non-contradiction are not just principles of rationality. They are principles of being. Let’s look to see what they are and why they must be grounded in reality and not thought.
It's important to distinguish between divine and human thought. The position is not that logic is reducible to human psychology. It's not intuitionism (e.g. Brouwer). God's thought and God's being are conterminous.
Yes, you could say logic is grounded in "being", but not just any kind of being will do. Physical existence won't suffice.
The law of identity states that something is identical with itself. If a thing is “A” then it is “A”. If something is a tree, then it is a tree. This seems rather mundane and uninformative; however, try imagining reality if this were not the case. The principle of excluded middle says that something is either “A” or “non-A”. It is either a tree or a non-tree. There is no middle ground (the middle ground is excluded). The law of non-contradiction says something can’t both be “A” and “not-A” at the same time in the same sense. That is, it can’t be a tree and a non-tree simultaneously.
That confuses logic with concrete exemplifications (or property instances) of abstract objects. A tree approximates the law of identity. Ideally, logical and mathematical truths map onto static, timeless relations or objects with discrete boundaries.
But physical objects undergo continuous incremental change. Physical objects have fuzzy boundaries in space and time. They have degrees of solidity. They exchange atoms with the surrounding environment. They blend into each other. So that comparison is counterproductive. There's never an exact match between a tree and the law of identity.
We get our understanding of these principles from the world around us. They are not just principles of thought, but of being. The law of non-contradiction is not just that a statement can’t be both true and false. The law of non-contradiction is that something in existence can’t be and not be simultaneously in the same way. In other words, a tree can’t be a tree and not a tree at the same time in the same sense. These laws are thus grounded in being and abstracted via our knowing process. We have experience of reality and then induce said principles of being and know that they apply to all thought and experience…While these laws are undeniable and are self-evident, the source of our knowledge of them is still physical reality.
He operates with an epistemology according to which all knowledge of universals is based on a psychological process of abstraction from particulars.
Now, I have no problem with sense knowledge or induction. Yes, we often generalize on the basis of samples. Fine.
But that can't be the basis of knowledge all the way down. You can't derive a concept of numbers from observing physical objects, for unless you already have numerical concepts to work with, you can't group physical objects numerically. Numbering objects requires a numerical preconception.
You can't bootstrap logical or mathematical knowledge from sensory perception. You can't group five apples by number unless you recognize that they comprise five apples, and you're not going to arrive at that classification by staring at some apples with a blank slate mind.
It takes knowledge to learn. It takes some prior knowledge to acquire additional knowledge. An initially empty mind has no frame of reference to evaluate sensory input. The mind of the percipient must have a logical structure which enables it to organize or reorganize sensory input. An inbuilt classification-system.
Another way we know the laws of logic is that they are undeniable. One cannot deny something like the law of non-contradiction without using it. If one attempted to do this, he would be forced into saying that his position is true and not false, and that the opposite opinion would be false and not true. We don’t argue from more foundational principles to arrive at these principles of logic. They are first principles of thought and being. The are first because they are foundational and self-evident. They can’t be denied. Further, they don’t require, nor could they require, antecedent proof. Such proof would have to use the laws of logic.
But necessary truths of logic can't derive from contingent truths of the physical world. In many respects, the physical world might have been different. Causation is a weaker principle than logical entailment.
Physical reality is known directly and is evident to our senses.
Actually, physical reality is known indirectly. Physical reality is mediated to the mind via sensory perception. A process of encoded and decoded information.
Note I said “evident” not “self-evident.” Propositions are self-evident when we know their meaning. “Bachelors are unmarried men” is a self-evident proposition because as soon as we know the meaning of the terms and the proposition as a whole, we know it is true.
But that's different from logic. That's stipulative. True by definition.
However, things are evident to our senses. I do not need an argument that there is a tree outside of my window. I simply see it. Thus, things are evident and the laws of logic are self-evident and undeniable. (I realize I am skipping over a veritable wonderland of skepticism and rationalism which I have no desire to deal with here. I simply don’t think I need to “justify” the existence of something I just ran my car into. If someone honestly doubts the existence of external reality, I would submit that his problem is not philosophical but psychological and he needs to seek medical treatment immediately.)
That confounds the metaphysics of math and logic with the psychology of sensory perception.
Of course, such principles can be applied to thoughts and propositions that don’t say things about reality. Logic can be applied to fictitious beings and propositions that say something like, “All monsters live in London.” However, such fictitious beings and propositions are still based in being—that is, things that exist extra-mentally. While a fictitious being doesn’t exist in reality (by definition), we get the concepts of things like monsters from reality. In other words, following the great empirical maxim, “All knowledge is grounded in reality,” we don’t have any new ideas, even of fictitious monsters, that are not tethered to or grounded in reality.
i) Fictions, hypotheticals, and counterfactuals have their source in God's power and imagination. Something is ultimately possible because God can enact that scenario. And God's infinite imagination is the repository of all concepts. God has created rational agents with some knowledge and power.
ii) I'd add that fictions are ideas, and therefore have a discrete identity lacking in physical objections.
This is why the presuppositional argument for the existence of God from logic fails. A common argument from them is that atheists cannot account for logic. Logic is immaterial and universal, they say, and as such, atheists can’t account for anything that is immaterial and universal. But if what I am arguing for is true, the presuppositionalist’s argument is not successful. This is because atheists can account for logic, because logic is grounded in reality and being. Yes, God is being as such, and as “being” the laws of logic are tethered to God. (God is God, God cannot be non-God, etc.) That is, in a sense they are antecedently grounded in God because they would be the case even if the physical realm did not exist.
But that means an atheist can't account for the laws of logic inasmuch as these are essentially independent of the physical world. To be sure, some atheists are Platonic realists, but that's different from Brian's paradigm. Moreover, Platonic realism is arguably ad hoc.
Another important note is that the laws of logic are not really immaterial. Sure the abstracted propositional form of being such as “A tree can’t be a tree and not a tree simultaneously” can be immaterial. But if logic is not merely a rational enterprise and is a second order based on the first order of physical reality, then the basis for logic is not immaterial.
God's rationality is not a second-order exercise based on God's first-order being. That's a false dichotomy. God's mind and God's being are both first-order realities, which underlie physical reality.
Our abstractions of the principles are mental, such as numbers, but many, if not most, philosophers do not think that numbers are real.
That's an illicit argument from authority. Moreover, it's not coincidental that mathematicians like Quine, Gödel, and Penrose subscribe to mathematical realism.
They like logical principles are abstracted from the real world. The number 2 does not exist. But I can say there are two trees. The two-ness is simply the addition of one more tree than the first. Math then is like logic in that the numbers are abstracted from the material world and then one can perform mental operations. But these numbers do not exist (unless one holds an extreme Platonic view). And as such, the atheist can account for logic by its foundation in sensible objects—just like he can account for numbers. Thus, the presuppositional argument for logic is going to reduce to some cosmological argument that says the universe needs a grounding in something other than itself.
If Big Ben strikes three o'clock, what do I actually hear? Do I hear three tones? No. I only hear a succession of discrete tones. I hear one tone, followed by another tone, followed by another tone. My mind apprehends three tones. That's not given in the raw stimulus, but requires an act of intellectual recognition. The mind isn't just a passive recipient of auditory input, but makes a contribution by its ability to classify the auditory input using innate mathematical categories.
Compare a human percipient to a canine percipient. Both hear the same sounds, but only the human has the additional understanding to discern the numerical significance of the tonal sequence. A dog doesn't register "three o'clock". It lacks the intelligence to group particulars. There must be something prior in the mind to interpret what was heard as three of something.
