Not that close.
This is what happens in non-Euclidean geometry.
Human beings have the ability to reason. This ability is part of who we are by nature. Perception is active not passive. It is not as if an organism’s immaterial mind informs material eyes.
If seeing that two things are equal is to grasp the universal ‘equality’ then is seeing that one thing resembles another grasping the universal ‘resemble’ ?
Yes, this is reference to the “living now”. The synthesis occurs because the now becomes a non-now, a past now. And in the living present, i.e. the pure presence, or thing which is present, one is retained within the other as a synthesis. Notice it is called an “impression”, “the primordial impression”. All of this activity referred to at this point, is within the subject.
But then he goes on to talk about a “trace”. The trace is a result of the difference being impure. The difference between the now and the non-now is not a pure negation, there remains a trace. The trace is described as “ the intimate relation of the living present with its outside”. The outside is what validates the “actual now”, discussed in Ch 5. He clearly concludes in Ch 6, that what is inside the subject (and that is the synthesis mentioned) is insufficient to conceive of time. Yes, you are correct to say that this is “within time”, but it is not adequate to produce a conception of time, because time itself is outside of this.
One has to have the idea of likeness already — which is the point the equals argument is making about equality.
That would be Descartes, not Plato or Aristotle.
One must also have the idea of being unlike as well. A resemblance might be weak, alike in some way but unlike in others. I though it might be easier to see with resemblances, the point holds with equality as well.
The problem of opposites is central to the Phaedo. Things are said to come to be from their opposite. Equal things from unequal. If the ability to recognize equal things comes from the idea of equality then the ability to recognize unequal things comes from the idea of inequality. Without the idea of unequal there would be no idea of equal. There is no explanation in terms of Forms unless in addition to unity there is multiplicity.
Not only things but Forms themselves are both same and other. Each Form is itself both other than the things of that Form, and other than the other Forms.
That is where your argument leads. According to you, the mind is immaterial. Eyes, however, are not immaterial.
The reason I referred to Descartes is that, in him, the idea of res cogitans and res extensa became clearly formulated. This division - between mind and body, spirit and matter - has become fundamental to the ‘grammar of culture’. It is part of the broader division introduced with modern science that divides the primary from secondary attributes of things, and the subjective and objective as domains of reference. It is referred to as ‘the Cartesian division’, subject of another post, Descartes’ Ghost.
But the dualism of Plato’s philosophy, modified but adapted by Aristotle, is the dualism of matter and form (hyle-morphē). And that is radically different. In Aristotle’s dualism, matter can’t exist without form (as there would be no answer to the question ‘what is that?’ for a thing without form), but forms are instantiated in matter.
Aristotle aside, what kinds of things are immaterial? The example I gave in this OP is the sign ‘=’. I argue that ‘equals’ is a distinct concept with a specific meaning, but that its nature is entirely intellectual (noetic or noumenal). And that idea can be extended to the entire domain of mathematical objects and relations. But I wouldn’t want to say that numbers are immaterial things. That’s where the Cartesian error creeps back in.
So, to respond to your challenge: yes, eyes, or at least, vision has a clearly physical or physiological basis - photosensitivity, transmission of signals via nerves, assimilation by the brain. This plainly operates in any organism with sight, and same too with h.sapiens.
But the non-material factor is interpretation - the identification of the object of perception, and its assimilation into the mind. This is the aspect that resists reduction to the physical because it is essential to the process by which the meaning of ‘physical’ is ascertained.
(That is the problem of recursion that was the subject of, for example, Douglas Hofstader’s I Am a Strange Loop, among other books.)
But where I’m going with that argument is that not only mathematics, but all formal symbolic systems, including the rules of logic, scientific conventions and laws - none of these can be reduced to or explained in terms of purely physical principles (which is what physicalism seeks to do, usually through a combination of neuroscience and evolutionary biology.)
This is at the basis of the interminable debates about platonism in philosophy of mathematics. The platonist (note small ‘p’) view is that numbers are real - to which they empiricist rejoinder is invariably, ‘well, where are they, then? Where in nature can numbers be found?’ I say, nowhere — but that they’re nonetheless real for anyone who can count.
Imagining, thinking, reasoning, speculating, theorizing, and interpreting are abilities of certain living organisms. To abstract from these abilities and postulate an immaterial mind as their cause is also an ability of these organisms.
Here is an interesting story: Some birds have been putting cigarette butts in their nests. Birds and Butts
Do their immaterial bird minds recollect from previously being dead the idea that toxic chemicals in tobacco keep parasites away?
Of course we can create stories in an attempt to explain what is happening, but the problem is that there is no way to demonstrate the truth of such stories once you abandon physical explanations.
Demonstration of truth is something only humans are capable of, although your account seems not to recognise this.
Of course demonstration of truth is something only human beings are capable of! What we (human beings) know is that birds are putting cigarette butts in their nests and that tobacco is a pesticide. The question that we (human beings) ask is how they (birds) know to do this. We (human beings) can make up stories to explain this, but there is no way we (human beings) can demonstrate if any of these stories are true if we (human beings) abandon physical explanations.
It is the same with the stories that you (Wayfarer) accept about knowledge of such things as the equal itself. Here too there is no way to demonstrate the truth of such stories.
What do you mean, ‘physical explanation’? What physical explanation, in particular, is relevant to animal behaviour?
I mean, there are literally endless numbers of examples of animals engaging in such adaptive behaviours . What point are you trying to prove in saying that? Is it that rational explanations themselves are also kinds of adaptive behaviours?
Do you think the meaning of the equals symbol is ‘a story’?
As far as I know there is no explanation. It is a recently observed behavior. The point is that any proposed explanation, if plausible, must be biological.
What is a story is what you call the “theory” of recollection. The meaning of the equals symbol is something we learn from our teachers. No story needed. Students learn the rule: this symbol = means equal.
None of this rises to the level of philosophical analysis.
Sorry I’m late to the party. Real life will occasionally drag me away.
To my mind the idea of equals is necessarily non-physical. Things can not be demonstrated to be equal universally, only within the framework of an agreed treatment, an agreed mental framework. Change the treatment, and the equality may disappear. For example 2+2 =4 in base ten, but not in base three, where 2+2 would equal 11.
Even at the level of physical objects, equality can not be demonstrated outside an agreement as to where an object starts and ends, which is very much an artefact of the visual system, and not a universal. Again, change the viewing conditions, and the equality may vanish.
However, we need to be cautious applying this to Identity Theory as part of a theoiry of mind. Identity theory is not the idea that thoughts and neural processes are equal, but rather than they share an identity - that they are the same thing, albiet possibly very different aspects of the same thing. There is no requirement for two things that share an identity to be equal.
The issue to my mind with Identity theory is not the very real differences between neural patterns and thought processes, but rather than materialism does not admit the qualities we are considering. The claim of the materialist (and I very much prefer the term physicalist for this reason) is that all the necessary qualities of thought are contained within or explained fully by a set of physical process. The reason why the claim fails is that the very qualities of thought that people want to understand and study, fall outside the universe that the materialist wants to consider. We are left with the conclusion that if the material realm encompasses and explains all of human thought, then the material realm can not be understood to be physical.
Because the material realm can not both be purely physical, and contain the details of human thought that people want to understand. The materialist’s claim confuses reductionism for explanation - if we want to understand thought, we can not reduce it away to something simpler.
Fair - although I had in mind Armstrong and Place, who’s theories of mind are very much in the brain-mind identity camp.
The meaning of the “equal symbol” is not something to be arrived at by philosophical analysis. It is a matter of learning a rule as part of a practice.
Immaterial mind or brain is a false dichotomy. The mind is embodied in living persons who have language, culture, and history.
I agree that thought is not a neural process, but without neural processing there would be no thought.
Perl claims, and you seem to agree, that “intelligible identities are the reality”. This reduces the ontological to the epistemological. It is the things of this world that are real and intelligible, although perhaps not completely intelligible to our limited intelligence.
But the primitive elements of arithmetic (such as the natural numbers and the concept of equality) are neither dependent on nor derived from neural processes. They are able to be discovered by any rational sentient being, such as ourselves, equipped to understand them.
I did provide a link to the book (Thinking Being: An Introduction to Metaphysics in the Classical Tradition, Eric Perl ref) which provides the background to the idea of intelligibility in Greek philosophy. I can’t be adequately expressed in a five-word phrase.
The point of the argument is that to derive a naturalist account of intelligence requires judgement as to what is and what is not the case at every step of the process. These judgements are foundational to the scientific account and can’t be meaningfully reduced to physical causation. This has been elaborated at length in various books and essays, notably Evolutionary Naturalism and the Fear of Religion, Thomas Nagel (ref).
How is it we know we have ‘limited intelligence’? Compared to what is it limited? Do you think a non-rational creature would grasp that idea?
Sure. If you believe that it is purely a mathematical symbol and utterly meaningless outside that context. Even then advanced mathematics will get you into uncertain territory. Because statements like infinity = infinity+1 depend on how you frame those rules and that practice.
If you want to use = for anything outside strict applications of basic arthimatic, then yes, it’s subject to philosophical analysis just like everything else.
That’s the point that Wayfarer is making. Can materialists really use = to mean two different things are the same, when referring to physical objects rather than a mathematical presentation of numbers?
They are dependent on neural processes but not reductive to them. We are not ventriloquist dummies.