•Logic is relationships which always replicate; a subset of science — Kaiser Basileus
By that he meant the evidence we receive from the world is a response to the way we formulate our inquiries toward it. It can respond very precisely to different formulations, but always in different ways, with different facts. — Joshs
The way we formulate our enquiries towards the world is in response to the way the world appears to us. We have no control over how the world appears to us. — Janus
Mathematics is the world to the same extent that French or German is in the world, as a peculiar grammar by which we organize it for our purposes.
— Joshs — wonderer1
Isn’t that analogous to how well science can reconfigure the way that world appears to us though a gestalt shift? — Joshs
So do you think ordinary languages, like French and German, would have facilitated equal progress in physics and cosmology since the 17th C, in the absence of mathematics? — Wayfarer
Science observes, and then attempts to explain what is observed. I see fire, for example, and I explain it in terms of phlogiston, then later I explain it in terms of agitated molecules. I continue to see the fire the same way; its appearance does not change regardless of the theory about its cause. — Janus
↪Joshs Seeing the same things and conceiving of them in different ways are two different things altogether. I haven't denied that we might come, and historically speaking have come, to conceive of things in novel ways — Janus
One of the most seductive forms of subjectivism in contemporary thought is the use made of the concepts of interpretation, whether by pragmatists or hermeneuticists. To its credit, interpretationism provides a penetrating critique of objectivism that is worth pursuing in some detail. To be objective, the interpretationist points out, one would have to have some set of mind-independent objects to be designated by language or known by science. But can we find any such objects? Let us look at an extended example from the philosopher Nelson Goodman.
A point in space seems to be perfectly objective. But how are we to define the points of our everyday world? Points can be taken either as primitive elements, as intersecting lines, as certain triples of intersecting planes, or as certain classes of nesting volumes. These definitions are equally adequate, and yet they are incompatible: what a point is will vary with each form of description. For example, only in the first "version," to use Goodman's term, will a point be a primitive element. The objectivist, however, demands, "What are points really?" Goodman's response to this demand is worth quoting at length:
If the composition of points out of lines or of lines out of points is conventional rather than factual, points and lines themselves are no less so. ... If we say that our sample space is a combination of points, or of lines, or of regions, or a combination of combinations of points, or lines, or regions, or a combination of all these together, or is a single lump, then since none is identical with any of the rest, we are giving one among countless alternative conflicting descriptions of what the space is. And so we may regard the disagreements as not about the facts but as due to differences in the conventions-adopted in organizing or describing the space. What, then, is the neutral fact or thing described in these different terms? Neither the space (a) as an undivided whole nor (b) as a combination of everything involved in the several accounts; for (a) and (b) are but two among the various ways of organizing it. But what is it that is so organized? When we strip off as layers of convention all differences among ways of describing it, what is left? The onion is peeled down to its empty core.
No. However, I don't see what that has to do with the sense in which mathematics can be said to be in the world. — wonderer1
Most often I've encountered the question from people motivated to use the fact that there is math in the world, as evidence for the necessity of a God.
IMO, there is nothing particularly theistic at expressing awe at the regularities in the world. We appear to have a universe with a begining. So at one point, there was a state at which things had begun to exist before which nothing seems to have existed. This forces us to ask the question "if things can start existing at one moment, for no reason at all, why did only certain types of things start to exist and why don't we see things starting to exist all the time? Or if things began to exist for a reason, what was the reason?"
I don't see how this is essentially a theistic question though. It seems like a natural outgrowth of human curiosity, God(s) or no. — Count Timothy von Icarus
One can trace a Platonism beginning in Greece, making its way through religious Christian thought and finally arriving at a humanism which retains the idea of the uncaused cause and the pure immanent identity of what presents itself to itself, but transfers these from God to mathematical idealities such as identity, pure quantitative magnitude and
extension. — Joshs
Not in my experience, but it might be selection bias. — Count Timothy von Icarus
The best example of this view I can think of is Nagel's "Mind and Cosmos," which looks at significant problems in the "life is the result of many random coincidences and looking at them as anything other than random is simply to give in to fantasy," view. But Nagel is an avowed atheist. Likewise, Glattfelter's "Information, Conciousness, Reality," Winger's "Unreasonable Effectiveness," etc. don't seem particularly theistic to me. — Count Timothy von Icarus
IMO, there is nothing particularly theistic at expressing awe at the regularities in the world. We appear to have a universe with a begining. So at one point, there was a state at which things had begun to exist before which nothing seems to have existed. This forces us to ask the question "if things can start existing at one moment, for no reason at all, why did only certain types of things start to exist and why don't we see things starting to exist all the time? Or if things began to exist for a reason, what was the reason?"
I don't see how this is essentially a theistic question though. It seems like a natural outgrowth of human curiosity, God(s) or no. — Count Timothy von Icarus
However, by a more excellent and more immediate method, judgement leads us to look upon eternal truth with greater certainty. For, whilst judgement and analysis arises through a reasoned abstraction from place, time and transformation and, thereby, through immutable, unlimited and endless reason, of dimension, succession and transmutation, there however remains nothing which is entirely immutable, unlimited and endless - apart from that which is eternal; and everything which is eternal is God, or in God. And, therefore, however more certainly we analyse all things, we analyse them according to this reason, which is clearly the reason of all things, the infallible rule and the light of truth in which all things are illumined infallibly, indelibly, indubitably, unbreakably, indistinguishably, unchangably, unconfinably, interminably, indivisibly and intellectually. And so, as we consider those laws, with which we judge with certainty those things which we perceive, while they are infallible and indubitable to the intellect of the one apprehending, indelible to the memory of the one recalling and unbreakable and indistinguishable to the intellect of the one judging, so, because, as Augustine says, no-one judges from them, but through them, it is required that they be unchangable and incorruptible because necessary, unconfinable because unlimited, endless because eternal, and, for this reason, indivisible because intellectual and incorporeal - not made, but uncreated, eternally existing in that art of eternity, from which, through which and consequent to which all elegant things are given form. For this reason, they cannot with certainty be gauged save through that which not only produced all other forms, but which also preserves and distinguishes all things, as in all things the essence holding the form and the rule directing it; and, through this, our mind judges/analyses all things which enter into it through the senses.
And so, as we consider those laws, with which we judge with certainty those things which we perceive, while they are infallible and indubitable to the intellect of the one apprehending, indelible to the memory of the one recalling and unbreakable and indistinguishable to the intellect of the one judging, so, because, as Augustine says, no-one judges from them, but through them, it is required that they be unchangable and incorruptible because necessary, unconfinable because unlimited, endless because eternal, and, for this reason, indivisible because intellectual and incorporeal - not made, but uncreated, eternally existing in that art of eternity, from which, through which and consequent to which all elegant things are given form ~ Bonaventura. — Count Timothy von Icarus
1. Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way; it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. Augustine concludes from these observations that intelligible objects cannot be part of reason's own nature or be produced by reason out of itself. They must exist independently of individual human minds.
2. Intelligible objects must be incorporeal because they are eternal and immutable. By contrast, all corporeal objects, which we perceive by means of the bodily senses, are contingent and mutable. Moreover, certain intelligible objects - for example, the indivisible mathematical unit - clearly cannot be found in the corporeal world (since all bodies are extended, and hence divisible.) These intelligible objects cannot therefore be perceived by means of the senses; the must be incorporeal and perceptible by reason alone.
3. Intelligible objects must be higher than reason because they judge reason. Augustine means by this that these intelligible objects constitute a normative standard against which our minds are measured. We refer to mathematical objects and truths to judge whether or not, and to what extent, our minds understand mathematics. We consult the rules of wisdom to judge whether or not, and to what extent, a person is wise. In light of these standards, we can judge whether our minds are as they should be. It makes no sense, however, to ask whether these normative intelligible objects are as they should be; they simply are and are normative for other things. In virtue of their normative relation to reason, Augustine argues that these intelligible objects must be higher than it, as a judge is higher than what it judges. Moreover, he believes that apart from the special sort of relation they bear to reason, the intrinsic nature of these objects shows them to be higher than it. These sorts of intelligible objects are eternal and immutable; by contrast, the human mind is clearly mutable. Augustine holds that since it is evident to all who consider it that the immutable is clearly superior to the mutable (it is among the rules of wisdom he identifies), it follows that these objects are higher than reason.
to stretch the analogy to the breaking point, puddles do indeed make potholes for themselves to collect in when they freeze, in a sort of self-reinforcing mechanism" — Count Timothy von Icarus
What exactly is wrong with the puddle's thought in Adam's analogy? The idea that the hole was made for the puddle is the most obvious target. But the puddle is still in the hole because of what the puddle is and what the hole is, and those seem like phenomena a sentient puddle might well strive to understand. — Count Timothy von Icarus
And do puddles make holes (which, to stretch the analogy to the breaking point, puddles do indeed make potholes for themselves to collect in when they freeze, in a sort of self-reinforcing mechanism)?" — Count Timothy von Icarus
It seems to me like this is partially right, and partially missing something. Sans some interpretation of consciousness where mind does not emerge from or interact closely with nature, it would seem to me that our descriptive languages have a close causal relationship with nature. — Count Timothy von Icarus
Yes, our math is axiomatic. The initial axioms drive the succeeding mathematical formula.To this point, I would argue that thinking of math as a "closed," system can be misleading in this context. — Count Timothy von Icarus
I don't think it's causal connection. Zero does not exist in nature. (Contrast that with "there are two apples on the table", which you could actually count) Certainly, saying that a 'nothing' exists in nature is a human invention. And the system of math did not include zero for thousands of years. Zero is a modern invention.
I don't know how to define "closed" in this context, but I agree. With over 26,000 Wikipedia pages, and counting, mathematics continues to expand its realms, especially into abstractions and generalizations. I suppose "closed" could mean based on axiomatic set theory, which it normally is, although frequently some distance from Cantor's creations. — jgill
I just learned about his new book. Haven't looked at it yet.At Home in the Universe
— Patterner
I've been reading a lot of science lately - switching from my usual fiction. I'll add this to my list. It was written in 1996, do you think it's out of date? Do you know any good, more recent books. — T Clark
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