Material things change every second (through natural (atomic) "decay"). However. things in the mind seem to not change at all. For example, 1+1=2 never varies.

What is the difference between 'Material things' and 'things in the mind'?

No; I do not want to talk about the differences; I want to talk about CHANGE. What do you think about 'change'? Someone may think 'everything changes'; but someone else may think that change only occurs in the real world and that things in mind can never change. So what do you think?

Do you agree with Hegel's assertion: 'quantity changes lead to quality changes' ?

  • 1
    This seems like a good candidate for closing based on the "do you agree" structure. Thought from others?
    – virmaior
    Commented Oct 31, 2015 at 14:58

3 Answers 3


Here's one way to look at it that might be of interest. I'm not sure that it'll be satisfying in getting to grips with the difference between objects "in the mind" and "material" things, but it is one philosophical explanation for why we might take statements such as "1+1=2" to be in some sense true independently of the way the observable world is perceived to be.

The philosopher Gottlob Frege proposed that we understood the world in terms of objects, which are the things that we name and identify using singular terms, and concepts, which are ways in which we split the world up to apply general or descriptive terms to those names, and get either Truth or Falsity for each object we want to apply it to. For instance, in order for the sentence "Jim is a boy" to be true, we need there to be a thing in the world that "Jim" refers to, and we also need to have some concept of "being a boy" that does, in fact, take that object to True (This is similar to the ideas in Plato and Aristotle that describe properties like being a boy in terms of metaphysical things called Forms or Universals, but let's follow Frege and just think about a concept as a logical notion, or something that lets us take objects to True or False)

Abstractions are objects that we take to exist because they can be identified in terms of the concepts that we can use. For example, Frege tries to give an example of what it means to be a Direction:

The direction of a line A is the same as the direction of some other line B if and only if A and B are Parallel Lines.

The idea is that because there is a relational concept of what it takes for two lines to be parallel (and also for them to not be parallel), and that the relation is an Equivalence (such that you can split all the lines up into distinct "parallel line" groups), we get the concept of something being a direction as safely understandable relative to that concept. As a result, then, we could explain that the objects corresponding to the different directions existed simply because of the concept of being a parallel line - our Abstractions are what they are simply because of how we come to meaningfully split the world up! This makes our knowledge of abstractions "Analytic" - we have knowledge about what they are simply in virtue of meaning, and observations about the direct, material world don't make any difference to how they are.

One of the problems that Frege had with this idea, though, was that while it explained how we could have concepts that could identify abstract objects, it didn't quite make clear why we were supposed to think that these abstract objects were different from any of the other objects that we already had. The direction of a straight line in a co-ordinate space that passed through both (0,0) and (1,1), clearly differed from the direction of another line passing through (1,0) and (0,1); but was the direction of either straight line different to, say, the Roman Emperor Julius Caesar? They're clearly supposed to be, but unless we specify otherwise, it is entirely possible that we could plug Julius into the new concept and get something true out. This shows that just explaining why directions are different from each other isn't quite enough to explain how they are what they are only because of the meaning of general terms.

Frege tried to fix this problem by instead appealing to a more mathematically detailed account of how we could create specific abstractions for sets of objects from an understanding of each concept, but Bertrand Russell demonstrated that Frege's own plan made the system inconsistent in Russell's Paradox.

There are still people who think that Frege's basic idea, often called Logicism, can be made to work by explaining how Abstractions can be made to pick out unique objects, without running into problems like Russell's paradox, and there are many others who don't. There are some good links available on the Wikipedia page for Logicism if you're keen to read further.

  • This answer might be less relevant now that the question is focusing on the the nature of change rather than the nature of different kinds of things, but it might still be helpful as a way of thinking about how abstractions can be understood as to some extent independent of changes in observable phenomena, and about theories of how they might change if we can explain variations in the kinds of concepts that there are.
    – Paul Ross
    Commented Aug 13, 2012 at 16:51

1+1=2 is a statement in a formal system. The central axioms of the system can't change without introducing a new formal system. Formal systems are abstractions created by people to describe or discuss the universe, and they are very robust.

However, the shapes of the symbols used to describe the system do change. In ancient Rome, for example, the sequence of 1+1 may not have led to the conclusion 2, since they didn't use arabic numbers. Instead, they would say I+I=II (although I don't know if Romans used the same symbol for equality or addition, even).

So the rules of a formal system can't change but the notation does and can, so in a million years, 1+1=2 as a string of symbols might not mean anything in the current notation.

  • Just to press this a little more, philosodad, we might note that while 1+1=2 and I+I=II are in distinct formal systems, these systems seem to have similar rules for evaluating expressions, which we can describe independently of the symbols we've used (e.g. satisfying the Peano-Dedekind axioms). This is going to give a system scheme, rather than an actual number system in itself, but to use it to talk about similarities between formal systems seems perfectly sensible. If the only distinction between abstracts was their formalisation, how could we account for these similarities?
    – Paul Ross
    Commented Aug 10, 2012 at 15:51
  • @PaulRoss I was making a distinction of notation rather than system--that is, integer arithmetic is the formal system and 2 or II are the notations. I'm not sure I follow where you are going, though.
    – philosodad
    Commented Aug 10, 2012 at 19:50

Quantity change does not always lead to quality change but only when the barrier of qualitative difference is crossed. Hegel uses the example of the temperature of water. When water is heated and the temperature rises there is no quality change. But when the temperature rises to 100 degrees the liquid water changes its quality and becomes gas (vapor). Or when the temperature falls to 0 or below the liquid is converted to ice (solid) (but it is still a different state of material).

A second example is the chemical elements. A quantitative change to the atomic number leads to a different element (quality) and different properties, but the old and new are all elements.

The same can be applied to ideas.

1 + 1 = 2 is already a different quality to the parts that consist it. 1 is the simpler type of measure but 1 + 1 = 2 is an arithmetic operation: an addition. The number two is a different quality than 1. That is the reason one and two are not equal (but these are both numbers).

Or think about a child's growth. When experience is gathered for a period a kid is still a kid. But after a fair amount of experience the kid is able to use language and gradually becomes a mature person (but the kid is always human).

Or think about music. One musical note alone is just an uncorrelated sound. With 2 or more notes you have a motive. A further expansion of the motive will make a musical phrase (but both a motive and musical phrase are always sound vibrations).

About the notion of change (according to Hegel), you must think of existence as a dialectical notion that consists of both being and becoming, and at the same time, of nothingness. Change (becoming) if applied on itself should provide no-change (being).

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