Henry Alford:  phys., see, for a contrast, ch. 1 Corinthians 8:1.

Thomas Aquinas:  First, indeed, as to pride, which is a disarranged desire for one’s own excellence. One seeks his own excellence in a disarranged manner, when it does not satisfy him to be contained in that station which has been established for him by God. Therefore it says in Sir (10:12): “The beginning of man’s pride is to depart from the Lord.” This happens when a man does not wish to be contained under the rule of God’s arrangement. And this is opposed to charity, by which one loves God above all things: “Puffed by without reason by this sensuous mind and not holding fast to the head” (Col. 2:18). It is right to compare pride to arrogance [being puffed up]. For that which is puffed up does not have solidity but its appearance; so the proud seem to themselves to be great, while they really lack true greatness, which cannot exist without the divine order: “He will dash them speechless to the ground” (Wis 4:19).

William Barclay:  Love is not inflated with its own importance. Napoleon always advocated the sanctity of the home and the obligation of public worship--for others. Of himself he said, "I am not a man like other men. The laws of morality do not apply to me." The really great man never thinks of his own importance. Carey was one of the greatest missionaries and certainly one of the greatest linguists the world has ever seen. He translated at least parts of the Bible into no fewer than thirty-four Indian languages. He began life as a cobbler. When he came to India he was regarded with dislike and contempt. Once at a dinner party a snob, with the idea of huiliating him, said in a tone that everyone could hear, "I suppose, Mr. Carey, you once worked as a shoe-maker." "No, your lordship," answered Care, "not a shoe-maker, only a cobbler." He did not even claim to make shoes--only to mend them. No one likes the "important" person. Man "dressed in a little brief authority" can be a sorry sight.

Barnes & Murphy:  Is not puffed up. \~fusioutai\~. This word means, to blow, to puff, to pant; then to inflate with pride, and vanity, and self-esteem. It perhaps differs from the preceding word, inasmuch as that word denotes the expression of the feelings of pride, vanity, etc., and this word the feeling itself. A man may be very proud and vain, and not express it in the form of boasting. That state is indicated by this word. If he gives expression to this feeling, and boasts of his endowments, that is indicated by the previous word. Love would prevent this, as it would the former, it would destroy the feeling, as well as the expression of it. It would teach a man that others had good qualities as well as he; that they had high endowments as well as he; and would dispose him to concede to them full credit for all that they have, and not to be vainglorious of his own. Besides, it is not the nature of love to fill the mind in this manner. Pride, vanity, and even knowledge (1 Corinthians 8:1) may swell the mind with the conviction of self-importance; but love is humble, meek, modest, unobtrusive. A brother that loves a sister is not filled with pride or vanity on account of it; a man that loves the whole world, and desires its salvation, is not filled with pride and vanity on account of it. Hence the Saviour, who had most love for the human race, was at the farthest possible remove from pride and vanity.

Joseph Beet:  Puffed-up: as in 8:1. In view of those we love, we never indulge inflated opinions about ourselves.

Joseph Benson:  Is not puffed up — With pride or self-conceit on account of any endowments or qualifications, mental or corporal, natural or acquired, civil or religious. On the contrary, love to God, whereby we esteem him as the greatest and best of beings, desire him as our chief good, delight in him as our portion and treasure in time and in eternity, cannot but humble us in the dust before him, while we contrast our various weaknesses, imperfections, and sins, with his infinite excellences and matchless glories, and compare his superlative goodness with our great unworthiness. And the love of our neighbour, naturally leading us to dwell on his virtues, and overlook his defects, must also, though in a lower degree, produce the same effect, and cause us to prefer others to ourselves in a variety of respects.

Jim Bomkamp:  'love is not arrogant':

1. Strong’s Greek Dictionary has the following definition for this word translated ‘arrogant’:
   1. To make natural, to cause a thing to pass into nature.
   2. To inflate, blow up, to cause to swell up.
   3. To puff up, make proud.
   4. To be puffed up, to bear one's self loftily, be proud.
2. We Christians must be careful not to become arrogant in our attitudes towards each other.
3. We read in Phil. 2:3 that the Lord wants each of us as Christians to think of others as actually being more important than we are, “3 Do nothing from selfishness or empty conceit, but with humility of mind let each of you regard one another as more important than himself.”
4. We saw already in 1 Cor. 8:1 that having knowledge causes one to be puffed up, or arrogant, "1 Now concerning things sacrificed to idols, we know that we all have knowledge. Knowledge makes arrogant, but love edifies."
   1. It is amazing how quickly, easily, and often we Christians can sometimes go from being in the place of realizing how totally unworthy we are to receive anything from the Lord, to being puffed up with pride and arrogance and thinking that we are really better or more spiritual than others.
   2. A person can become puffed up with pride and arrogance when he possesses just a little bit of knowledge as well as when he possesses a lot of knowledge. Jeremiah wrote in Jer. 17:9 about how the human heart is utterly deceitful and beyond understanding, "9 The heart is more deceitful than all else And is desperately sick; Who can understand it?".
   3. We Christians must not allow our pride to cause us to be puffed up towards others because we think that we have arrived spiritually or because we believe we understand more than others. God will bring us to a place where He will cause us to be mightily humbled if we travel this path.
5. Sometimes I have observed that Christians can begin to act arrogant towards non-Christians as if they feel like they are better than the non-Christian because they don’t do some of the things that the non-Christian does, or even just because Christ has come into their life.
6. We Christians do not really comprehend the “agape” love that the Lord has for us if we are getting arrogant and prideful and ‘puffed up’ with ourselves and our abilities. The arrogant person sees himself as being smarter, better looking, or better off than others, and thus he looks down his nose at others. We don’t need to puff ourselves up when we know just how much that the Lord loves us.

John Calvin:  He adds, farther, that it has nothing of the nature of pride. That man, then, who is governed by love, is not puffed up with pride, so as to despise others and feel satisfied with himself.

Alan Carr:  Is Not Puffed Up: Love is not arrogant or proud, but it realizes that all it has and all that it is has been given to it by God. No matter how great our talents or how spectacular our gifts, everything we are is the result of divine grace.

Adam Clarke:  Is not puffed up] ou fusioutai
Is not inflated with a sense of its own importance; for it knows it has nothing but what it has received; and that it deserves nothing that it has got. Every man, whose heart is full of the love of God, is full of humility; for there is no man so humble as he whose heart is cleansed from all sin. It has been said that indwelling sin humbles us; never was there a greater falsity: PRIDE is the very essence of sin; he who has sin has pride, and pride too in proportion to his sin: this is a mere popish doctrine; and, strange to tell, the doctrine in which their doctrine of merit is founded! They say God leaves concupiscence in the heart of every Christian, that, in striving with and overcoming it from time to time, he may have an accumulation of meritorious acts: Certain Protestants say, it is a true sign of a very gracious state when a man feels and deplores his inbred corruptions. How near do these come to the Papists, whose doctrine they profess to detest and abhor! The truth is, it is no sign of grace whatever; it only argues, as they use it, that the man has got light to show him his corruptions; but he has not yet got grace to destroy them. He is convinced that he should have the mind of Christ, but he feels that he has the mind of Satan; he deplores it, and, if his bad doctrine do not prevent him, he will not rest till he feels the blood of Christ cleansing him from all sin.

True humility arises from a sense of the fullness of God in the soul; abasement from a sense of corruption is a widely different thing; but this has been put in the place of humility, and even called grace; many, very many, verify the saying of the poet: "Proud I am my wants to see; Proud of my humility."

F.C. Cook:  If physiOUtai also is in middle voice, as is most probable, it may be rendered, being a word of some coarseness, "does not swell and swagger".

Henry Drummond:  After you have been kind, after Love has stolen forth into the world and done its beautiful work, go back into the shade again and say nothing about it. Love hides even from itself. Love waives even self-satisfaction.

Exell & Spence:  Is not puffed up. Has no purse proud or inflated arrogance." Love, therefore, is free from the characteristic vice of the Corinthian Church (1 Corinthians 4:6, 18, 19; 5:2; 8:1).

Lee Gatiss:  Love ou fusioutai unlike the Corinthians of course, who Paul has rebuked for just this problem throughout the letter. They were arrogant when they really should have been ashamed at the damage their attitudes were causing in the Church.

Geneva Notes:  He describes the force and nature of charity, partly by a comparison of opposites, and partly by the effects of charity itself. And by this the Corinthians may understand both how profitable it is in the church, and how necessary: and also how far they are from it, and therefore how vainly and without cause they are proud.

John Gill:  Is not puffed up, swelled with pride, and elated with a vain conceit of himself, of his parts and abilities, of his learning, eloquence, wisdom, and knowledge, as the false teachers in this church were; knowledge without grace, unsanctified knowledge, mere notional speculative knowledge, puffeth up; but charity, or the grace of love, does not; that edifies and preserves persons from being puffed up with themselves, or one against another.

Frédéric Louis Godet:  ou physioutai: Inflation as the inward source of the two preceding evils. The word physiOUSthai was used, 4:6, to denote the presumptuous self-satisfaction with which certain Corinthians were filled.

John W. Gregson:  It is not puffed up like a bellows--"a windbag."

Matthew Henry:  Charity subdues pride and vain-glory; It vaunteth not itself, is not puffed up, is not bloated with self-conceit, does not swell upon its acquisitions, nor arrogate to itself that honour, or power, or respect, which does not belong to it. It is not insolent, apt to despise others, or trample on them, or treat them with contempt and scorn. Those who are animated with a principle of true brotherly love will in honour prefer one another, Romans 12:10. They will do nothing out of a spirit of contention or vain-glory, but in lowliness of mind will esteem others better than themselves, Philippians 2:3. True love will give us an esteem of our brethren, and raise our value for them; and this will limit our esteem of ourselves, and prevent the tumours of self-conceit and arrogance. These ill qualities can never grow out of tender affection for the brethren, nor a diffusive benevolence. The word rendered in our translation vaunteth itself bears other significations; nor is the proper meaning, as I can find, settled; but in every sense and meaning true charity stands in opposition to it. The Syriac renders it, non tumultuatur--does not raise tumults and disturbances. Charity calms the angry passions, instead of raising them. Others render it, Non perperàm et perversè agit--It does not act insidiously with any, seek to ensnare them, nor tease them with needless importunities and addresses. It is not froward, nor stubborn and untractable, nor apt to be cross and contradictory. Some understand it of dissembling and flattery, when a fair face is put on, and fine words are said, without any regard to truth, or intention of good. Charity abhors such falsehood and flattery. Nothing is commonly more pernicious, nor more apt to cross the purposes of true love and good will.

H.A. Ironside:  And love “is not puffed up.” There is a Scripture that says, “Knowledge puffeth up, but [love] edifieth,” or buildeth up (1 Cor. 8:1). I think I know a great deal more than other people and so become conceited, puffed up over it, but real love does not puff up, it builds up.

Jamieson, Fausset, & Brown:  Not puffed up -- with party zeal, as some at Corinth were (1 Cor. 4:6).

B.W. Johnson:  Nor is it inflated.

S. Lewis Johnson:  And finally in chapter 4 in verse 6, we have the beginning of the use of the expression. "Now these things brethren I have figuratively transferred to myself and Apollos for your sakes that you may learn in us not to think beyond what is written that none of you may be puffed up."

Verse 18 and verse 19, "Now some are puffed up as though I were not coming to you, but I will come to you shortly if the Lord wills and I will know not the words of those who are puffed up, but the power." Paul, he could say some things that could be called rather sharp, could he not?

Verse 2 of chapter 5, "And you are puffed up, and have not rather mourned that he who has done this deed might be taken away from you."

In 1 Cor. 8:1 again, “Now concerning things offered to idols, we know that we all have knowledge, knowledge puffs up, but love edifies.”

Puffed up, many of us are like that. We get that like that. Preachers particularly. Preachers, in Believers Chapel particularly, in fact, there is one of them standing before you. I know that this is something addressed to me. Now, the apostle speaks specifically, of course, to the Corinthians, but he’s talking about all of us who may fall into this kind of sin.

Now, my little sports thing that I read has a quotation from John McEnroe in it. John McEnroe, former outstanding tennis player, known for his tantrums on the court, as most of you know, involving the referees, involving his opponents, involving the tennis balls and the racquets and anything, anything, the crowd especially. This is what John McEnroe once said — see if you can believe it, if you know anything about tennis. “It is vital, in my opinion, that tennis maintains a strong and watchful stand against swearing.” [Laughter] Now, this is a man who is known for these things.

Muhammad Ali. Muhammad Ali was never known for being a modest kind of person. He was riding on a plane one time, and you remember he often said “I am the greatest,” and he came — one of the stewardesses walking up the aisle of the plane looked at him, saw he didn’t have his seatbelt fastened, and said to him “Mr. Ali, you’ll have to fix your seatbelt.” He said “Superman don’t need no seatbelt.” [Laughter] So the stewardess then replied — and I marvel at her ability to do this — “Superman don’t need no airplane either.” [Laughter, Johnson laughs]

Those of us who are puffed up can be easily deflated. And if only for that reason we should avoid being puffed up. So the apostle says, “Is not puffed up, Christian love is not puffed up.” We look at ourselves as the Scriptures set us forth.

William Kelly:  There is no self-display (or, as some think, forwardness), nor the arrogance whence it springs.

Keith Krell:  Love is not arrogant. The term “arrogant” refers to a grasping for power. It is more serious than bragging, which is only grasping for praise. Arrogant people push themselves into leadership, using people as stepping-stones, and always consider themselves exempt from the requirements on mere mortals. Arrogance disrespects others and carries a disdain for others. God calls us to serve others and be gracious toward them.

Paul Kretzmann:  Love is not puffed up, is not guilty of moral indecency, of bad taste, is not proud in its own conceit, looking down upon others as inferior.

Lange & Schaff:  Is not puffed up--i.e., inflated with vanity. As this expresses the subjective state of conceit and self-exaltation, so does the former express the natural manifestation of this in boasts over advantages possessed, and in attempts to get honor for them. [Of course there is a contrast here implied. Through these negatives he would give them to understand that "love is modest and humble; modest because humble." Or as Chrysostom beautifully says, "He adorns love not only from what she hath, but also from what she hath not. For he saith that she both brings in virtue, and extirpates vice, nay, rather she suffers it not to spring up at all."]

R.C.H. Lenski: Behind boastful bragging there lies conceit, an overestimation of one's own importance, abilities, or achievements. Hence the next step: "is not puffed up." From envy to boasting, from boasting to puffing oneself up is a natural sequence in the psychology of lovelessness. He that exalteth himself shall be abased; he that humbleth himself shall be exalted. Thus in this case the positive virtue is Christian humility and lowliness of mind.

Paul has mentioned being puffed up repeatedly in 4:6, 18, 19; 5:2; 8:1. Yet the conclusion which some draw, that Paul's description of love, especially its negative side, is derived from manifestations which he found among the Corinthians, is too narrow. Paul describes love as it really is with all of its main characteristic features. Even if Corinth had not existed, every line of this description would be true. In regard to some points, where we know the loveless tendencies of the Corinthians, we see these very tendencies contradicted by Paul's picture of love. These applications are, however, only incidental and may in a similar way be made to any other congregation and do not as such dominate the picture here sketched.

Steve Lewis:  Is not arrogant (phusioo) = to be inflated, puffed up with pride, haughty. This is the same term that was used in 1 Cor 4:6, 18, 19; 5:2; 8:1, and from these references we know that this was a large problem in the Corinthian church. In the previous phrase ("Love does not brag") Paul was describing the expression of an attitude of superiority, but here in this phrase Paul is describing the inward attitude that produces those kinds of expressions.